Mathematics : Suggested Books by Subject

Establishing Texts:

Introduction to calculus and analysis - Courant
Complex variables and applications - Churchill
Mathematical analysis : an introduction - Browder
Mathematical analysis - Apostol
Invitation to complex analysis - Boas

Deeper Reading:
Complex analysis, an introduction to the theory of analytic functions of one complex variable - Ahlfors*
Real analysis : modern techniques and their applications - Folland*
Complex analysis - Gamelin*
Real analysis - Royden*
Principles of mathematical analysis - Rudin*
Real and complex analysis - Rudin*
Real analysis : measure theory, integration, and Hilbert spaces - Stein & Shakarchi*
Complex analysis - Stein & Shakarchi*

Establishing Texts:
Differential equations : a dynamical systems approach - Strang*
Basic partial differential equations - Bleecker
Boundary value problems - Gahkov

Further Reading:
Fourier series and boundary value problems - Churchill*
Calculus of variations - Gelfand & Fomin*
Partial differential equations : analytical solution techniques - Kevorkian*
Complex variables - Levinson & Redheffer*
Partial differential equations and boundary-value problems with applications - Pinsky*
Green’s functions and boundary value problems - Stakgold*
Partial differential equations of applied mathematics - Zauderer*

Establishing Texts:
Principles and techniques in combinatorics - Chen
Combinatorics and graph theory - Harris
Foundations of applied combinatorics - Bender
Graphs & digraphs - Chartrand
Graph theory : an introductory course - Bollobás

Further Reading:
Enumerative combinatorics. Volume 1 - Stanley
Graph theory - Tutte
Spectral graph theory - Chung
Random graphs - Bollobás
Ramsey theory - Graham, Rothschild, & Spencer
Handbook of combinatorics - Graham, Grötschel, & Lovász
Probabilistic methods in combinatorics - Erdös & Spencer

Establishing Texts:

Introduction to algorithms - Cormen, Leiserson, Rivest, & Stein
A friendly introduction to numerical analysis - Bradie*
Numerical analysis - Burden & Faires

Further Reading:
The art of computer programming - Knuth
Finite difference methods for ordinary and partial differential equations steady-state and time-dependent problems - LeVeque*
Finite difference schemes and partial differential equations - Strikwerda*
Spectral methods in MATLAB - Trefethen*
A practical guide to pseudospectral methods - Fornberg*
Finite volume methods for hyperbolic problems - LeVeque*
Computational differential equations - Eriksson, Estep, Hansbo, & C. Johnson*
Finite Element Methods and Their Applications - Chen*
Monte Carlo methods - Kalos & Whitlock*

Establishing Texts:
An invitation to algebraic geometry - Smith
Conics and cubics : a concrete introduction to algebraic curves - Bix
The shape of space : how to visualize surfaces and three-dimensional manifolds - Weeks
Basic topology - Armstrong
The four pillars of geometry - Stillwell
Topology - Munkres

Further Reading:
Topology and geometry - Bredon*
Differential topology - Guillemin and Pollack*
Algebraic topology - Hatcher*
Homology theory : an introduction to algebraic topology - Vick*
A comprehensive introduction to differential geometry. Volume 1 - Spivak*

Establishing Texts:
A mathematical introduction to logic - Enderton
Classic set theory : a guided independent study - Goldrei

Further Reading:
Categories for the working mathematician - Mac Lane
Mathematical logic - Ebbinghaus, Flum, & Thomas*
Mathematical logic - Shoenfield*
Set theory - Kunen*
Recursively enumerable sets and degrees : a study of computable functions and computably generated sets - Soare*
Theory of recursive functions and effective computability - Rogers*
Set theory - Kunen*
Set theory - Jech*
Model theory - Chang & Keisler*
Model theory : an introduction - Marker*

Establishing Texts:
The higher arithmetic : an introduction to the theory of numbers - Davenport
An introduction to the theory of numbers - Hardy & Wright
Higher mathematics from an elementary point of view - Rademacher
The beauty of doing mathematics : three public dialogues - Lang

Further Reading
Algebraic number theory - Lang
Elliptic curves - Knapp
Topics in analytic number theory - Rademacher
Chapter 1 From number theory to physics: An introduction to zeta functions - Cartier
Modular functions and Dirichlet series in number theory - Apostol
The theory of partitions - Andrews