School of Science Indiana University-Purdue University Indianapolis

1. School of Science Indiana University-Purdue University Indianapolis The Expanding Role of Mathematics in Science and Society Carl C. Cowen, Dean IUPUI School of Science President, Mathematical Association of America NCTM Annual Meeting, Anaheim April 9, 2005 1

2. School of Science Indiana University-Purdue University Indianapolis • Introduction • The Challenge and the Opportunity • Automatic Teller Machines: The math of ATM security • CAT Scans and MRI’s: The math of medical diagnostics • SARS, HIV, Cancer, Parkinson’s: The math of epidemics and disease • Sources for classroom materials 2

3. School of Science Indiana University-Purdue University Indianapolis • Not educating enough people in science, technology, engineering and math • Need to diversify our math and science workforce • Middle school and high school are the critical times • Spread message of opportunity to parents and counselorswww.science.iupui.edu/ccowen/Careers.html 3

4. School of Science Indiana University-Purdue University Indianapolis • Not educating enough people in science, technology, engineering and math • Need to diversify our math and science workforce • Middle school and high school are the critical times • Spread message of opportunity to parents and counselorswww.science.iupui.edu/ccowen/Careers.html 4

5. School of Science Indiana University-Purdue University Indianapolis • Not educating enough people in science, technology, engineering and math • Need to diversify our math and science workforce • Middle school and high school are the critical times • Spread message of opportunity to parents and counselorswww.science.iupui.edu/ccowen/Careers.html 5

6. School of Science Indiana University-Purdue University Indianapolis • Not educating enough people in science, technology, engineering and math • Need to diversify our math and science workforce • Middle school and high school are the critical times • Spread message of opportunity to parents and counselorswww.science.iupui.edu/ccowen/Careers.html 6

7. School of Science Indiana University-Purdue University Indianapolis • Explosion in biological research and progress • The mathematical sciences will be a part • Opportunity: few mathematical scientists are biologically educated few biological scientists are mathematically educated Dr. Rita Colwell: “We're not near the fulfillment of biotechnology's promise. We're just on the cusp of it…” 7

8. School of Science Indiana University-Purdue University Indianapolis • Explosion in biological research and progress • The mathematical sciences will be a part • Opportunity: few mathematical scientists are biologically educated few biological scientists are mathematically educated Report Bio2010: “How biologists design, perform, and analyze experiments is changing swiftly. Biological concepts and models are becoming more quantitative…” 8

9. School of Science Indiana University-Purdue University Indianapolis • Explosion in biological research and progress • The mathematical sciences will be a part • Opportunity: few mathematical scientists are biologically educated few biological scientists are mathematically educated NSF/NIH: “Emerging areas transcend traditional academic boundaries and require interdisciplinary approaches that integrate biology, mathematics, and computer science.” 9

10. School of Science Indiana University-Purdue University Indianapolis ATM Security Increasing use of electronic communications in financial and other applications has increased the need for encryption to ensure privacy 10

11. School of Science Indiana University-Purdue University Indianapolis ATM Security Increasing use of electronic communications in financial and other applications has increased the need for encryption to ensure privacy The most widely used encryption system in the world is RSA, developed in 1976 by three mathematicians, Rivest, Shamir, and Adelman. 11

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43. School of Science Indiana University-Purdue University Indianapolis CAT Scans and MRI’s X-rays have been used for about a century in medical diagnostics. They are high frequency, high energy electromagnetic waves 43

44. School of Science Indiana University-Purdue University Indianapolis CAT Scans and MRI’s X-rays have been used for about a century in medical diagnostics. They are high frequency, high energy electromagnetic waves –– like visible light, except that the electromagnetic waves of visible light are lower frequency and lower energy. 44

45. School of Science Indiana University-Purdue University Indianapolis CAT Scans and MRI’s X-rays have been used for about a century in medical diagnostics. They are high frequency, high energy electromagnetic waves –– like visible light, except that the electromagnetic waves of visible light are lower frequency and lower energy. Since we see differences of frequency in light as ‘color’ and differences of energy as ‘brightness’, so you might say X-rays are very bright and a different color from what we see! 45

46. School of Science Indiana University-Purdue University Indianapolis X-rays are so energetic that our bodies are nearly transparent to them – like glass is to ordinary light. Bones are much less transparent to X-rays than soft parts of our bodies, indeed, each part of our bodies has slightly different transparencies than other parts. 46

47. School of Science Indiana University-Purdue University Indianapolis X-rays are so energetic that our bodies are nearly transparent to them – like glass is to ordinary light. Bones are much less transparent to X-rays than soft parts of our bodies, indeed, each part of our bodies has slightly different transparencies than other parts. Physicists would say that the rays are attenuated when they pass through dense matter, and the amount of attenuation is related to the properties of the matter they are passing through. 47

48. School of Science Indiana University-Purdue University Indianapolis When X-rays strike film, the chemicals in the film are changed – and the amount of the change is related to the strength of the rays that strike the film. When the film is developed, an image appears that records the intensity of the X-rays reaching the film at that spot. 48

49. School of Science Indiana University-Purdue University Indianapolis When X-rays strike film, the chemicals in the film are changed – and the amount of the change is related to the strength of the rays that strike the film. When the film is developed, an image appears that records the intensity of the X-rays reaching the film at that spot. The process is exactly analogous to the creation of a black-and-white negative in ordinary cameras thirty years ago – the bright areas of the picture are black, the dark areas are white. 49

50. School of Science Indiana University-Purdue University Indianapolis X-ray film 50