# Putnam Club

*Organizers: Gheorghe Craciun, Alexander Hanhart, Mihaela Ifrim, Botong Wang*

The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. It is given each year on the first Saturday in December. The exam consists of 12 problems, 6 in the 3 hour morning session and 6 in the 3 hour afternoon session. Each problem is worth 10 points, so the maximum score is 120. National winners usually get around 100 points. The median score is generally around 0-2 points. This is a difficult exam with many interesting and fun problems.

Old exams and more information on the Putnam competition.

The UW is also participating in the Virginia Tech Regional Mathematics Contest. This is an individual competition with seven problems in 2.5 hours. Many schools use it as a kind of rehearsal for the Putnam. You can find more information over here.

We also hold our own UW Madison Undergraduate Math Competition in the spring; for this academic year, it is tentatively scheduled in April 2019.

## Contents

## Spring 2019

The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. **The first meeting will be on the 6th of February in Van Vleck hall, room B139.**

**! Important announcement:** We will begin preparing you for the Putnam exam earlier this year. The material covered will be presented gradually. More details will be explained to you during your first meeting of this semester (Feb 6th). We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu.

- February 6: The basics by Botong
- February 13: Botong
- February 20: Alex Ordered Sets
- March 6th: Mihaela Algebra
- March 13: Mihaela
- March 27: Botong Matrices

If this material is completely new to you then read through the definitions in the first section and try the interspersed exercises which are direct applications of the definitions. If you are familiar with the basic material then review the problem solving strategies and the example problems which directly utilize the techniques. Finally, if you are a veteran, go ahead and jump right to the exercises!

- February 27: Alex: Review results from 2/20. Bring written solutions and/or be prepared to present your
- March 6th: Mihaela
- March 13: Mihaela

etc.

## Fall 2018

The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139. **The first meeting will be on the 26th of September in Van Vleck hall, room B139.**

**! Important announcement:** We put together a Piazza account that will help the participants to discuss and collaborate with their pairs. Here is the link you need to access in order to register for this "class": piazza.com/wisc/fall2018/putnam2018 . Our intervention on Piazza will be minimal (some of the instructors will, from time to time, visit the piazza questions and provide some help). Also, based on your requests, we have decided to structure our meetings in a way that will provide more insight on methods and certain tricks that are very often used in this type of math competitions. The book we will mainly use as a guide in preparing our meetings is: "Putnam and Beyond" by Razvan Gelca and Titu Andreescu.

- September 26: topic Introductory meeting by Mihaela Ifrim. We covered only the first 3 problems. I encourage you to work out all the problems!

- October 3: Linear Algebra by George Craciun.

- October 10: Polynomials by Botong Wang.

- October 17: Sequences by Alex Hanhart.

- October 24: Convergence and Continuity by Mihaela Ifrim.

- October 27: Virginia Tech Math Contest: 9-11:30am in VV B115.

- October 31: Geometry: cartesian coordinates, complex coordinates, circles and conics by George Craciun.

- November 7: Combinatorics: Set theory and geometric combinatorics by Botong Wang.

- November 14: Techniques from Group Theory by Alex Hanhart.

- November 21:
**No meeting**: Happy Thanksgiving!

- November 28: Number Theory by Mihaela Ifrim.

- December 1: Putnam Competition! Starts at 9am!!!!
**The competition will take place December 1st 2018 (Saturday December 1st). The competition is administered in two sessions (A and B) on the same day, December 1st! Session A will start at 9 am and it will end at 12pm, and Session B will start at 2pm and it will end at 5pm. You should arrive at least 10 minutes prior to each session. You should bring your own pencils and pens (blue or black ink are permitted). Number 2 pencils with erasers will be needed to complete the identification forms. Erasers are also permitted, but nothing else will not be allowed in the exam room. I plan on bringing 20 such no 2 pencils. The exam room is B239 which is a class room located in Van Vleck Hall, at the level B2. Thank you all for participating and see you all there! If you have friends that would like to take the exam please encourage them to do so.**

## Spring 2018

The Putnam Club does not meet in the spring, but we had the fourth annual UW Undergraduate Math Competition on **April 24th**, 2018, 5:30-8pm in VV B239.

## Fall 2017

The Putnam Club will help you prepare for the exam by practicing on problems from previous years and other olympiad-style problems. The meeting time is 5pm on Wednesdays in VV B139.

