U.T. Putnam preparations, 2021

First read more about the Putnam competition on this page's parent page

This year's UT Putnam competition will take place at 9am on Dec 4, 2021 in ETC 2.136 . Please try to arrive by 8:45am so we can take care of paperwork and then start promptly at 9. First session is 9am to noon; then we'll go out to lunch and come back in time for the second session of 6 more questions, from 2pm to 5pm. Bring something to write with. You don't need much else.

New this year: you must register yourself online before the competition!. Register at:

                https://artofproblemsolving.com/contests/putnam/student

UT Students who want to prepare for the Putnam competition -- and even those who just want to learn some mathematics or have fun trying hard problems! -- are invited to join us for weekly practices during the Fall term. We meet THURSDAY afternoons at 4:00 in PMA 9.166, starting October 7. We don't have to follow any particular format or syllabus, but typically each week will be devoted to problems in one branch of mathematics. We will remind each other of some of the key terms and theorems and tools from that area of math, and then work on a collection of problems of varying levels of difficulty from that subject area. When people are ready to share their ideas, students head up to the blackboard to explain their solutions or their incomplete ideas.

Students are encouraged to write up their solutions, too. You can bring your solutions to me so we can discuss how to improve your presentation, or you can send them to me to be posted here for the benefit of other students -- and to encourage others to give you feedback!

I will post the problems we work on each week right here. I can also post solutions to the problems but what I would prefer to do is to have some of YOU submit write-ups to solutions that you have worked out! Get them to me and I will post them.

Here are the problem sets we've worked on so far.

The first meeting was October 7. We tackled a grab-bag of problems, and a couple dozen students had some great ideas to solve them. I welcome those who would like to write up their complete solutions to send them to me and I will post them here. The hardest one, surely, was at the bottom; it was an actual Putnam exam question from last year. I wrote up an answer key to that one myself, that discusses how the solution might actually have been discovered by a normal human being!
Oct 14: we considered some tricky problems in Calculus
Oct 21: NO MEETING. (Well, you are welcome to assemble in PMA 9.166 to discuss problems but I will be out of state!)
Oct 28: A motley collection of questions in combinatorics
Nov 04: I talked too much about Number Theory but we still had time to work on some Number Theory problems that I had prepared in the past. I touched up a set of solutions to (most of) those problems too.
Nov 11: Some Linear Algebra questions, with a bonus challenge about the axioms for a vector space. (Typo: the fourth axiom should stop before the word "likewise"; otherwise a careful expansion of the quantity "(1+1)*(u+v)" would make axiom 2 redundant.
Nov 18: Problems in various types of Geometry I wrote up a long-ish analysis of the problem about long parabolas inside circles, and a little sidebar about an optimization problem we ran into while addressing the first problem.
Nov 25: No meeting; Happy Thanksgiving!
Dec 02: Last pre-competition meeting. We will try our hand at working an actual Putnam competition exam paper!
Dec 04 2021: This is the big day! Putnam exam starts at 9pm; come a few minutes early. We will meet in ETC 2.136 .

For more information about the competition please contact Dave Rusin in PMA 9.140. (rusin@math.utexas.edu)