5. Mathematics: Warning: trite phrase ahead Knowledge That Lasts

6. Before Internet:Many Books After Internet: “The Book” (Web-Kindle...) _______________________________________ Many Sciences Or One Science ?

7. Mathematics is (in part...) --A language --An aid in understanding complexity, abstraction --A medium for precision --A paradigm for creativity --A set of tools for modeling reality (whatever that is) --A pillar of stability in a rapidly changing world --And more

8. The study of mathematics prepares for lifelong learning Mathematics is empowering. With a strong math background: --Science & Technology become more accessible --Retooling/Retraining/Change is more easily accommodated

9. Will learning more mathematics --get me a better job? --get me a higher salary? What will my starting salary be in my first job after graduation? What will my starting salary be in my second job after graduation?

10. Some things are (virtually) impossible without advanced mathematics Example: Imaging Devices (CAT scan, MRI,...)

11. Simple math model for CAT scan: Determine the 4 unknown data A,B,C,D From the six “X-Ray” sums A+B,A+C,A+D,B+C,B+D,C+D Ex: A=([A+B]+[A+C]-[B+C])/2

12. Symmetry Group Theory Algebra

13. Symmetry: Discrete & Continuous Discrete Symmetry: rotations and reflections of a square, Continuous Symmetry: rotations of a circle

14. Biggest Discrete Symmetry in the Universe: Monster Group |M|= 808017424794512875886459904961710757005754368000000000 ( Monsters I know, but what’s a (math) group? ) Biggest Continuous Symmetry in the Universe: E_8 How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness

15. What is E 8 ? Buckyballs

17. Topological Insulators. (What’s Topology?)

18. Protein Folding

20. I don't need to take math ___. (How can you be sure?) --Calculus:study non-linear phenomena by locally approximating linearly --Linear Algebra: study linearity in depth --Differential Equations: study dynamics --Probability: humans are not “wired” for it. Theory is needed. --More

21. You may know more mathematics than you claim to know