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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