Mathematics: a Global Science

Cody CliftonUniversity of Kansas

Department of MathematicsFebruary 12, 2013

http://imgs.xkcd.com/comics/purity.png

Is everything just applied mathematics… ?

Modern Communication via Signal Processing

Modern Communication via Signal Processing

In the language of communication systems, a signal is a function that conveys information about the behavior of some phenomenon

Processing of a signal can involve:- signal transmission, acquisition, and reconstruction- quality improvement, such as noise reduction or image enhancement- signal compression for efficient data transference- feature extraction, such as speech recognition

Diagram courtesy of Brews ohare

Cryptography: making and breaking codes

Basic encryption method: the shift cipher

Shift of 3 letters to the right

Cryptography: making and breaking codes

Basic decryption methods:

1. Brute force: try every possibleshift of the ciphertext until a likely plaintext is discovered

2. Frequency analysis

Public-key cryptography is generally thought to be the most practical methodof encryption, and relies on “one-way” problems from number theory

The future of cryptography: if quantum computing beats the RSA, what next?

Cryptography: making and breaking codes

Modern cryptography employs sophisticated mathematical concepts

The most famous public-key cryptosystem is the RSA, which uses prime numbers and modular arithmetic (sometimes called clock arithmetic)

First published in 1977, the RSA is considered quite old as a mathematical algorithm… is it still useful or relevant?

Synthetic Aperture Radar (SAR)

Synthetic Aperture Radar (SAR)

Sandia National Laboratorieswww.sandia.gov/RADAR/

Plane or satellite flies along a straight track

Antenna emits pulses of electromagnetic radiation in a directed beam

Waves scatter off the terrain and are detected with the same antenna

Received signals are used to produce an image of the terrain

Source: NASA

Reaching the International Space Station (ISS)

Source: NASA

Reaching the International Space Station (ISS)

Numerous mathematical infrastructures are involved when spacecraft arriveand dock at the ISS

Complex sensor systems control navigation between Earth and outer space, with the ISS orbiting at an altitude of over 200 miles

Precise communication ensures compatible orbital velocities between spacecraft

Other considerations include optimizing the amount of fuel carried by the spacecraft, based on its total weight and expected launch trajectory Johannes Kepler ATV (2011)

The space rendezvous process can take between a couple of days and a month

Middelgrunden Wind Farm off Copenhagen Photo Credit: Kim Hansen

Smart Grid: the Future of Energy Efficiency

Middelgrunden Wind Farm off Copenhagen Photo Credit: Kim Hansen

Smart Grid: the Future of Energy Efficiency

Open Systems International

Automated communication between power providers and consumers

Automation involves networking, which requires mathematics

Statistical analysis of power consumption results in more efficient energy allocation

For more on this, seewww.smartgrid.gov

Flesch Readability Tests

Flesch Readability Tests

FRES, on a scale of 0 – 100, is determined by the formula:

FKGL gives a value that represents the number of years of American education generally required for complete understanding of the writing:

The Flesch Reading Ease Score (FRES) and Flesch-Kincaid Grade Level (FKGL) are two related mathematical formulas that objectively assign a value of “readability” to written passages of the English language

Flesch Readability Tests

www.editcentral.comHow well does it work?

Abstract of my latest technical report: FRES = 2.3, FKGL = 22.9

Readability of three papers from my first college writing course:

Paper 1: FRES = 85.3, FKGL = 5.5 Paper 2: FRES = 83.3, FKGL = 6 Paper 3: FRES = 53.3, FKGL = 10.1

Sampling of my other college writing: FRES = 33.6 - 62.1, FKGL = 9.4 - 16.3

Summary