maths statistics and logic for kids

http://dx.doi.org/10.1007/978-0-8176-8412-9 From Calculus to Analysis Steen Pedersen Springer, 2015, ISBN 978-3-319-13641-7 http://dx.doi.org/10.1007/978-3-319-13641-7 From Calculus to Analysis Rinaldo B. Schinazi Springer, 2012, ISBN 978-0-8176-8289-7 http://dx.doi.org/10.1007/978-0-8176-8289-7 Numbers and Functions: Steps into Analysis, Second Edition R. P. Burn Cambridge University Press, 2004, ISBN 9780511755248

http://dx.doi.org/10.1017/CBO9780511755248 Introduction to Calculus and Classical Analysis, Second Edition Omar Hijab Springer, 2007, ISBN 978-0-387-69316-3 http://dx.doi.org/10.1007/978-0-387-69316-3

Calculus for the Ambitious T. W. Korner Cambridge University Press, 2014, ISBN 9781107517271 http://dx.doi.org/10.1017/CBO9781107517271 A Concise Approach to Mathematical Analysis

Mangatiana A. Robdera Springer, 2003, ISBN 978-0-85729-347-3 http://dx.doi.org/10.1007/978-0-85729-347-3

Mathematical Analysis Fundamentals A. E. Bashirov Elsevier, 2014, ISBN 978-0-12-801001-3 http://www.sciencedirect.com/science/book/9780128010013

Foundations of Mathematical Analysis S. Ponnusamy Springer, 2012, ISBN 978-0-8176-8292-7 http://dx.doi.org/10.1007/978-0-8176-8292-7 A Course in Mathematical Analysis, Volume I: Foundations and Elementary Real Analysis D. J. H. Garling Cambridge University Press, 2013, ISBN 9781139424493 http://dx.doi.org/10.1017/CBO9781139424493 A Course in Mathematical Analysis, Volume II: Metric and Topological Spaces, Functions of a Vector Variable D. J. H. Garling Cambridge University Press, 2013, ISBN 9781139424509 http://dx.doi.org/10.1017/CBO9781139424509 A Course in Mathematical Analysis, Volume III: Complex Analysis, Measure and Integration D. J. H. Garling

Cambridge University Press, 2014, ISBN 9781139424516 http://dx.doi.org/10.1017/CBO9781139424516

Mathematical Analysis I, Second Edition Claudio Canuto and Anita Tabacco Springer, 2015, ISBN 978-3-319-12757-9 http://dx.doi.org/10.1007/978-3-319-12772-9 Mathematical Analysis II, Second Edition Claudio Canuto and Anita Tabacco Springer, 2015, ISBN 978-3-319-12757-6 http://dx.doi.org/10.1007/978-3-319-12757-6 A Course in Calculus and Real Analysis Sudhir R. Ghorpade and Balmohan V. Limaye Springer, 2006, ISBN 978-0-387-36425-4 http://dx.doi.org/10.1007/0-387-36425-0 Calculus of One Variable ** Terse, use of Maple is recommended ** Keith E. Hirst Springer, 2006, ISBN 978-1-884628-222-5 http://dx.doi.org/10.1007/1-84628-222-5 From Real to Complex Analysis R. H. Dyer and D. E. Edmunds Springer, 2014, ISBN 978-3-319-06209-9

http://dx.doi.org/10.1007/978-3-319-06209-9

The Integral: A Crux for Analysis Steven G. Krantz Morgan & Claypool, 2011, ISBN 9781608456147 http://dx.doi.org/10.2200/S00327ED1V01Y201101MAS009

Real Analysis: Measures, Integrals and Applications Boris Makarov and Anatolii Podkorytov Springer, 2013, ISBN 978-1-4471-5122-7 http://dx.doi.org/10.1007/978-1-4471-5122-7

Measure, Integral, Derivative: A Course in Lebesgue’s Theory Sergei Ovchinnikov Springer, 2013, ISBN 978-1-4614-7196-7 http://dx.doi.org/10.1007/978-1-4614-7196-7 Measure and Integral Martin Brokate and Gotz Kersting Springer, 2015, ISBN 978-3-319-15365-0 http://dx.doi.org/10.1007/978-3-319-15365-0 A Course on Integration Theory: including more than 150 exercises with detailed answers Nicolas Lerner Springer, 2014, ISBN 978-3-0348-0694-7 http://dx.doi.org/10.1007/978-3-0348-0694-7 Mathematical Analysis: Approximation and Discrete Processes Mariano Giaquinta and Giuseppe Modica Springer, 2004, ISBN 978-0-8176-4414-7

http://dx.doi.org/10.1007/978-0-8176-4414-7 Discovering Mathematics: A Problem-Solving Approach to Mathematical Analysis with MATHEMATICA and Maple Jiri Gregor and Jaroslav Tiser Springer, 2011, ISBN 978-0-85729-064-9 http://dx.doi.org/10.1007/978-0-85729-064-9

Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras Joseph Muscat Springer, 2014, ISBN 978-3-319-06728-5 http://dx.doi.org/10.1007/978-3-319-06728-5

An Introduction to Modern Analysis Vicente Montesinos, Peter Zizler, and Vaclav Zizler Springer, 2015, ISBN 978-3-319-12481-0 http://dx.doi.org/10.1007/978-3-319-12481-0 A Course of Modern Analysis, Fourth Edition E. T. Whittaker and G. N. Watson Cambridge University Press, 1996 (1927), ISBN 9780511608759 http://dx.doi.org/10.1017/CBO9780511608759 Exercises in Analysis, Part I Leszek Gazinski and Nikolaos S. Papageorgiou

Springer, 2014, ISBN 978-3-319-06176-4 http://dx.doi.org/10.1007/978-3-319-06176-4

Examples and Theorems in Analysis Peter Walker Springer, 2004, ISBN 978-0-85729-380-0 http://dx.doi.org/10.1007/978-0-85729-380-0

Back to the Table of Contents =======================================

Real Analysis ==========================

Advanced Real Analysis Anthony W. Knapp Springer, 2005, ISBN 978-0-8176-4442-0 http://dx.doi.org/10.1007/0-8176-4442-3 Analysis: An Introduction Richard Beals Cambridge University Press, 2004, ISBN 9780511755163 http://dx.doi.org/10.1017/CBO9780511755163 Basic Real Analysis Anthony W. Knapp Springer, 2005, ISBN 978-0-8176-4441-3

http://dx.doi.org/10.1007/0-8176-4441-5 Basic Real Analysis, Second Edition Houshang H. Sohrab Springer, 2014, ISBN 978-1-4939-1841-6 http://dx.doi.org/10.1007/978-1-4939-1841-6 The Continuum: A Constructive Approach to Basic Concepts of Real Analysis Rudolf Taschner Springer, 2005, ISBN 978-3-322-82036-5 http://dx.doi.org/10.1007/978-3-322-82036-5 Lectures on Real Analysis Finnur Larusson Cambridge University Press, 2012, ISBN 9781139208604 http://dx.doi.org/10.1017/CBO9781139208604 A Problem Book in Real Analysis Asuman G. Aksoy and Mohamed A. Khamsi Springer, 2010, ISBN 978-1-4419-1296-1

http://dx.doi.org/10.1007/978-1-4419-1296-1 Problems in Real Analysis: Advanced Calculus on the Real Axis Teodora-Liliana T. Radulescu, Vicentiu D. Radulecu, and Titu Andrrescu Springer, 2009, ISBN 978-0-387-77379-7

http://dx.doi.org/10.1007/978-0-387-77379-7

Real Analysis for the Undergraduate: With an Invitation to Functional Analysis Matthew A. Pons Springer, 2014, ISBN 978-1-4614-9638-0 http://dx.doi.org/10.1007/978-1-4614-9638-0

Real Analysis on Intervals A.D.R. Choudary and Constantin P. Niculescu Springer, 2014, ISBN 978-81-322-2148-7 http://dx.doi.org/10.1007/978-81-322-2148-7

Real and Convex Analysis Erhan Cinlar and Robert J. Vanderbei Springer, 2013, ISBN 978-1-4614-5257-7 http://dx.doi.org/10.1007/978-1-4614-5257-7

The Real Numbers and Real Analysis Ethan D. Bloch Springer, 2011, ISBN 978-0-387-72177-4 http://dx.doi.org/10.1007/978-0-387-72177-4 Set Theoretical Aspects of Real Analysis Alexander B. Kharazishvili CRC Press, 2015, ISBN 978-1-4822-4202-7 http://dx.doi.org/10.1201/b17298

Complex Analysis =======================

Complex Analysis and Differential Equations Luis Barreira and Claudia Valls Springer, 2012, ISBN 978-1-4471-4008-5 http://dx.doi.org/10.1007/978-1-4471-4008-5 Complex Analysis: In the Spirit of Lipman Bers, Second Edition Rubi E. Rodriguez, Irwin Kra, and Jane P. Gilman Springer, 2013, ISBN 978-1-4419-7323-8 http://dx.doi.org/10.1007/978-1-4419-7323-8 A Course in Complex Analysis: From Basic Results to Advanced Topics Wolfgang Fischer and Ingo Lieb Springer, 2012, ISBN 978-3-8348-8661-3 http://dx.doi.org/10.1007/978-3-8348-8661-3 Geometric Function Theory: Explorations in Complex Analysis Steven G. Krantz Springer, 2006, ISBN 978-0-8176-4440-6

http://dx.doi.org/10.1007/0-8176-4440-7

Fourier Analysis ======================== An Introduction to Laplace Transform and Fourier Series, Second Edition Phil Dyke Springer, 2014, ISBN 978-1-4471-6395-4 http://dx.doi.org/10.1007/978-1-4471-6395-4 An Intuitive Explanation of Fourier Theory Steven Lehar http://cns-alumni.bu.edu/~slehar/fourier/fourier.html Classical Fourier Analysis, Third Edition Loukas Grafakos Springer, 2014, ISBN 978-1-4939-1194-3

http://dx.doi.org/10.1007/978-1-4939-1194-3 Modern Fourier Analysis, Third Edition Loukas Grafakos Springer, 2014, ISBN 978-1-4939-1230-8 http://dx.doi.org/10.1007/978-1-4939-1230-8

A Trip from Classical to Abstract Fourier Analysis Kenneth A. Ross Notices of the AMS, Volume 61, Number 9 (October 2014)

http://dx.doi.org/10.1090/noti1161 Digital Fourier Analysis: Fundamentals Ken’iti Kido Springer, 2015, ISBN 978-1-4614-9260-3 http://dx.doi.org/10.1007/978-1-4614-9260-3 Digital Fourier Analysis: Advanced techniques Ken’iti Kido Springer, 2015, ISBN 978-1-4939-1127-1 http://dx.doi.org/10.1007/978-1-4939-1127-1 Fourier Analysis and Its Applications Anders Vretblad Springer, 2003, ISBN 978-0-387-21723-9

http://dx.doi.org/10.1007/b97452 Foundations of Time-Frequency Analysis Karlheinz Grochenig Springer, 2001, ISBN 978-1-4612-0003-1 http://dx.doi.org/10.1007/978-1-4612-0003-1

The Fourier Transform and its Applications (Lecture Notes for EE 261) Brad Osgood Electrical Engineering Department, Stanford University http://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf

Course Home

http://see.stanford.edu/see/courseInfo.aspx?coll=84d174c2-

d74f-493d-92ae-c3f45c0ee091

Stanford Engineering Everywhere (SEE) http://see.stanford.edu/ Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry John P. D’Angelo Springer, 2013, ISBN 978-1-4614-8526-1 http://dx.doi.org/10.1007/978-1-4614-8526-1 An introduction to wavelets Amara Graps IEEE Computational Science & Engineering, Volume 2, Number 2 (Summer 1995) http://dx.doi.org/10.1109/99.388960 Wavelets for Kids: A Tutorial Introduction Brani Vidakovic and Peter Mueller http://gtwavelet.bme.gatech.edu/wp/kidsA.pdf Wavelets Made Easy Yves Nivergelt Springer, 2013 (2001), ISBN 978-1-4614-6006-0

http://dx.doi.org/10.1007/978-1-4614-6006-0 A Friendly Guide to Wavelets Gerald Kaiser Springer, 2011 (1994), ISBN 978-0-8176-8111-1

http://dx.doi.org/10.1007/978-0-8176-8111-1 An introduction to Wavelets Through Linear Algebra Michael W. Frazier Springer, 1999, ISBN 978-3-642-85570-2 http://dx.doi.org/10.1007/978-3-642-85570-2 Applied Mathematics: Data Compression, Spectral Methods, Fourier Analysis, Wavelets, and Applications Charles K. Chui and Quingtang Jiang Springer, 2013, ISBN 978-94-6239-009-6 http://dx.doi.org/10.2991/978-94-6239-009-6 A Mathematical Introduction to Wavelets P. Wojtaszczyk Cambridge University Press, 1997, ISBN 0780511623790 http://dx.doi.org/10.1017/CBO9780511623790 Wavelets: from Math to Practice Desanka P. Radunovic Springer, 2009, ISBN 978-3-642-00614-2

http://dx.doi.org/10.1007/978-3-642-00614-2 A Wavelet Tour of Signal Processing: The Sparse Way Stephane Mallat Elsevier, 2009, ISBN 978-0-12-374370-1 http://www.sciencedirect.com/science/book/9780123743701

From Fourier Analysis to Wavelets

Jonas Gomes and Luiz Velho Springer, 2015, ISBN 978-3-319-22075-8 http://dx.doi.org/10.1007/978-3-319-22075-8

Wavelet Transforms and Their Applications, Second Edition Lokenath Debnath and Firdous Ahmad Shah Springer, 2015, ISBN 978-0-8176-8418-1 http://dx.doi.org/10.1007/978-0-8176-8418-1

Discrete Fourier Analysis M.W. Wong Springer, 2011, ISNM 978-3-0348-0116-4 http://dx.doi.org/10.1007/978-3-0348-0116-4 Mastering the Discrete Fourier Transform in One, Two or Several Dimensions: Pitfalls and Artifacts Issav Amidror Springer, 2013, ISBN 978-1-4471-5167-8 http://dx.doi.org/10.1007/978-1-4471-5167-8 Decay of the Fourier Transform: Analytic and Geometric Aspects Alex Iosevich and Elijah Liflyand Springer, 2014, ISBN 978-3-0348-0625-1 http://dx.doi.org/10.1007/978-3-0348-0625-1 Excursions in Harmonic Analysis, Volume 1: The February Fourier Talks at the Norbert Wiener Center Travis D. Andrews, Radu Balan, John J. Benedetto,

Wojciech Czaja, and Kasso A. Okoudjou (Editors) Springer, 2013, ISBN 978-0-8176-8376-4 http://dx.doi.org/10.1007/978-0-8176-8376-4

Excursions in Harmonic Analysis, Volume 2: The February Fourier Talks at the Norbert Wiener Center Travis D. Andrews, Radu Balan, John J. Benedetto, Wojciech Czaja, and Kasso A. Okoudjou (Editors) Springer, 2013, ISBN 978-0-8176-8379-5 http://dx.doi.org/10.1007/978-0-8176-8379-5

Wavelets and Multiscale Analysis: Theory and Applications Jonathan Cohen and Ahmed I. Zayed (Editors) Springer, 2011, ISBN 978-0-8176-8095-4 http://dx.doi.org/10.1007/978-0-8176-8095-4

Shearlets: Multiscale Analysis for Multivariate Data Gitta Kutyniok and Demetrio Labate (Editors) Springer, 2012, ISBN 978-0-8176-8316-0 http://dx.doi.org/10.1007/978-0-8176-8316-0 Unified Signal Theory Gianfranco Cariolaro Springer, 2011, ISBN 978-0-85729-464-7 http://dx.doi.org/10.1007/978-0-85729-464-7 Fast Fourier Transform: Algorithms and Applications K.R. Rao, D.N. Kim, and J.J. Hwang Springer, 2010, ISBN 978-1-4020-6629-0

http://dx.doi.org/10.1007/978-1-4020-6629-0 A First Course in Statistics for Signal Analysis, Second Edition Springer, 2011, ISBN 978-0-8176-8101-2 Wojbor A. Woyczynski http://dx.doi.org/10.1007/978-0-8176-8101-2 A Basis Theory Primer: Expanded Edition Christopher Heil Springer, 2011, ISBN 978-0-8176-4687-5 http://dx.doi.org/10.1007/978-0-8176-4687-5 Distributions: Theory and Applications J.J. Dustremaat and J.A.C. Kolk Springer, 2010, ISBN 978-0-8176-4675-2

http://dx.doi.org/10.1007/978-0-8176-4675-2 Introduction to Hyperfunctions and Their Integral Transforms: An Applied and Computational Approach Urs Graf Springer, 2010, ISBN 978-3-0346-0408-6

http://dx.doi.org/10.1007/978-3-0346-0408-6 Explorations in Harmonic Analysis: With Applications to Complex Function Theory and the Heisenberg Group Steven G. Krantz Springer, 2009, ISBN 978-0-8176-4669-1

http://dx.doi.org/10.1007/978-0-8176-4669-1

Principles of Harmonic Analysis Anton Deitmar and Siegfried Echterhoff Springer, 2009, ISBN 978-0-387-85469-4 http://dx.doi.org/10.1007/978-0-387-85469-4

The Evolution of Applied Harmonic Analysis: Models of the Real World Elena Prestini Springer, 2004, ISBN 978-0-8176-8140-1 http://dx.doi.org/10.1007/978-0-8176-8140-1

Fourier Analysis and Approximation of Functions Roald M. Trigub and Eduard S. Bellinsky Springer, 2004, ISBN 978-1-4020-2876-2 http://dx.doi.org/10.1007/978-1-4020-2876-2

Applied Mathematics: Data Compression, Spectral Methods, Fourier Analysis, Wavelets, and Applications Charles K. Chui and Quingtang Jiang Springer, 2013, ISBN 978-94-6239-009-6 http://dx.doi.org/10.2991/978-94-6239-009-6

Inequalities ============================

Inequalities: Theorems, Techniques and Selected Problems Zdravko Cvetkovski Springer, 2012, ISBN 978-3-642-23792-8 http://dx.doi.org/10.1007/978-3-642-23792-8

Equations and Inequalities: Elementary Problems and Theorems in Algebra and Number Theory Jiri Herman, Radan Kucera, and Jaromir Simsa Springer, 2000, ISBN 978-1-4612-1270-6 http://dx.doi.org/10.1007/978-1-4612-1270-6

Inequalities: With Applications to Engineering, Second Edition Michael J. Cloud, Byron C. Drachman, and Leonid P. Lebedev Springer, 2014, ISBN 978-3-319-05311-0 http://dx.doi.org/10.1007/978-3-319-05311-0

The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities J. Michael Steele Cambridge University Press, 2004, ISBN 9780511917106 http://dx.doi.org/10.1017/CBO9780511817106

Inequalities E. F. Beckenbach and R. Bellman Springer, 1965, ISBN 978-3-642-64971-4 http://dx.doi.org/10.1007/978-3-642-64971-4

Proof: A Many-Splendored Thing ==========

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Book of Proof, Second Edition Richard Hammack (2013) http://www.people.vcu.edu/~rhammack/BookOfProof/ Home Page of Richard Hammack http://www.people.vcu.edu/~rhammack/

A Gentle Introduction to the Art of Mathematics Joseph E. Fields (2013) http://ares.southernct.edu/~fields/GIAM/

Home Page of Joe Fields http://ares.southernct.edu/~fields/ Mathematical Reasoning: Writing and Proof Ted Sundstrom (2014) https://sites.google.com/site/mathematicalreasoning3ed/

Home Page of Ted Sundstrom https://sites.google.com/site/tedsundstrom/

The Art of Proof:

Basic Training for Deeper Mathematics Matthias Beck and Ross Geoghegan Springer, 2010, ISBN 978-1-4419-7023-7 http://dx.doi.org/10.1007/978-1-4419-7023-7

The Proof is in the Pudding: The Changing Nature of Mathematical Proof Steven G. Krantz Springer, 2011, ISBN 978-0-387-48744-1 http://dx.doi.org/10.1007/978-0-387-48744-1

