Mathematics for Informatics
Code  Completion  Credits  Range  Language 

MIMPI  Z,ZK  7  3P+2C  Czech 
 Lecturer:
 Štěpán Starosta (guarantor)
 Tutor:
 Štěpán Starosta (guarantor), Michal Kupsa, Jan Spěvák, František Štampach
 Supervisor:
 Department of Applied Mathematics
 Synopsis:

The course comprises topics from general algebra with focus on finite structures used in computer science. It includes topics from multivariate analysis, smooth optimization and multivariate integration. The third large topic is computer arithmetics and number representation in a computer along with error manipulation. The last topic includes selected numerical algorithm and their stability analysis. The topics are completed with demonstration of applications in computer science. The course focuses on clear presentation and argumentation.
 Requirements:

linear algebra, elements of discrete mathematics, elements of calculus
 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. Multivariable calculus: partial derivative and gradient.
7. Continuous optimization methods. Selected optimization problems in informatics.
8. Constrained multivariable optimization.
9. Integration of multivariable functions.
10. Representation of numbers in computers, floating point arithmetics and related errors.
11. Solving systems of linear equations, finding eigenvalues and stability of numerical algorithms.
12. Error estimation in numerical algorithms. Numerical differentiation.
 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. Constrained multivariable optimization
11. Constrained multivariable optimization with inequality constraints
12. Multivariable integration
 Study Objective:

The course covers selected topics from general algebra and number theory with
emphasis on modular arithmetics and finite structures, computer arithmetics and representation of numbers,
multivariable calculus and continuous optimization. It provides some examples of informatics applications of
mathematics.
 Study materials:

1. Dummit, D. S.  Foote, R. M. Abstract Algebra. Wiley, 2003. ISBN 9780471433347.
2. Mareš, J. Algebra. Úvod do obecné algebry. Vydavatelství ČVUT, 1999. ISBN 9788001019108.
3. Paar, Ch.  Pelzl, J. Understanding Cryptography. Springer, 2010. ISBN 9783642041006.
4. Cheney, E. W.  Kincaid, D. R. Numerical Mathematics and Computing. Cengage Learning, 2007. ISBN
9780495114758.
5. Higham, N. J. Accuracy and Stability of Numerical Algorithms. SIAM, 2002. ISBN 9780898715217.
6. Marsden, J.  Weinstein, A. Calculus III. Springer, 1998. ISBN 9780387909851.
7. Ross, T. J. Fuzzy Logic with Engineering Applications (3rd Edition). Wiley, 2010. ISBN 9780470743768.
 Note:
 Further information:
 https://courses.fit.cvut.cz/MIMPI/
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Knowledge Engineering, in Czech, Presented in Czech, Version 2016 and and 2017 (compulsory course in the program)
 Computer Security, Presented in Czech, Version 2016 to 2019 (compulsory course in the program)
 Computer Systems and Networks, Presented in Czech, Version 2016 to 2019 (compulsory course in the program)
 Design and Programming of Embedded Systems, in Czech, Version 2016 to 2019 (compulsory course in the program)
 Specialization Web and Software Engineering, in Czech, Version 2016 to 2019 (compulsory course in the program)
 Specialization Software Engineering, in Czech, Version 2016 to 2019 (compulsory course in the program)
 Specialization Web Engineering, Presented in Czech, Version 2016 to 2019 (compulsory course in the program)
 Master Informatics, Presented in Czech, Version 2016 to 2019 (compulsory course in the program)
 Specialization System Programming, Presented in Czech, Version 2016 to 2019 (compulsory course in the program)
 Specialization Computer Science, Presented in Czech, Version 20162017 (compulsory course in the program)
 Specialization Computer Science, Presented in Czech, Version 2018 to 2019 (compulsory course in the program)
 Knowledge Engineering, in Czech, Presented in Czech, Version 2018 to 2019 (compulsory course in the program)