Göm meny
Didactical Materials.html

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: Counting Revisited. Principle Inclusion-Exclusion & Applications
Lecture Notes and a small tutorial video on Principle on Inclusion-Exclusion
Notes to Exercises 3: Examples of Binomial Th.(proved by Math. Induct.),   Examples on Pigeonhole Principle   Examples on PIE   More Examples on PIE

Material online for Lecture 4: Mathematical Induction. Recurrence (Difference Equations) Lecture Notes
Lists of Exercises on Recurrence
Notes to Exercises 4: Examples on Mathematical Induction (IP),   Proving Binomial Th. by Math. Induct. (IP)

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