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Mathematical Foundations
Calculus
Linear Algebra
Probability Theory
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Automatic Differentiation
Discrete Mathematics
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Table of Contents
1. Set Theory Fundamentals
1.1 Set Operations
1.2 Power Set and Cartesian Product
2. Relations and Functions
2.1 Properties of Relations
2.2 Equivalence Relations and Partial Orders
2.3 Functions
3. Graph Theory Fundamentals
3.1 Basic Concepts
3.2 Connectivity
3.3 Special Paths and Cycles
3.4 Graph Coloring and Planar Graphs
4. Combinatorics
4.1 Permutations and Combinations
4.2 The Binomial Theorem
4.3 The Inclusion-Exclusion Principle
4.4 The Pigeonhole Principle
4.5 Introduction to Generating Functions
5. Boolean Algebra
5.1 Boolean Operations
5.2 Normal Forms
5.3 Logic Circuits
6. Recurrence Relations
6.1 Linear Recurrences
6.2 The Master Theorem
7. Connections Between Discrete Mathematics and AI
References
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