Mathematics Book List

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This list was formerly on my "NCEA notes" GitHub page. I have updated it and moved it here (Nov. 2021).

This list is an effort to make a list similar and supplementary to the Chicago undergrad bibliography, but with a less useful organisational structure. Library call numbers listed in brackets after review; (*) denotes a book that the library does not own. Now that the University of Auckland moved the mathematics research collection off-site in the latest set of library closures and service reductions, I see no reason to include library call numbers any more.

It is less a list of reviews, and more a reminder to me about which books I have enjoyed reading and which books I would like to read more of. I mark my favourite books with a green star, thus.

Disclaimers. The presence of a book on this list does not mean:

I maintain a list of books which I own on LibraryThing.



Children's books (first and second year undergraduate)

Single-variable calculus

Multi-variable calculus

Linear algebra

Logic, "proofs", and naive set theory

Elementary number theory

Differential equations


Higher undergraduate books

Mathematical logic


Combinatorics and finite geometry

Number theory

Single-variable analysis


Point-set topology.

Geometric topology.

Complex calculus and analysis

The first few books here, broadly speaking, are complex calculus books; the latter books are complex analysis books.

Classical geometry

Algebraic geometry for undergraduates

Differential geometry.

Postgraduate texts


General algebra.

Group theory.

Category theory

Linear algebra.

Commutative algebra.

Rings and group representations.

Number theory


General combinatorics.

Polytopes. See also the books by Stanley and Miller/Sturmfels in the commutative algebra section above.

Algebraic topology

Differential and Riemannian geometry

Geometric group theory

General books

Arithmetic flavour (e.g. buildings, \(p\)-adic fields).

Geometric flavour (Kleinian groups and hyperbolic manifolds). See also the section on low-dimensional geometry below.

Low-dimensional and hyperbolic geometry

Geometric manifolds. See also the section on geometric group theory above.


Complex analysis and Teichmüller theory

Algebraic geometry

Scheme theory.

Toric varieties and combinatorial algebraic geometry.

Abelian varieties; Elliptic curves; Arithmetic geometry.


Dynamical systems

Now it's the challenger's turn to reply to to this verbal bombardment:
Neatly each phrase he dissects. with intelligence subtle and keen;
Harmless around him the adjectives tumble, as he ducks for cover
And squeaks, 'It depends what you mean.'

-- Aristophanes, Frogs (trans. Barrett, p.166).