Mathematics: a Global Science

1. Mathematics: a Global Science Cody Clifton University of Kansas Department of Mathematics February 12, 2013

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

3. Is everything just applied mathematics… ?

4. Modern Communication via Signal Processing

5. 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

6. Cryptography: making and breaking codes

7. Cryptography: making and breaking codes Basic encryption method: the shift cipher Shift of 3 letters to the right Basic decryption methods: 2. Frequency analysis 1. Brute force: try every possible shift of the ciphertext until a likely plaintext is discovered

8. Cryptography: making and breaking codes Modern cryptography employs sophisticated mathematical concepts Public-key cryptography is generally thought to be the most practical method of encryption, and relies on “one-way” problems from number theory 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? The future of cryptography: if quantum computing beats the RSA, what next?

9. Synthetic Aperture Radar (SAR)

10. Synthetic Aperture Radar (SAR) 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 Sandia National Laboratories www.sandia.gov/RADAR/

11. Reaching the International Space Station (ISS) Source: NASA

12. Reaching the International Space Station (ISS) Numerous mathematical infrastructures are involved when spacecraft arrive and 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 Source: NASA

13. Smart Grid: the Future of Energy Efficiency Middelgrunden Wind Farm off Copenhagen Photo Credit: Kim Hansen

14. Smart Grid: the Future of Energy Efficiency 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, see www.smartgrid.gov Open Systems International Middelgrunden Wind Farm off Copenhagen Photo Credit: Kim Hansen

15. Flesch Readability Tests

16. Flesch Readability Tests 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 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:

17. Flesch Readability Tests www.editcentral.com How well does it work? 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 Abstract of my latest technical report: FRES = 2.3, FKGL = 22.9

18. Summary