Proof Patterns Mark Joshi Springer, 2015, ISBN 978-3-319-16250-8

http://dx.doi.org/10.1007/978-3-319-16250-8

Proof: A Many-Splendored Thing Israel Kleiner and Nitsa Movshovitz-Hadat Mathematical Intelligencer, Volume 19, Number 3 (June 1997) http://dx.doi.org/10.1007/BF03025344

Proofs from THE BOOK, Fifth Edition Martin Aigner and Gunther M. Ziegler Springer, 2014, ISBN 978-3-662-44205-0 http://dx.doi.org/10.1007/978-3-662-44205-0

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Deduction, Computation, Experiment: Exploring the Effectiveness of Proof Rosella Lupacchini and Giovanna Corsi (Editors) Springer, 2008, ISBN 978-88-470-0784-0 http://dx.doi.org/10.1007/978-88-470-0784-0 Proofs (Not) from the Book S. Tabachnikov Mathematical Intelligencer, Volume 36, Number 2 (June 2014) http://dx.doi.org/10.1007/s00283-013-9424-2 A Logical Introduction to Proof Daniel W. Cunningham Springer, 2012, ISBN 978-1-4614-3631-7 http://dx.doi.org/10.1007/978-1-4614-3631-7

Informal Logic http://dx.doi.org/10.1007/978-1-4419-7127-2_1 Strategies for Proofs http://dx.doi.org/10.1007/978-1-4419-7127-2_2 Proofs and Fundamentals: A First Course in Abstract Mathematics, Second Edition Ethan D. Bloch Springer, 2011, ISBN 978-1-4419-7127-2 http://dx.doi.org/10.1007/978-1-4419-7127-2

Introduction to Mathematical Structures and Proofs, Second Edition Larry J. Gerstein Springer, 2012, ISBN 978-1-4614-4265-3

http://dx.doi.org/10.1007/978-1-4614-4265-3 Is it Plausible? Barry Mazur Mathematical Intelligencer, Volume 36, Number 1 (February 2014) http://dx.doi.org/10.1007/s00283-013-9398-0

Paradigms of Proof Johnston Anderson and Keith Austin The Mathematical Gazette, Volume 79, Number 486 (November 1995) http://www.jstor.org/stable/3618075

Introduction – Creativity, Thought and Mathematical Proof Ian Winchester (Editor) Special Issue: Creativity, Thought and Mathematical Proof Interchange, Volume 21, Number 1 (Spring 1990) http://dx.doi.org/10.1007/BF01809603

Why Do We Prove Theorems? Yehuda Ray Philosophia Mathematica, Volume 7, Issue 1 (February 1999) http://dx.doi.org/10.1093/philmat/7.1.5

Why Prove It Again? – Alternative Proofs in Mathematical Practice John W. Dawson, Jr. Springer, 2015, ISBN 978-3-319-17368-9

http://dx.doi.org/10.1007/978-3-319-17368-9

The Four-Colour Problem ================

Problem: Can every map be coloured with at most four colours in such a way that neighbouring countries are coloured differently?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The existence of unavoidable sets of geographically good configurations K. Appel and W. Haken Illinois Journal of Mathematics, Volume 20, Number 2 (1976) http://www.projecteuclid.org/euclid.ijm/1256049898 The Four-Color Problem

Kenneth Appel and Wolfgang Haken http://dx.doi.org/10.1007/978-1-4613-9435-8_7

Mathematics Today: Twelve Informal Essays Lynn Arthur Steen (Editor) Springer, 1978, ISBN 978-1-4613-9435-8 http://dx.doi.org/10.1007/978-1-4613-9435-8 An Unavoidable Set of Configurations in Planar Triangulations K. Appel and W. Haken Journal of Combinatorial Theory B, Volume 26, Number 1 (February 1979) http://dx.doi.org/10.1016/0095-8956(79)90038-8 The Four Color Proof Suffices K. Appel and W. Haken Mathematical Intelligencer, Volume 8, Number 1 (March 1986) http://dx.doi.org/10.1007/BF03023914 A Digest of the Four Color Theorem Frank R. Bernhart Journal of Graph Theory, Volume 1, Number 3 (Fall 1977) http://dx.doi.org/10.1002/jgt.3190010305 The Four-Color Theorem Rudolf Fritsch and Gerda Fritsch Springer, 1998, ISBN 978-1-4612-1720-6

http://dx.doi.org/10.1007/978-1-4612-1720-6

Map Color Theorem Gerhard Ringel Springer, 1974, ISBN 978-3-642-65759-7 http://dx.doi.org/10.1007/978-3-642-65759-7

Chapter 3 On Proof and Progress in Mathematics William P. Thurston http://dx.doi.org/10.1007/0-387-29831-2_3

Chapter 7 Computers and the Sociology of Mathematical Proof Donald Mackenzie http://dx.doi.org/10.1007/0-387-29831-2_7 18 Unconventional Essays on the Nature of Mathematics Reuben Hersh (Editor) Springer, 2006, ISBN 978-0-387-29831-3

http://dx.doi.org/10.1007/0-387-29831-2

Geometry, Fractals, and Topology =========

Explorations in Topology: Map Coloring, Surfaces, and Knots; Second Edition David A. Gay

Elsevier, 2014, ISBN 978-0-12-416648-6 http://www.sciencedirect.com/science/book/978012416

Euler’s Gem: The Polyhedron Formula and the Birth of Topology David S. Richeson Princeton University Press, 2008, ISBN 9781400838561 http://muse.jhu.edu/books/9781400838561 Topology through the centuries: Low dimensional manifolds John Milnor Bulletin of the AMS, Volume 52, Number 4 (October 2015) *** Large PDF – many photographs *** http://dx.doi.org/10.1090/bull/1507

Mysteries of the Equilateral Triangle Brian J. McCartin http://www.m-hikari.com/bmp.html The Four Pillars of Geometry John Stillwell Springer, 2005, ISBN 978-0-387-29052-2 http://dx.doi.org/10.1007/0-387-29052-4 Gems of Geometry, Second Edition John Barnes Springer, 2012, ISBN 978-3-642-30964-9

http://dx.doi.org/10.1007/978-3-642-30964-9 An Axiomatic Approach to Geometry: Geometric Trilogy I Francis Borceux Springer, 2014, ISBN 978-3-319-01730-3 http://dx.doi.org/10.1007/978-3-319-01730-3 An Algebraic Approach to Geometry: Geometric Trilogy II Francis Borceux Springer, 2014, ISBN 978-3-319-01733-4 http://dx.doi.org/10.1007/978-3-319-01733-4 A Differential Approach to Geometry: Geometric Trilogy III Francis Borceux Springer, 2014, ISBN 978-3-319-01736-5

http://dx.doi.org/10.1007/978-3-319-01736-5 Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination Marjorie Senechal (Editor) Springer, 2013, IS N978-0-387-92714-5 http://dx.doi.org/10.1007/978-0-387-92714-5 Manifold Mirrors: The Crossing Paths of the Arts and Mathematics Felipe Cucker Cambridge University Press, 2013, ISBN 9781139014632 http://dx.doi.org/10.1017/CBO9781139014632

The Art of Science: From Perspective Drawing to Quantum Randomness Rossella Lupacchini and Annarita Angelini (Editors) Springer, 2014, ISBN 978-3-319-02111-9

http://dx.doi.org/10.1007/978-3-319-02111-9 Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry Jurgen Richter-Gebert Springer, 2011, ISBN 978-3-642-17286-1 http://dx.doi.org/10.1007/978-3-642-17286-1

Symmetry and Pattern in Projective Geometry Eric Lord Springer, 2013, ISBN 978-1-4471-4631-5 http://dx.doi.org/10.1007/978-1-4471-4631-5

Geometry Revealed: A Jacob’s Ladder to Modern Higher Geometry Marcel Berger Springer, 2010, ISBN 978-3-540-70997-8 http://dx.doi.org/10.1007/978-3-540-70997-8

Curves and Surfaces Marco Abate and Francesca Tovena Springer, 2012, ISBN 978-88-470-1941-6 http://dx.doi.org/10.1007/978-88-470-1941-6

Dense Sphere Packings: A blueprint for formal proofs Thomas C. Hales Cambridge University Press, 2012, ISBN 9781139193894 http://dx.doi.org/10.1017/CBO9781139193894

The Colours of Infinity: The Beauty and Power of Fractals Nigel Lesmoir-Gordon (Editor) Springer, 2011, ISBN 978-1-84996-486-9 http://dx.doi.org/10.1007/978-1-84996-486-9 Chaos and Fractals: New Frontiers of Science, Second Edition Heinz-Otto Peitgen, Hartmut Jurgens, and Dietmar Saupe Springer, 2004, ISBN 978-0-387-21823-6 http://dx.doi.org/10.1007/b97624 The Science of Fractal Images Heinz-Otto Peitgen and Dietmar Saupe (Editors) Springer, 1988, ISBN 978-1-4612-3784-6 http://dx.doi.org/10.1007/978-1-4612-3784-6 The Beauty of Fractals: Images of Complex Dynamical Systems H.-O. Peitgen and P.H. Richter Springer, 1986, ISBN 978-3-642-61717-1 http://dx.doi.org/10.1007/978-3-642-61717-1 Superfractals

Michael Fielding Barnsley Cambridge University Press, 2006, ISBN 9781107590168 http://dx.doi.org/10.1017/CBO9781107590168

Fractal Geometry Steven G. Krantz Mathematical Intelligencer, Volume 11, Number 4 (Fall 1989) http://dx.doi.org/10.1007/BF03025877

Some “Facts” That Evaporate Upon Examination Benoit B. Mandelbrot Mathematical Intelligencer, Volume 11, Number 4 (Fall 1989) Pages 17-19 http://dx.doi.org/10.1007/BF03025878

Art Meets Mathematics in the Fourth Dimension, Second Edition Stephen Leon Lipscomb Springer, 2014, ISBN 978-3-319-06254-9 http://dx.doi.org/10.1007/978-3-319-06254-9

Introduction to Topology and Geometry, Second Edition Saul Stahl and Catherine Stenson Wiley, 2013, ISBN 9781118545904 http://dx.doi.org/10.1002/9781118545904 A Course in Point Set Topology John B. Conway

Measure, Topology, and Fractal Geometry, Second Edition Gerald Edgar Springer, 2008, ISBN 978-0-387-74749-1 http://dx.doi.org/10.1007/978-0-387-74749-1 The Four-Color Theorem: History, Topological Foundations, and Idea of Proof Rudolf Fritsch and Gerda Fritsch Springer, 1998, ISBN 978-1-4612-1720-6 http://dx.doi.org/10.1007/978-1-4612-1720-6 Knots – 3rd, fully revised and extended edition Gerhard Burde, Heiner Zieschang, and Michael Heusner Walter de Gruyter, 2014, ISBN 978-3-11-027078-5 http://www.degruyter.com/viewbooktoc/product/179871 An Introduction to Knot Theory W.B. Raymond Lickorish Springer, 1997, ISBN 978-1-4612-0691-0 http://dx.doi.org/10.1007/978-1-4612-0691-0 Graphs on Surfaces: Dualities, Polynomials, and Knots Joanna A. Ellis-Monaghan and Iain Moffatt Springer, 2013, ISBN 978-1-4614-6971-1

http://dx.doi.org/10.1007/978-1-4614-6971-1

A Short Course in Computational Geometry and Topology Herbert Edelsbrunner Springer, 2014, ISBN 978-3-319-05957-0 http://dx.doi.org/10.1007/978-3-319-05957-0

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, Fourth Edition David A. Cox, John Little, and Donal O’Shea Springer, 2015, ISBN 978-3-319-16721-3 http://dx.doi.org/10.1007/978-3-319-16721-3

Polyhedral and Algebraic Methods in Computational Geometry Michael Joswig and Thorsten Theobald Springer, 2013, ISBN 978-1-4471-4817-3 http://dx.doi.org/10.1007/978-1-4471-4817-3

Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists Paul Renteln Cambridge University Press, 2014, ISBN 9781107324893 http://dx.doi.org/10.1017/CBO9781107324893

Convex Analysis Steven G. Krantz CRC Press, 2015, ISBN 978-1-4987-0638-4 http://dx.doi.org/10.1201/b17694

Encyclopedia of Distances, Third Edition Michel Marie Deza and Elene Deza Springer, 2014, ISBN 978-3-662-44342-2 http://dx.doi.org/10.1007/978-3-662-44342-2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Lie Groups, Lie Algebras, and Representations: An Elementary Introduction; Second Edition Brian Hall Springer, 2015, ISBN 978-3-319-13467-3 http://dx.doi.org/10.1007/978-3-319-13467-3

Linear Algebra =========================

Linear Algebra David Cherney, Tom Denton, and Andrew Waldron https://www.math.ucdavis.edu/~linear/

Linear Algebra Done Right, Third Edition Sheldon Axler Springer, 2015, ISBN 978-3-319-11080-6

http://dx.doi.org/10.1007/978-3-319-11080-6

Linear Algebra: Algorithms, Applications, and Techniques; Third Edition Richard Bronson, Gabriel B. Costa, and John T. Saccoman Elsevier, 2014, ISBN 978-0-12-391420-0 http://www.sciencedirect.com/science/book/978012391

4200 Essential Linear Algebra with Applications: A Problem-Solving Approach Titu Andreescu Springer, 2014, ISBN 978-0-8176-4636-3 http://dx.doi.org/10.1007/978-0-8176-4636-3

Linear Algebra: for everyone Lorenzo Robbiano Springer, 2011, ISBN 978-88-470-1839-6 http://dx.doi.org/10.1007/978-88-470-1839-6

Finite-Dimensional Vector Spaces Paul R. Halmos Springer, 1987, ISBN 978-1-4612-6387-6 http://dx.doi.org/10.1007/978-1-4612-6387-6 Vectors, Pure and Applied: A General Introduction to Linear Algebra

T. W. Körner

Cambridge University Press, 2013, ISBN 9781139520034

http://dx.doi.org/10.1017/CBO9781139520034 A First Course in Linear Algebra Robert A. Beezer (2004-2013) http://linear.ups.edu/download.html

Linear Algebra Thoroughly Explained Milan Vujicic Springer, 2007, ISBN 978-3-540-74639-3 http://dx.doi.org/10.1007/978-3-540-74639-3

Linear Algebra: Concepts and Methods Martin Anthony and Michele Harvey Cambridge University Press, 2012, ISBN 9780511844249 http://dx.doi.org/10.1017/CBO9780511844249

A Concise Introduction to Linear Algebra Geza Schay Springer, 2012, ISBN 978-0-8176-8325-2 http://dx.doi.org/10.1007/978-0-8176-8325-2 Linear Algebra Peter Petersen Springer, 2012, ISBN 978-1-4614-3612-6 http://dx.doi.org/10.1007/978-1-4614-3612-6

The Linear Algebra a Beginning Graduate Student Ought to Know, Third Edition Jonathan S. Golan Springer, 2012, ISBN 978-94-007-2636-9 http://dx.doi.org/10.1007/978-94-007-2636-9

Applied Linear Algebra and Matrix Analysis Thomas Shores Springer, 2007, ISBN 978-0-387-48947-6 http://dx.doi.org/10.1007/978-0-387-48947-6

Matrix Analysis, Second Edition Roger A. Horn and Charles R. Johnson Cambridge University Press, 2013, ISBN 9781139020411 http://dx.doi.org/10.1017/CBO9781139020411

Matrix Reference Manual Mike Brookes http://www.ee.ic.ac.uk/hp/staff/dmb/matrix/ Home Page http://www.ee.ic.ac.uk/hp/staff/dmb/

A Concise Text on Advanced Linear Algebra Yisong Yang Cambridge University Press, 2015, ISBN 9781316103845 http://dx.doi.org/10.1017/CBO9781316103845

Advanced Linear Algebra Nicholas Loehr

CRC Press, 2014, ISBN 978-1-4665-5902-8 http://dx.doi.org/10.1201/b16505

Advanced Linear Algebra, Third Edition Steven Roman Springer, 2008, ISBN 978-0-387-72831-5 http://dx.doi.org/10.1007/978-0-387-72831-5 Algebra and Number Theory: An Integrated Approach Martyn R. Dixon, Leonid A. Kurdachenko, and Igor Ya. Subbotin Wiley, 2010, ISBN 9780470640548 http://dx.doi.org/10.1002/9780470640548 Linear Algebra and Geometry Igor R. Shafarevich and Alexey O. Remizov Springer, 2013, ISBN 978-3-642-30994-6 http://dx.doi.org/10.1007/978-3-642-30994-6 Separable Type Representations of Matrices and Fast Algorithms Volume 1: Basics. Completion Problems. Multiplication and Inversion Algorithms Yuli Eidelman, Israel Goldberg, and Julian Haimovici Springer, 2014, ISBN 978-3-0348-0606-0 http://dx.doi.org/10.1007/978-3-0348-0606-0 Separable Type Representations of Matrices and Fast Algorithms

Volume 2: Eigenvalue Method Yuli Eidelman, Israel Goldberg, and Julian Haimovici Springer, 2014, ISBN 978-3-0348-0612-1 http://dx.doi.org/10.1007/978-3-0348-0612-1

Algebra =============================== Classical Algebra: Its Nature, Origins, and Uses Roger Cooke Wiley, 2008, ISBN 9780470277980 http://dx.doi.org/10.1002/9780470277980

Basic Algebra Anthony W. Knapp Springer, 2006, ISBN 978-0-8176-4529-8 http://dx.doi.org/10.1007/978-0-8176-4529-8

Advanced Algebra Anthony W. Knapp Springer, 2007, ISBN 978-0-8176-4613-4 http://dx.doi.org/10.1007/978-0-8176-4613-4

Groups:

An Introduction to Ideas and Methods of the Theory of Groups Antonio Machi Springer, 2012, ISBN 978-88-470-2421-2 http://dx.doi.org/10.1007/978-88-470-2421-2

The Elementary Theory of Groups: A Guide through the Proofs of the Tarski Conjectures Benjamin Fine, Anthony Gaglione, Alexei Myasnikov, Gerhard Rosenberger, and Dennis Spellman Walter de Gruyter, 2014, ISBN 978-3-11-034203-1 http://www.degruyter.com/viewbooktoc/product/247008

Basic Modern Algebra with Applications Mahima Ranjan Adhikari and Avishek Adhikari Springer, 2014, ISBN 978-81-322-1599-8 http://dx.doi.org/10.1007/978-81-322-1599-8

Drawing with Complex Numbers Michael Eastwood and Roger Penrose The Mathematical Intelligencer, Volume 22, Number 4 (December 2000) http://dx.doi.org/10.1007/BF03026760

Why do Mathematicians Need Different Ways of Presenting Mathematical Objects? The Case of Cayley Graphs Irina Starikova http://dx.doi.org/10.1007/s11245-009-9065-4

Mathematical Knowledge: Intuition, visualization, and understanding (special issue)

Leon Horsten and Irina Starikova(Editors) Topoi, Volume 29, Number 1 (April 2010) Exterior Analysis: Using Applications of Differential Forms Erdogan S. Suhubi Elsevier, 2013, ISBN 978-0-12-415902-0 http://www.sciencedirect.com/science/book/9780124159020 Representation Theory: A Homological Algebra Point of View Alexander Zimmerman Springer, 2014, ISBN 978-3-319-07968-4 http://dx.doi.org/10.1007/978-3-319-07968-4

Category Theory Steve Awodey Oxford University Press, 2006, ISBN 9780198568612 http://dx.doi.org/10.1093/acprof:oso/9780198568612.001.000

1 Abstract Algebra: Structure and Applications David R. Finston and Patrick J. Morandi Springer, 2014, ISBN 978-3-319-04498-9 http://dx.doi.org/10.1007/978-3-319-04498-9 Abstract Algebra: An Introduction with Applications, Second Edition Derek J. S. Robinson Walter de Gruyter, 2015, ISBN 978-3-11-034087-7 http://www.degruyter.com/viewbooktoc/product/246334

An Invitation to General Algebra and Universal Constructions, Second Edition George M. Bergman Springer, 2015, ISBN 978-3-319-11478-1

http://dx.doi.org/10.1007/978-3-319-11478-1 Lattices and Ordered Sets Steven Roman Springer, 2008, ISBN 978-0-387-78901-9 http://dx.doi.org/10.1007/978-0-387-78901-9

