Discrete Mathematics Course for Beginners

Learn discrete mathematics in this beginner's course. Discrete mathematics plays a key role in IT solutions, used in machine learning, accelerating queries in search engines and databases, in algorithms such as finding the shortest paths (graph theory), encryption, compression, and many other modern systems/solutions.

This field is constantly evolving along with the development of its key application: computer science. This course is an introduction to this group of mathematical sciences, and we will focus on the most important issues on which other branches of discrete mathematics are based: combinatorics, number theory, prime numbers, and several selected topics: pigeonhole principle, stars and bars principle, Stirling's number, and the Chinese remainder theorem. At the end of the course, there are tips and encouragement for further exploration of this field.

Karol Kurek teaches this course. He is a former math teacher and senior Python developer.

🔗 Course resources: https://github.com/Redysz/Discrete-Ma...

Contact: http://karolkurek.pl
YT Channel:    / @twowaysmath  
Support: http://buymeacoffee.com/karol_kurek

⭐️ Contents ⭐️
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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