Putnam

The Seventy Eight Putnam Examination will be held on Saturday, December 1st, 2018.

It will consist of two sessions of three hours each:

  • Morning Session: 8:00am-11:00am, 510R
  • Afternoon Session: 1:00pm-4:00pm, 510R

The test is supervised by faculty members of each participating school. Every problem is graded on a scale of 0-10. The problems are usually listed in increasing order of difficulty, with A1 and B1 the easiest, and A6 and B6 the hardest. Top 5 scoring students on the Putnam exam are named Putnam Fellows. A student can take this exam maximum four times and the Putnam official team of the university consists of 3 members.

The purpose of this class is to provide a comprehensive introduction into the world of problem solving in different branches of mathematics such as: real & complex analysis, linear algebra, abstract algebra, combinatorics, probability, geometry and trigonometry and number theory.

This course (Math 194) teaches important skills in problem solving that are not taught in a systematic way in any other course. These skills are extremely valuable in preparing students for jobs and for graduate-level research. The teaching style will be a mixture of a lecture and a problem-solving session. By the end of this course, students should develop fundamental problem solving skills, and become accustomed to concentrating on a problem for an extended period of time. Indeed, this seminar concentrates on the raw creative problem-solving skills which can serve as an essential ingredient in almost every field of activity.

Important Information

You can take the Putnam Exam even if you don't take Math 194. (If you are enrolled in Math 194, I will sign you up automatically.) To sign up, send me an e-mail at vmatei@uci.edu. All email signup requests will be acknowledged. If you're not enrolled in Math 194 and you change your mind later and don't take the exam, that's OK.

Syllabus for the class

  • Meeting time: Tuesdays 7 to 8:20 PM in Rowland Hall 306
  • Office Hours: Tuesday 5:30 to 6:50 in 540 N Rowland Hall
  • Grades: This course is pass or no pass. You should be present for the whole lectures if you are registered and take the Putnam exam, to pass the class. Homework will be regularly assigned, but it is not mandatory. It is highly advised trying to work on the problems; they are fun and it is good practice for the Putnam.
  • Book: There is no official book for this class; I will draw from random topics in the above categories and will update the list of lectures as we go along. Some recommendations though are the following:
  1. R. Gelca, T. Andreescu, Putnam and Beyond, Springer Verlag, 2007.
  2. K. Kedlaya, B. Poonen, R. Vakil- The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions and Commentary, The Mathematical Association of America, Washington, D.C., 2002.
  3. L. Larson, Problem-Solving Through Problems, Springer Verlag, 1983.

Lectures:

  • Lecture 1: General Problem Solving. We've talked about induction, pigeonhole principle and the extremal element principle. Attached you will find the handout with the problems Problem Sheet
  • Lecture 2: Polynomials. We've talked about degree, roots, Vieta's relations, polynomial equations. You will find attached extra material on the rational root theorem, Lagrange Interpolation, a clarification on the class example, and the proof of the ABC conjecture for polynomials. Lecture-ExtraMaterial ProblemSheet
  • Lecture 3: We talked about convergence of sequences- Definition, Cauchy criteria, Monotone convergence theorem, squeeze theorem, and the Stolz Cezaro lemma-which is a discrete version of L'Hopital Theorem. Attached is the problem handout Problem Sheet
  • Lecture 4: We talked about matrices- Cayley Hamilton, Eigenvalues, minimal polynomial, triangularization. Attached is the problem handout Problem Sheet
  • Lecture 5: We talked about continuity- Definition, Weierstrass theorem, Intermediate Value theorem; differentiability- increasing, decreasing, Fermat's theorem, Rolle, Mean Value Theorem. Attached is the problem handout Problem Sheet
  • Lecture 6: Probabilities Problem Sheet
  • Lecture 7: Determinants Problem Sheet
  • Lecture 8: Integration Problem Sheet

Resources:

  1. Ed Barbeau has kindly selected and sorted the Putnam Problems according to topic and you can find them here http://www.math.utoronto.ca/barbeau/university.html
  2. Karl's Rubin webpage for previous Fall https://www.math.uci.edu/~krubin/194/
  3. Harvey Mudd Webpage https://www.math.hmc.edu/putnam/
  4. Po-Shen Loh http://www.math.cmu.edu/~lohp/2018-putnam.shtml. A very rich site and the class is split on working on different levels of problems.