As an Yale grad student self-studying topology and differential geometry with an undergrad background in Biochemical Engineering at UCL, I had to catch up on a series of math major courses. On this page, I’d like to share some textbooks recommended by teachers and friends that helped me through this process.
- Undergrad engineering math:
- Engineering Mathematics by K.A. Stroud, Dexter J. Booth
- Discrete math:
- Discrete Mathematics and Its Applications by Kenneth H. Rosen
- Analysis:
- Basic Analysis I, II by Jiří Lebl
- Understanding Analysis by Stephen Abbot
- Introduction to Real Analysis by William F. Trench
- Principles of Mathematical Analysis by Walter Rudin
- Abstract Algebra:
- A First Course in Abstract Algebra by John B. Fraleigh
- Differential Geometry:
- Elementary Diff Geom by Andrew Pressley
- Topology:
- Topology by John G. Hocking and Gail S. Young
- Algebraic Topology: An Introduction by W. S. Massey
- Topology by James Munkres
- Lecture Notes in Algebraic Topology by Laurentiu Maxim
- Homotopic Topology by A. T. Fomenko, D. B. Fuchs and
V. L. Gutenmacher - Algebraic Topology by Allen Hatcher
- Knots and Links by Dale Rolfsen
- The Knot Book by Colin C. Adams
- Topological Data Analysis for Genomics and Evolution – Topology in Biology by Raúl Rabadán and Andrew J. Blumberg
Online classes that I have checked out:
- MIT OpenCourseWare Linear Algebra by Professor Strang
- MIT OpenCourseWare Real Analysis by Dr. Rodriguez
