Introduction to Math Olympiad Problems

A Brief Introduction to Olympiad Inequalities

The goal of this document is to provide a easier introduction to olympiad inequalities than the standard exposition Olympiad Inequalities, by Thomas Mildorf. I was motivated to write it by feeling guilty for getting free 7’s on problems by simply regurgitating a few tricks I happened to know, while other students were unable to solve the problem. Warning: These are notes, not a full handout. Lo...

Introduction to Discrete Math

are non-zero. Solution: First suppose the above some has no non-zero entries on its diagonal. Since A(G)i,j is the number of walks of length k from i to j, if the sum above has non-zero diagonal entries, then for any pair of vertices i, j there is a walk of some length from i to j. This implies there is a path from i to j. Since i, j are arbitrary, we conclude that G is connected. Now assume G ...

Math 220: Introduction to Pde

Partial differential equations are ubiquitous in applications of mathematics, and indeed they play an important role in ‘pure mathematics’ as well. In this course we study these equations, and we start by describing general types of these equations. However, before the outset it is good to keep in mind that while PDE are generalizations of ODE, and thus some ODE notions often have analogues, on...

Math 104: Introduction to Analysis

MATH 239: Introduction to Combinatorics