Read

**Fill in Gaps**:

Lang - Basic Mathematics

Apostol - Calculus

**Royal Road To Differential Geometry and Physics**:

Lawvere - Sets for Mathematics Shilov - Linear Algebra (and)

Lev Landau - courses in physics Volume 1+2 (then) Bishop - Tensor Analysis (or)\*

Sternberg - Differential Geometry (then)\*\*

Isu Vaisman - Cohomology and Differential Forms

**Backbone**:

Arnold - Ordinary Differential Equations

Kaplansky - Set Theory and Metric Spaces (and)

Edmund Landau - Foundations of Analysis (then) Rudin - Principles of Mathematical Analysis

Bradley, Bryson, Terrilla - Topology: A Categorical Approach

Ahlfors - Complex Analysis Olver - Applications of Lie Groups to Differential Equations

Aluffi - Algebra Chapter 0 (or) \*

Lang - Algebra\*\*

\* = easier

\*\* = direct

**Good General Videos**:

https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

notes:

https://drive.google.com/file/d/1nchF1fRGSY3R3rP1QmjUg7fe28tAS428/view

https://www.youtube.com/channel/UCIyDqfi_cbkp-RU20aBF-MQ