1. Mathematics: a Global Science

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

3. Is everything just applied mathematics… ?

4. Modern Communication via Signal Processing

5. 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. 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 possible shift of the ciphertext until a likely plaintext is discovered 2. Frequency analysis

8. Public-key cryptography is generally thought to be the most practical method of 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?

9. Synthetic Aperture Radar (SAR)

10. Sandia National Laboratories www.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

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

12. Source: NASA 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

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

14. 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, see www.smartgrid.gov

15. Flesch Readability Tests

16. 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

17. Flesch Readability Tests www.editcentral.com How 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

18. Summary