This page gives citations for some of the books/resources I have referred to on this blog. The idea is that if I cite them fully here, then in my actual blog posts I can use shorthand references and trust that the reader will come here to look up the full citation (if they want to go look at the resource). In addition, I will say something about how I came across each resource.

  • Christopher C. Leary; Lars Kristiansen. A Friendly Introduction to Mathematical Logic (2nd ed). I found this book recommended in Peter Smith’s Teach Yourself Logic guide.
  • George Boolos; John Burgess; Richard Jeffrey. Computability and Logic (5th ed). I found this book in MIRI’s research guide. I later also found it in Peter Smith’s guide.
  • Peter Smith. An Introduction to Gödel’s Theorems (2nd ed). I found this book in Peter Smith’s Teach Yourself Logic guide (yes, the same person).
  • David Patrick. Intermediate Counting & Probability. I found this book while looking for practice problems for basic probability.
  • Richard L. Epstein; Walter A. Carnielli. Computability: Computable Functions, Logic, and the Foundations of Mathematics (3rd ed). Advanced Reasoning Forum. 2008. I found this book while looking for textbooks on computability (I later also found it in Peter Smith’s guide).
  • Hartley Rogers, Jr. Theory of Recursive Functions and Effective Computability. McGraw-Hill Book Company. 1967. I think I found this book either when looking for books on computability or via Wei Dai.
  • Sheldon Axler. Linear Algebra Done Right (3rd ed). This is a well-known book, so I’m not sure how I first found out about it (you can’t avoid hearing about it if you spend any time reading about math online). I think what led me to actually working through it was (1) it being listed in the MIRI research guide; and (2) reading TurnTrout’s review of the book.
  • Terence Tao. Analysis I (2nd ed). I have known about this book since around 2011 or 2012, so I can’t say for sure how I first found it. Back in 2011 I was interested in the foundations of math, and I think I liked that Tao constructs most of the number systems.
  • Charles Chapman Pugh. Real Mathematical Analysis. This book is again something I first found in 2011 or 2012 so I can’t say how I found it.
  • Michael Spivak. Calculus (4th ed). This is a famous proof-based calculus textbook, so I think I found it just by being exposed to math culture online (it is recommended many times).
  • James Munkres. Topology (2nd ed). This seems to be the standard topology textbook, so I think I found it just by being exposed to math culture online. One specific place I remember it being recommended is the Cognito Mentoring info wiki.
  • John Stillwell. Reverse Mathematics. I found this book via a strange coincidental route: (1) I had been thinking about the similarity between various theorems in real analysis and how different analysis books prove the theorems through different pathways, and had found this Math Stack Exchange question, where Thomas Andrews mentions reverse mathematics; (2) on the same day I chanced upon this Reddit comment recommending Stillwell’s book; (3) I had already known about Stillwell via his Mathematics and Its History, which I had seen recommended in Tristan Needham’s Visual Complex Analysis.
  • Tom M. Apostol. Mathematical Analysis. I found this book recommended in some online discussion threads (I don’t remember the specific one).
  • Pete L. Clark. Honors Calculus. I think I know about Pete L. Clark from his activity on Math Stack Exchange, and I found his text that way.
  • Vipul Naik. Math 196 (linear algebra) notes and quizzes. I know about this through my interactions with Vipul.
  • Michael Sipser. Introduction to the Theory of Computation (3rd ed). I think I found this via MIRI’s research guide, but this also seems to be the standard text for computability and computational complexity in computer science programs, so I have seen it mentioned a bunch in other places.
  • Terence Tao. Linear algebra notes for math 115A. See also the course webpage. I found these notes by looking at the courses Tao has taught (which I was doing because I liked his analysis book and wanted to see if he had other course material at a similar level).
  • Nigel Cutland. Computability: An introduction to recursive function theory. I think I found this book via Peter Smith’s guide.
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