Meeting Times: Wednesdays 5:45-7:45 PM in 528 Math
Instructor: Dmitry Zakharov
Office: 206A Math
Office Phone: (212) 854-5886
Office Hours: By appointment
Email: zakharov@math.columbia.edu
Prerequisites: Interest in mathematics! Also desirable: abstract and linear algebra, number theory, analysis.

Course Description:

Literature: Aigner, M., Ziegler, G.M., Hofmann, K.H., Proofs from THE BOOK, 3rd ed., Springer, 2004. This is our basic source. I've put a copy on reserve in the library, and you can buy one for about $30 at AddAll.com. However, our course is by no means limited to this book, if you find an interesting proof you would like to present.

Grading: Every attending student is expected to give at least two talks, and you will be graded primarily on the quality of your preparation and presentation.

Attendance: Attendance is mandatory. Please inform me if you need to miss a lecture.
September 13: I will introduce the course by an example of both a quintessential Book proof (the infinitude of the primes) and an infamous non-Book proof (the four-color theorem). I will offer several topics for the next few talks and maybe we'll find a more convenient time.
September 20: Tlacael Esparza - Bertrand's postulate.
September 27: Cindy Lee - Cauchy's rigidity theorem.
October 4: Jay Mullen - Hilbert's third problem.
October 11: Matt Zickermann - A theorem of Polya on polynomials.
October 18: Kristen Curtis - Every finite division ring is a field.
October 25: Miriam Parnes - Writing prime numbers as the sum of two squares.
November 1: Tlacael Esparza - Cotangent and the Herglotz trick.
November 8: Jay Mullen - Every large point set has an obtuse angle.
November 15: Cindy Lee - Some irrational numbers.
November 21: Matt Zickermann - Sets, functions and the continuum hypothesis.
November 29: Miriam Parnes - Completing Latin squares.
December 6: Kristen Curtis - How to guard a musuem.
Homework 2 (Due November 1): Homework_2_book.pdf