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Incomplete list of books that people on ##math have bought, sold, tried, read, taught, suffered through and would feel like suggesting.

If you are a self-learner and are looking for a few books to get started, the first section contains exclusively such books.

Other useful such lists on the web: [1]

Introductory Books for Self Learners Edit

So you don't have a mathematical education and want to get started somewhere?

These books are for you.

They have no prerequisites and provide a gentle, thorough introduction to the foundations you want to have in order to explore intermediate topics or get a head start on a degree.

  • Calculus: Guichard's free book: https://www.whitman.edu/mathematics/multivariable/
    • No prerequisites.
  • Kenneth Rosen, Discrete Mathematics and its Applications,
    • No prerequisites.
    • Especially relevant to programmers and aspiring computer scientists.
    • Provides, in a simple and progressive style, the basics of mathematical reasoning (proofs, etc) as well as an introduction to all the topics (such as logic and graph theory) that are imprescindible to computer science.
    • Continue with CLRS, Ben Ari and Cutland
  • Daniel Velleman, How To Prove It
    • No prerequisites
    • Logic, proofs, relations - basic mathematical tools.
    • A better, more in-depth treatment of a subset of the topics in Rosen. Probably still go with Rosen if have more than a passing interest in computer science.
  • Linear Algebra: Gilbert Strang's Introduction to Linear Algebra
    • Slightly "harder" than the previous entries.
  • Ross, First Course in Probability
    • Some familiarity with calculus and linear algebra (see previous entries) is useful

Linear Algebra Edit

Calculus and Mathematical Analysis Edit

Probability Edit

Logic Edit

Introductory:

Combinatorics Edit

Introductory:

  • Tucker, Applied Combinatorics. Very readable but IMHO poorly structured. You sometimes have to fish the definitions out of some very discursive text.

Computability Edit

  • Cutland's Computability. Progressive, enjoyable but rigorous introduction. Recommended.

Algorithms Edit

(Abstract) Algebra Edit

Note that this refers to the "algebra" as found in university courses under this title. This is mostly disjoint from what is known as "algebra" in high school. Algebra courses

  • Dummit and Foote, Abstract Algebra
  • Michael Artin, Algebra
  • Galian, Contemporary Abstract Algebra is a good entry into to the subject

Topology Edit

  • Munkres is the standard text
  • Lee, Topological and Smooth Manifolds present the main principles

Algebraic Topology Edit

Introductory:

  • Allen Hatcher, Algebraic Topology
    • Prerequisites: familiarity with what a topological space is, and basic group theory. Knowledge of Rings and Modules is helpful, especially in chapters 2 and 3.
    • Gentle book on algebraic topology. Free pdf is available on the author's website.

Advanced:

Machine Learning + Data Mining Edit

Introductory:

  • Mitchell: very readable, gentle introduction to ML. Slightly outdated. No SVM, no clustering. If in doubt, read this first
  • Tibishirani, Hastie: Introduction to Statistical Learning, introductory, very much example-driven (in R), perhaps too much.
  • Scarpa, Azzalini: Data Analysis and Data Mining, roughly same league as ISL, but as the back cover blurb says, "More detailed than practically-oriented books". Can confirm.
  • Yaser S. Abu-Mostafa, Learning from Data A very readable introduction to machine learning.

Intermediate:

Notably absent from the list is Bishop's Pattern Recognition and Machine Learning. It is a ubiquitous applied reference text that is not good for reading sequentially.

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