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Expand Up @@ -221,13 +221,29 @@ Courses | Duration | Effort | Prerequisites
[Differential Geometry](https://ocw.mit.edu/courses/mathematics/18-950-differential-geometry-fall-2008/) [(Supplementary Video Lectures)](https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP) | 10 weeks | 6-8 hours/week | Multivariable Calculus, Introduction To Analysis and Linear Algebra

### Probability and Statistics
Combinatorics, probability, statistics, game theory, applied stats
| Subtopic | Course / Book | Duration (Weeks) | Effort (Hours/Week) | Prerequisites |
|--------------------------|--------------|------------------|---------------------|---------------|
| **Combinatorics** | *A Walk Through Combinatorics* - Miklós Bóna | 6-8 | 6-8 | Discrete Math |
| **Probability** | [Introduction to Probability - Blitzstein (Harvard)](https://projects.iq.harvard.edu/stat110/home) | 10 | 8-10 | Basic Calculus |
| **Statistics** | *All of Statistics* - Larry Wasserman | 12-14 | 6-10 | Probability, Linear Algebra |
| **Game Theory** | [Multiagent Systems - Shoham & Leyton-Brown (Stanford)](https://web.stanford.edu/~shoham/) | 8 | 6-8 | Probability, Basic Graph Theory |
| **Applied Statistics** | *The Elements of Statistical Learning* - Hastie, Tibshirani, Friedman | 14 | 10-12 | Linear Algebra, Probability |

### Mathematical Analysis
Real analysis, numerical analysis, complex analysis, optimization theory
| Subtopic | Course / Book | Duration (Weeks) | Effort (Hours/Week) | Prerequisites |
|-------------------------|--------------|------------------|---------------------|---------------|
| **Real Analysis** | *Principles of Mathematical Analysis* - Walter Rudin | 14 | 10-12 | Calculus 1-3, Linear Algebra |
| **Numerical Analysis** | *Numerical Linear Algebra* - Trefethen & Bau | 10 | 8-10 | Linear Algebra |
| **Complex Analysis** | *Visual Complex Analysis* - Tristan Needham | 10-12 | 6-8 | Basic Real Analysis |
| **Optimization Theory** | [Convex Optimization - Boyd & Vandenberghe (Stanford)](https://web.stanford.edu/~boyd/cvxbook/) | 12 | 8-12 | Linear Algebra, Calculus, Probability |

### Abstract Algebra
Abstract algebra, category theory, algebraic geometry and topology
| Subtopic | Course / Book | Duration (Weeks) | Effort (Hours/Week) | Prerequisites |
|---------------------------|--------------|------------------|---------------------|---------------|
| **Abstract Algebra** | *Abstract Algebra* - Dummit & Foote | 14 | 10-12 | Linear Algebra |
| **Category Theory** | *Category Theory for Scientists* - David Spivak | 10 | 6-8 | Abstract Algebra, Graph Theory |
| **Algebraic Geometry** | *Algebraic Geometry* - Robin Hartshorne | 16+ | 12+ | Abstract Algebra, Real & Complex Analysis |
| **Algebraic Topology** | *Algebraic Topology* - Allen Hatcher | 14 | 10-12 | Group Theory, Topology |


## Congratulations
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