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- 00:00:00 Introduction to Discrete Mathematics
- 00:05:20 Permutations: Definition and Examples
- 00:08:27 Applications of Permutations
- 00:10:14 Cycles and Multiset Permutations
- 00:13:13 Counting Permutations: The Formulas
- 00:19:12 Permutations in Python with itertools
- 00:25:18 Custom Python Function for Counting Permutations
- 00:33:23 Heap's Algorithm
- 00:40:59 K-Permutations and K-Tuples
- 00:46:08 The Rule of Product
- 00:53:35 The Rule of Sum
- 00:54:25 Exercises: Rule of Product & Sum
- 01:14:11 The Inclusion-Exclusion Principle
- 01:26:52 Exercises: Inclusion-Exclusion Principle
- 01:44:36 Mathematical Notations Sigma & Pi
- 02:30:28 Equinumerosity & Countable Sets
- 03:00:47 Proving Rational Numbers are Countable
- 03:09:16 Prime Numbers & Sieve of Eratosthenes
- 03:27:33 Prime Number Generation in Python
- 03:40:43 Advanced Properties of Prime Numbers
- 03:58:30 GCD & LCM Greatest Common Divisor & Least Common Multiple
- 04:22:53 Co-prime Numbers
- 04:29:30 Congruences Modular Arithmetic
- 05:00:53 Binomial Coefficients & Pascal's Triangle
- 05:11:11 Combinations
- 05:40:43 Solving a Complex Combinatorics Problem
- 05:51:53 Stirling Numbers
- 06:53:52 Bell Numbers
- 07:00:00 The Chinese Remainder Theorem
- 07:22:16 Conclusion & What's Next
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