MATH 131: Mathematical Analysis

Harvey Mudd College — Spring 2026

Welcome

This is the course website for MATH 131: Mathematical Analysis at Harvey Mudd College, Spring 2026, taught by Dr. Lisette de Pillis.

This course is a rigorous analysis of the real numbers, as well as an introduction to writing and communicating mathematics well.

Course Structure

The course covers four main areas:

  1. Sets and Topology (Lectures 1–10): Countability, fields, metric spaces, open/closed sets, compactness
  2. Sequences (Lectures 11–16): Convergence, subsequences, Cauchy sequences, constructing the reals
  3. Series (Lectures 17–19): Convergence tests, sums, products, rearrangements
  4. Functions (Lectures 20–24): Limits, continuity, pointwise and uniform convergence

Textbook

  • Required: Principles of Mathematical Analysis (3rd Ed), by Walter Rudin
  • Supplemental (free): Understanding Analysis (2nd Ed), by Stephen Abbott — available from the Claremont Colleges Library

Contact

  • Instructor: Dr. Lisette de Pillis — depillis@g.hmc.edu
  • Office: Shanahan 3418
  • Class: Tuesdays and Thursdays in Shan 2460