bookshelf

Here I have collected a list of textbooks I have found useful and/or interesting. While my reading of these books ranges from “cover-to-cover” to “a chapter or two”, I have gained valuable insights from each of them. You can find a pdf for most of these books freely online.

I am also an avid reader of classic literature. You can find out more about my non-academic readings on my Goodreads page.

Undergraduate-level Texts

• Andrews, Number Theory *
• Axler, Linear Algebra Done Right *
• Blitzstein and Hwang, Introduction to Probability Theory
• Hammack, Book of Proof *
• Hungerford, Abstract Algebra: An Introduction
• Rudin, Principles of Mathematical Analysis *

Algebra

• Atiyah and Macdonald, Commutative Algebra *
• Dummit and Foote, Abstract Algebra
• Lang, Algebra

Number Theory

• Diamond and Sherman, A First Course in Modular Forms
• Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-Functions
• Marcus, Number Fields *
• Neukirch, Algebraic Number Theory *
• Serre, A Course in Arithmetic

Topology

• Hatcher, Algebraic Topology
• Milnor, Topology from the Differentiable Viewpoint
• Munkres, Topology *

Analysis

• Folland, Real Analysis
• Rudin, Real and Complex Analysis
• Stein and Shakarchi, Complex Analysis *

Geometry

• Lee, Introduction to Topological Manifolds
• Milne, Algebraic Geometry
• Tu, Differential Geometry

Physics

• Arnold, Mathematical Methods of Classical Mechanics
• Hall, Quantum Theory for Mathematicians
• Landau, Mechanics *
• Lugo, Differential Geometry in Physics

Texts marked with an asterisk were especially valuable to my mathematical development, and are exemplary treatments of their respective subjects in my view.