Fall 2009 Math 490-01 Senior seminar on
Learning, teaching, research, and applications of mathematics

Chi-Kwong Li
Office: Jones 128, Tel:221-2042, Fax: 221-7400, E-mail: ckli@math.wm.edu
http://www.math.wm.edu/~ckli
Office hours: TT 11:30 a.m. - 12:30 p.m., Wed. 10:30 - 11:30 a.m. and by appointments

Meeting Time and Place Tuesday/Thursday 3:30 - 4:50 p.m. Morton 239.

Course Description

Topics on learning, teaching, research, and applications of mathematics will be discussed.

Format

Instructor and students will take turn to discuss material related to learning, teaching, research and applications of mathematics. The first two round presentations will be based on the book:

• COMAP, For All Practical Purposes (Paper): Mathematical Literacy in Today's World (paperback version) (Comap, the Consortium for Mathematics and Its Applications) (Paperback), W. H. Freeman, Seventh or Eighth Edition.

• Liping Ma, Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States.
• George F. Simmons, Calculus Gems: Brief Lives and Memorable Mathematics (Paperback), McGraw-Hill Co., 1992.
• M. Nakahara and T. Ohmi, Quantum computing: From Linear Algebra to Physical Realizations, CRC Press, Taylor and Francis Group, New York, 2008.
• M.A. Nielsen and I.L. Chuang, Quantum computation and quantum information, Cambridge University Press, Cambridge, 2000.
• C.K. Li, A website on mathematical education related topics.
• Wikipedia.

Assessment

   Participation/evaluation/discussion/homeowrk            20%
   Presentation/Leadership of discussion                   
             (evaluated by instructor and participants)
   Presentation 1 (from COMAP book)                        20%
   Presentation 2 (from COMAP book)                        20%
   Presentation 3 (self selected topic)                    20%
   Paper associated with presentation 3                    20%
        First draft ready by March 15
        Final paper due on May 3
   Extra credits (inspiring ideas/problems/solutions)       5%

Letter Grades

 
     Grades (for homework, quizzes, exams, final grade, etc.):
 
     %: 0 - 60 - 65 - 70 - 75 - 80 - 83 - 87 - 90 - 93 - 100
          F    D    C-   C    C+   B-   B    B+   A-    A       
 

Discussion schedule

• January 21. C.K. Li, Introduction of the course. A Sample Presentation on Abacus.
• January 26. Discussion about the evaluation form.
  Chaper 1, C.K. Li.
• January 28. Chapter 2, C.K. Li.
• February 2. Chapter 3, Jennifer Holland.
• February 4. Chapter 4, Paul Moore
• February 9. Chapter 5, Brandon Gregor.
• February 11. Chapter 6, C.K. Li.
• February 16. Chapter 7, Austin Cole.
• February 18. Chapter 8, Sarah Cameron.
• February 23. Chapter 9, Michelle Blessing.
• February 25. Chapters 10/11 Katherine Goulde.
• March 2. Chapter 12 + related material. Paul Moore
• March 4. Chapters 13/14. Austin Cole.
• March 8-12. Spring break.
• March 16. Chapter 15 + related material. Katherine Goulde.
• March 18. Chapters 16/17. Sarah Cameron.
• March 23. Chapters 18/19/20. Brandon Georger.
• March 25. Chapters 21/22. Jennifer Holland.
• March 30. Chapter 23 + related material. Michelle Blessing.
• April 1. C.K Li will present the talk by Professor Yiu-Tung Poon (Iowa State University) on:
  What is $1+11 +.....+(111....111)$?
  Abstract: We use the simple question given in the title to illustrate the use and limitation of computer in mathematics research. We will discuss the following concepts: solution, pattern recognition, conjecture, proof and counter-example. Additional examples will be discussed if time permits.
• April 6. Brandon Gregor. Financial mathematics.
  I will give a broad overview of financial mathematics with topics including, measuring risk and return, methods of valuation for various assets, discounted cash flow models, and portfolio optimization. I will discuss the background of how these concepts are derived from a mathematical basis and how they are implemented by investment professionals.
• April 8. Katherine Goulde. Mathematics of Music.
  The lecture will discuss the mathematics of rhythmic styles, various types of scales, and styles and forms of composition.
• April 13. Sarah Cameron. Math in Art.
• April 15. Paul Moore. Mathematics in Sports.
• April 20. Jennifer Holland.
  Integrating TI calculators into mathematics curriculum from middle school through high school (and beyond).
• April 22. No class.
• April 27. Austin Cole. Probability and statistics.
  We will discuss different distributions: geometric, binomial, negative binomial, and hypergeometric.
• April 29. Mischelle Blessing.