Multivariable Calculus =================== Mathematical Analysis: An Introduction to Functions of Several Variables Mariano Giaquinta and Guiseppe Modica Springer, 2009, ISBN 978-0-8176-4612-7

http://dx.doi.org/10.1007/978-0-8176-4612-7 A Course in Multivariable Calculus and Analysis Sudhir R. Ghorpade and Balmohan V. Limaye Springer, 2010, ISBN 978-1-4419-1621-1

http://dx.doi.org/10.1007/978-1-4419-1621-1 Multivariable Calculus and Differential Geometry Gerard Walschap Walter de Gruyter, 2015, ISBN 978-3-11-036954-0 http://www.degruyter.com/viewbooktoc/product/430770 Differential Forms: Theory and Practice, Second Edition Steven H. Weintraub Elsevier, 2014, ISBN 978-0-12-394403-0 http://www.sciencedirect.com/science/book/9780123944030 A Geometric Approach to Differential Forms David Bachman Springer, 2006, ISBN 978-0-8176-4520-5

http://dx.doi.org/10.1007/978-0-8176-4520-5 Introduction to Tensor Analysis and the Calculus of Moving Surfaces Pavel Grinfeld Springer, 2013, ISBN 978-1-4614-7867-6

http://dx.doi.org/10.1007/978-1-4614-7867-6

Ordinary Differential Equations =========== Introductory Differential Equations, Fourth Edition Martha L. Abell and James P. Braselton Elsevier, 2014, ISBN 978-0-12-417219-7

http://www.sciencedirect.com/science/book/9780124172197 Ordinary Differential Equations: Analysis, Qualitative Theory and Control Hartmut Logemann and Eugene P. Ryan Springer, 2014, ISBN 978-1-4471-6398-5

http://dx.doi.org/10.1007/978-1-4471-6398-5 Differential Equations: A Primer for Scientists and Engineers Christian Constanda Springer, 2013, ISBN 978-1-4614-7297-1 http://dx.doi.org/10.1007/978-1-4614-7297-1

A First Course in Differential Equations, Second Edition J. David Logan Springer, 2011, ISBN 978-1-4419-7592-8 http://dx.doi.org/10.1007/978-1-4419-7592-8

An Introduction to Ordinary Differential Equations Ravi P. Agarwal and Donal O’Regan Springer, 2008, ISBN 978-0-387-71276-5 http://dx.doi.org/10.1007/978-0-387-71276-5

Differential Equations: Theory and Applications, Second Edition David Bettounes Springer, 2010, ISBN 978-1-4419-1163-6 http://dx.doi.org/10.1007/978-1-4419-1163-6

A Textbook on Ordinary Differential Equations Shair Ahmad and Antonio Ambroscetti Springer, 2014, ISBN 978-3-319-02129-4 http://dx.doi.org/10.1007/978-3-319-02129-4

A First Course in Ordinary Differential Equations: Analytical and Numerical Methods Martin Hermann and Masoud Saravi Springer, 2014, ISBN 978-81-322-1835-7 http://dx.doi.org/10.1007/978-81-322-1835-7

Ordinary Differential Equations and Mechanical Systems Jan Awrejcewicz Springer, 2014, ISBN 978-3-319-07659-1 http://dx.doi.org/10.1007/978-3-319-07659-1

Partial Differential Equations =============

Introduction to Partial Differential Equations Peter J. Olver Springer, 2014, ISBN 978-3-319-02099-0 http://dx.doi.org/10.1007/978-3-319-02099-0

Partial Differential Equations, Second Edition Emmanuele DiBenedetto Springer, 2010, ISBN 978-0-8176-4552-6 http://dx.doi.org/10.1007/978-0-8176-4552-6

Partial Differential Equations, Third Edition Jurgen Jost Springer, 2013, ISBN 978-1-4614-4809-9 http://dx.doi.org/10.1007/978-1-4614-4809-9

Lectures on Partial Differential Equations Vladimir I. Arnold Springer, 2004, ISBN 978-3-662-05441-3 http://dx.doi.org/10.1007/978-3-662-05441-3 Solving Numerical PDEs: Problems, Applications, Exercises Luca Formaggia, Fausto Saleri, and Alessandro Veneziani Springer, 2012, ISBN 978-88-470-2412-0 http://dx.doi.org/10.1007/978-88-470-2412-0 Applied Partial Differential Equations J. David Logan Springer, 2015, ISBN 978-3-319-12493-3

http://dx.doi.org/10.1007/978-3-319-12493-3 Partial Differential Equations in Action: From Modelling to Theory; Second Edition Sandro Salsa Springer, 2015, ISBN 978-3-319-15093-2 http://dx.doi.org/10.1007/978-3-319-15093-2

Functional Analysis ===================== Real Analysis for the Undergraduate: With an Invitation to Functional Analysis Matthew A. Pons Springer, 2014, ISBN 978-1-4614-9638-0 http://dx.doi.org/10.1007/978-1-4614-9638-0

An Introduction to Modern Analysis Vicente Montesinos, Peter Zizler, and Vaclav Zizler Springer, 2015, ISBN 978-3-319-12481-0 http://dx.doi.org/10.1007/978-3-319-12481-0 Functional Analysis: Fundamentals and Applications Michel Willem

Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras Joseph Muscat Springer, 2014, ISBN 978-3-319-06728-5 http://dx.doi.org/10.1007/978-3-319-06728-5

A Primer on Hilbert Space Theory: Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups Carlo Alabiso and Ittay Weiss Springer, 2015, ISBN 978-3.319-03713-4 http://dx.doi.org/10.1007/978-3-319-03713-4

Functional Analysis, Calculus of Variations and Optimal Control Francis Clarke Springer, 2013, ISBN 978-1-4471-4820-3 http://dx.doi.org/10.1007/978-1-4471-4820-3

Methods of Nonlinear Analysis: Applications to Differential Equations, Second Edition Pavel Drabek and Jaroslav Milota Springer, 2013, ISBN 978-3-0348-0387-8 http://dx.doi.org/10.1007/978-3-0348-0387-8

A Glimpse at Hilbert Space Operators: Paul R. Hamos in Memoriam Sheldon Axler, Peter Rosenthal, and Donald Sarason (Editors) Birkhauser, 2010, ISBN 978-3-0346-0347-8 http://dx.doi.org/10.1007/978-3-0346-0347-8

Wikipedia: http://en.wikipedia.org/wiki/Paul_Halmos The Elements of Operator Theory, Second Edition Carlos S. Kubrusly Springer, 2011, ISBN 978-0-8176-4998-2 http://dx.doi.org/10.1007/978-0-8176-4998-2 Basic Operator Theory Israel Gohberg and Seymour Goldberg Springer, 1980, ISBN 978-1-4612-5985-5

http://dx.doi.org/10.1007/978-1-4612-5985-5

Discrete Mathematics =================== Also see: the Solving Mathematical Problems section. Applied Discrete Structures

Alan Doerr and Kenneth Levasseur (2013) http://faculty.uml.edu/klevasseur/ads2/

Home Page of Ken Levasseur http://faculty.uml.edu/klevasseur/

The Bridge Between Continuous and Discrete http://dx.doi.org/10.1007/978-0-387-33062-4_1 Mathematical Masterpieces: Further Chronicles by the Explorers Arthur Knoebel, Reinhad Laubenbacher, Jerry Lodder, and David Pengelley Springer, 2007, ISBN 978-0-387-33062-4 http://dx.doi.org/10.1007/978-0-387-33062-4

Sets, Logic and Maths for Computing, Second Edition David Makinson Springer, 2012, ISBN 978-1-4471-2500-6 http://dx.doi.org/10.1007/978-1-4471-2500-6

Fundamentals of Discrete Math for Computer Science: A Problem-Solving Primer Tom Jenkyns and Ben Stephenson Springer, 2013, ISBN 978-1-4471-4069-6 http://dx.doi.org/10.1007/978-1-4471-4069-6

Mathematics of Discrete Structures for Computer Science Gordon J. Pace Springer, 2012, ISBN 978-3-642-29840-0

http://dx.doi.org/10.1007/978-3-642-29840-0 A Beginner’s Guide to Discrete Mathematics, Second Edition W.D. Wallis Springer, 2012, ISBN 978-0-8176-8286-6 http://dx.doi.org/10.1007/978-0-8176-8286-6 A First Course in Discrete Mathematics Ian Anderson Springer, 2002, ISBN 978-0-85729-315-2 http://dx.doi.org/10.1007/978-0-85729-315-2 Transfinite Numbers – What Is Infinity? S M Srivastava Resonance, Volume 2, Number 3 (March 1997)

http://dx.doi.org/10.1007/BF02838969

The Logic of Infinity Barnaby Sheppard Cambridge University Press, 2014, ISBN 9781107415614 http://dx.doi.org/10.1017/CBO9781107415614 The Mathematics of Infinity: A Guide to Great Ideas, Second Edition Theodore G. Faticoni Wiley, 2012, ISBN 9781118243879 http://dx.doi.org/10.1002/9781118243879

In Search of Infinity N. Ya. Vilenkin Springer, 1995, ISBN 978-1-4612-0837-2 http://dx.doi.org/10.1007/978-1-4612-0837-2 Introduction to Finite Mathematics John G. Kemeny, J. Laurie Snell, and Gerald L. Thompson http://www.math.dartmouth.edu/~doyle/docs/finite/cover/co

ver.html Topics in Finite and Discrete Mathematics Sheldon M. Ross Cambridge University Press, 2000, ISN 9780511755354 http://dx.doi.org/10.1017/CBO9780511755354 Mathematics Is Not a Spectator Sport George M. Phillips Springer, 2005, ISBN 978-0-387-28697-7 http://dx.doi.org/10.1007/0-387-28697-7 Discrete Mathematics: Elementary and Beyond L. Lovasz, J. Pelikan, and K. Vesztergombi Springer, 2003, ISBN 978-0-387-21777-2 http://dx.doi.org/10.1007/b97469

Looking at Numbers Tom Johnson and Franck Jedrzejewski Springer, 2014, ISBN 978-3-0438-0554-4

http://dx.doi.org/10.1007/978-3-0348-0554-4

The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications Martin Gardner Springer, 1997, ISBN 978-0-387-30389-5 http://dx.doi.org/10.1007/978-0-387-30389-5 How to Guard an Art Gallery: And Other Discrete Mathematical Adventures T. S. Michael Johns Hopkins University Press, 2009, ISBN 9780801897047 http://muse.jhu.edu/books/9780801897047 Difference Equations: From Rabbits to Chaos Paul Cull, Mary Flahive, and Robby Robson Springer, 2005, ISBN 978-0-387-27645-9 http://dx.doi.org/10.1007/0-387-27645-9 An Introduction to Difference Equations, Third Edition Saber Elaydi Springer, 2005, ISBN 978-0-387-23059-7 http://dx.doi.org/10.1007/0-387-27602-5 The Thrills of Abstraction P. R. Halmos The Two-Year College Mathematics Journal, Volume 13, Number 4 (September 1982)

http://www.jstor.org/stable/3027126 The Truth about Venn Diagrams Ian Stewart The Mathematical Gazette, Volume 60, Number 411 (March 1976) http://www.jstor.org/stable/3615644 Is the Venn Diagram Good Enough? Mou-liang Kung and George C. Harrison The College Mathematics Journal, Volume 15, Number 1 (January 1984) http://www.jstor.org/stable/3027430

On Picture-Writing George Polya The American Mathematical Monthly, Volume 63, Number 10 (December 1956) http://www.jstor.org/stable/2309555

The On-Line Encyclopedia of Integer Sequences (OEIS) https://oeis.org/ Website of Neil J. A. Sloane http://neilsloane.com/

Website of Herbert Wilf http://www.math.upenn.edu/~wilf/

Problems from the Discrete to the Continuous: Probability, Number Theory, Graph Theory, and Combinatorics Ross G. Pinsky Springer, 2014, ISBN 978-3-319-07965-3

http://dx.doi.org/10.1007/978-3-319-07965-3 Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra Matthias Beck and Sinai Robins Springer, 2007, ISBN 978-0-387-46112-0 http://dx.doi.org/10.1007/978-0-387-46112-0

The Surprising Mathematics of Longest Increasing Subsequences Dan Romik Cambridge University Press, 2014, ISBN 9781139872003 http://dx.doi.org/10.1017/CBO9781139872003

Combinatorics =========================

Combinatorics Through Guided Discovery Kenneth P. Bogart (2004)

http://www.math.dartmouth.edu/news-

resources/electronic/kpbogart/

Foundations of Combinatorics with Applications Edward A. Bender and S. Gill Williamson Dover, 2006, ISBN 0-486-44603-4 http://www.math.ucsd.edu/~ebender/CombText/

Applied Combinatorics: Preliminary Edition Michael T. Keller and William T. Trotter (February 2015) http://people.math.gatech.edu/~trotter/

generatingfunctionology, Second Edition Academic Press, 1994 Herbert Wilf http://www.math.upenn.edu/~wilf/DownldGF.html Website of Herbert Wilf http://www.math.upenn.edu/~wilf/

The Combinatorial Object Server http://www.theory.csc.uvic.ca/~cos/

Website of Neil J. A. Sloane http://neilsloane.com/ A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory, Second Edition

Miklos Bona World Scientific, 2006, ISBN 981-256-885-9 *** click on the book cover and then on “Front Cover” *** https://books.google.com/books?isbn=9789814335232

How to Count: An Introduction to Combinatorics and Its Applications Robert A. Beeler Springer, 2015, ISBN 978-3-319-13844-2 http://dx.doi.org/10.1007/978-3-319-13844-2

Combinatorics of Permutations, Second Edition Miklos Bona CRC Press, 2012, ISBN 978-1-4398-5052-7 http://dx.doi.org/10.1201/b12210

Combinatorics of Set Partitions Toufik Mansour CRC Press, 2013, ISBN 978-1-4398-6334-3 http://dx.doi.org/10.1201/b12691

Latin Squares and their Applications, Second Edition A. Donald Keedwell and Jozsef Denes Elsevier, 2015, ISBN 978-0-444-63555-6 http://www.sciencedirect.com/science/book/978044463

On Picture-Writing

George Polya The American Mathematical Monthly, Volume 63, Number 10 (December 1956) http://www.jstor.org/stable/2309555 Constructive Combinatorics Dennis Stanton and Dennis White Springer, 1986, ISBN 978-1-4612-4968-9

http://dx.doi.org/10.1007/978-1-4612-4968-9 Counting: The Art of Enumerative Combinatorics George E. Martin Springer, 2001, ISBN 978-1-4757-4878-9 http://dx.doi.org/10.1007/978-1-4757-4878-9

An Introduction to Enumeration Alan Camina and Barry Lewis Springer, 2011, ISBN 978-0-85729-599-6 http://dx.doi.org/10.1007/978-0-85729-600-9

Combinatorics, Second Edition Russell Merris Wiley, 2003, Online ISBN 978-0-471-44968-3 http://dx.doi.org/10.1002/0471449687

Problem-Solving Methods in Combinatorics: An Approach to Olympiad Problems Pablo Soberon

Counting and Configurations: Problems in Combinatorics, Arithmetic, and Geometry Jiri Herman, Radan Kucera, and Jaromir Simsa Springer, 2003, ISBN 978-1-4757-3925-1 http://dx.doi.org/10.1007/978-1-4757-3925-1

Algebraic Combinatorics: Walks, Trees, Tableaux, and More Richard P. Stanley Springer, 2013, ISBN 978-1-4614-6998-8 http://dx.doi.org/10.1007/978-1-4614-6998-8 Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture David M. Bressoud Cambridge University Press, 1999, ISBN 9780511613449 http://dx.doi.org/10.1017/CBO9780511613449 Inverse Relations and Combinatorial Identities John Riordan American Mathematical Monthly, Volume 71, Number 5 (May 1964) http://www.jstor.org/stable/2312584 The Pigeonhole Principle (What It Is, How It Works, and How It Applies to Map Coloring) Kenneth R. Rebman

The Two-Year College Mathematics Journal, Volume 10, Number 1 (January 1979) http://www.jstor.org/stable/3026807

Notes on Introductory Combinatorics George Polya, Robert E. Tarjan, and Donald R. Woods Springer, 2010, ISBN 978-0-8176-4953-1 http://dx.doi.org/10.1007/978-0-8176-4953-1

Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds G. Polya and R.C. Read Springer, 1987, ISBN 978-1-4612-4664-0 http://dx.doi.org/10.1007/978-1-4612-4664-0 Combinatorics: The Rota Way Joseph P. S. King, Gian-Carlo Rota, and Catherine H. Yan Cambridge University Press, 2009, ISBN 9780511803895 http://dx.doi.org/10.1017/CBO9780511803895 Combinatorial Snapshots Gian-Carlo Rota The Mathematical Intelligencer, Volume 21, Number 2 (June 1999) http://dx.doi.org/10.1007/BF03024840 On the foundations of combinatorial theory I. Theory of Mobius Functions Gian-Carlo Rota

Probability Theory and Related Fields, Volume 2, Number 4 (1964) http://dx.doi.org/10.1007/BF00531932

A Course in Enumeration Martin Aigner Springer, 2007, ISBN 978-3-540-39032-9 http://dx.doi.org/10.1007/978-3-540-39035-0

Enumerative Combinatorics, Volume 1, Second Edition Richard P. Stanley Cambridge University Press, 2012, ISBN 9781139058520 http://dx.doi.org/10.1017/CBO9781139058520 Enumerative Combinatorics, Volume 2 Richard P. Stanley Cambridge University Press, 1999, ISBN 978-0-511-60958-9 http://dx.doi.org/10.1017/CBO9780511609589 Combinatorial Theory Martin Aigner Springer, 1997, ISBN 978-3-642-59101-3 http://dx.doi.org/10.1007/978-3-642-59101-3 A Course in Combinatorics, Second Edition J. H. van Lint and R. M. Wilson Cambridge University Press, 2001, ISBN 9780511987045

http://dx.doi.org/10.1017/CBO9780511987045

Combinatorial Theory, Second Edition Marshall Hall, Jr. Wiley, 1983 (1998), ISBN 9781118032862 http://dx.doi.org/10.1002/9781118032862

Partition bijections, a survey Igor Pak The Ramanujan Journal, Volume 12, Number 1 (August 2006) http://dx.doi.org/10.1007/s11139-006-9576-1

Permutations, matrices, and generalized Young tableaux Donald E. Knuth Pacific Journal of Mathematics, Volume 34, Number 3 (1970) http://projecteuclid.org/DPubS?service=UI&version=1.0

&verb=Display&handle=euclid.pjm/1102971948 Advanced Combinatorics: The Art of Finite and Infinite Expansions; Revised and Enlarged Edition Louis Comtet Springer, 1974, ISBN 978-94-010-2196-8 http://dx.doi.org/10.1007/978-94-010-2196-8

Analytic Combinatorics Philippe Flajolet and Robert Sedgewick Cambridge University Press, 2009, ISBN 9780511801655

http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.h

http://dx.doi.org/10.1017/CBO9780511801655 Geometric Etudes in Combinatorial Mathematics Alexander Soifer Springer, 2010, ISBN 978-0-387-75469-7 http://dx.doi.org/10.1007/978-0-387-75470-3 Ramsey Theory: Yesterday, Today, and Tomorrow Alexander Soifer (Editor) Springer, 2011, ISBN 978-0-8176-8092-3

http://dx.doi.org/10.1007/978-0-8176-8092-3 Configurations from a Graphical Viewpoint Tomaz Pisanski and Brigitte Servatius Springer, 2013, ISBN 978-0-8176-8364-1 http://dx.doi.org/10.1007/978-0-8176-8364-1

Matroids: A Geometric Introduction Gary Gordon and Jennifer McNulty Cambridge University Press, 2012, ISBN 9781139049443 http://dx.doi.org/10.1017/CBO9781139049443

The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications Martin Gardner Springer, 1997, ISBN 978-0-387-30389-5

http://dx.doi.org/10.1007/978-0-387-30389-5 Games of No Chance Richard J. Nowakowski (Editor) http://library.msri.org/books/Book29/ More Games of No Chance Richard J. Nowakowski (Editor)

http://library.msri.org/books/Book42/ Games of No Chance 3 Michael H. Albert and Richard J. Nowakowski (Editors) Cambridge University Press, 2009, ISBN 9780511807251 http://dx.doi.org/10.1017/CBO9780511807251

