Colorado State University Putnam Seminar

2018 team (left to right): Henry Adams, Yuling Wu, Jingya Li, Yujia Chen, William van Noordt, Ethan Coldren, Andre Leautaud, Matt Beirne, Luke Askew, George Laird. Not pictured: Sean Walters.

What is the Putnam?

The Putnam is an annual mathematics competition for college students, and a fun way to expose yourself to new challenging math problems. The exam is held on the first Saturday of December, meaning Saturday, December 1, 2018.

Here is the Putnam Mathematical Competition website, and here is the Wikipedia page.


What is the Putnam seminar?

We will be holding weekly practice sessions, during which we will try to solve interesting problems together. The emphasis will be on learning from each other (not on competition), so please stop by and share your ideas. It's definitely okay if you can't make some of the practice sessions.

You are welcome to attend the practice sessions even if you can't make the exam, and you are welcome to take the exam even if you can't make the practice sessions.

In Fall 2018 we will be meeting weekly on Mondays at 4:00pm, in Weber 201. Our first meeting will be on Monday, August 27.

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How do I get involved?

Stop by one of the practice sessions! Alternatively, feel free to contact Henry Adams (henry dot adams at colostate dot edu) with questions, or to have him add you to our email list.


Resources

Here are Putnam problems 1985-present and solutions 1995-present.

Here are Putnam problems and solutions 1994-present.

Here are Putnam problems 1980-2010.

Here are Putnam problems and solutions 1938-2003.

The book Putnam and Beyond by Gelca and Andreescu organizes problems by topic, presents examples, and contains practice problems. It is freely available to CSU students as a pdf.


Coaches


Fall 2018 Schedule

Date Topic, problems discussed, discussion leader

Aug 27 Pigeonhole principle, and Putnam 2015 exam, B1
Sep 10 Sean Walters: Putnam 2015 exam, and pigeonhole principle
Sep 24 Putnam 1997 exam, B2
Oct 1 Putnam 1997 exam, A4 and A5
Oct 8 Putnam 1994 exam, A2
Oct 15 Putnam 1994 exam, A1, B1, B2, B3
Oct 29 Putnam 1983 exam, B1 and part of A2
Nov 12 Putnam 1983 exam, A1 and A2
Nov 26 Sean Walters: Putnam 1990 and 2006 exams, A1 from 2006
Saturday, December 1 Putnam exam!

Spring 2018 Schedule

Date Topic, problems discussed, discussion leader

Jan 29 Putnam 2017 exam, B2
Feb 5 Putnam 2017 exam, B1 and part of A1
Feb 12 Will van Noordt, Section 3.4 on equations with functions as unknowns, #536
Feb 19 Jingya Li, Combined integral method
Feb 26 Sheldon Deeny, Section 2.2.5 on irreducible polynomials, #182, 183
Mar 5 Sean Walters, Section 2.3.3 on the inverse of a matrix, #229
Mar 26 Henry Adams, Section 6.1.1 on set theory and combinatorics of sets, #823
Apr 2 Ethan Coldren, Section 6.1.3 on combinatorial geometry, #837, 841
Apr 9 No meeting - Henry has a visitor in town
Apr 16 Dinner at Henry's at 6pm

Fall 2017 Schedule

Date      Topic, problems discussed

Aug 28 Putnam 1999 A1 and pigeonhole principle: "Prove that among any 5 integers there are always three with sum divisible by 3"
Sep 11 Putnam 1999 A3 and pigeonhole principle: "At least 6 Coloradans with the same number of hairs on their head", and "At least two arrows within 1 meter"
Sep 18 Putnam 1999 B1, "Probability two random triangles inscribed on the circle intersect", and "Probability two integers are relatively prime"
Oct 2 Putnam 2011 B1 and "Given three points sampled uniformly at random from a circle centered at the origin, what is the probability that the origin is contained in the resulting triangle?"
Oct 9 Putnam 2011 A4 and "Prove that (n-1)/(n+1)<cos(π/n) for all integers n≥4"
Oct 30 Putnam 1986 B1, Putnam 1988 A1, Putnam 2007 B1
Nov 6 Putnam 1991 B1, Putnam 2009 A1, Putnam 2001 A1
Nov 18 Putnam 1988 B1, Putnam 1991 A1, Putnam 2008 A1, Putnam 2010 A1
Nov 27 Putnam 1992 B1, Putnam 2001 A2, Putnam 1997 A4
Dec 2 Putnam exam!

Spring 2017 Schedule

Date      Topic, problems discussed

Jan 23 Putnam 2016 exam, B1 and A4
Jan 30 Nabeel Moin, Section 3.2.1 on Taylor series
Feb 6 Ethan Coldren, Section 2.4 on abstract algebra
Feb 13 Sean Walters, Section 4.1.2 on the coordinate geometry of lines and circles
Feb 27 Will van Noordt, Section 4.1.2 on factorization and divisibility, and Sylvester's theorem
Mar 6 Dinner at Henry's!
Mar 20 Bowen Li, sequences and series, including Section 3.1.4, and 2016 B6, and #360 on page 120
Mar 27 Bowen Li, sequences and series, #353 and #354 on page 119
Apr 3 Ethan Coldren, Section 6.2.2 on generating functions
Apr 17 Section 6.2.2 on generating functions, #867, #870, #872
Apr 17 Putnam 2005 exam, B1

Fall 2016 Schedule

Date      Topic, problems discussed

Aug 24 Putnam 2013, A1 and B1
Aug 31 The pigeonhole principle
Sep 7 The pigeonhole principle, part 2
Sep 14 Ethan Coldren, Section 4.1.3 on conics & other planar curves, #604
Sep 21 Section 4.1.3 on conics & other planar curves, #606, #616
Sep 28 Peter Muller, sheet of problems, 2009 A1
Oct 5 Sheet of problems, 2015 A1, 2014 A1, 2012-A1, 2010 B2, 2012 A1
Oct 12 Putnam 1998, A2 and B1, and from prior weeks
Oct 19 Putnam 1995 exam, A1 and B2
Oct 26 Putnam 2007 exam, B1
Nov 2 Nabeel Moin, Section 2.3.1 and 2.3.2 on matrices and determinants, #203, #205, #207
Sunday Nov 6 Practice exam! 2003 side A, and 2000 side A and B1
Nov 16 Discussed practice exam
Nov 16 Peter Muller: Analysis section from Putnam and Beyond
Dec 6 Putnam exam!

2017 team (left to right): Zhi Li, Bowen Li, Sheldon Deeny, Nathan Larson, Will van Noordt, Amber Moin, Ethan Coldren. Not pictured: Henry Adams, Sean Walters.

2016 team (left to right): Zhi Li, Henry Adams, Bowen Li, Will van Noordt, Ethan Coldren, Brooks Adams, Joseph Gelfand, Colin Roberts, Doran Wood, Chase Ashby. Not pictured: Sean Walters, Amber Moin, Sid Katz, Peter Muller, Nabeel Moin.


2015 team (left to right): Henry Adams, Ethan Coldren, Gavin Stewart, Nabeel Moin, Amber Moin, Katy Sieviec. Not pictured: Sean Walters.