Linear Algebra With Elizabeth Meckes. Published by Cambridge University Press. See this page for various online resources, including glossary, complete solutions manual for instructors, and errata list.

Random Matrices from the Classical Compact Groups: a Panorama

Lecture notes

• A brief introduction to group representations and character theory

  These are notes for a brief unit on representation theory at the end of a standard graduate abstract algebra course. The notes assume no special preparation for representation theory, but take advantage of efficiencies of exposition made possible by an assumed basic graduate-level background in module theory, canonical forms, etc.

• Lecture notes on matrix analysis

  These are my lecture notes for MATH 405, Advanced Matrix Analysis, in Spring 2019. They're pretty rough in places. I plan to revise them and polish them up for public consumption over time, but in the mean time, here they are. (Don't take the word "Advanced" in the course title too seriously — it's just there to signal to potential students that this shouldn't be mistaken for a first course in linear algebra. The material is at a similar level to most books titled "Matrix Analysis".)

• More to come...

Links for students (and teachers!)

• Common Errors in Undergraduate Mathematics
• Good advice from the New York Times for college students in general:
  • Forget What You Know About Good Study Habits
  • How to Get the Most Out of College
  • An Underappreciated Key to College Success: Sleep
  • U Can't Talk to Ur Professor Like This and the author's guidelines about email etiquette for students
• Useful posts about basic logic from Tim Gowers's blog:
  • Welcome to the Cambridge Mathematical Tripos
  • Basic logic — connectives — AND and OR
  • Basic logic — connectives — NOT
  • Basic logic — connectives — IMPLIES
  • Basic logic — quantifiers
  • Basic logic — relationships between statements — negation
  • Basic logic — relationships between statements — converses and contrapositives
  • Basic logic — tips for handling variables
  • Basic logic — summary
• A few words about proofs: a short handout with some hints about basic techniques in writing proofs. (This makes reference to specific course numbers at CWRU, but of course the content is potentially useful to students elsewhere.)