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- 00:08:27 Applications of Permutations
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Classroom Contents
Discrete Mathematics Course for Beginners
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- 1 - 00:00:00 Introduction to Discrete Mathematics
- 2 - 00:05:20 Permutations: Definition and Examples
- 3 - 00:08:27 Applications of Permutations
- 4 - 00:10:14 Cycles and Multiset Permutations
- 5 - 00:13:13 Counting Permutations: The Formulas
- 6 - 00:19:12 Permutations in Python with itertools
- 7 - 00:25:18 Custom Python Function for Counting Permutations
- 8 - 00:33:23 Heap's Algorithm
- 9 - 00:40:59 K-Permutations and K-Tuples
- 10 - 00:46:08 The Rule of Product
- 11 - 00:53:35 The Rule of Sum
- 12 - 00:54:25 Exercises: Rule of Product & Sum
- 13 - 01:14:11 The Inclusion-Exclusion Principle
- 14 - 01:26:52 Exercises: Inclusion-Exclusion Principle
- 15 - 01:44:36 Mathematical Notations Sigma & Pi
- 16 - 02:30:28 Equinumerosity & Countable Sets
- 17 - 03:00:47 Proving Rational Numbers are Countable
- 18 - 03:09:16 Prime Numbers & Sieve of Eratosthenes
- 19 - 03:27:33 Prime Number Generation in Python
- 20 - 03:40:43 Advanced Properties of Prime Numbers
- 21 - 03:58:30 GCD & LCM Greatest Common Divisor & Least Common Multiple
- 22 - 04:22:53 Co-prime Numbers
- 23 - 04:29:30 Congruences Modular Arithmetic
- 24 - 05:00:53 Binomial Coefficients & Pascal's Triangle
- 25 - 05:11:11 Combinations
- 26 - 05:40:43 Solving a Complex Combinatorics Problem
- 27 - 05:51:53 Stirling Numbers
- 28 - 06:53:52 Bell Numbers
- 29 - 07:00:00 The Chinese Remainder Theorem
- 30 - 07:22:16 Conclusion & What's Next
