discrete structures fall 2021 course information
TRANSCRIPT
Discrete StructuresSpring 2022
Course Information
Amotz Bar-Noy
Department of Computer and Information ScienceBrooklyn College
February 1, 2022
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Instructor — Amotz Bar-Noy
E-mail: [email protected]
Internet:http://www.sci.brooklyn.cuny.edu/˜amotz/TR11discretemath.html
Class Hours: Tuesdays and Thursdays 11:00am–12:15pm
Classroom: Ingersoll 3143
Office Hours: Thursdays 12:30pm–1:30pm
Zoom Link:https://us02web.zoom.us/j/88913444494?pwd=VTJZaWRZblZMeDc3Z010aDFXanRGZz09
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Prerequisite Courses and Knowledge
Computer and Information Science1110 [1.5] or 1115 or 1.10 or 1.20 or
Mathematics1011 [2.9] or 2.92or assignment to Mathematics 3.20, 1201 [3.3], or 4.10 by theDepartment of Mathematics.
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Computer and Information Science Prerequisite
Syllabus 1110/1115:Algorithms, computers and programs. Writing, debugging, andtesting programs. Loops and conditional control structures.Method definition and parameter passing. Arrays, ArrayLists, andStrings. Sorting, searching and other basic algorithms. Input andoutput. Programming applications selected from variousdisciplines. History and basic concepts of computer science.
General linkhttp://www.brooklyn.cuny.edu/courses/ShowCourse.do?redirect=/acad/course_info.jsp&dsc=
CISC.&crs_num=1115&div=U
Detailed linkhttp://www.brooklyn.cuny.edu/web/aca_naturalsciences_cis/CISC1110.pdf
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Math Prerequisite
SyllabusPreparation for calculus. Trigonometry. The concept of function,including, linear and quadratic functions, composition of functions,polynomials and rational functions, exponential, logarithmic,trigonometric, and inverse trigonometric functions. Conic sections.Binomial theorem.
General linkhttp://www.brooklyn.cuny.edu/courses/ShowCourse.do?redirect=/acad/course_info.jsp&dsc=
MATH.&crs_num=1011&div=U
Detailed linkhttp://www.brooklyn.cuny.edu/web/aca_naturalsciences_math/Math1011_Syllabus.pdf
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Some Textbooks
A “good fit to this course” text book: “Discrete Mathematics forComputer Science,” by Bogart, and Stein. and Drysdale.https://www.kth.se/social/files/557ec6b0f27654784e263d66/fullbook.pdf
A “popular” BC-CIS text book: “Discrete Mathematics and itsApplications,” by Kenneth H. Rosen (6th, 7th, 8th editions).https://notendur.hi.is/mbh6/html/_downloads/Discrete%20Mathematics%20and%20Its%
20Applications%20-%20Kenneth%20Rosen%20(2012).pdf
A book with an online tutorial (see below): “Discrete MathematicsAn Open Introduction,” by Oscar Levin (3rd Edition).http://discrete.openmathbooks.org/pdfs/dmoi-tablet.pdf
A list of books on “Discrete mathematics for Computer Science”from Google:https://www.google.com/search?q=list+of+books+on+discrete+mathematics+for+computer+
science&rlz=1C1CHBF_enUS762US762&source=univ&tbm=shop&tbo=u&sa=X&ved=
0ahUKEwiEk5HHiKDfAhUIm-AKHWYIAGgQsxgIzAE
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Some Course Notes
MIT “Mathematics for Computer Science (2015)”:https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/
6-042j-mathematics-for-computer-science-spring-2015/readings/MIT6_042JS15_textbook.pdf
Yale “Notes on Discrete Mathematics (2020)”:http://www.cs.yale.edu/homes/aspnes/classes/202/notes.pdf
Stanford “Mathematical Foundations of Computing (2013)”:http://theory.stanford.edu/˜trevisan/cs103-14/keith.pdf
Duke “Discrete Mathematics for Computer Science (2009)”:https://www2.cs.duke.edu/courses/spring09/cps102/Lectures/Book.pdf
University of Pennsylvania “Discrete Mathematics for ComputerScience Some Notes (2008)”:https://arxiv.org/pdf/0805.0585.pdf
Cornell “A Course in Discrete Structures”:https://www.cs.cornell.edu/˜rafael/discmath.pdf
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Some Online Video Lectures
Video lectures for Mathematics for Computer Science from MIT:https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/
6-042j-mathematics-for-computer-science-fall-2010/video-lectures/
Trevtutor: Discrete Math I and Discrete Math II (lectures andexercise sessions)https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz
https://www.youtube.com/playlist?list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2
Introduction to Higher Mathematics (first 12 lectures):https://www.youtube.com/playlist?list=PLZzHxk_TPOStgPtqRZ6KzmkUQBQ8TSWVX
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Some Online Text Tutorials
“Discrete Mathematics An Open Introduction” by Oscar Levin:http://discrete.openmathbooks.org/dmoi2/frontmatter.html
“Discrete Mathematics Tutorial” by tutorialspointhttps://www.tutorialspoint.com/discrete_mathematics/index.htm
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Some Books with Problems and Solutions
“Theory and Problems of Discrete Mathematics” by S. Lipschutzand M. Lipson (Schaum’s book):https://alas.matf.bg.ac.rs/˜mi10164/Materijali/DS.pdf
∗ Many examples with full solutions.
