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.

## 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 2, 2017.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 Spring 2018 we will be meeting weekly on Mondays at 3:00pm, in Weber 201. Our first meeting will be on Monday, January 29.

## 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

In 2017 the coaches of the CSU Putnam team are Henry Adams and Sean Walters.In 2016 the coaches of the CSU Putnam team were Henry Adams, Peter Muller, and Nabeel Moin.

## 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! |

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.