My current study plan is in order below. I will be completing these textbooks in this order one at a time.
I have been told that I don't have textbooks in my plan that approach topology in a general matter, but instead my focus is very narrow, meaning I may miss many important ideas.
Question: Is this a valid concern? Is the same true for either Algebra, or Analysis?
- Cohn - Classic Algebra
- Rudin - Principles of Mathematical Analysis
- Lee - Topological Manifolds
- Cohn - Basic Algebra
- Rudin - Complex Analysis
- Lee - Smooth Manifolds
- Cohn - Further Algebra
- Rudin - Functional Analysis
- Lee - Riemannian Manifolds
Note: My calculus is sufficiently built. For meta discussion on the close votes, please go here.
List constructed with advice from comments and the one answer(added are bold). It seems to be potentially excessively long(added bold):
- Cohn – Classic Algebra
- Axler – Linear Algebra Done Right
- Zorich – Mathematical Analysis I
- Rudin – Principles of Mathematical analysis
- Dugundji - Topology
- Lee – Topological Manifolds
- Zorich – Mathematical Analysis II
- Rudin – Real & Complex Analysis
- Cohn – Basic Algebra
- J.P May – A Concise Course in Algebraic Topology
- Ddo Carmo - Differential Geometry of Curves and Surfaces
- Lee – Smooth Manifolds
- Cohn – Further Algebra
- Rudin – Functional Analysis
- Lee – Riemannian Manifolds