Fall 2009 Math 49001 Senior seminar on
Learning, teaching, research, and applications of mathematics
Instructor
ChiKwong Li
Office: Jones 128, Tel:2212042, Fax: 2217400, Email: 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.
Additional references include:
 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),
McGrawHill 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
Sample evaluation from
at http://www.math.wm.edu/~ckli/Courses/490form.pdf.
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 812. 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 YiuTung 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
counterexample. 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.