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Mathematics
Combinatorics
1. Introduction to Combinatorics
2. Fundamental Counting Principles
3. Permutations
4. Combinations
5. The Binomial Theorem
6. Advanced Counting Techniques
7. Recurrence Relations
8. Generating Functions
9. Special Counting Numbers and Sequences
10. Graph Theory and Combinatorics
11. Design Theory
12. Probabilistic Combinatorics
13. Algebraic Combinatorics
14. Extremal Combinatorics
15. Applications and Advanced Topics
14.
Extremal Combinatorics
14.1.
Ramsey Theory
14.1.1.
Ramsey Numbers
14.1.2.
Ramsey's Theorem
14.1.3.
Applications and Examples
14.2.
Turán-type Problems
14.2.1.
Turán's Theorem
14.2.2.
Extremal Graph Theory
14.2.3.
Forbidden Substructures
14.3.
Erdős-Ko-Rado Theorem
14.3.1.
Intersecting Families
14.3.2.
Applications and Generalizations
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13. Algebraic Combinatorics
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15. Applications and Advanced Topics