# Didactical Materials Online

You find here links to didactical material for the different lectures and tutorials.

Material online for Lecture 1:
Principles of Counting. Permutations and Combinations

Lecture Notes and a
**
small tutorial video on permutations and combinations
**

Videos to Exercises 1: **
some examples on permutations** **
more examples on permutations** **
combinations** and **
combinations with repetition**

Material online for Lecture 2:
Recalling Set Theory. Principle on Inclusion-Exclusion

Lecture Notes and
small tutorial videos on **
Venn diagrams for union of sets** as well as on **
Principle on Inclusion-Exclusion**

Videos to Exercises 2: **
Principle Inclusion-Exclusion (PIE)** **
more properties of PIE** **
representation of sets** and **
properties of Cartesian products**

Material online for Lecture 3:
Mathematical Induction. Recurrence (Difference Equations)
Lecture Notes

**Lists of Exercises on Recurrence**

Notes to Exercises 3:
**Examples for Exercises 3,
Proving Binomial Th. by Math. Induct. (IP)**

Material online for Lecture 4:
Counting Revisited. Principle Inclusion-Exclusion & Applications

Lecture Notes
and a ** small tutorial video on
Principle on Inclusion-Exclusion**

Notes to Exercises 4:** Examples of
Binomial Th.(proved by Math. Induct.),
Examples on Pigeonhole Principle
Examples on PIE
More Examples on PIE**

Material online for Lecture 5:
Introduction to Modeling: Setting up Difference Equations
Lectures Notes

**Lists of Exercises on Recurrence**

Notes to Exercises 5: ** Find solved exercises in the corresponding list of
exercises on recurrence and
here two more detailed examples**

Material online for Lecture 6:
Solving Linear Recursive Equations with Constant Coefficients
Lecture Notes

**Lists of Exercises on Recurrence**

Notes to Exercises 6: ** Find solved exercises in the corresponding list of
exercises on recurrence and here two more detailed
examples**

Videos to Exercises 6:
**Examples of linear recurrence equation**

Material online for Lectures 7 and 8:
Relations: Equivalence Relations & Posets
Lecture Notes

Notes to Exercises 7:
**Examples for Exercises 7,**

Material online for Lecture 9:
Number Theory: Divisibility and Diophantine Equations
Lecture Notes

Notes to Exercises 8:**
Examples on Divisibility Examples of
Diophantine Equations
**

Videos to Exercises 8:
**Algorithm to Determine the Binary Expression of an integer**
**Solving linear Diophantine Equations**

Material online for Lecture 10:
Number Theory: Modular Arithmetic and Chinese Remainder Theorem
Lecture Notes

Notes to Exercises 9:** Examples of
Diophantine Equations
Examples on Modular Arithmetic
**

Videos to Exercises 9:
**Solving linear Diophantine Equations**
**Solving linear Congruence Equations**
**Fast Calculations: Squaring **

Material online for Lecture 11:
Application of Number Theory: RSA Cypher
Lecture Notes

**Lists of Exercises in English on Chinese Remainder
Theorem and Cryptography**

Notes to Exercises 10:** Examples on
Chinese Remainder Th.
Examples of RSA cypher
**

Videos to Exercises 10:
**Example of Chinese Remainder Theorem**
**Example of RSA Cypher**

Material online for Lecture 12:
Graphs: Basic Concepts: Eulerian and Hamiltonian Graphs.
Lecture Notes

Notes to Exercises 11:** Examples on
Basic Concepts in Graph Theory and Eulerian and Hamiltonian Graphs.
**

Videos to Exercises 11:
**Example of Modeling Networks**
** One more example of graphs **

Material online for Lecture 13:
Graphs: Trees with applications.
Lecture Notes

Notes to Exercises 12:** Examples on
Trees with Applications.
**

Videos to Exercises 12:
**Data Transmission: Prefix Codes**

Material online for Lecture 14:
Graphs: Planar and Bipartite Graphs. Graph Colorings.
Lecture Notes

Notes to Exercises 13:**
Examples on Planar Graphs and Graph Colorings.
Example of Calculation of Chromatic Polynomial
**

Videos to Exercises 13:
**Calculation of Chromatic Polynomial**

Sidansvarig: milagros.izquierdo@liu.se

Senast uppdaterad: 2020-05-19