Mathematics for Informatics
- Francesco Dolce
- Francesco Dolce
- Department of Applied Mathematics
The course focuses on selected topics from general algebra, number theory, numerical mathematics, multivariate calculus and continuous optimization. The topics are selected to emphasize the connection with computer science. Some examples of applications of mathematics to computer sciences are given: cryptography, discrete Fourier transform and fuzzy control.
- Syllabus of lectures:
1. Basic notions of abstract algebra: grupoid, monoid, group, homomorphism.
2. Cyclic and finite groups and their properties.
3. Discrete logarithm problem in various groups and its applications in cryptography.
4. Rings and fields and their properties.
5. Modular arithmetics and equations in finite fields.
6. Representing numbers in computers, floating point arithmetics.
7. Solving systems of linear equations, finding eigenvalues and stability of numerical algorithms.
8. Multivariable calculus: partial derivative and gradient.
9. Continuous optimization methods. Selected optimization problems in informatics.
10. Constrained multivariable optimization.
11. Integration of multivariable functions.
12. Discrete Fourier transform.
13. Mathematics of uncertainty: fuzzy set theory
- Syllabus of tutorials:
1. Fucntions, derivative, polynomials
2. Grupoid, semigroup, monoid, group
3. Cyclic group, generators
4. Homomorphism, discrete logarithm, fields and rings
5. Finite fields
6. Discrete exponenciation, CRT, discrete logarithm
7. Machine numbers.
8. Multivariable functions, partial derivatives
9. Multivariable optimization
10. Multivariable optimization with constraints
11. Multivariable integration
12. Fuzzy sets
- Study Objective:
Mathematics as a language for description of the world is a key discipline for an informatics engineer. The aim of this module is introduce students to the relevant parts of modern mathematics that form the theoretical background of many informatics disciplines and to develop students in general problem solving.
- Study materials:
1. Schroeder, R. M.: ''Number Theory in Science and Communication'', Springer, Berlin, 2006.
2. Graham, R., Knuth, D., Patashnik, O.: ''Concrete Mathematics: A Foundation for Computer Science'', Addison-Wesley, Reading, Mass., 1989.
- Further information:
- Time-table for winter semester 2019/2020:
Mon Tue Fri ThuroomT9:347
- Time-table for summer semester 2019/2020:
- Time-table is not available yet
- The course is a part of the following study plans:
- Computer Security, Presented in English, Version 2016 to 2019 (compulsory course in the program)
- Computer Systems and Networks, Presented in English, Version 2016 to 2019 (compulsory course in the program)
- Design and Programming of Embedded Systems, in English, Version 2016 to 2019 (compulsory course in the program)
- Specialization Software Engineering, in English, Version 2016 to 2019 (compulsory course in the program)