What This Document Is
This document contains detailed solutions to the 1986 William Lowell Putnam Mathematical Competition, a highly challenging undergraduate mathematics exam. It’s a compilation of worked problems from that year’s contest, prepared for students in an advanced mathematics course at the University of California, Berkeley. The solutions are presented with a focus on clarity and mathematical rigor.
Why This Document Matters
This resource is invaluable for students preparing for the Putnam Competition, or those seeking to deepen their understanding of advanced mathematical problem-solving techniques. It’s particularly beneficial for students enrolled in challenging upper-division courses like real analysis, abstract algebra, or number theory. Studying these solutions can provide insight into the types of problems encountered on the Putnam exam and the level of mathematical sophistication required to succeed. It’s best used *after* attempting the problems independently, as a way to check your work and learn alternative approaches.
Topics Covered
* Algebraic Manipulation and Equations
* Combinatorics and Counting Principles
* Calculus and Analysis (including limits and series)
* Number Theory and Divisibility
* Geometric Problem Solving
* Advanced Mathematical Proof Techniques
What This Document Provides
* Complete solutions to all problems from the 1986 Putnam Competition.
* Detailed mathematical reasoning and justifications for each step.
* A demonstration of strategies for tackling complex mathematical problems.
* An opportunity to learn from a high-performing student’s approach to the competition.
* Insight into the expected level of mathematical maturity for Putnam participants.
