Università telematica internazionale UNINETTUNO

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

Discrete Mathematics


Slides

Lesson n. 1: Discrete Mathematics
   Induction and Recursion

   The principle of recursive definition
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Lesson n. 2: Induction and recursion
   Principle of recursive definition

   Example
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Lesson n. 3: Mathematical Induction
   Mathematical induction

   Principle of Mathematical Induction

   Using the other method
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Lesson n. 4: Mathematical induction - Part II
   More examples
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Lesson n. 5: The extend principle of Mathematical induction
   More examples on induction

   Other principles of induction
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Lesson n. 6: More examples on the other principles of induction
   Example on the extend principle

   The relation between the two principles
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Lesson n. 7: The second principle on Mathematical Induction
   The second principle

   Tower of Hanoi
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Lesson n. 8: Tower of Hanoi
   Tower of Hanoi

   Exercises
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Lesson n. 9: The n-th Fibonacci numbers
   Fibonacci numbers
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Lesson n. 10: Counting
   Introduction - Counting

   Permutations and combinations
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Lesson n. 11: Some important examples using combinations
   Examples of using combinations

   Combinations of similar groupings
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Lesson n. 12: Binomial expansions
   The binomial theorem

   Newtons binomial
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Lesson n. 13: Pascal’s triangle
   Pascal’s triangle

   Recursion Relations
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Lesson n. 14: Recursion relations and generating functions
   Solving Recursion relations

   Definition
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Lesson n. 15: Solving recursion relations
   Characteristic equation

   Example and Solution
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Lesson n. 16: Solving recursion relations and generating functions
   Characteristic equation

   Generating Functions
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Lesson n. 17: Generating Functions
   Generating functions

   Theorem
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Lesson n. 18: More applications of the generating functions
   Corollary

   Theorem
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Lesson n. 19: Elementary number theory
   Elementary Number Theory

   Prime Numbers
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Lesson n. 20: Prime Numbers
   Definition

   How Can we decide if a number is prime?

   Listing Primes
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Lesson n. 21: Prime Numbers – Part II
   Notes

   By a previous theorem
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Lesson n. 22: Divisibility Properties Go to this slide
Lesson n. 23: Divisibility Properties – Part II
   Example

   Theorem

   Congruence
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Lesson n. 24: Congruence
   Theorem

   Example
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Lesson n. 25: Congruence – Part II
   Theorem

   Example
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