Study Guide

Objective

After completing the course the student: can some of the basic concepts of mathematical logic identifies some of basic concepts of sets can describe some of basic concepts of proof in mathematics can what means mathematical induction can describe what means concepts: permutation, combination, probability can describe some of basic concepts of number theory can describe what means concepts: group, ring, field and calculate basic exercises in finite fields can describe elements of coding theory and calculate linear codes: encoding and decoding can describe what means BCH codes and calculate BCH codes: encoding and decoding.

Content

mathematical logic: statements, truth tables, logical equivalences, valid arguments sets: subsets, the power set, operations on sets techniques of proofs in mathematics: mathematical induction permutations and combinations elementary probability number theory: divisibility and the Euclidean algorithm, prime numbers, congruence, applications of congruence basic concepts of modern algebra: group, ring and field coding theorem: linear codes and BCH codes Matlab programming in coding theory.

Materials

1. Discrete Mathematics and Its Applications, Kenneth H. Rose, Sixth Edition
2. Theory and Problems of Discrete Mathematics, Seymour Lipschutz, Marc Lars Lipson. Schaum’s Outline Series, Third Edition

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding of the discrete mathematics and help students to solve equations by using the principle of mathematical induction theorem and understand coding channels (sending and receiving), the students can use relevant mathematical denotation correctly
The students will team up for a project work and writing reports on some current and relevant aspect of basic math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Student workload

Classroom activities: Classroom activities participation: 50 h
Homework: Working on homework sets 1-6: 30 h
Project work: Research, presentation material, presentation: 20h
Final exam: Preparing for the final exam : 25 h

Content scheduling

• Set theory
• Number Theory: Mathematica Induction
• Graph Theory and Applications
• Groups Theory
• Coding Theory (Finite fields, linear codes, syndrome decoding, Hamming codes, BCH codes, cyclic code, Reed-Solomon codes)

Evaluation scale

H-5