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MOOC Massive Open Online Courses (Academic Year 2018/2019)

Discrete Mathematics



Videolesson

Lesson n. 1: Discrete Mathematics
   Induction and Recursion
   The principle of recursive definition 		Go to this lesson Mashhoor Refai
Lesson n. 2: Induction and recursion
   Principle of recursive definition
   Example 		Go to this lesson Mashhoor Refai
Lesson n. 3: Mathematical Induction
   Mathematical induction
   Principle of Mathematical Induction
   Using the other method 		Go to this lesson Mashhoor Refai
Lesson n. 4: Mathematical induction - Part II
   More examples 		Go to this lesson Mashhoor Refai
Lesson n. 5: The extend principle of Mathematical induction
   More examples on induction
   Other principles of induction 		Go to this lesson Mashhoor Refai
Lesson n. 6: More examples on the other principles of induction
   Example on the extend principle
   The relation between the two principles 		Go to this lesson Mashhoor Refai
Lesson n. 7: The second principle on Mathematical Induction
   The second principle
   Tower of Hanoi 		Go to this lesson Mashhoor Refai
Lesson n. 8: Tower of Hanoi
   Tower of Hanoi
   Exercises 		Go to this lesson Mashhoor Refai
Lesson n. 9: The n-th Fibonacci numbers
   Fibonacci numbers 		Go to this lesson Mashhoor Refai
Lesson n. 10: Counting
   Introduction - Counting
   Permutations and combinations 		Go to this lesson Mashhoor Refai
Lesson n. 11: Some important examples using combinations
   Examples of using combinations
   Combinations of similar groupings 		Go to this lesson Mashhoor Refai
Lesson n. 12: Binomial expansions
   The binomial theorem
   Newtons binomial 		Go to this lesson Mashhoor Refai
Lesson n. 13: Pascal’s triangle
   Pascal’s triangle
   Recursion Relations 		Go to this lesson Mashhoor Refai
Lesson n. 14: Recursion relations and generating functions
   Solving Recursion relations
   Definition 		Go to this lesson Mashhoor Refai
Lesson n. 15: Solving recursion relations
   Characteristic equation
   Example and Solution 		Go to this lesson Mashhoor Refai
Lesson n. 16: Solving recursion relations and generating functions
   Characteristic equation
   Generating Functions 		Go to this lesson Mashhoor Refai
Lesson n. 17: Generating Functions
   Generating functions
   Theorem 		Go to this lesson Mashhoor Refai
Lesson n. 18: More applications of the generating functions
   Corollary
   Theorem 		Go to this lesson Mashhoor Refai
Lesson n. 19: Elementary number theory
   Elementary Number Theory
   Prime Numbers 		Go to this lesson Mashhoor Refai
Lesson n. 20: Prime Numbers
   Definition
   How Can we decide if a number is prime?
   Listing Primes 		Go to this lesson Mashhoor Refai
Lesson n. 21: Prime Numbers – Part II
   Notes
   By a previous theorem 		Go to this lesson Mashhoor Refai
Lesson n. 22: Divisibility Properties Go to this lesson Mashhoor Refai
Lesson n. 23: Divisibility Properties – Part II
   Example
   Theorem
   Congruence 		Go to this lesson Mashhoor Refai
Lesson n. 24: Congruence
   Theorem
   Example 		Go to this lesson Mashhoor Refai
Lesson n. 25: Congruence – Part II
   Theorem
   Example 		Go to this lesson Mashhoor Refai