Introduction to the basic concepts, terminology, theorems, and application of number theory, abstract algebra, cryptography, codes.
Mathematics for Computer Science II (GAINBAN-SZAMMAT2-1)
Basic data
Name and type of the study programme
Computer Science Engineering, undergraduate program
Curriculum
2022
Classes / consultation hours
0 + 2 + 2 (L+S+Labs)
Credits
5 credits
Theory – Practice
Theory: 0%, Practice: 100%
Recommended semester
Semester 4
Study mode
full-time
Prerequisites
Mathematics for Computer Science I
Evaluation type
Colloquium
Course category
Compulsory
Language
English
Instructors
Responsible instructor
Dr. Végh Attila
Responsible department
Department of Basic Sciences
Instructor(s)
Dr. Végh Attila
Checked by
Kovács Márk
Course objectives
Course content
Seminars
1. Introduction to number theory. Fundamental theorem of arithmetic. 2. Diophantine equations. 3. Congruences, residue classes. Solvability of linear congruences. 4. Euclidean algorithm. 5. Fermat's little theorem, Fermat-Euler theorem. 6. Basics of cryptography, public key encryption, RSA algorithm. 7. Prime numbers, prime testing. 8. Basic concepts of abstract algebra. Subgroup, Lagrange theorem. Permutation groups. Direct product, Abel groups. 9. Rings, fields, finite fields. 10. Polynomials, irreducible polynomials. 11. Polynomials over a finite field, finite field of prime order. 12. Basic coding concepts, error correcting codes. Binary linear and Hamming codes. Linear codes, Hamming codes. 13. Reed-Solomon codes, cyclic codes, BCH codes.
Labs
Solving practical problems and exercises related to the knowledge acquired in the seminars using MATLAB.
Acquired competences
Knowledge
- Knowledge of the principles and methods of natural sciences (mathematics, physics, other natural sciences) relevant to the field of IT.
Skills
- He/she uses the principles and methods of natural sciences (mathematics, physics, other natural sciences) relevant to the field of information technology in his/her engineering work for the design of information systems.
Attitude
- He/she makes an effort to work efficiently and to high standards.
Autonomy and responsibilities
–
Additional professional competences
- Efficient use of digital technology, knowledge of digital solutions to fulfill educational objectives
Requirements, evaluation and grading
Mid-term study requirements
There will be three 30-30 point tests during the semester in weeks 6, and 12. In the last week of the semester, tests can be corrected and made up.
Exam requirements
The exam is a 40-point written test.
Generative AI usage
Use of GAI tools is not permitted for solving assignments. This means GAI tools cannot be used to complete formative or summative assessments, and using GAI constitutes academic misconduct. The use of AI tools for spelling and grammar checking does not fall under this prohibition.
Study aids, laboratory background
Mark Kelbert, Yuri Suhov, Information Theory and Coding by Example, Cambridge University Press , 2013, ISBN:9780521139885
Readings
Compulsory readings
Mark Kelbert, Yuri Suhov, Information Theory and Coding by Example, Cambridge University Press , 2013, ISBN:9780521139885
Recommended readings
Mark Kelbert, Yuri Suhov, Information Theory and Coding by Example, Cambridge University Press , 2013, ISBN:9780521139885