Learning Mathematics [closed]

I am a physics master's final year student and will be graduating in July. Recently I have become very interested in learning mathematics after studying group theory and tensors. I want to learn mathematics atleast till the undergraduate level. I was recommended to start from Susanna s Epps set theory book and I am going through it while doing exercises. I am unsure of where to go next from here. Can anybody guide me on how and what all should I study after this. Please also include book references

Solution 1:

Here is what I consider compulsory to reach a good level in mathematics.

Linear Algebra and Geometry

$\bullet$ S. Axler - Linear Algebra done right

$\bullet$ S. Lang - Linear Algebra

$\bullet$ M. Artin - Algebra

$\bullet$ Herstein - Algebra

Complex Analysis and Mathematical Methods

$\bullet$ D. Wunsch - Complex Analysis (this text you shall know and study like your address)

$\bullet$ Bleistein - Asymptotic Expansion of Integrals

$\bullet$ S. Abate - Curves and Surfaces

$\bullet$ Piskunov - Differential and Integral Culculus

$\bullet$ Weir - Lebesgue Integration and Measure

$\bullet$ Brezis - Functional Analysis, PDE and Sobolev Spaces

$\bullet$ Simmons - Differential Equations with historical notes

Differential Geometry and Topology

$\bullet$ L. Tu - Introduction to manifolds

$\bullet$ Huybrechts - Complex Geometry

$\bullet$ Do Carmo - Differential Geometry

Extras which you wouldn't miss

$\bullet$ L. Hörmander - Linear partial differential operators

$\bullet$ Weinberger - Introduction to PDE

$\bullet$ Struwe - Variational Methods

$\bullet$ Strang, Introduction to Linear Algebra.

$\bullet$ T. Needham, Visual Complex Analysis.

Just another advice: focus very much onto Fourier transform, differential equation (ordinary and partial), and try to study in a rather deep way the theory of distributions. They are fundamental.