“Problems on Algorithms” by I. Parberry and W. Gasarch.http://www.inf.ufes.br/˜raulh/ufes/teaching/courses/ds/texts/poa.pdf
∗ Although most of the problems are about Algorithms, there aremany that are relevant to Discrete Math.
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What is Discrete Math?
A long answer part I
Discrete mathematics is the study of mathematical structures thatare fundamentally discrete rather than continuous.
In contrast to real numbers that have the property of varyingsmoothly, the objects studied in discrete mathematics – such asintegers, graphs, and statements in logic – do not vary smoothly inthis way, but have distinct, separated values.
Discrete mathematics therefore excludes topics in continuousmathematics such as calculus or Euclidean geometry.
Discrete objects can often be enumerated by integers.
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What is Discrete Math?
A long answer part II
More formally, discrete mathematics has been characterized asthe branch of mathematics dealing with countable sets (finite setsor sets with the same cardinality as the natural numbers.
However, there is no exact definition of the term discretemathematics.
Indeed, discrete mathematics is described less by what isincluded than by what is excluded: continuously varying quantitiesand related notions.
The set of objects studied in discrete mathematics can be finite orinfinite. The term finite mathematics is sometimes applied to partsof the field of discrete mathematics that deals with finite sets,particularly those areas relevant to business.
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What is Discrete Math for Computer Science?
A shorter answer
Discrete mathematics is the part of mathematics devoted to thestudy of discrete (i.e. distinct) objects.
In general, it is used whenever objects are counted, whenrelationships between finite (or countable) sets are studied, andwhen processes involving a finite number of steps are analyzed.
It is important for computer science because in computingmachines, information is stored and manipulated in a discretefashion.
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Why study Discrete Math?
Proofs, proofs, and more proofs:What distinguishes Math from other “exact” sciences.
More subjective answers:Problem solving: Talent, Intuition, Luck, Experience, Hard Work.Mathematical thinking, critical thinking, mathematical reasoning,...“Fun” with math (e.g., via puzzles) and Math as an art.
Do we or I really need Math?What if I want to be a programmer?What if I want to be a system person?
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This Course
Flexible curriculum:Quantity vs. quality.Many orders among the topics are good.
Are we starting from the beginning?No!!! We assume you already know a lot!
Resources for study:Textbooks, lecture notes, video lectures, online tutorials, practiceexercises, blogs, wikipedia, . . .There are too many choices, how to select the “right” one?
What if I care only about the final grade?Master the material studied in this course?!
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Syllabus
Part IProofs; Sets; Logic;
Part IICounting; Combinatorics; Induction; Recursion; Number Theory;
Part IIIProbability; Algorithms; Graphs;
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Tentative ScheduleClass 1 Feb 1, 2022 IntroductionClass 2 Feb 3, 2022 Prerequisite QuizClasses 3-4 Feb 10,15, 2022 ProofsClasses 5-8 Feb 17,22,24, Mar 1, 2022 Sets & LogicClass 9 Mar 3, 2022 CountingClass 10 Mar 8, 2022 Midterm Exam IClasses 11-13 Mar 10,15,17, 2022 CombinatoricsClasses 14-17 Mar 22,24,29,31, 2022 Induction & RecursionClasses 18-19 Apr 5,7, 2022 Number TheoryClass 20 Apr 12, 2022 Midterm Exam IIClasses 21-24 Apr 14,16,28, May 3, 2022 ProbabilityClasses 25-26 May 5,10, 2022 AlgorithmsClasses 27-28 May 12,14, 2022 Graphs
May 24, 2022 Final Exam
RemarksThere are no classes on Feb 8, Apr 19, and Apr 21.Final exam date&time: Tuesday May 24, 2022 10:30am – 12:30pm
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In-Person Classes and Zoom Sessions
ClassesIn each 75-minute class, I will present a slide-based lecturecoupled with Internet videos.The slides will be posted on the course websitehttp://www.sci.brooklyn.cuny.edu/˜amotz/TR11discretemath.html
ZoomThe zoom link for the class ishttps://us02web.zoom.us/j/88913444494?pwd=VTJZaWRZblZMeDc3Z010aDFXanRGZz09
There will be Zoom sessions in parallel to the in-person classes.The Zoom sessions will not be recorded and the focus will be onthe students who attend the in-person classes.If the in-person classes are canceled, we meet via Zoom on thesame days and times.