Combinatorial Games: Tic-Tac-Toe Theory Jozsef Beck Cambridge University Press, 2008, ISBN 978-0-511-73520-2 http://dx.doi.org/10.1017/CBO9780511735202

Number Theory ======================== The Whole Truth About Whole Numbers:

An Elementary Introduction to Number Theory Sylvia Forman and Agnes M. Rash Springer, 2015, ISBN 978-3-319-11035-6 http://dx.doi.org/10.1007/978-3-319-11035-6

Elementary Number Theory in Nine Chapters, Second Edition James J. Tattersall Cambridge University Press, 2005, ISBN 9780511756344 http://dx.doi.org/10.1017/CBO9780511756344

Number Theory: Structures, Examples, and Problems Dorin Andrica and Titu Andreescu Springer, 2009, ISBN 978-0-8176-4645-5 http://dx.doi.org/10.1007/b11856 An Introduction to Diophantine Equations: A Problem-Based Approach Titu Andreescu, Dorin Andrica, and Ion Cucurezeanu Springer, 2010, ISBN 978-0-8176-4549-6 http://dx.doi.org/10.1007/978-0-8176-4549-6 Complex Numbers From A to … Z, Second Edition Titu Andreescu and Dorin Andrica Springer, 2014, ISBN 978-0-8176-8415-0 http://dx.doi.org/10.1007/978-0-8176-8415-0 Number Theory: An Introduction to Mathematics, Second Edition William A. Coppel

A Comprehensive Course in Number Theory Alan Baker Cambridge University Press, 2012, ISBN 9781139093835 http://dx.doi.org/10.1017/CBO9781139093835 Equations and Inequalities: Elementary Problems and Theorems in Algebra and Number Theory Jiri Herman, Radan Kucera, and Jaromir Simsa Springer, 2000, ISBN 978-1-4612-1270-6 http://dx.doi.org/10.1007/978-1-4612-1270-6 Arithmetic Tales Olivier Bordelles Springer, 2012, ISBN 978-1-4471-4096-2 http://dx.doi.org/10.1007/978-1-4471-4096-2 An Introduction to Number Theory Graham Everest and Thomas Ward Springer, 2005, ISBN 978-1-84628-044-3 http://dx.doi.org/10.1007/b137432

PRIMES: What is Riemann’s Hypothesis? Barry Mazur and William Stein (2014) http://wstein.org/books/rh/

Elementary Number Theory: Primes, Congruences, and Secrets William Stein (2011) http://wstein.org/ent/

Number Theory: An Introduction via the Distribution of Primes Benjamin Fine and Gerhard Rosenberger Springer, 2006, ISBN 978-0-8176-4541-0 http://dx.doi.org/10.1007/978-0-8176-4541-0

Prime Numbers: A Computational Perspective, Second Edition Richard Crandall and Carl Pomerance Springer, 2005, ISBN 978-0-387-28979-8 http://dx.doi.org/10.1007/0-387-28979-8 Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity; Fifth Edition Manfred Schroeder Springer, 2009, ISBN 978-3-540-85298-8 http://dx.doi.org/10.1007/978-3-540-85298-8 Algebraic Number Theory Frazer Jarvis Springer, 2014, ISBN 978-3-319-07545-7 http://dx.doi.org/10.1007/978-3-319-07545-7 Algebraic Number Theory, A Computational Approach William Stein (2012) http://wstein.org/books/ant/ant.pdf

Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories, Second Edition Yuri Ivanovic Manin and Alexei A. Panchishkin Springer, 2005, ISBN 3-540-27692-0

http://dx.doi.org/10.1007/3-540-27692-0 A Primer of Analytic Number Theory: From Pythagoras to Riemann Jeffrey Stopple Cambridge University Press, 2003, ISBN 9780511755132 http://dx.doi.org/10.1017/CBO9780511755132

On Certain Sequences of Integers Defined by Sieves Verna Gardiner, R. Lazarus, N. Metropolis, and S. Ulam Mathematics Magazine, Volume 29, Number 3 (January-February 1956) http://www.jstor.org/stable/3029719

A Visual Display of Some Properties of the Distribution of Primes M. L. Stein, S. M. Ulam, and M. B. Wells American Mathematical Monthly, Volume 71, Number 5 (May 1964)

http://www.jstor.org/stable/2312588 An Introduction to Sieve Methods and Their Applications Alina Carmen Cojocaru and M. Ram Murty Cambridge University Press, 2005, ISBN 978-0-511-61599-3

http://dx.doi.org/10.1017/CBO9780511615993 Neverending Fractions: An Introduction to Continued Fractions Jonathan Borwein, Alf Van der Poorten, Jeffrey Shallit, and Wadim Zudilin Cambridge University Press, 2014, ISBN 9780511902659 http://dx.doi.org/10.1017/CBO9780511902659

Transcendental Numbers M. Ram Murty and Purusottam Rath Springer, 2014, ISBN 978-1-4939-0832-5 http://dx.doi.org/10.1007/978-1-4939-0832-5 Lattice Theory: Foundation George Gratzer Springer, 2011, ISBN 978-3-0348-0018-1 http://dx.doi.org/10.1007/978-3-0348-0018-1 Lattice Theory: Special Topics and Applications, Volume 1 George Gratzer and Friedrich Wehrung (Editors) Springer, 2014, ISBN 978-3-319-06413-0 http://dx.doi.org/10.1007/978-3-319-06413-0 Reciprocity Laws: From Euler to Eisenstein Franz Lemmermeyer Springer, 2000, ISBN 978-3-662-12893-0

http://dx.doi.org/10.1007/978-3-662-12893-0

The Quadratic Reciprocity Law: A Collection of Classical Proofs Oswald Baumgart Springer, 2015, ISBN 978-3-319-16283-6 http://dx.doi.org/10.1007/978-3-319-16283-6

Introduction to Classical Mathematics I: From the Quadratic Reciprocity Law to the Uniformization Theorem Helmut Koch Springer, 1991, ISBN 978-94-011-3218-3 http://dx.doi.org/10.1007/978-94-011-3218-3

Applied Number Theory Harald Niederreiter and Arne Winterhof Springer, 2015, ISBN 9783-319-22321-6 http://dx.doi.org/10.1007/978-3-319-22321-6

Graph Theory ========================== Leonhard Euler and the Koenigsberg Bridges Leonhard Euler Scientific American, Volume 189, Number 1 (January 1953) http://www.nature.com/scientificamerican/journal/v189/n1/in

dex.html#articles

*** http://dx.doi.org/10.1038/scientificamerican0753-66

A Beginner’s Guide to Graph Theory, Second Edition W. D. Wallis Springer, 2007, ISBN 978-0-8176-4580-9 http://dx.doi.org/10.1007/978-0-8176-4580-9 Combinatorics and Graph Theory, Second Edition John M. Harris, Jeffry L. Hirst, and Michael J. Mossinghoff Springer, 2008, ISBN 978-0-387-79711-3 http://dx.doi.org/10.1007/978-0-387-79711-3 Graph Theory with Algorithms and Its Applications: In Applied Science and Technology Santanu Saha Ray Springer, 2013, ISBN 978-81-322-0750-4 http://dx.doi.org/10.1007/978-81-322-0750-4 A Textbook of Graph Theory, Second Edition R. Balakrishnan and K. Ranganathan Springer, 2012, ISBN 978-1-4614-4529-6 http://dx.doi.org/10.1007/978-1-4614-4529-6 Covering Walks in Graphs Futaba Fujie and Ping Zhang Springer, 2014, ISBN 978-1-4939-0305-4

http://dx.doi.org/10.1007/978-1-4939-0305-4

Magic Graphs, Second Edition Alison M. Marr and W.D. Wallis Springer, 2013, ISBN 978-0-8176-8391-7 http://dx.doi.org/10.1007/978-0-8176-8391-7

Graphs and Cubes Sergei Ovchinnikov Springer, 2011, ISBN 978-1-4614-0797-3 http://dx.doi.org/10.1007/978-1-4614-0797-3

The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators Alexander Soifer Springer, 2009, ISBN 978-0-387-74642-5 http://dx.doi.org/10.1007/978-0-387-74642-5 Thirty Essays on Geometric Graph Theory Janos Pach (Editor) Springer, 2013, ISBN 978-1-4614-01110-0 http://dx.doi.org/10.1007/978-1-4614-0110-0 The Four-Color Theorem: History, Topological Foundations, and Idea of Proof Rudolf Fritsch and Gerda Fritsch Springer, 1998, ISBN 978-1-4612-1720-6 http://dx.doi.org/10.1007/978-1-4612-1720-6 Graph Theory Applications

L.R. Foulds Springer, 1992, ISBN 978-1-4612-0933-1 http://dx.doi.org/10.1007/978-1-4612-0933-1

Spectral Radius of Graphs Dragan Stevanovic Elsevier, 2015, ISBN 9780-12-802068-5 http://www.sciencedirect.com/science/book/9780128020685

Network Science =======================

Also see: the Biological Networks shelf in the Biophysics, Bioinformatics, … section; the Computational Social Science shelf in the Computer Science, … section.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Network Science Albert-Laszlo Barabasi Center for Complex Network Research, Northeastern University

http://barabasilab.neu.edu/networksciencebook/ Network Science Albert-Laszlo Barabasi More Is Different Conference Nanyang Technological University, Singapore (2012) https://www.youtube.com/watch?v=NCq1kpuCUq4 The Architecture of Complexity: From the Topology of the WWW to Human Diseases Albert-Laszlo Barabasi Institute for Mathematics and Its Applications (April 2009) https://www.youtube.com/watch?v=KOfRITP9o5U

Catching the “Network Science” Bug: Insight and Opportunity for the Operations Researcher Operations Research, Volume 56, Number 5 (Sep/Oct 2008) http://dx.doi.org/10.1287/opre.1080.0606 Network Science Katy Borner, Soma Sanyal, and Alessandro Vespignani Annual Review of Information Science and Technology, Volume 41 (2007) http://dx.doi.org/10.1002/aris.2007.1440410119 Complex Networks: An Algorithmic Perspective Kayhan Erciyes CRC Press, 2015, ISBN 089-1-4665-7167-9 http://dx.doi.org/10.1201/b17409

Complex networks: Structure and dynamics S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang Physics Reports, Volume 424, Numbers 4-5 (February 2006)

http://dx.doi.org/10.1016/j.physrep.2005.10.009 Computational Network Science: An Algorithmic Approach Henry Hexmoor Elsevier, 2015, ISBN 978-0-12-800891-1 http://www.sciencedirect.com/science/book/9780128008911

Exploring complex networks Steven H. Strogatz Nature, Volume 410, Number 6825 (8 March 2001) http://dx.doi.org/10.1038/35065725

Fundamentals of Complex Networks: Models, Structures and Dynamics Guanrong Chen, Xiaofan Wang, and Xiang Li Wiley, 2015, ISBN 9781118718124 http://dx.doi.org/10.1002/9781118718124

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Algebraic connectivity of graphs Miroslav Fiedler Czechoslovak Mathematical Journal, Volume 23, Number 2 (1973)

http://dml.cz/handle/10338.dmlcz/101168 Community detection in graphs Santo Fortunato Physics Reports, Volume 486, Numbers 3-5 (February 2010) http://dx.doi.org/10.1016/j.physrep.2009.11.002 Eigenvectors of acyclic matrices Miroslav Fiedler Czechoslovak Mathematical Journal, Volume 25, Number 4 (1975) http://dml.cz/handle/10338.dmlcz/101356 Evolution of networks S.N. Dorogovtsev and J.F.F. Mendes Advances in Physics, Volume 51 (2002) http://arxiv.org/abs/cond-mat/0106144 Evolutionary Network Analysis: A Survey Charu Aggarwal and Karthik Subbian ACM Computing Surveys, Volume 47, Number 1 (July 2014)

http://dx.doi.org/10.1145/2601412 A fast and efficient heuristic algorithm for detecting community structures in complex networks Duanbing Chen, Yan Fu, and Mingsheng Shang Physica A, Volume 388, Number 13 (1 July 2009)

http://dx.doi.org/10.1016/j.physa.2009.03.022

Frontiers in Network Science (special issue) Bernd Blasius and Dirk Brockmann (Guest Editors) European Physical Journal B, Volume 84, Number 4 (December 2011) http://link.springer.com/journal/10051/84/4/

Graph clustering Satu Elisa Schaeffer Computer Science Review, Volume 1 (2007) http://dx.doi.org/10.1016/j.cosrev.2007.05.001

A Graph-Theoretic Approach to Enterprise Network Dynamics Horst Bunke, Peter J. Dickinson, Miro Kraetzl, and Walter D. Wallis Springer, 2007, ISBN 978-0-8176-4519-9 http://dx.doi.org/10.1007/978-0-8176-4519-9

Lectures on Complex Networks S. N. Dorogovtsev Clarendon Press, 2010 https://sites.google.com/site/sergeydorogovtsev/lectures_on_

complex_networks Network Science: Complexity in Nature and Technology Ernesto Estrada, Maria Fox, Desmond J. Higham, and Gian-Luca Oppo (Editors) Springer, 2010, ISBN 978-1-84996-396-1

http://dx.doi.org/10.1007/978-1-84996-396-1

Networks: An Introduction M.E.J. Newman Oxford University Press, 2010, ISBN 9780199206650 http://dx.doi.org/10.1093/acprof:oso/9780199206650.001.000

1 Network Science, Nonlinear Science and Infrastructure Systems Terry L. Friesz (Editor) Springer, 2007, ISBN 978-0-387-71134-8 http://dx.doi.org/10.1007/0-387-71134-1 Performance Analysis of Complex Networks and Systems Piet van Mieghem Cambridge University Press, 2014, ISBN 9781107415874

http://dx.doi.org/10.1017/CBO9781107415874 Principles of Systems Science George E. Mobus and Michael C. Kalton Springer, 2015, ISBN 978-1-4349-1920-8 http://dx.doi.org/10.1007/978-1-4939-1920-8

A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory Miroslav Fiedler Czechoslovak Mathematical Journal, Volume 25, Number 4 (1975)

http://dml.cz/handle/10338.dmlcz/101357

Spectral methods for graph clustering – A survey Maria C.V. Nascimento and Andre C.P.L.F. de Carvalho European Journal of Operational Research, Volume 2011, Number 2 (1 June 2011) http://dx.doi.org/10.1016/j.ejor.2010.08.012

Statistical mechanics of complex networks Reka Albert and Albert-Laszlo Barabasi Reviews of Modern Physics, Volume 74 (2002) http://arxiv.org/abs/cond-mat/0106096

Structural Equation Models: From Paths to Networks J. Christopher Westland Springer, 2015, ISBN 978-3-319-16507-3 http://dx.doi.org/10.1007/978-3-319-16507-3

The structure and function of complex networks M. E. J. Newman SIAM Review, Volume 45 (2003) http://arxiv.org/abs/cond-mat/0303516 A survey of kernel and spectral methods for clustering Maurizio Filippone, Francesco Camastra, Francesco Masulli, and Stefano Rovetta Pattern Recognition, Volume 41, Number 1 (January 2008) http://dx.doi.org/10.1016/j.patcog.2007.05.018 Synchronization in complex networks Alex Arenas, Albert Diaz-Guilera, Jurgen Kurths,

Yamir Moreno, and Changsong Zhou Physics Reports, Volume 469, Number 3 (December 2008) http://dx.doi.org/10.1016/j.physrep.2008.09.002

A very fast algorithm for detecting community structures in complex networks Xutao Wang, Guanrong Chen, and Hongtao Lu Physica A, Volume 384 (2007) http://dx.doi.org/10.1016/j.physa.2007.05.013

Weak Links: The Universal Key to the Stability of Networks and Complex Systems Peter Csermely Springer, 2009, ISBN 978-3-540-31157-7 http://dx.doi.org/10.1007/978-3-540-31157-7

Logic and Set Theory ==================== forallx: Cambridge 2014-2015 (with a complete solutions booklet) P.D. Magnus (modified by Tim Button for Cambridge) and Metatheory for truth-functional logic

Tim Button http://people.ds.cam.ac.uk/tecb2/logicebooks.shtml

Tim Button’s Home Page http://people.ds.cam.ac.uk/tecb2/index.shtml forallx: An Introduction to Formal Logic P.D. Magnus http://www.fecundity.com/logic/

Introduction to Logic and to the Methodology of Deductive Sciences Alfred Tarski Oxford University Press, 1946 *** click on the book cover and then on “Front Cover” *** https://books.google.com/books?isbn=0198021399

Three Views of Logic: Mathematics, Philosophy, and Computer Science Donald W. Loveland, Richard E. Hodel, and S. G. Sterrett Princeton University Press, 2014, ISBN 978-1-4008-4875-1 http://www.degruyter.com/viewbooktoc/product/459326

The Three Laws of Thought, Plus One: The Law of Comparisons Thomas L. Saaty Axioms, Volume 3, Number 1 (2014) http://dx.doi.org/10.3390/axioms3010046

Sets, Relations, Functions Ivo Düntsch and Günther Gediga (2000)

http://www.cosc.brocku.ca/~duentsch/papers/methprimer1.ht

Propositional and Predicate Calculus: A Model of Argument Derek Goldrei Springer, 2005, ISBN 978-1-84628-229-4 http://dx.doi.org/10.1007/1-84628-229-2

Logic and Structure, Fifth Edition Dirk van Dalen Springer, 2013, ISBN 978-1-4471-4558-5 http://dx.doi.org/10.1007/978-1-4471-4558-5

Elements of Logical Reasoning Jan Von Plato Cambridge University Press, 2013, ISBN 97851139567862 http://dx.doi.org/10.1017/CBO9781139567862 First-Order Logic Raymond M. Smullyan Springer, 1968, ISBN 978-3-642-86718-7 http://dx.doi.org/10.1007/978-3-642-86718-7 Sets, Logic and Categories Peter J. Cameron Springer, 1998, ISBN 978-1-4471-0589-3 http://dx.doi.org/10.1007/978-1-4471-0589-3

Lectures in Logic and Set Theory, Volume 1: Mathematical Logic George Tourlakis Cambridge University Press, 2003, ISBN 9780511615559 http://dx.doi.org/10.1017/CBO9780511615559

Lectures in Logic and Set Theory, Volume 2: Set Theory George Tourlakis Cambridge University Press, 2003, ISBN 9780511615566 http://dx.doi.org/10.1017/CBO9780511615566

Mathematical Logic George Tourlakis Wiley, 2008, ISBN 9781118032436 http://dx.doi.org/10.1002/9781118032435

A Course in Mathematical Logic for Mathematicians Yu. I. Manin Springer, 2010, ISBN 978-1-4419-0615-1 http://dx.doi.org/10.1007/978-1-4419-0615-1 Proofs and Computations Helmut Schwichtenberg and Stanley S. Wainer Cambridge University Press, 2012, ISBN 9781139031905 http://dx.doi.org/10.1017/CBO9781139031905 Type Theory and Formal Proof: An Introduction Rob Nederpelt and Herman Geuvers Cambridge University Press, 2014, ISBN 9781139567725

http://dx.doi.org/10.1017/CBO9781139567725 Introduction to Mathematical Logic Vilnis Detlovs and Karlis Podnieks http://www.ltn.lv/~podnieks/mlog/ml.htm What is Mathematics: Godel’s Theorem and Around Karlis Podnieks http://www.ltn.lv/~podnieks/gt.html

Website http://www.ltn.lv/~podnieks/ Computability and Logic, Fifth Edition George S. Boolos, John P. Burgess, and Richard C. Jeffrey Cambridge University Press, 2007, ISBN 9780511804076 http://dx.doi.org/10.1017/CBO9780511804076 Godel’s Proof Ernest Nagel and James R. Newman Scientific American, Volume 194, Number 6 (June 1956) http://www.nature.com/scientificamerican/journal/v194/n6/in

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The Completeness Theorem of Godel: 1. An Introduction to Mathematical Logic S. M. Srivastava Resonance, Volume 6, Number 7 (July 2001) http://dx.doi.org/10.1007/BF02835268

