### Discrete Mathematics

#### Course Description

Notions, techniques and algorithms of discrete mathematics are studied, with special interest on parts of it involving algebra: number theory, algebraic structures and cryptography. A student will get the crucial knowledge from elementary number theory, founding structural properties of groups, rings and finite fields, and will be introduced and learn to analize some most common cryptosystems.

#### General Competencies

Learning how to use techniques and ways of thinking in discrete mathematics, particularly in algebraic combinatorics, and applying that knowledge to specific examples.

#### Learning Outcomes

1. use the basic facts in elementary number theory
2. solve linear and some particular non-linear congruences
3. solve the basic diophantine equations
4. identify the basic algebraic structures; groups, rings and fields
5. understand the basic concepts in Cryptography
6. use the algorithms for some Public-Key Cryptosystems

#### Forms of Teaching

Lectures

The lectures are performed in croatian language

Exams

two exams (each 120 minutes)

Consultations

one a week

Other

two short tests during the semester

Continuous Assessment Exam
Quizzes 0 % 10 % 0 % 10 %
Mid Term Exam: Written 0 % 45 % 0 %
Final Exam: Written 0 % 45 %
Exam: Written 0 % 90 %

#### Week by Week Schedule

1. Divisibility. The Euclidean Algorithm
2. Primes
3. Congruences
4. Functions in Number Theory and Applications
6. Diophantine Equations
7. Semigroups and Groups
8. Exam
9. Rings and Fields
10. Finite Fields
11. A Short Introduction to Cryptography
12. Data Encryption Standard and Advanced Encryption Standard
13. The RSA Public-Key Cryptosystem
14. Other Public-Key Cryptosystems
15. Exam

#### Study Programmes

Computer Engineering (profile)
Mathematics and Science (1. semester)
Computer Science (profile)
Mathematics and Science (1. semester)
Control Engineering and Automation (profile)
Mathematics and Science (1. semester)
Electrical Engineering Systems and Technologies (profile)
Mathematics and Science (1. semester)
Electrical Power Engineering (profile)
Mathematics and Science (1. semester)
Electronic and Computer Engineering (profile)
Mathematics and Science (1. semester)
Electronics (profile)
Mathematics and Science (1. semester)
Information Processing (profile)
Mathematics and Science (1. semester)
Software Engineering and Information Systems (profile)
Mathematics and Science (1. semester)
Telecommunication and Informatics (profile)
Mathematics and Science (1. semester)
Wireless Technologies (profile)
Mathematics and Science (1. semester)

#### Literature

(.), Cryptography. Theory and Practice D. R. Stinson CRC Press 2002,
(.), Diskretna matematika D. Žubrinić Element 2002,
(.), Course in Number Theory and Cryptography N. Koblitz Springer 1994,
(.), A Course in Group Theory J. F. Humphreys Oxford Univ. Press 1996,

#### Lecturers in Charge

ID 34556
Winter semester
4 ECTS
L0 English Level
L1 e-Learning
45 Lectures
0 Exercises
0 Laboratory exercises
0 Project laboratory

85 Excellent
70 Very Good
55 Good
45 Acceptable