- September 20: Introductory meeting by D.Arinkin
- September 27: Equations with functions as unknowns by M.Ifrim (by request: here is a solution to problem 6; problem 7 is problem B5 of 2016 Putnam exam; you can see the solution here).
- October 4: Inequalities by G.Craciun.
- October 11: Polynomials by D.Arinkin.
- October 18: Equations by M. Ifrim
- October 21: Virginia Tech Math Contest: 9-11:30am in VV B203.
- October 25: Review of this year's Virginia Tech Contest by G.Craciun.
- November 1: Functions and calculus by D.Arinkin.
- November 8: Past Competitions by M.Ifrim
- November 15: Recurrences by G.Craciun.
- November 22:
**No meeting**: Happy Thanksgiving! - November 29: Complex numbers by D.Arinkin.
- December 2:
**Putnam Exam**in VVB115. Morning session: 9-12pm; Afternoon session: 2-5pm.

## Spring 2016

The Putnam Club does not meet in the spring, but we had the third annual UW Undergraduate Math Competition on April 19th, 2017.

## Fall 2016

- September 20: Introductory meeting
- September 27: Calculus and analysis
- October 4: Generating functions (by Vlad Matei)
- October 11: Review of last year's UW Math competition
- October 18: Functional equations
- October 22: Virginia Tech Math Contest
- October 25: Review of this year's VT contest
- November 1: Matrices (by Vlad Matei)
- November 15: Two algebra problems
- November 22: No meeting: Happy Thanksgiving!
- November 29: Assorted problems
- December 3: Putnam Exam: Morning session: 9am-noon, Afternoon session: 2-5pm in VV B135.

## Spring 2016

The Putnam Club does not meet in the spring, but we had the second annual UW Undergraduate Math Competition on April 12th, 2016.

## Fall 2015

.

- September 23rd: Introductory meeting
- September 30th: Pigeonhole principle
- October 7th: Review of 2015 UW math competition
- October 14th: Matrices and determinants
- October 21st: Virginia Tech practice
- October 24th: Virginia Tech Regional Mathematics Contest: 9-11:30 am
- October 28th: Review of the 2015 Virginia Tech contest.
- November 4th: Polynomials
- November 11th: Assorted problems
- November 18th: Assorted problems
- No meeting on November 25th
- December 2nd: TBA
- December 5th: Putnam competition: Morning session: 9am-12pm, afternoon session: 2-5pm in VV B115.

## Spring 2015

The Putnam Club does not meet in the spring, but we had our first UW Undergraduate Math Competition!

## Fall 2014

- September 17: Introductory meeting
- September 22: Coloring and pigeonhole principle
- October 1st: Went through HW problems from last time
- October 8th: Number theory
- October 15th: Games
- October 22nd: Problems from last year's Virginia Tech contest
- October 25th: Virginia Tech Regional Mathematics Contest
- October 29th: Review of this year's Virginia Tech contest
- November 5th: Inequalities and functional equations
- November 12th: Polynomials
- November 19th: Combinatorics
- December 3rd: Recursions
- December 6th: Putnam competition: Morning session: 9am-12pm, Afternoon session: 2pm-5pm in Van Vleck B119
- December 10th: Review of this year's Putnam

## Fall 2013

- September 11: Introductory Meeting
- September 18: Assorted Problems (by Yihe Dong)
- September 25: Combinatorics
- October 2: Matrices and Linear Algebra
- October 9: Number Theory
- October 16: Functions and Calculus
- October 23: Polynomials
- October 26: Virginia Tech Regional Mathematics Contest
- October 30: Problems from this year's Virginia Tech contest
- November 6: Games
- November 13: Pigeonhole Principle
- November 20: Extreme Principle
- November 27: No meeting (Thanksgiving)
- December 4: TBA
- December 7: Putnam competition Morning session: 9am-12pm, afternoon session: 2-5pm in VV B239.

## Fall 2012

- September 11: Introduction Problems
- September 18: Some Basic Techniques Problems
- September 25: Polynomials and Algebra Problems
- October 2: Number Theory Problems
- October 9: Calculus Problems
- October 16: Games and Algorithms Problems
- October 23: Combinatorics Problems
- October 30: Probability Problems
- November 6: Linear Algebra Problems
- November 13: Grab Bag Problems
- November 27: Grab Bag 2 Problems

## Fall 2011

- September 21: Pigeonhole Principle (Brian Rice) Problems
- September 28: Introduction to Counting (Brian Rice) Problems
- October 5: Elementary Number Theory (Brian Rice) Problems, Problems (Hardcore)
- October 12: Polynomials (Brian Rice) Problems, Problems (Hardcore)
- October 19: A Grab Bag of Discrete Math (Brian Rice) Problems
- October 26: Calculus, Week 1 (Brian Rice) Problems
- November 2: Calculus, Week 2 (Brian Rice) Problems
- November 9: Linear and Abstract Algebra (Brian Rice) Problems
- November 16: Mock Putnam Problems, Solutions