The Completeness Theorem of Godel:

2. Henkin’s Proof for First Order Logic S. M. Srivastava Resonance, Volume 6, Number 8 (August 2001) http://dx.doi.org/10.1007/BF02902516

Godel’s Proof: 1. An Introduction to Mathematical Logic S M Srivastava Resonance, Volume 12, Number 2 (February 2007) http://dx.doi.org/10.1007/s12045-007-0028-z

Godel’s Proof: 2. Semantics of First order Theory and Hilbert’s program S M Srivastava Resonance, Volume 12, Number 3 (March 2007) http://dx.doi.org/10.1007/s12045-007-0018-1

Godel’s Proof: 3. Incompleteness Theorems S M Srivastava Resonance, Volume 12, Number 5 (May 2007) http://dx.doi.org/10.1007/s12045-007-0052-z An Introduction to Godel’s Theorems, Second Edition Peter Smith Cambridge University Press, 2013, ISBN 9781139149105 http://dx.doi.org/10.1017/CBO9781139149105 Kurt Godel: Essays for His Centennial Solomon Feferman, Charles Parsons, and Stephen G. Simpson (Editors)

The Mathematics of Logic: A guide to completeness theorems and their applications Richard Kaye Cambridge University Press, 2007, ISBN 9780511619243 http://dx.doi.org/10.1017/CBO9780511619243

Formal Languages in Logic: A Philosophical and Cognitive Analysis Catarina Dutilh Novaes Cambridge University Press, 2012, ISBN 9781139108010 http://dx.doi.org/10.1017/CBO9781139108010 Set Theory: Exploring Independence and Truth Ralf Schindler Springer, 2014, ISBN 978-3-319-06725-4 http://dx.doi.org/10.1007/978-3-319-06725-4 Set Theory: With an Introduction to Real Point Sets Abhijit Dasgupta Springer, 2014, ISBN 978-1-4614-8854-5 http://dx.doi.org/10.1007/978-1-4614-8854-5 The Joy of Sets: Fundamentals of Contemporary Set Theory, Second Edition Keith Devlin Springer, 1993, ISBN 978-1-4612-0903-4

http://dx.doi.org/10.1007/978-1-4612-0903-4

In Search of Infinity N. Ya. Vilenkin Springer, 1995, ISBN 978-1-4612-0837-2 http://dx.doi.org/10.1007/978-1-4612-0837-2 The Mathematics of Infinity: A Guide to Great Ideas, Second Edition Theodore G. Faticoni Wiley, 2012, ISBN 9781118243879 http://dx.doi.org/10.1002/9781118243879

Sets for Mathematics F. William Lawvere and Robert Rosebrugh Cambridge University Press, 2003, ISBN 9780511755460 http://dx.doi.org/10.1017/CBO9780511755460

Ordered Sets: An Introduction Bernd S. W. Schroder Springer, 2003, ISBN 978-1-4612-0053-6 http://dx.doi.org/10.1007/978-1-4612-0053-6 Ordered Sets Robert Harzheim Springer, 2005, ISBN 978-0-387-24222-4 http://dx.doi.org/10.1007/b104891

Lattices and Ordered Sets Steven Roman Springer, 2008, ISBN 978-0-387-78901-9 http://dx.doi.org/10.1007/978-0-387-78901-9

Classical Descriptive Set Theory Alexander S. Kechris Springer, 1995, ISBN 978-1-4612-4190-4 http://dx.doi.org/10.1007/978-1-4612-4190-4

Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics Jose Ferreiros Springer, 2007, ISBN 978-3-7643-8350-3 http://dx.doi.org/10.1007/978-3-7643-8350-3

The Elements of Cantor Sets – With Applications Robert W. Vallin Wiley, 2013, ISBN 9781118405710 http://dx.doi.org/10.1002/9781118548745 The Logical Status of Diagrams Sun-Joo Shin Cambridge University Press, 1995, ISBN 9780511574696 http://dx.doi.org/10.1017/CBO9780511574696 Visual Reasoning with Diagrams Amiouche Moktefi and Sun-Joo Shin (Editors) Springer, 2013, ISBN 978-3-0348-0600-8

http://dx.doi.org/10.1007/978-3-0348-0600-8 Principia Mathematica to *56 Alfred North Whitehead and Bertrand Russell Cambridge University Press, 1997, ISBN 9780511623585 http://dx.doi.org/10.1017/CBO9780511623585 The Evolution of Principia Mathematica: Bertrand Russell’s Manuscripts and Notes for the Second Edition Bernard Linsky Cambridge University Press, 2011, ISBN 9780511760181 http://dx.doi.org/10.1017/CBO9780511760181 A Course in Model Theory Katrin Tent and Martin Ziegler Cambridge University Press, 2012, ISBN 9781139015417 http://dx.doi.org/10.1017/CBO9781139015417 Practical Foundations for Programming Languages Robert Harper Cambridge University Press, 2013, ISBN 9781139342131 http://dx.doi.org/10.1017/CBO9781139342131 Apartness and Uniformity: A Constructive Development Douglas S. Bridges and Luminita Vita Springer, 2011, ISBN 978-3-642-22415-7

http://dx.doi.org/10.1007/978-3-642-22415-7

Elementary Set Theory with a Universal Set Randall Holmes http://math.boisestate.edu/~holmes/holmes/head.pdf

Randall Holmes’s Home Page http://math.boisestate.edu/~holmes/ Kripke’s Worlds: An Introduction to Modal Logics via Tableaux Olivier Gasquet, Andreas Herzig, Bilal Said, and Francois Schwarzentruber Springer, 2014, ISBN 978-3-7643-8504-0 http://dx.doi.org/10.1007/978-3-7643-8504-0 Universal Logic as a Science of Patterns Brian R. Gaines http://dx.doi.org/10.1007/978-3-319-10193-4_7

The Road to Universal Logic: Festschrift for 50th Birthday of Jan-Yves Beziau, Volume I Arnold Kozlow and Arthur Buchsbaum (Editors) Springer, 2015, ISBN 978-3-319-10193-4 http://dx.doi.org/10.1007/978-3-319-10193-4

Truth, Proof, and Infinity: A Theory of Constructions and Constructive Reasoning Peter Fletcher Springer, 1998, ISBN 978-94-017-3616-9 http://dx.doi.org/10.1007/978-94-017-3616-9

Back to the Table of Contents

=======================================

Thoughts, Ideas, Opinions, Surveys, and Blogs =======================================

Math Trek Blog https://www.sciencenews.org/search?st=math+trek&=S

earch Science News Magazine http://www.sciencenews.org/ Discrete Thoughts: Essays on Mathematics, Science, and Philosophy Mark Kac, Gian-Carlo Rota, and Jacob T. Schwartz Springer, 2008, ISBN 978-0-8176-4775-9 http://dx.doi.org/10.1007/978-0-8176-4775-9

The Mathematics of Paul Erdos I, Second Edition Ronald L. Graham, Jaroslav Nesetril, and Steve Butler (Editors) Springer, 2013, ISBN 978-1-4614-7258-2 http://dx.doi.org/10.1007/978-1-4614-7258-2

The Mathematics of Paul Erdos II, Second Edition

Ronald L. Graham, Jaroslav Nesetril, and Steve Butler (Editors) Springer, 2013, ISBN 978-1-4614-7254-4 http://dx.doi.org/10.1007/978-1-4614-7254-4 The Crossing of Heaven: Memoirs of a Mathematician Karl Gustafson Springer, 2012, ISBN 978-3-642-22558-1

http://dx.doi.org/10.1007/978-3-642-22558-1 A Mathematician Reflects on the Useful and Reliable Illusion of Reality in Mathematics Keith Devlin Erkenntnis, Volume 68, Number 3 (May 2008)

http://dx.doi.org/10.1007/s10670-008-9105-2 Mathematics – The Music of Reason Jean Diedonne Springer, 1992, ISBN 978-3-662-35358-5 http://dx.doi.org/10.1007/978-3-662-35358-5

Mathematics: Queen and Servant of the Sciences Michael Atiyah Proceedings of the American Philosophical Society, Volume 137, Number 4 (December 1993) http://www.jstor.org/stable/987071

MATHKNOW:

Mathematics, Applied Sciences and Real Life Michele Emmer and Alfio Quarteroni (Editors) Springer, 2009, ISBN 978-88-470-1122-9 http://dx.doi.org/10.1007/978-88-470-1122-9 Imagine Math: Between Culture and Mathematics Michele Emmer (Editor) Springer, 2012, ISBN 978-88-470-2427-4

http://dx.doi.org/10.1007/978-88-470-2427-4 Imagine Math 2: Between Culture and Mathematics Michele Emmer (Editor) Springer, 2013, ISBN 978-88-470-2889-0 http://dx.doi.org/10.1007/978-88-470-2889-0

The Mathematician as a Type William Story http://aleph0.clarku.edu/~djoyce/story/MathAsType.html

William Edward Story - Biography http://www.gap-system.org/~history/Biographies/Story.html David E. Joyce, Professor of Mathematics and Computer Science, Clark University http://aleph0.clarku.edu/~djoyce/

Truth as a Value and Duty: Lessons of Mathematics **** Includes a question and answer period **** Yuri Manin

http://dx.doi.org/10.1007/978-1-4020-9896-3_3 Truth in Science, the Humanities, and Religion: Balzan Symposium 2008 M.E.H. Nicolette Mout and Werner Stauffacher (Editors) Springer, 2010, ISBN 978-1-4020-9896-3 http://dx.doi.org/10.1007/978-1-4020-9896-3 Georg Cantor and his heritage Yuri I. Manin arXiv:math/0209244 http://arxiv.org/abs/math/0209244 Mathematical knowledge: internal, social and cultural aspects Yu. I. Manin arXiv:math/0703427v1 http://arxiv.org/abs/math/0703427v1 Comments on a recent item by Yu I Manin Elemer E Rosinger arXiv:math/0703547

http://arxiv.org/abs/math/0703547 The Mathematical Truth Enrico Bombiery, Institute for Advanced Study Slides of a lecture at Swiss Federal Institute of Technology (November 24, 2008) http://www.math.ethz.ch/news_events/bombieri_math_truth.

Mathematics, Matter and Method, Philosophical Papers, Volume I, Second Edition Hilary Putnam Cambridge University Press, 1979, ISBN 9780511625268

http://dx.doi.org/10.1017/CBO9780511625268 Unfashionable Pursuits Freeman J. Dyson The Mathematical Intelligencer, Volume 5, Number 3 (September 1983) http://dx.doi.org/10.1007/BF03026573

Birds and Frogs Freeman Dyson Notices of the AMS, Volume 56, Number 2 (February 2009) http://www.ams.org/notices/200902/rtx090200212p.pd

f Wikipedia: http://en.wikipedia.org/wiki/Freeman_Dyson A Revolution in Mathematics? What Really Happened a Century Ago and Why It Matters Today Frank Quinn Notices of the AMS, Volume 59, Number 1 (January 2012) http://www.ams.org/notices/201201/rtx120100031p.pdf

Encounters with Science: Dialogues in Five Parts Lars Garding http://dx.doi.org/10.1007/3-540-30434-7_14 Perspectives in Analysis: Essays in Honor of Lennart Carleson’s 75th Birthday Michael Benedicks, Peter W. Jones, Stanislaw Smirnov, and Bjorn Winckler (Editors) Springer, 2005, ISBN 978-3-540-30434-0 http://dx.doi.org/10.1007/3-540-30434-7

The Hilbert-Brouwer controversy resolved? Per Martin-Lof http://dx.doi.org/10.1007/978-3-7643-8653-5_15 One Hundred years of Intuitionism (1907-2007) – The Cerisy Conference Mark van Atten, et al. (Editors) Springer, 2008, ISBN 978-3-7643-8653-5 http://dx.doi.org/10.1007/978-3-7643-8653-5

18 Unconventional Essays on the Nature of Mathematics Reuben Hersh (Editor) Springer, 2006, ISBN 978-0-387-29831-3 http://dx.doi.org/10.1007/0-387-29831-2 The Two Cultures of Mathematics

http://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf When are two proofs essentially the same?

http://gowers.wordpress.com/2007/10/04/when-are-two-

proofs-essentially-the-same/ Prof. W.T. Gowers, FRS, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge http://www.dpmms.cam.ac.uk/people/w.t.gowers/ Weblog http://gowers.wordpress.com/

Mathematical Events of the Twentieth Century **** The Russian perspective **** A.A. Bolibruch, Yu. S.Osipov, and Ya. G. Sinai (Editors) Springer, 2006, ISBN 978-3-540-23235-3 http://dx.doi.org/10.1007/3-540-29462-7

Contemporary Debates on the Nature of Mathematics A.N. Kolmogorov (1929) Problems of Information Transmission, Volume 42, Number 4 (October-December 2006) http://dx.doi.org/10.1134/S0032946006040107

Unified Foundations for Mathematics Mark Burgin arXiv:math/0403186v1 http://arxiv.org/abs/math/0403186

The Abel Prize: 2003-2007 The First five Years

Helge Holden and Ragni Piene (Editors) Springer, 2010, ISBN 978-3-642-01372-0 http://dx.doi.org/10.1007/978-3-642-01373-7

Proof, Computation and Agency - Logic at the Crossroads - First Indian Conference on Logic and its Relationship with Other Disciplines Johan van Benthem, Amitabha Gupta, and Rohit Parikh (Editors) Springer, 2011, ISBN 978-94-007-0079-6 http://dx.doi.org/10.1007/978-94-007-0080-2

Computational Discovery in Pure Mathematics Simon Colton http://dx.doi.org/10.1007/978-3-540-73920-3_9

Computational Discovery Saso Dzeroski and Ljupco Todorovski (Editors) Springer, 2007, ISBN 978-3-540-73919-7, LNCS 4660 http://dx.doi.org/10.1007/978-3-540-73920-3 Risk and Reward: The Science of Casino Blackjack N. Richard Werthamer Springer, 2009, ISBN 978-1-4419-0252-8 http://dx.doi.org/10.1007/978-1-4419-0253-5 Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win Steven Skiena Cambridge University Press, 2001, ISBN 9780511547089

http://dx.doi.org/10.1017/CBO9780511547089 The Doctrine of Chances: Probabilistic Aspects of Gambling Stewart N. Ethier Springer, 2010, ISBN 978-3-540-78763-9 http://dx.doi.org/10.1007/978-3-540-78783-9 Mixing Apples and Oranges: What Poetry and Applied Mathematics Have in Common Joel E. Cohen Proceedings of the American Philosophical Society, Volume 155, Number 2 (June 2011) http://www.amphilsoc.org/publications/proceedings/v/155/n/

History of Mathematics ================== 5000 Years of Geometry: Mathematics in History and Culture Christoph J. Scriba and Peter Schreiber Springer, 2015, ISBN 978-3-0348-0898-9 http://dx.doi.org/10.1007/978-3-0348-0898-9

The Scholar and the State: In Search of Van der Waerden

Alexander Soifer Springer, 2015, ISBN 978-3-0348-0712-8 http://dx.doi.org/10.1007/978-3-0348-0712-8

Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century Victor J. Katz and Karen Hunger Parshall Princeton University Press, 2014, ISBN 9781400850525 http://muse.jhu.edu/books/9781400850525

The Chinese Roots of Linear Algebra Roger hart Johns Hopkins University Press, 2011, ISBN 9780801899584 http://muse.jhu.edu/books/9780801899584 Abraham Robinson: The Creation of Nonstandard Analysis – A Personal and Mathematical Odyssey Princeton University Press, 1995, ISBN 9781400864096 http://muse.jhu.edu/books/9781400864096 Mathematical Encounters of the Second Kind Philip J. Davis Springer, 1997, ISBN 978-1-4612-2462-4 http://dx.doi.org/10.1007/978-1-4612-2462-4 Journey through Mathematics: Creative Episodes in Its History Enrique A. Gonzalez- Velasco Springer, 2011, ISBN 978-0-387-92154-9 http://dx.doi.org/10.1007/978-0-387-92154-9

Mathematics and Its History John Stillwell Springer, 2010, ISBN 978-1-4419-6053-5 http://dx.doi.org/10.1007/978-1-4419-6053-5

Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century Victor J. Katz and Karen Hunger Parshall Princeton University Press, 2014, ISBN 978-1-4008-5052-5 http://www.degruyter.com/viewbooktoc/product/452092

Sources in the Development of Mathematics: Infinite Series and Products from the Fifteenth to the Twenty-first Century Ranjan Roy Cambridge University Press, 2011, ISBN 9780511844195 http://dx.doi.org/10.1017/CBO9780511844195

Geometry: Our Cultural Heritage, Second Edition Audun Holme Springer, 2010, ISBN 978-3-642-14441-7 http://dx.doi.org/10.1007/978-3-642-14441-7

Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century Jeremy Gray Springer, 2010, ISBN 978-0-85729-060-1 http://dx.doi.org/10.1007/978-0-85729-060-1

Analysis by Its History E. Hairer and G. Wanner Springer, 2008, ISBN 978-0-387-77036-9 http://dx.doi.org/10.1007/978-0-387-77036-9

Gauss: A Biographical Study W. K. Buhler Springer, 1981, ISBN 978-3-642-49207-5 http://dx.doi.org/10.1007/978-3-642-49207-5

A History of Chinese Mathematics Jean-Claude Martzloff Springer, 2006, ISBN 978-3-540-33783-6 http://dx.doi.org/10.1007/978-3-540-33783-6 Throwing Some Light on the Vast Darkness that is Analysis: Niels Henrik Abel’s Critical Revision and the Concept of Absolute Convergence Henrik Kragh Sorensen Centaurus – An International Journal of the History of Science and Its Cultural Aspects, Volume 52, Issue 1 (February 2010) http://dx.doi.org/10.1111/j.1600-0498.2009.00163.x

The Battle for Cantorian Set Theory Joseph W. Dauben http://dx.doi.org/10.1007/0-387-28272-6_10 Hilbert and his Twenty-Four Problems Rudiger Thiele http://dx.doi.org/10.1007/0-387-28272-6_11

Mathematics and the Historian’s Craft – The Kenneth O. May Lectures Glen Van Brummelen and Michael Kinyon (Editors) Springer, 2005, ISBN 978-0-387-25284-1 http://dx.doi.org/10.1007/0-387-28272-6

A History of the Central Limit Theorem: From Classical to Modern Probability Theory Hans Fischer Springer, 2011, ISBN 978-0-387-87856-0 http://dx.doi.org/10.1007/978-0-387-87857-7

A History of Algebra: From al-Khwarizmi to Emmy Noether B.L. van der Waerden Springer, 1985, ISBN 978-3-642-51599-6 http://dx.doi.org/10.1007/978-3-642-51599-6

Science Awakening I B.L. van der Waerden Springer, 1988, ISBN 978-94-009-1379-0 http://dx.doi.org/10.1007/978-94-009-1379-0

The World as a Mathematical Game: John von Neumann and Twentieth Century Science Giorgio Israel and Ana Milan Gasca Springer, 2009, ISBN 978-3-7643-9896-5 http://dx.doi.org/10.1007/978-3-7643-9896-5

Hilbert

Constance Reid Springer, 1996, ISBN 978-1-4612-0739-9 http://dx.doi.org/10.1007/978-1-4612-0739-9

Sur les problems futures des mathematiques David Hilbert Deuxieme Congres International des Mathematiciens (1900) http://mathunion.org/ICM/ICM1900/

ICM Proceedings 1893-2010 http://mathunion.org/ICM/ International Mathematical Union http://mathunion.org/

Modeling and Simulation ================ Modeling and Simulation in the Systems Engineering Life Cycle: Core Concepts and Accompanying Lectures Margaret L. Loper (Editor) Springer, 2015, ISBN 978-1-4471-5634-5 http://dx.doi.org/10.1007/978-1-4471-5634-5

Ways of Thinking, Ways of Seeing:

Mathematical and Other Modelling in Engineering and Technology Chris Bissell and Chris Dillon (Editors) Springer, 2012, ISBN 978-3-642-25209-9 http://dx.doi.org/10.1007/978-3-642-25209-9

