Learning roadmap request: compiling a "Mathematics Stack Exchange Undergraduate Bibliography" [closed]
Please, add your contributions to this answer (which I made community wiki). In case you wish to add some personal comments about your entries, add a tag like [Your_Username].
Foundations
Daniel J. Velleman, How to Prove It: A Structured Approach
Problem solving
- G. Polya, How to Solve It: A New Aspect of Mathematical Method
Recreational
Algebra
- Roger Godement , Algebra (Translation of Cours d' Algebre)
- Lang - Algebra
- Jacobson - Basic Algebra I, Basic Algebra II
- Rotman - Introduction to the Theory of Groups
- Dummit and Foote - Algebra
- Hungerford - Abstract Algebra
- Serre - Linear Representations of Finite Groups
- Fulton, Harris - Representation Theory - A First Course
- Humphreys - Introduction to Lie Algebras and Representation Theory
- Atiyah, MacDonald - Introduction to Commutative Algebra
- Eisenbud - Commutative Algebra: with a View Toward Algebraic Geometry
- Weibel - An Introduction to Homological Algebra
Linear algebra
- Sheldon Axler, Linear Algebra Done Right.
- Sergei Treil, *Linear Algebra Done Wrong*
- Roman - Advanced Linear Algebra
Geometry
- Mumford - The Red Book of Varieties and Schemes
Point-set topology
Differential geometry
- John Lee, *Introduction to Smooth Manifolds *
Number theory
- Andre Weil, *Basic Number Theory*
- Ireland and Rosen - A Classical Introduction to Moder Number Theory
- Edmund Landau - Introduction to Number Theory
- Burton - Elementary Number Theory
Combinatorics and discrete mathematics
- Graham, Knuth, Patashnik, Concrete Mathematics.
Probability and Statistics
Real analysis
- Gerald B. Folland, *Real Analysis: Modern Techniques and Their Applications*
- Shilov and Gurevich: Integral, Measure and Derivative.
Multivariable calculus
- Spivak, Calculus On Manifolds.
Complex analysis
- Tristan Needham, Visual Complex Analysis.
- Remmert - Introduction to the Theory of Functions.
- Remmert - Classical Topics in Function Theory
Differential equations
Functional analysis
- Walter Rudin, *Functional Analysis*
- Erwin Kreyszig, *Introductory Functional Analysis with Applications*
- Reinhold Meise & Dietmar Vogt: Introduction to Functional Analysis
Mathematical and theoretical physics
- Arnold - Mathematical Methods of Classical Mechanics