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**Fill in Gaps**:

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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**:

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