Modeling and Simulation: An Application-Oriented Introduction Hans-Joachim Bungartz, Stefan Zimmer, Martin Bucholz, and Dirk Pfluger Springer, 2014, ISBN 978-3-642-39524-6 http://dx.doi.org/10.1007/978-3-642-39524-6

Principles of Modeling and Simulation: A Multidisciplinary Approach John A. Sokolowski and Catherine M. Banks (Editors) Wiley, 2009, ISBN 9780470403563 http://dx.doi.org/10.1002/9780470403563

Modeling Reality: How Computers Mirror Life Iwo Bialynicki-Birual and Iwona Bialynicka-Birula Oxford University Press, 2004, ISBN 9780198531005 http://dx.doi.org/10.1093/acprof:oso/9780198531005.001.000

1 Handbook of Real-World Applications in Modeling and Simulation John A. Sokolowski and Catherine M. Banks (Editors) Wiley, 2012, ISBN 9781118241042

http://dx.doi.org/10.1002/9781118241042 Discrete and Continuous Simulation: Theory and Practice Susmita Bandyopadhyay and Ranjan Bhattacharya CRC Press, 2014, ISBN 978-1-4665-9640-5 http://dx.doi.org/10.1201/b17127 It’s a Nonlinear World Richard H. Enns Springer, 2011, ISBN 978-0-387-75340-9 http://dx.doi.org/10.1007/978-0-387-75340-9 Mathematics and Technology Christiane Rousseau and Yvan Saint-Aubin Springer, 2008, ISBN 978-0-387-69216-6

http://dx.doi.org/10.1007/978-0-387-69216-6 The Mathematics of Medical Imaging: A Beginner’s Guide Timothy G. Freeman Springer, 2010, ISBN 978-0-387-92712-1 http://dx.doi.org/10.1007/978-0-387-92712-1

Mathematical Modelling of Zombies Robert Smith University of Ottawa Press, 2014, ISBN 9780776621685 http://muse.jhu.edu/books/9780776621685

Braaaiiinnnsss!: from Academics to Zombies Robert Smith (Editor)

University of Ottawa Press, 2011, ISBN 9780776619613 http://muse.jhu.edu/books/9780776619613

Probability ============================

What Is Probability? Rudolf Carnap Scientific American, Volume 189, Number 3 (September 1953) http://www.nature.com/scientificamerican/journal/v189/n3/in

dex.html#articles *** http://dx.doi.org/10.1038/scientificamerican0953-128

An Introduction to Probability Theory and its Applications, Volume 1, Second Edition William Feller Wiley, 1957 https://archive.org/details/AnIntroductionToProbabilityTheory

AndItsApplicationsVolume1

Chance Rules: An Informal Guide to Probability, Risk and Statistics; Second Edition

Brian Everitt Springer, 2008, ISBN 978-0-387-77415-2 http://dx.doi.org/10.1007/978-0-387-77415-2

Probabilities: The Little Numbers that Rule Our Lives Peter Olofsson Wiley, 2007, ISBN 9780470099797 http://dx.doi.org/10.1002/0470099798

A Basic Course in Measure and Probability Ross Leadbetter, Stamatis Cambanis, and Vladas Pipiras Cambridge University Press, 2014, ISBN 9781139103947 http://dx.doi.org/10.1017/CBO9781139103947

Elementary Probability, 2nd Edition David Stirzaker Cambridge University Press, 2003, ISBN 9780511755309 http://dx.doi.org/10.1017/CBO9780511755309

The Unity and Diversity of Probability Glenn Shafer http://www.jstor.org/stable/2245372 Comment by Hirotugu Akaike http://www.jstor.org/stable/2245373

Comment by David Aldous http://www.jstor.org/stable/2245374 Comment by George Box

http://www.jstor.org/stable/2245375 Comment by A. P. Dempster

http://www.jstor.org/stable/2245376 Comment by B. Efron

http://www.jstor.org/stable/2245377 Comment by Ian Hacking http://www.jstor.org/stable/2245378

Comment by David S. Moore http://www.jstor.org/stable/2245379 Rejoinder by Glenn Shafer http://www.jstor.org/stable/2245380

Statistical Science, Volume 5, Number 4 (1990) Janus-Faced Probability Paolo Rocchi Springer, 2014, ISBN 978-3-319-04861-1 http://dx.doi.org/10.1007/978-3-319-04861-1

Understanding Probability, Third Edition Henk Tijms Cambridge University Press, 2012, ISBN 9781139206990 http://dx.doi.org/10.1017/CBO9781139206990 Introduction to Probability, Second Edition George G. Roussas Elsevier, 2014, ISBN 978-0-12-800041-0 http://www.sciencedirect.com/science/book/9780128000410 Basic Probability Theory with Applications Mario Lefebvre Springer, 2009, ISBN 978-0-387-74995-2

http://dx.doi.org/10.1007/978-0-387-74995-2 40 Puzzles and Problems in Probability and Mathematical Statistics Wolfgang Schwarz Springer, 2008, ISBN 978-0-387-73512-2 http://dx.doi.org/10.1007/978-0-387-73512-2 An Introduction to Probability and Statistical Inference, Second Edition George G. Roussas Elsevier, 2015, ISBN 978-0-12-800114-1 http://www.sciencedirect.com/science/book/9780128001141 An introduction to Measure-Theoretic Probability, Second Edition George G. Roussas Elsevier, 2014, ISBN 978-0-12-800042-7 http://www.sciencedirect.com/science/book/9780128000427 Probability and Random Variables: A Beginner’s Guide David Stirzaker Cambridge University Press, 1999, ISBN 9780511813627 http://dx.doi.org/10.1017/CBO9780511813627 Analysis and Probability Aurel Spataru Elsevier, 2013, ISBN 978-0-12-401665-1 http://www.sciencedirect.com/science/book/9780124016651

Probability Theory: A Comprehensive Course, Second Edition Achim Klenke Springer, 2014, ISBN 978-1-4471-5361-0 http://dx.doi.org/10.1007/978-1-4471-5361-0

The Theory of Probability Santosh S. Venkatesh Cambridge University Press, 2013, ISBN 9781139169325 http://dx.doi.org/10.1017/CBO9781139169325

A Probability Path Sidney I. Resnick Springer, 2014, ISBN 978-0-8176-8409-9 http://dx.doi.org/10.1007/978-0-8176-8409-9

Probability: The Classical Limit Theorems Henry McKean Cambridge University Press, 2014, ISBN 9781107282032 http://dx.doi.org/10.1017/CBO9781107282032 Fundamentals of Applied Probability and Random Processes, Second Edition Oliver C. Ibe Elsevier, 2014, ISBN 978-0-12-800852-2 http://www.sciencedirect.com/science/book/9780128008522 Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, via Conditioning, Second Edition

Loic Chaumont and Marc Yor Cambridge University Press, 2012, ISBN 9781139135351 http://dx.doi.org/10.1017/CBO9781139135351

Fundamentals of Probability: A First Course Anirban DasGupta Springer, 2010, ISBN 978-1-4419-5780-1 http://dx.doi.org/10.1007/978-1-4419-5780-1

Introduction to Probability Models, Eleventh Edition Sheldon M. Ross Elsevier, 2014, ISBN 978-0-12-407948-9 http://www.sciencedirect.com/science/book/9780124079489 Probability Models, Second Edition John Haigh Springer, 2013, ISBN 978-1-4471-5343-6 http://dx.doi.org/10.1007/978-1-4471-5343-6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A Treatise on Probability John Maynard Keynes (1921) http://www.archive.org/details/treatiseonprobab007528

mbp Wikipedia: http://en.wikipedia.org/wiki/John_Maynard_Keynes

Probability and Statistics =================

Probability and Statistics by Example I: Basic probability and Statistics, Second Edition Yuri Suhov and Mark Kelbert Cambridge University Press, 2014, ISBN 9781139087773

http://dx.doi.org/10.1017/CBO9781139087773 Probability and Statistics by Example, Volume 2 Yuri Suhov and Mark Kelbert Cambridge University Press, 2008, ISBN 9780521612341

http://dx.doi.org/10.1017/CBO9780511813641 A Modern Introduction to Probability and Statistics: Understanding Why and How F.M. Dekking, C. Kraaikamp, H.P. Lopuhaa, and L.E. Meester Springer, 2005, ISBN 978-1-84628-168-6

http://dx.doi.org/10.1007/1-84628-168-7

Statistics ==============================

Chance Rules: An Informal Guide to Probability, Risk and Statistics; Second Edition Brian Everitt Springer, 2008, ISBN 978-0-387-77415-2 http://dx.doi.org/10.1007/978-0-387-77415-2

Common Errors in Statistics (and How to Avoid Them), Fourth Edition Philip I. Good and James W. Hardin Wiley, 2012, ISBN 9781118294390 http://dx.doi.org/10.1002/9781118360125

Core Statistics Simon N. Wood Cambridge University Press, 2015, ISBN 9781107741973 http://dx.doi.org/10.1017/CBO9781107741973

Past, Present, and Future of Statistical Science Xihong Lin, Christian Genest, David L. Banks, Geert Molenberghs, David W. Scott, and Jane-Ling Wang (Editors) CRC Press, 2014, ISBN 978-1-4822-0498-8 http://dx.doi.org/10.1201/b16720

Normal and Student’s t Distributions and Their Applications

Mohammad Ahsanullah, B. M. Golam Kibria, and Mohammad Shakil Springer, 2014, ISBN 978-94-6239-061-4 http://dx.doi.org/10.2991/978-94-6239-061-4

Regression: Models, Methods and Applications Ludwig Fahrmeir, Thomas Kneib, Stefan Lang, and Brian Marx Springer, 2013, ISBN 978-3-642-34333-9 http://dx.doi.org/10.1007/978-3-642-34333-9

Do We Really Need the S-word? Megan D. Higgs American Scientist, Volume 101, Number 1 (January-February 2013) http://dx.doi.org/10.1511/2013.100.6

What Everyone Should Know about Statistical Correlation Vladica M. Velickovic American Scientist, Volume 103, Number 1 (January-February 2015) http://dx.doi.org/10.1511/2015.112.26

To Throw Away Data: Plagiarism as a Statistical Crime Andrew Gelman and Thomas Basboll American Scientist, Volume 101, Number 3 (May-June 2013) http://www.americanscientist.org/issues/pub/2013/3/to-

throw-away-data-plagiarism-as-a-statistical-crime

Outlier Analysis Charu C. Aggarwal Springer, 2013, ISBN 978-1-4614-6396-2 http://dx.doi.org/10.1007/978-1-4614-6396-2

Data is a singular noun (2010) Norman Gray http://nxg.me.uk/note/2005/singular-data/

Website http://nxg.me.uk/ The Art of Data Science Matthew J. Graham http://dx.doi.org/10.1007/978-1-4614-3323-1_4

Astrostatistics and Data Mining Luis Manuel Sarro, Laurent Eyer, William O’Mullane, and Joris De Ridder (Editors) Springer, 2012, ISBN 978-1-614-3323-1 http://dx.doi.org/10.1007/978-1-4614-3323-1

The Future of Data Analysis John W. Tukey Annals of Mathematical Statistics, Volume 33, Number 1 (March 1962) http://www.jstor.org/stable/2237638

Symmetry Studies:

An Introduction to the Analysis of Structured Data in Applications Marlos A. G. Viana Cambridge University Press, 2008, ISBN 9780511755477 http://dx.doi.org/10.1017/CBO9780511755477

An Introduction to Categorical Data Analysis, Second Edition Alan Agresti Wiley, 2007, ISBN 9780470114759 http://dx.doi.org/10.1002/0470114754

Categorical Data Analysis, Second Edition Alan Agresti Wiley, 2002, ISBN 9780471249689 http://dx.doi.org/10.1002/0471249688

First Link in the Markov Chain: Probability and poetry were unlikely partners in the creation of a computational tool Brian Hayes American Scientist, Volume 101, Number 2 (March-April 2013) http://www.americanscientist.org/issues/pub/2013/2/first-

links-in-the-markov-chain Understanding Markov Chains: Examples and Applications Nicolas Privault Springer, 2013, ISBN 978-981-4451-51-2

http://dx.doi.org/10.1007/978-981-4451-51-2

Finite Markov Chains and Algorithmic Applications Olle Haggstrom Cambridge University Press, 2002, ISBN 9780511613586 http://dx.doi.org/10.1017/CBO9780511613586

Markov Chains R. Norris Cambridge University Press, 1998 http://www.statslab.cam.ac.uk/~james/Markov/

A Course in Time Series Analysis Daniel Pena, George C. Tiao, and Ruey S. Tsay (Editors) Wiley, 2001, ISBN 9781118032978 http://dx.doi.org/10.1002/9781118032978

Probability and Information: An Integrated Approach, Second Edition David Applebaum Cambridge University Press, 2008, ISBN 978-0-511-75526-2 http://dx.doi.org/10.1017/CBO9780511755262

Essentials of Stochastic Processes, Second Edition Rick Durrett (2011) http://www.math.duke.edu/~rtd/EOSP/eosp.html Springer, 2012, ISBN 978-1-4614-3615-7 http://dx.doi.org/10.1007/978-1-4614-3615-7

Informal Introduction to Stochastic Processes with Maple

Jan Vrbik and Paul Vrbik Springer, 2013, ISBN 978-1-4614-4057-4 http://dx.doi.org/10.1007/978-1-4614-4057-4

Introduction to Probability and Stochastic Processes with Applications Liliana Blanco Castaneda, Viswanathan Arunachalam, and Delvamuthu Dharmaraja Wiley, 2012, ISBN 9781118344972 http://dx.doi.org/10.1002/9781118344972

An Introduction to Markov Processes, Second Edition Daniel W. Stroock Springer, 2014, ISBN 978-3-642-40523-5 http://dx.doi.org/10.1007/978-3-642-40523-5

Markov Processes for Stochastic Modeling, Second Edition Oliver C. Ibe Elsevier, 2013, ISBN 978-0-12-407795-9 http://www.sciencedirect.com/science/book/9780124077959 Multivariate Statistics: Exercises and Solutions, Second edition Wolfgang Hardle and Zdenek Hlavka Springer, 2015, ISBN 978-3-642-36005-3 http://dx.doi.org/10.1007/978-3-642-36005-3 Applied Multivariate Statistical Analysis, Fourth Edition Wolfgang Karl Hardle and Leopold Simar Springer, 2015, ISBN 978-3-662-45171-7

http://dx.doi.org/10.1007/978-3-662-45171-7 Fundamentals of Modern Statistical Methods: Substantially Improving Power and Accuracy, Second Edition Rand R. Wilcox Springer, 2010, ISBN 978-1-4419-5525-8 http://dx.doi.org/10.1007/978-1-4419-5525-8 Chi-Squared Goodness of Fit Tests with Applications V. Voinov, M. Nikulin, and N. Balakrishnan Elsevier, 2013, ISBN 978-0-12-397194-4 http://www.sciencedirect.com/science/book/9780123971944 Numerical Methods of Statistics, Second Edition John F. Monahan Cambridge University Press, 2011, ISBN 9780511977176 http://dx.doi.org/10.1017/CBO9780511977176 A Matrix Handbook for Statisticians George A. F. Seber Wiley, 2008, ISBN 9780470226797

http://dx.doi.org/10.1002/9780470226797 Data Representations, Transformations, and Statistics for Visual Reasoning Ross MacieJewski Morgan & Claypool, 2011, ISBN 9781608456260

http://dx.doi.org/10.2200/S00357ED1V01Y201105VIS002

The Significance Test Controversy Revisited: The Fiducial Bayesian Alternative Bruno Lecoutre and Jacques Poitevineau Springer, 2014, ISBN 978-3-662-44046-9 http://dx.doi.org/10.1007/978-3-662-44046-9

Statistical Modeling and Computation Dirk P. Kroese and Joshua C.C. Chan Springer, 2014, ISBN 978-1-4614-8775-3 http://dx.doi.org/10.1007/978-1-4614-8775-3

Matrix Tricks for Linear Statistical Models: Our Personal Top Twenty Simo Puntanen, George P. H. Styan, and Jarko Isotalo Springer, 2011, ISBN 978-3-642-10473-2 http://dx.doi.org/10.1007/978-3-642-10473-2

The Big Picture (Chapter 4) http://dx.doi.org/10.1007/0-387-34239-7_4

Estimation of Dependences Based on Empirical Data Vladimir Vapnik Springer, 2006, ISBN 978-0-387-34329-9 http://dx.doi.org/10.1007/0-387-34239-7

Fisher, Neyman, and the Creation of Statistics Erich L. Lehmann Springer, 2011, ISBN 978-1-4419-9500-1 http://dx.doi.org/10.1007/978-1-4419-9500-1

Principal Component Analysis, Second Edition I.T. Jolliffe Springer, 2002, ISBN 978-0-387-22440-4 http://dx.doi.org/10.1007/b98835

Probability Theory As Extended Logic **************************************************** Edwin T. Jaynes was one of the first people to realize that probability theory, as originated by Laplace is a generalization of Aristotelian logic that reduces to deductive logic in the special case that our hypotheses are either true or false. This website has a large selection of his articles, as well as articles by a number of other people who use probability theory in this way **************************************************** http://bayes.wustl.edu/ Statistics in Food Science and Nutrition Are Hugo Pripp Springer, 2013, ISBN 978-1-4614-5010-8 http://dx.doi.org/10.1007/978-1-4614-5010-8 Statistics for Anthropology, Second Edition Lorena Madrigal Cambridge University Press, 2012, ISBN 9781139022699 http://dx.doi.org/10.1017/CBO9781139022699 Statistical Modeling and Computation

Dirk P. Kroese and Joshua C.C. Chan Springer, 2014, ISBN 978-1-4614-8775-3 http://dx.doi.org/10.1007/978-1-4614-8775-3

The Foundations of Statistics: A Simulation-based Approach Shravan Vasishth and Michael Broe Springer, 2011, ISBN 978-3-642-16313-5 http://dx.doi.org/10.1007/978-3-642-16313-5

Explorations in Monte Carlo Methods Ronald W. Shonkwiler and Franklin Mendivil Springer, 2009, ISBN 978-0-387-87837-9 http://dx.doi.org/10.1007/978-0-387-87837-9 Essentials of Monte Carlo Simulation: Statistical Methods for Building Simulation Models Nick T. Thomopoulos Springer, 2013, ISBN 978-1-4614-6022-0 http://dx.doi.org/10.1007/978-1-4614-6022-0 Foundations of Applied Statistical Methods Hang Lee Springer, 2014, ISBN 978-3-319-02402-8 http://dx.doi.org/10.1007/978-3-319-02402-8 Principles of Applied Statistics D. R. Cox and Christal A. Donnelly Cambridge University Press, 2011, ISBN 9781139005036 http://dx.doi.org/10.1017/CBO9781139005036

Statistical Principles for the Design of Experiments R. Mead, S. G. Gilmour, and A. Mead Cambridge University Press, 2012, ISBN 9781139020879 http://dx.doi.org/10.1017/CBO9781139020879

Lies, Damned Lies and Statistics http://www.york.ac.uk/depts/maths/histstat/lies.htm

Material for the History of Statistics http://www.york.ac.uk/depts/maths/histstat/welcome.htm A Career in Statistics: Beyond the Numbers Gerald J. Hahn and Necip Doganaksov Wiley, 2011, ISBN 9781118490143 http://dx.doi.org/10.1002/9781118490143

Strength in Numbers: The Rising of Academic Statistics Departments in the U.S. Alan Agresti and Xiao-Li Meng (Editors) Springer, 2013, ISBN 978-1-4614-3649-2 http://dx.doi.org/10.1007/978-1-4614-3649-2

Odds Are, It’s Wrong: Science fails to face the shortcomings of statistics Tom Siegfried Science News, Volume 177, Number 7 (March 27, 2010) http://www.sciencenews.org/view/feature/id/57091/descripti

on/Odds_Are_Its_Wrong

The Dilemma of Statistics: Rigorous Mathematical Methods Cannot Compensate Messy Interpretations and Lousy Data Peter Schuster Complexity, Volume 20, Number 1 (September-October 2014) http://dx.doi.org/10.1002/cplx.21553

The Pleasures of Statistics: The Autobiography of Frederick Mosteller Frederick Mosteller Springer, 2010, ISBN 978-0-387-77956-0 http://dx.doi.org/10.1007/978-0-387-77956-0

