Berea Math Team

Putnam Competition Training Resources

Essential materials and structured practice for competitive mathematics success. Focus on consistent training, clean proof-writing, and strategic problem-solving.

Current Training Proof Techniques External Resources

Training Schedule

Regular Sessions

  • Main sessions: Fridays 4:00–6:00 PM at MAC 206
  • Power Hour: Saturdays (peer-led practice)
  • Mock exams: Monthly full 6-problem tests

Key Dates

  • Competition: Saturday, December 6
  • Registration: Mid-October
  • Final prep: November intensive sessions
MAC Building Entrance
MAC 206 Meeting Room

Current Training Materials

This Week

Mini-Mock Problems

Focus: Inequalities + Induction

Download PDF Submit Solutions
Solutions

Model Write-ups

Clean proof examples with commentary

View Solutions
Support

Practice Sessions

  • Friday group sessions
  • Saturday power hour
  • 1:1 proof feedback

Proof Techniques Playbook

Core strategies for Putnam A1-A3 and B1-B2 problems. Master these patterns for consistent success.

Induction & Invariants

  • Strong/structural induction
  • Monovariant arguments
  • Loop invariants

Inequalities

  • AM-GM, Cauchy-Schwarz
  • Jensen's inequality
  • Rearrangement inequality

Number Theory

  • Modular arithmetic
  • Pigeonhole principle
  • Divisibility arguments

Combinatorics

  • Extremal arguments
  • Double counting
  • Bijective proofs

Analysis

  • Telescoping series
  • Integral estimates
  • Mean value theorem

Algebra

  • Vieta's formulas
  • Polynomial factoring
  • Root analysis

Linear Algebra

  • Rank-nullity theorem
  • Eigenvalue bounds
  • Matrix inequalities

Functional Equations

  • Substitution strategies
  • Monotonicity tests
  • Injectivity proofs

Proof Writing

Structure: Claim → Key idea → Proof steps → Conclusion

LaTeX Template

Mock Examinations

Monthly full-length practice tests under timed conditions to build competition readiness.

Mock Exam #1

Late October • 3 hours

Register

Mock Exam #2

Mid November • 3 hours

Register

Scoring Guide

Grading rubric and common mistake patterns

View Rubric

LaTeX Template

Standard template for clean, professional proof write-ups:

\documentclass[11pt]{article}
\usepackage{amsmath,amssymb,amsthm}
\usepackage[margin=1in]{geometry}
\newtheorem*{claim}{Claim}

\begin{document}
\section*{Putnam Practice \#N \quad [Your Name]}

\subsection*{Problem A1}
\begin{claim}
% State the result you will prove clearly
\end{claim}

\textbf{Key Idea:} % One sentence describing the main approach

\textbf{Proof:} 
% Step-by-step argument with clear justification
% Use proper mathematical notation
% Address edge cases if relevant

\qed
\end{document}

External Resources

Official Putnam Site

maa.org/putnam

Competition rules, registration, and official information

Problem Archive

Kedlaya's Archive

Complete solutions 1985–present

Practice Problems

AoPS Putnam Wiki

Categorized by topic and difficulty

Training Books

  • "Putnam and Beyond" by Gelca & Andreescu
  • "The Art and Craft of Problem Solving" by Zeitz
  • "Problem-Solving Strategies" by Engel

Online Communities

Competition Math

  • IMO problems and solutions
  • USA Mathematical Olympiad
  • Monthly contest archives