Mathematics for Informatics
Code  Completion  Credits  Range  Language 

MIMPI  Z,ZK  7  3P+2C  Czech 
 Lecturer:
 Tutor:
 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:

 Master branch Knowledge Engineering, in Czech, 20162017 (compulsory course in the program)
 Master branch Computer Security, in Czech, 20162019 (compulsory course in the program)
 Master branch Computer Systems and Networks, in Czech, 20162019 (compulsory course in the program)
 Master branch Design and Programming of Embedded Systems, in Czech, 20162019 (compulsory course in the program)
 Master branch Web and Software Engineering, spec. Info. Systems and Management, in Czech, 20162019 (compulsory course in the program)
 Master branch Web and Software Engineering, spec. Software Engineering, in Czech, 20162019 (compulsory course in the program)
 Master branch Web and Software Engineering, spec. Web Engineering, in Czech, 20162019 (compulsory course in the program)
 Master program Informatics, unspecified branch, in Czech, version 20162019 (compulsory course in the program)
 Master branch System Programming, spec. System Programming, in Czech, 20162019 (compulsory course in the program)
 Master branch System Programming, spec. Computer Science, in Czech, 20162017 (compulsory course in the program)
 Master specialization Computer Science, in Czech, 20182019 (compulsory course in the program)
 Master branch Knowledge Engineering, in Czech, 20182019 (compulsory course in the program)