Wikipedia: http://en.wikipedia.org/wiki/Frederick_Mosteller

Reminiscences of a Statistician: The Company I Kept E. L. Lehman Springer, 2007, ISBN 978-0-387-71597-1 http://dx.doi.org/10.1007/978-0-387-71597-1

An Accidental Statistician: The Life and Memories of George E.P. Box George E.P. Box Wiley, 2013, ISBN 9781118514948 http://dx.doi.org/10.1002/9781118514948 Mathematical Statistics with Applications in R, Second Edition

Kandethody M. Ramachandran and Chris P. Tsokos Elsevier, 2015, ISBN 978-0-12-417113-8 http://www.sciencedirect.com/science/book/9780124171138

Basics of Modern Mathematical Statistics Vladimir Spokoiny and Thorsten Dickhaus Springer, 2014, ISBN 978-3-642-39909-1 http://dx.doi.org/10.1007/978-3-642-39909-1

Basics of Modern Mathematical Statistics: Exercises and Solutions Wolfgang Karl Hardle, Vladimir Spokoiny, Vladimir Panov, and Weining Wang Springer, 2014, ISBN 978-3-642-36850-9 http://dx.doi.org/10.1007/978-3-642-36850-9

Mathematical Statistics B.L. van der Waerden Springer, 1969, ISBN 978-3-662-22137-2 http://dx.doi.org/10.1007/978-3-662-22137-2 40 Puzzles and Problems in Probability and Mathematical Statistics Wolfgang Schwarz Springer, 2008, ISBN 978-0-387-73512-2 http://dx.doi.org/10.1007/978-0-387-73512-2 Understanding Uncertainty, Revised Edition Dennis V. Lindley

Wiley, 2014, ISBN 9781118650158 http://dx.doi.org/10.1002/9781118650158

Statistical Inference =====================

Applied Statistical Inference: Likelihood and Bayes Leonhard Held and Daniel Sabanes Bove Springer, 2014, ISBN 978-3-642-37887-4 http://dx.doi.org/10.1007/978-3-642-37887-4

Causal Inference: for Statistics, Social, and Biomedical Sciences – An Introduction Guido W. Imbens and Donald B. Rubin Cambridge University Press, 2015, ISBN 9781139025751 http://dx.doi.org/10.1017/CBO9781139025751

Counterfactuals and Causal Inference: Models and Principles for Social Research, Second Edition Stephen L. Morgan and Christopher Winship Cambridge University Press, 2015, ISBN 9781107587991 http://dx.doi.org/10.1017/CBO9781107587991

Essential Statistical Inference: Theory and Methods

Dennis D. Boos and L.A. Stefanski Springer, 2013, ISBN 978-1-4614-4818-1 http://dx.doi.org/10.1007/978-1-4614-4818-1

Essentials of Statistical Inference G. A. Young and R. L. Smith Cambridge University Press, 2005, ISBN 9780511755392 http://dx.doi.org/10.1017/CBO9780511755392

Foundations of Inference Kevin H. Knuth and John Skilling Axioms, Volume 1, Number 1 (June 2012) http://dx.doi.org/10.3390/axioms1010038 Principles of Statistical Inference D. R. Cox Cambridge University Press, 2006, ISBN 9780511813559 http://dx.doi.org/10.1017/CBO9780511813559 Statistical Inference: The Minimum Distance Approach Ayanendranath Basu, Hiroyuki Shioya, and Chanseok Park CRC Press, 2011, ISBN 978-1-4200-9966-9 http://dx.doi.org/10.1201/b10956 Statistical Theory and Inference David J. Olive Springer, 2014, ISBN 978-3-319-04972-4

http://dx.doi.org/10.1007/978-3-319-04972-4

Design of Experiments ===================

Design and Analysis of Experiments Volume 1: Introduction to Experimental Design, Second Edition Klaus Hinkelmann and Oscar Kempthorne Wiley, 2008, ISBN 9780470191750 http://dx.doi.org/10.1002/9780470191750 Volume 2: Advanced Experimental Design Klaus Hinkelmann and Oscar Kempthorne Wiley, 2005, ISBN 9780471709947 http://dx.doi.org/10.1002/0471709948

Volume 3: Special Designs and Applications Klaus Hinkelmann (Editor) Wiley, 2012, ISBN 9781118147634 http://dx.doi.org/10.1002/9781118147634

Design of Experiments for Engineers and Scientists, Second Edition Jiju Antony Elsevier, 2014, ISBN 978-0-08-099417-8 http://www.sciencedirect.com/science/book/9780080994178

Latin Squares and their Applications, Second Edition A. Donald Keedwell and Jozsef Denes Elsevier, 2015, ISBN 978-0-444-63555-6 http://www.sciencedirect.com/science/book/9780444635556 Statistical Design and Analysis of Experiments: With Applications to Engineering and Science, Second Edition Robert L. Mason, Richard F. Gunst, and James L. Hess Wiley, 2003, ISBN 9780471458500 http://dx.doi.org/10.1002/0471458503 Statistical Principles for the Design of Experiments R. Mead, S. G. Gilmour, and A. Mead Cambridge University Press, 2012, ISBN 9781139020879 http://dx.doi.org/10.1017/CBO9781139020879

Thomas Bayes: Life and Work ============= The Reverend Thomas Bayes, FRS: A Biography to Celebrate the Tercentenary of His Birth D. R. Bellhouse

http://projecteuclid.org/euclid.ss/1089808271 Special Issue: Bayes Then and Now

Statistical Science, Volume 19, Number 4 (February 2004) http://projecteuclid.org/euclid.ss/1089808267

Most Honourable Remenbrance: The Life and Work of Thomas Bayes Andrew I. Dale Springer, 2003, ISBN 978-0-387-21561-7 http://dx.doi.org/10.1007/b97274

A History of Inverse Probability: From Thomas Bayes to Carl Pearson Andrew I. Dale Springer, 1991, ISBN 978-1-4684-4115-9 http://dx.doi.org/10.1007/978-1-4684-0415-9 An Essay towards Solving a Problem in the Doctrine of Chances. By the Late Rev. Mr. Bayes, F. R. S. Communicated by Mr. Price, in a Letter to John Canton, A. M. F. R. S. Philosophical Transactions, Volume 53 (1763) http://dx.doi.org/10.1098/rstl.1763.0053

Bayes’ Theorem in the 21st Century Bradley Efron Science, Volume 340, Number 6137 (7 June 2013) http://dx.doi.org/10.1126/science.1236536 Thomas Bayes’s Bayesian Inference Stephen M. Steiger

Journal of the Royal Statistical Society, Series A, Volume 145, Number 2 (1982) http://www.jstor.org/stable/2981538

Was Bayes a Bayesian? Donald A. Gillies Historia Mathematca, Volume 14 (1987) http://dx.doi.org/10.1016/0315-0860(87)90065-6

Bayes’ Bayesianism John Earman Studies in History and Philosophy of Science Part A, Volume 21, Number 3 (September 1990) http://dx.doi.org/10.1016/0039-3681(90)90001-O Who Discovered Bayes’s Theorem? Stephen M. Stigler The American Statistician, Volume 37, Number 4 (November 1983) http://www.jstor.org/stable/2682766 Laplace’s 1774 Memoir on Inverse Probability Stephen M. Steiger Statistical Science, Volume 1, Number 3 (1986) http://projecteuclid.org/euclid.ss/1177013620 Pierre-Simon Laplace: Philosophical Essay on Probabilities Andrew I. Dale Springer, 1995, ISBN 978-1-4612-4184-3

http://dx.doi.org/10.1007/978-1-4612-4184-3 An Intuitive Explanation of Bayes’ Theorem http://yudkowsky.net/rational/bayes A Technical Explanation of Technical Explanation http://yudkowsky.net/rational/technical

Eliezer S. Yudkowsky, Research Fellow, Singularity Institute for Artificial Intelligence http://yudkowsky.net/ Bayesian Essentials with R, Second Edition Jean-Michel Marin and Christian P. Robert Springer, 2014, ISBN 978-1-4614-8687-9 http://dx.doi.org/10.1007/978-1-4614-8687-9 Bayesian Probability Theory: Applications in the Physical Sciences Wolfgang von der Linden, Volker Dose, and Udo von Toussaint Cambridge University Press, 2014, ISBN 9781139565608 http://dx.doi.org/10.1017/CBO9781139565608 Introduction to Bayesian Statistics, Second Edition William M. Bolstad Wiley, 2007, ISBN 9780470181188

http://dx.doi.org/10.1002/9780470181188 Bayes Linear Statistics: Theory and Methods Michael Goldstein and David Wooff Wiley, 2007, ISBN 9780470065662

http://dx.doi.org/10.1002/9780470065662 Bayesian Theory and Methods with Applications Vladimir P. Savchuk and Chris P. Tsokos Springer, 2011, ISBN 978-94-91216-14-5 http://dx.doi.org/10.2991/978-94-91216-14-5 Introduction to Probability and Statistics: From a Bayesian Viewpoint, Part 2 Inference D. V. Lindley Cambridge University Press, 1965, ISBN 9780511662973 http://dx.doi.org/10.1017/CBO9780511662973 Bayesian Inference: With Ecological Examples William A. Link and Richard J. Barker Elsevier, 2010, ISBN 978-0-12-374854-6 http://www.sciencedirect.com/science/book/9780123748546 Bayesian Inference in Statistical Analysis George E.P. Box and George C. Tiao Wiley, 1973, ISBN 9781118033197

http://dx.doi.org/10.1002/9781118033197 Bayesian Networks: An Introduction Timo Koski and John M. Noble Wiley, 2009, ISBN 9780470684023 http://dx.doi.org/10.1002/9780470684023

Interpreting Probability:

Controversies and Developments in the Early Twentieth Century David Howie Cambridge University Press, 2002, ISBN 9780511498840 http://dx.doi.org/10.1017/CBO9780511498480

A History of Probability and Statistics and Their Applications before 1750 Anders Hald Wiley, 2003, ISBN 9780471725169 http://dx.doi.org/10.1002/0471725161

Bayesian Statistics ======================

The Mathematics of Making Up Your Mind Will Hively Discover (May 1996) http://discovermagazine.com/1996/may/themathematicsof76

Subjective Probability: The Real Thing Richard Jeffrey Cambridge University Press, 2004, ISBN 9780511816161

http://dx.doi.org/10.1017/CBO9780511816161 A Primer on Bayesian Statistics in Health Economics and Outcomes Research Anthony O’Hagan and Bryan R. Luce MEDTAP International (2003) http://www.paceinitiative.org/Resources_Pubs.html

Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and STAN; Second Edition John K. Kruschke Elsevier, 2015, ISBN 978-0-12-405888-0 http://www.sciencedirect.com/science/book/9780124058880 Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and Stan Franzi Korner-Nievergelt, et al. Elsevier, 2015, ISBN 978-0-12-801370-0

http://www.sciencedirect.com/science/book/9780128013700 The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation, Second Edition Christian P. Robert Springer, 2007, ISBN 978-0-387-71599-5 http://dx.doi.org/10.1007/0-387-71599-1 Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science, Second Edition

Franco Taroni, Alex Biedermann, Silvia Bozza, Paolo Garbolino, and Colin Aitken Wiley, 2014, ISBN 9781118914762 http://dx.doi.org/10.1002/9781118914762

Bayesian Probability Theory: Applications in the Physical Sciences Wolfgang von der Linden, Volker Dose, and Udo von Toussaint Cambridge University Press, 2014, ISBN 9781139565608 http://dx.doi.org/10.1017/CBO9781139565608

Bayesian Methods for the Physical Sciences: Learning from Examples in Astronomy and Physics Stefano Anderson and Brian Weaver Springer, 2015, ISBN 978-3-319-15287-5 http://dx.doi.org/10.1007/978-3-319-15287-5

Statistical Programming Using R ===========

The R Project for Statistical Computing http://www.r-project.org/

The Art of R Programming

Norman Matloff (2009) http://heather.cs.ucdavis.edu/~matloff/132/NSPpart.pdf

The R Book, Second Edition Michael J. Crawley Wiley, 2013, ISBN 9781118448908 http://dx.doi.org/10.1002/9781118448908 Beginning R: An Introduction to Statistical Programming Larry Pace Springer, 2012, ISBN 978-1-4302-4555-1

http://dx.doi.org/10.1007/978-1-4302-4555-1 Understanding Statistics Using R Randall Schumacker and Sara Tomek Springer, 2013, ISBN 9781-4614-6227-9 http://dx.doi.org/10.1007/978-1-4614-6227-9

Using R for Statistics Sarah Stowell Springer, 2014, ISBN 978-1-4842-0139-8 http://dx.doi.org/10.1007/978-1-4842-0139-8

The R Software: Fundamentals of Programming and Statistical Analysis Pierre Lafaye de Micheaux, Remy Drouilhet, and Benoit Liquet Springer, 2013, ISBN 978-1-4614-9020-3 http://dx.doi.org/10.1007/978-1-4614-9020-3

Bayesian Computation with R, Second Edition Jim Albert Springer, 2009, ISBN 978-0-387-92298-0 http://dx.doi.org/10.1007/978-0-387-92298-0

Statistics and Data with R: An applied approach through examples Yosef Cohen and Jeremiah Y. Cohen Wiley, 2008, ISBN 9780470758052 http://dx.doi.org/10.1002/9780470721896

R Quick Syntax Reference Margot Tollefson Springer, 2014, ISBN 978-1-4302-6641-9 http://dx.doi.org/10.1007/978-1-4302-6641-9

A Tiny Handbook of R Mike Allerhand Springer, 2011, ISBN 978-3-642-17980-8 http://dx.doi.org/10.1007/978-3-642-17980-8

Advanced R Hadley Wickham CRC Press, 2015, ISBN 978-1-4665-8696-3 http://dx.doi.org/10.1201/b17487 Beginning Data Science with R Manas A. Pathak

R for Cloud Computing: An Approach for Data Scientists A. Ohri Springer, 2014, ISBN 978-1-4939-1702-0 http://dx.doi.org/10.1007/978-1-4939-1702-0 Guide to Programming and Algorithms Using R Ozgur Ergul Springer, 2013, ISBN 978-1-4471-5328-3 http://dx.doi.org/10.1007/978-1-4471-5328-3 Data Mining and Business Analytics with R Johannes Ledolter Wiley, 2013, ISBN 9781118596289 http://dx.doi.org/10.1002/9781118596289 XML and Web Technologies for Data Sciences with R Deborah Nolan and Duncan Temple Lang Springer, 2014, ISBN 978-1-4614-7900-0

http://dx.doi.org/10.1007/978-1-4614-7900-0 Analyzing Compositional Data with R K. Gerald van den Boogaart and Raimon Tolosana-Delgado Springer, 2013, ISBN 978-3-642-36809-7 http://dx.doi.org/10.1007/978-3-642-36809-7

Statistical Analysis of Network Data with R

Eric D. Kolaczyk and Gabor Csardi Springer, 2014, ISBN 978-1-4939-0983-4 http://dx.doi.org/10.1007/978-1-4939-0983-4

Statistical Methods for Ranking Data Mayer Alvo and Philip L.H. Yu Springer, 2014, ISBN 978-1-4939-1471-5 http://dx.doi.org/10.1007/978-1-4939-1471-5

**** A companion set of R programs **** http://web.hku.hk/~plhyu/StatMethRank/ Bayesian Essentials with R, Second Edition Jean-Michel Marin and Christian P. Robert Springer, 2014, ISBN 978-1-4614-8687-9 http://dx.doi.org/10.1007/978-1-4614-8687-9

Mathematical Statistics with Applications in R, Second Edition Kandethody M. Ramachandran and Chris P. Tsokos Elsevier, 2015, ISBN 978-0-12-417113-8 http://www.sciencedirect.com/science/book/9780124171138

Data Mining Applications with R Yanchang Zhao and Yonghua Cen Elsevier, 2014, ISBN 978-0-12-411511-8 http://www.sciencedirect.com/science/book/9780124115118

Introduction to Data Analysis and Graphical Presentation in Biostatistics with R: Statistics in the Large Thomas W. MacFarland

Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and Stan Franzi Korner-Nievergelt, et al. Elsevier, 2015, ISBN 978-0-12-801370-0 http://www.sciencedirect.com/science/book/9780128013700

Data Analysis and Graphics Using R – an Example-Based Approach, Third Edition John Maindonald and W. John Braun Cambridge University Press, 2010, ISBN 9781139194648 http://dx.doi.org/10.1017/CBO9781139194648 Guidebook to R Graphics Using Microsoft® Windows Kunio Takezawa Wiley, 2012, ISBN 9781118270165 http://dx.doi.org/10.1002/9781118270165 Six Sigma with R: Statistical Engineering for Process Improvement Emilio L. Cano, Javier M. Moguerza, and Andres Redchuk Springer, 2012, IS N978-1-4614-3652-2 http://dx.doi.org/10.1007/978-1-4614-3652-2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

10 How computing has changed statistics Brian D. Ripley http://dx.doi.org/10.1093/acprof:oso/9780198566540.003.001

1 Celebrating Statistics: Papers in honour of Sir David Cox on his 80th birthday Anthony Davison, Yadolah Dodge, and Nanny Wermuth (Editors) Oxford University Press, 2005, ISBN 9780198566540 http://dx.doi.org/10.1093/acprof:oso/9780198566540.001.000

1 Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing Daniela Calvetti and Erkki Somersalo Springer, 2007, ISBN 978-0-387-73394-4 http://dx.doi.org/10.1007/978-0-387-73394-4 Using R for Numerical Analysis in Science and Engineering Victor A. Bloomfield CRC Press, 2014, ISBN 978-1-4398-8449-2 http://www.crcnetbase.com/isbn/978-1-4398-8448-5 Computational Actuarial Science with R Arthur Charpentier (Editor) CRC Press, 2015, ISBN 978-1-4665-9260-5 http://www.crcnetbase.com/isbn/978-1-4665-9259-9 Text Analysis with R for Students of Literature

Matthew L. Jockers Springer, 2014, ISBN 978-3-319-03164-4 http://dx.doi.org/10.1007/978-3-319-03164-4

Modeling Count Data Joseph M. Hilbe Cambridge University Press, 2014, ISBN 9781139236065 http://dx.doi.org/10.1017/CBO9781139236065

Negative Binomial Regression, Second Edition Joseph M. Hilbe Cambridge University Press, 2011, ISBN 9780511973420 http://dx.doi.org/10.1017/CBO9780511973420 How to speed up R code: an introduction Nathan Uyttendaele (March 2015) http://arxiv.org/abs/1503.00855 inside-R – A Community Site for R http://www.inside-r.org/

Experimental Math and Math Computing ==== Also see:

MATLAB shelf in the Engineering section. Experimental Mathematics in Action David H. Bailey, Jonathan M. Borwein, Neil J. Calkin, Roland Girgensohn, D. Russell Luke, and Victor H. Moll 2006 (preprint; published by AK Peters in 2007) http://web.cs.dal.ca/~jborwein/Preprints/Books/EMA/ema.pdf Website of David H. Bailey (Publications) http://www.davidhbailey.com/

Website of Jonathan Borwein (Publications) http://www.carma.newcastle.edu.au/jon/ CARMA – Priority Research Centre for Computer-Assisted Research Mathematics and Its Applications, University of Newcastle, NSW, Australia http://www.carma.newcastle.edu.au/carmamembers.shtml Experimental Mathematics (journal, Taylor & Francis) http://www.tandfonline.com/loi/uexm20

OR http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=

Display&page=past&handle=euclid.em

The Linear Algebra Survival Guide: Illustrated with Mathematica Fred E. Szabo Elsevier, 2015, ISBN 978-0-12-409520-5 http://www.sciencedirect.com/science/book/9780124095205

Modern Computer Algebra, Third Edition Joachim von zur Gathen and Jurgen Gerhard Cambridge University Press, 2013, ISBN 9781139856065 http://dx.doi.org/10.1017/CBO9781139856065

An Introduction to Modern Mathematical Computing: With Maple Jonathan M. Borwein and Matthew P. Skerritt Springer, 2011, ISBN 978-1-4614-0122-3 http://dx.doi.org/10.1007/978-1-4614-0122-3

