2014mchidamb / math-exercise-guides

Math-Exercise-Guides

My solutions to exercises across several math/CS textbooks. Also, some brief reviews.

Disclaimer: Completion percentages are from memory and may not actually be accurate.

Algebra by Garrett Birkhoff and Saunders MacLane

Status: ~50-60% of exercises in chapters 1 and 2.

Review: Enjoying the progression/setup of topics so far in this book. Most people recommended Dummit & Foote, but I've personally found Algebra to be a more enjoyable read. Exercises feel a little on the easier side.

Calculus on Manifolds by Michael Spivak

Status: ~60% of exercises in chapter 1, chapter 2 in progress.

Review: Love the brevity of this book. Nice range of exercises after each section, with many exercises being important results that Spivak refers to over and over again as he develops the material. My only complaint so far is that some of the notation is a bit cumbersome.

Complex Analysis by Lars Ahlfors

Status: Some exercises in chapter 1, just started chapter 2.

Review: Can't say I've liked this book so far. Chapter 1 had a bunch of tedious exercises that I chose to skip, and the ones I chose to do didn't feel illuminating. Still, enough people have heaped praise on this book that I'll try to stick with it.

Elements of Statistical Learning by Trevor Hastie, Robert Tibshirani, and Jerome Friedman

Status: I've done the first exercise.

Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller

Status: ~10% complete.

Review: Fun problems.

Lecture Notes on Elementary Topology and Geometry by Isadore Singer and John Thorpe

Status: Started reading chapter 1, but there are no exercises.

Linear Algebra by Peter Lax

Note: this book is not the same as Linear Algebra and its Applications by Lax.

Status: Close to 100% of exercises in chapters 1-9.

Review: Huge fan of the bite-sized chapter format, and I really like the exposition. Unfortunately, this book has very few exercises per chapter, and most of the exercises are quite straightforward.

Nature of Computation by Christopher Moore and Stephan Mertens

Status: 100% of exercises in chapters 1-3 and a handful of problems in chapters 1-3.

Review: Amazing book, reads like a novel. Really appreciate the historical background woven into each section, as well as the in-text exercises for keeping the reader on their toes. Also, the end-of-chapter problems look awesome; I need to do more of them.

Principles of Mathematical Analysis by Walter Rudin

Status: ~50% of exercises in chapters 1-7.

Review: Many, many reviews have been written about this book. I personally love it; the chapters are relatively short and the exercises have definitely strengthened my grasp on analysis.

Reinforcement Learning: An Introduction by Richard Sutton and Andrew Barto

Status: 100% of exercises in chapter 1.

Statistical Inference by George Casella and Richard Berger

Status: ~20% of exercises in chapters 1-3.

Review: Don't really like the writing, but has lots of exercises and each chapter is packed with information. Feels pretty comprehensive.