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Attendance
AttendanceExcept for the first two classes and the exams (not quizzes),attendance is not mandatory.Absent students are responsible for the material covered in class.
RewardStudents who attend the in-person classes will be awarded agrade of 100 that will be worth up to 5% of their final gradedepending on the number of attended in-person classes.
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Communication With The Instructor
From the InstructorI will broadcast announcements using WebCentral (or CUNYFirst).Make sure that both systems have your preferred email address.I will post course material (lectures, assignments, exams&quizzes,announcements) on the course website:http://www.sci.brooklyn.cuny.edu/˜amotz/TR11discretemath.html
To the instructorEmail questions to [email protected] sent to my other email addresses will be ignored.
Office hoursOn Thursdays at 12:30pm – 15 minutes after the end of the class.
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Online Procedure
Joining a zoom sessionStudents must join the class prior to the start time, otherwise, theyrisk not being admitted.
AudioAudio should be muted unless I request a verbal response.
CameraStudents are encouraged to turn their camera on.
ChatStudents may ask questions using the chat option.
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Assignments
Type of AssignmentsReading assignments: to help students be better prepared forfuture topics.Writing assignments: for students to practice topics covered inprevious classes.
Submission procedureThe due dates for the writing assignments will be class dates.Students may submit a written (preferably typed) assignmentbefore or after the class.Alternatively, students may submit a scanned version as a PDFattachment to [email protected].
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Assignments
Grading assignmentsAssignments will be graded with a Pass-Fail grade.After the due date, detailed solutions will be posted on the coursewebsite.
Preparing assignmentsTry your best to do the assignments alone.Get help only if necessary.You must understand and be ready to explain to me everythingyou write.
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Exams and Quizzes
ExamsThe final exam is scheduled on Tuesday Nay 24, 2022 from10:30am to 12:30pm in room ???Both midterm exams will be taken during class sessions on thedates that appear in the course schedule.
QuizzesThe number of quizzes has not been yet determined.Some quizzes will be announced ahead of time and some will besurprised quizzes.Quizzes are not mandatory. You may skip them or decide not tosubmit them.A quiz grade counts only if it is higher than the final exam grade.
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Grading Exams and Quizzes
GradingExams and quizzes will be fully and accurately graded.Detailed solutions will be posted.
Answering questionsAnswer a question only within the given space for the answer.Use legible handwriting for exams and quizzes and typed text forassignments.You will get 20% of the credit if you leave the answer blank and nocredit for a wrong answer.
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Project
ScopeThe project is “open ended” and as such there will be noinstructions of what to do.However, few examples will be offered to illustrate the types ofprojects that would qualify.
SubmissionSubmitting a project is not mandatory.However it is a great opportunity for students to boost their finalgrade.
DeadlineThe deadline will be about two weeks before the final exam.This is a firm deadline; there will be no exceptions.
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Final Grade
Components of the final grade∗ 15%− 20% for the first midterm exam.∗ 15%− 20% for the second midterm exam.∗ 0%− 20% for the quizzes.∗ 0%− 10% for the assignments.∗ 0%− 15% for the project.∗ 0%− 5% for attendance.∗ 10%− 70% for the final exam.
The final exam percentageThe percentage allocated to the final exam depends on thenumber of quizzes taken, the number of assignments submitted,the scope of the project, and attendance.
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Honor Code
This course policyStudents are expected to do the exams, the quizzes, and theproject by themselves without any external help from other people,the Internet, or books and notes unless stated otherwise.Cheaters will be punished severely. At minimum, they will fail thespecific exam or quiz, but they may fail the whole class.In addition, student who cheat risk disciplinary measures byBrooklyn College and CUNY.
CUNY policy on Academic IntegrityAcademic Dishonesty is prohibited in the City University ofNew York and is punishable by penalties, including failinggrades, suspension, and explusion, as provided herein.
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