Calculus with Vectors Jay S. Treiman Springer, 2014, ISBN 978-3-319-09438-0 http://dx.doi.org/10.1007/978-3-319-09438-0 **** Maple *** Computer Algebra Recipes: An Introductory Guide to Mathematical Models of Science Richard H. Enns and George C. McGuire Springer, 2006, ISBN 978-0-387-31262-5 http://dx.doi.org/10.1007/0-387-31262-5 Modeling of Curves and Surfaces with MATLAB Vladimir Rovenski Springer, 2010, ISBN 978-0-387-71278-9 http://dx.doi.org/10.1007/978-0-387-71278-9

An Introduction to Modern Mathematical Computing: With Mathematica Jonathan M. Borwein and Matthew P. Skerritt Springer, 2012, ISBN 978-1-4614-4253-0 http://dx.doi.org/10.1007/978-1-4614-4253-0

Programming with Mathematica: An Introduction Paul Wellin Cambridge University Press, 2013, ISBN 9780511972942 http://dx.doi.org/10.1017/CBO9780511972942

Mathematica in Action: Problem Solving Through Visualization and Computation, Third Edition Stan Wagon Springer, 2010, ISBN 978-0-387-75477-2 http://dx.doi.org/10.1007/978-0-387-75477-2

Discovering Mathematics: A Problem-Solving Approach to Mathematical Analysis with MATHEMATICA and Maple Jiri Gregor and Jaroslav Tiser Springer, 2011, ISBN 978-0-85729-064-9 http://dx.doi.org/10.1007/978-0-85729-064-9

Maple and Mathematica: A Problem Solving Approach for Mathematics, Second Edition Inna Shingareva and Carlos Lizarraga-Celaya Springer, 2009, ISBN 978-3-211-99432-0 http://dx.doi.org/10.1007/978-3-211-99432-0

Sage – free open-source mathematics software system http://www.sagemath.org/

Sage for Power Users William Stein (2012) http://wstein.org/books/sagebook/sagebook.pdf Numerical Analysis Using Sage George A. Anastassiou and Razvan A. Mezei Springer, 2015, ISBN 978-3-319-16739-8 http://dx.doi.org/10.1007/978-3-319-16739-8 Algebra for Symbolic Computation Antonio Machi Springer, 2011, ISBN 978-88-470-2397-0

http://dx.doi.org/10.1007/978-88-470-2397-0

LaTeX ================================ Practical LaTeX George Gratzer Springer, 2014, ISBN 978-3-319-06425-3 http://dx.doi.org/10.1007/978-3-319-06425-3

More Math Into LaTeX, 4th Edition George Gratzer Springer, 2007, ISBN 978-0-387-68852-7 http://dx.doi.org/10.1007/978-0-387-68852-7

What Is New in LaTeX? G. Gratzer VII. The STIX Math Symbols Notices of the AMS, Volume 62, Number 6 (June/July 2015) http://dx.doi.org/10.1090/noti1261

VI. LaTeX on an iPad. Empire Notices of the AMS, Volume 60, Number 4 (April 2013) http://dx.doi.org/10.1090/noti963 V. LaTeX on an iPad. Foundation Notices of the AMS, Volume 60, Number 3 (March 2013) http://dx.doi.org/10.1090/noti957 IV. WYSIWYG LaTeX Notices of the AMS, Volume 58, Number 6 (June/July 2011) http://www.ams.org/notices/201106/rtx110600828p.pdf

III. Formatting References Notices of the AMS, Volume 56, Number 8 (September 2009) http://www.ams.org/notices/200908/rtx090800954p.pdf II. TeX Implementations, Evolution or Revolution Notices of the AMS, Volume 56, Number 5 (May 2009) http://www.ams.org/notices/200905/rtx090500627p.pdf I. Breaking Free Notices of the AMS, Volume 56, Number 1 (January 2009) http://www.ams.org/notices/200901/tx090100052p.pdf

LaTeX and Friends M.R.C. van Dongen Springer, 2012, ISBN 978-3-642-23816-1 http://dx.doi.org/10.1007/978-3-642-23816-1

Digital Typography Using LaTeX Apostolos Syropoulos, Antonis Tsolomitis, and Nick Sofroniou Springer, 2003, ISBN 978-0-387-22436-7 http://dx.doi.org/10.1007/b98959

People and Places ====================== Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920s Dennis E. Hesseling Springer, 2003, ISBN 978-3-0348-7989-7 http://dx.doi.org/10.1007/978-3-0348-7989-7

Kurt Godel and the Foundations of Mathematics: Horizons of Truth Matthias Baaz, Christos H. Papadimitriou, Hilary W. Putnam, Dana S. Scott, and Charles L. Harper, Jr. (Editors)

Kurt Godel Centenary: Lectures from the Institute for Advanced Study http://www.youtube.com/watch?v=IvbnxT3VL1E Bernhard Riemann 1826-1866 – Turning Points in the Conception of Mathematics Detlef Laugwitz Springer, 2008, ISBN 978-0-8176-4777-3 http://dx.doi.org/10.1007/978-0-8176-4777-3 Gosta Mittag-Leffler: A Man of Conviction Arild Stubhaug Springer, 2010, ISBN 978-3-642-11672-8 http://dx.doi.org/10.1007/978-3-642-11672-8 Remembering Sofya Kovalevskaya Michele Audin Springer, 2011, ISBN 978-0-85729-929-1

http://dx.doi.org/10.1007/978-0-85729-929-1 Mathematical Lives – Protagonists of the Twentieth Century – From Hilbert to Wiles Claudio Bartocci, Renato Betti, Angelo Guerragio, and Roberto Lucchetti (Editors) Springer, 2011, ISBN 978-3-642-13606-1 http://dx.doi.org/10.1007/978-3-642-13606-1

Ernst Zermelo: An Approach to His Life and Work Heinz-Dieter Ebbinghaus Springer, 2007, 978-3-540-49553-6 http://dx.doi.org/10.1007/978-3-540-49553-6

Collected Works – Volume I – Set Theory, Miscellanea Ernst Zermelo Springer, 2010, ISBN 978-3-540-79384-7 http://dx.doi.org/10.1007/978-3-540-79384-7

The Map of My Life Goro Shimura Springer, 2008, ISBN 978-0-387-79715-1 http://dx.doi.org/10.1007/978-0-387-79715-1

Oscar Zariski (24 April 1899-4 July 1986) Garrett Birkhoff Proceedings of the American Philosophical Society Volume 137, Number 2 (June 1993) Pages 306-320 http://www.jstor.org/stable/986739

The Unreal Life of Oscar Zariski Carol Parikh Springer, 2009, ISBN 978-0-387-09430-4 http://dx.doi.org/10.1007/978-0-387-09430-4 Claude Elwood Shannon, 30 April 1916 – 24 February 2001 Robert G. Gallagher

Proceedings of the American Philosophical Society Volume 147, Number 2 (June 2003) Pages 187-191 http://www.jstor.org/stable/1558263

Kolmogorov’s Heritage in Mathematics Eric Charpentier, Annick Lesne, and Nikolai K. Nikolski (Editors) Springer, 2007, ISBN 978-3-540-36351-4 http://dx.doi.org/10.1007/978-3-540-36351-4

Wikipedia: http://en.wikipedia.org/wiki/Andrey_Kolmogorov Selected Works of A. N. Kolmogorov, Volume I: Mathematics and Mechanics V. M. Tikhomirov (Editor) Springer, 1991, ISBN 978-94-011-3030-1 http://dx.doi.org/10.1007/978-94-011-3030-1 Selected Works of A. N. Kolmogorov, Volume II: Probability Theory and Mathematical Statistics A.N. Shiryayev (Editor) Springer, 1992, ISBN 978-94-011-2260-3 http://dx.doi.org/10.1007/978-94-011-2260-3 Selected Works of A. N. Kolmogorov, Volume III: Information Theory and Theory of Algorithms A.N. Shiryayev (Editor) Springer, 1993, ISBN 978-94-017-2973-4 http://dx.doi.org/10.1007/978-94-017-2973-4

The Vexing Case of Igor Shafarevich, A Russian Political Thinker Krista Berglund Springer, 2012, ISBN 978-3-0348-0215-4

http://dx.doi.org/10.1007/978-3-0348-0215-4

Wikipedia: http://en.wikipedia.org/wiki/Igor_Shafarevich A Glimpse at Hilbert Space Operators: Paul R. Halmos in Memoriam Sheldon Axler, Peter Rosenthal, and Donald Sarason (Editors) Birkhauser, 2010, ISBN 978-3-0346-0347-8 http://dx.doi.org/10.1007/978-3-0346-0347-8

Wikipedia: http://en.wikipedia.org/wiki/Paul_Halmos

Random Curves: Journeys of a Mathematician Neal Koblitz Springer, 2008, ISBN 978-3-540-74078-0 http://dx.doi.org/10.1007/978-3-540-74078-0

Wikipedia: http://en.wikipedia.org/wiki/Neal_Koblitz

The Pleasures of Statistics: The Autobiography of Frederick Mosteller Frederick Mosteller Springer, 2010, ISBN 978-0-387-77956-0 http://dx.doi.org/10.1007/978-0-387-77956-0

Wikipedia: http://en.wikipedia.org/wiki/Frederick_Mosteller

Reminiscences of a Statistician: The Company I Kept E. L. Lehman Springer, 2007, ISBN 978-0-387-71597-1 http://dx.doi.org/10.1007/978-0-387-71597-1

An Accidental Statistician: The Life and Memories of George E.P. Box George E.P. Box Wiley, 2013, ISBN 9781118514948 http://dx.doi.org/10.1002/9781118514948

The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development John L. Bell Springer, 1999, ISBN 978-94-011-4209-0 http://dx.doi.org/10.1007/978-94-011-4209-0

Ramanujan – Life and Work ============== The Indian Mathematician Ramanujan G. H. Hardy

The American Mathematical Monthly, Volume 44, Number 3 (March 1937) Pages 137-155 http://www.jstor.org/stable/2301659

Documentary: Letters from an Indian Clerk http://www.youtube.com/watch?v=OARGZ1xXCxs

Ramanujan: For Lowbrows Bruce C. Berndt and S. Bhargava The American Mathematical Monthly, Volume 100, Number 7 (August-September 1993)

http://www.jstor.org/stable/2323885 Srinivasa Ramanujan: Going Strong at 125, Part I Notices of the American Mathematical Society, Volume 59, Number 11 (December 2012) http://www.ams.org/notices/201211/index.html

Srinivasa Ramanujan: Going Strong at 125, Part II Notices of the American Mathematical Society, Volume 60, Number 1 (January 2013) http://www.ams.org/notices/201301/index.html

Ramanujan’s Place in the World of Mathematics: Essays Providing a Comparative Study Krishnaswami Alladi Springer, 2013, ISBN 978-81-322-0767-2 http://dx.doi.org/10.1007/978-81-322-0767-2

The Mathematical Legacy of Srinivasa Ramanujan M. Ram Murty and V. Kumar Murty Springer, 2013, ISN978-81-322-0770-2 http://dx.doi.org/10.1007/978-81-322-0770-2

Ramanujan’s Notebooks, Part I Bruce C. Berndt Springer, 1985, ISBN 978-1-4612-1088-7 http://dx.doi.org/10.1007/978-1-4612-1088-7

Ramanujan’s Notebooks, Part II Bruce C. Berndt Springer, 1989, ISBN 978-1-4612-4530-8 http://dx.doi.org/10.1007/978-1-4612-4530-8

Ramanujan’s Notebooks, Part III Bruce C. Berndt Springer, 1991, ISBN 978-1-4612-0965-2 http://dx.doi.org/10.1007/978-1-4612-0965-2 Ramanujan’s Notebooks, Part IV Bruce C. Berndt Springer, 1994, ISBN 978-1-4612-0879-2 http://dx.doi.org/10.1007/978-1-4612-0879-2 Ramanujan’s Notebooks, Part V Bruce C. Berndt Springer, 1998, ISBN 978-1-4612-1624-7

http://dx.doi.org/10.1007/978-1-4612-1624-7 Ramanujan’s Lost Notebook, Part I George E. Andrews and Bruce C. Berndt Springer, 2005, ISBN 978-0-387-28124-7 http://dx.doi.org/10.1007/0-387-28124-X Ramanujan’s Lost Notebook, Part II George E. Andrews and Bruce C. Berndt Springer, 2009, ISBN 978-0-387-77766-5 http://dx.doi.org/10.1007/b13290 Ramanujan’s Lost Notebook, Part III George E. Andrews and Bruce C. Berndt Springer, 2012, ISBN 978-1-4614-3810-6

http://dx.doi.org/10.1007/978-1-4614-3810-6 Ramanujan’s Lost Notebook, Part IV George E. Andrews and Bruce C. Berndt Springer, 2013, ISBN 978-1-4614-4081-9 http://dx.doi.org/10.1007/978-1-4614-4081-9

Elements de Mathematique by N. Bourbaki ==

Theorie des Ensembles Springer, 2006, ISBN 978-3-540-34035-5 http://dx.doi.org/10.1007/978-3-540-34035-5

Groupes et Algebres de Lie: Chapitre 1 Springer, 2007, ISBN 978-3-540-35337-9 http://dx.doi.org/10.1007/978-3-540-35337-9

Groupes et Algebres de Lie: Chapitre 4 a 6 Springer, 2007, ISBN 978-3-540-34491-9 http://dx.doi.org/10.1007/978-3-540-34491-9 Elements d’histoire des mathematiques Springer, 2007, ISBN 978-3-540-33981-6

http://dx.doi.org/10.1007/978-3-540-33981-6

Mathematical Fun ====================== Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist Ellie Baker and Susan Goldstine CRC Press, 2014, ISBN 978-1-4665-8849-3

http://dx.doi.org/10.1201/b17578 Flexagons Inside Out Les Pook Cambridge University Press, 2003, ISBN 9780511543302 http://dx.doi.org/10.1017/CBO9780511543302 Serious Fun with Flexagons: A Compendium and Guide Les Pook Springer, 2009, ISBN 978-90-481-2503-6 http://dx.doi.org/10.1007/978-90-481-2503-6 Manifold Mirrors: The Crossing Paths of the Arts and Mathematics Felipe Cucker Cambridge University Press, 2013, ISBN 9781139014632 http://dx.doi.org/10.1017/CBO9781139014632 A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics Peter Hilton and Jean Pedersen Cambridge University Press, 2010, ISBN 9780511777004 http://dx.doi.org/10.1017/CBO9780511777004 Dicing with Death: Chance, Risk and Health Stephen Senn Cambridge University Press, 2003, ISBN 9780511543319

http://dx.doi.org/10.1017/CBO9780511543319

Fallacies in Mathematics E. A. Maxwell Cambridge University Press, 1959, ISBN 9780511569739 http://dx.doi.org/10.1017/CBO9780511569739

Insights into Game Theory: An Alternative Mathematical Experience Ein-Ya Gura and Michael Maschler Cambridge University Press, 2008, ISBN 9780511754229 http://dx.doi.org/10.1017/CBO9780511754326

Social Choice and the Mathematics of Manipulation Alan D. Taylor Cambridge University Press, 2005, ISBN 9780511614316 http://dx.doi.org/10.1017/CBO9780511614316

Naïve Decision Making: Mathematics Applied to the Social World T. W. Korner Cambridge University Press, 2008, ISBN 9780511755439 http://dx.doi.org/10.1017/CBO9780511755439

Legal Matters ==========================

Patenting mathematical algorithms: What’s the harm? – A thought experiment in algebra Pal B. de Laat International Review of Law and Economics, Volume 20 (2000) http://dx.doi.org/10.1016/S0144-8188(00)00031-4

Patent Strategy: For Researchers and Research Managers, Third Edition H. Jackson Knight Wiley, 2013, ISBN 9781118314289 http://dx.doi.org/10.1002/9781118314289

Reference Material =====================

Computational Statistics: Concepts and Methods, Handbook of; Second Edition James E. Gentle, Wolfgang Karl Hardle, and Yuichi Mori (Editors) Springer, 2012, ISBN 978-3-642-21550-6 http://dx.doi.org/10.1007/978-3-642-21551-3

Continued Fractions for Special Functions, Handbook of Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadeland, and William B. Jones Springer, 2008, ISBN 978-1-4020-6949-9 http://dx.doi.org/10.1007/978-1-4020-6949-9 Geomathematics, Handbook of Willi Freeden, M. Zuhair Nashed, and Thomas Sonar (Editors) Springer, Live Reference – Constantly updated, ISBN 978-3-642-27793-1 http://dx.doi.org/10.1007/978-3-642-27793-1 Mathematics, Handbook of; Sixth Edition I. N. Bronshtein, K. A. Semendyayev, Gerhard Musiol, and Heiner Muhlig Springer, 2015, ISBN 978-3-662-46221-8 http://dx.doi.org/10.1007/978-3-662-46221-8 Operator Theory Daniel Alpay (Editor) Springer, Live Reference – Constantly updated, ISBN 978-3-0348-0692-3 http://dx.doi.org/10.1007/978-3-0348-0692-3 Statistical Sciences, Encyclopedia of

Samuel Kotz, Campbell B. Read, N. Balakrishnan, and Brani Vidakovic (Editors) Wiley, 1999-present, ISBN 9780471667193 http://dx.doi.org/10.1002/0471667196

http://projecteuclid.org/euclid.ss/1177012021 Statistical Science, International Encyclopedia of Miodrag Lovric (Editor) Springer, 2011 ISBN 978-3-642-04898-2 http://dx.doi.org/10.1007/978-3-642-04898-2 Statistics, The Concise Encyclopedia of Yadolah Dodge Springer, 2008, ISBN 978-0-387-32833-1 http://dx.doi.org/10.1007/978-0-387-32833-1

Additional Web Resources ===============

Design Theory – theoretical, computational, and statistical aspects of combinatorial designs

http://designtheory.org/ MacTutor History of Mathematics Archive School of Mathematics and Statistics University of St Andrews, Scotland http://www-history.mcs.st-and.ac.uk/ The Probability Web http://probweb.berkeley.edu/probweb.html Random – Probability, Mathematical Statistics, Stochastic Processes (formerly Virtual Laboratories in Probability and Statistics) http://www.math.uah.edu/stat/index.html Reprints in Theory and Applications of Categories http://www.tac.mta.ca/tac/reprints/

Online Publications – Directly =============

Theory and Applications of Categories http://www.tac.mta.ca/tac/index.html Undergraduate Math Journal Rose-Hulman Institute of Technology http://www.rose-hulman.edu/mathjournal/index.php

Odds & Ends =========================== Nonstandard Analysis for the Working Mathematician, Second Edition Peter A. Loeb and Manfred P.H. Wolff (Editors) Springer, 2015, ISBN 978-94-017-7327-0 http://dx.doi.org/10.1007/978-94-017-7327-0 Introduction to Neutrosophic Statistics Florentin Smarandache (2014) http://arxiv.org/abs/1406.2000 Smarandache Notions Journal (plus a lot more) http://fs.gallup.unm.edu/

Two Millennia of Mathematics: From Archimedes to Gauss George M. Phillips Springer, 2000, ISBN 978-1-4612-1180-8 http://dx.doi.org/10.1007/978-1-4612-1180-8

Mathematical Intuition: Poincare, Polya, Dewey Reuben Hersh http://dx.doi.org/10.1007/978-0-8176-8394-8_2

The Courant-Friedrichs-Lewy (CFL) Condition: 80 Years After Its Discovery Carlos A. de Moura and Carlos S. Kubrusly (Editors) Springer, 2013, ISBN 978-0-8176-8394-8 http://dx.doi.org/10.1007/978-0-8176-8394-8

Theory of Transformation Groups I: General Properties of Continuous transformation Groups. A Contemporary Approach and Translation Sophus Lie Springer, 2015, ISBN 978-3-662-46211-9 http://dx.doi.org/10.1007/978-3-662-46211-9

Elliptic Tales: Curves, Counting, and Number Theory Avner Ash and Robert Gross Princeton University Press, 2012, ISBN 978-1-4008-4171-4 http://www.degruyter.com/viewbooktoc/product/452369

In Pursuit of the Travelling Salesman: Mathematics at the Limits of Computation William J. Cook

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