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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

NI-MPI Mathematics for Informatics Extent of teaching: 3P+2C
Instructor: Spěvák J., Starosta Š. Completion: Z,ZK
Department: 18105 Credits: 7 Semester: Z

Annotation:
The course comprises topics from general algebra with focus on finite structures used in computer science. It includes topics from multi-variate analysis, smooth optimization and multi-variate 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.

Lecture syllabus:
1. Basic notions of abstract algebra: grupoid, monoid, group, homomorphism.
2. Cyclic and finite groups and their properties.
3. Rings and fields.
4. (2) Finite fields. Applications in cryptography.
5. Multivariate calculus: partial derivative, gradient, and Hessian.
6. Unconstrained extremas of multivariate functions.
7. (2) Constrained extremas of multivariate functions.
8. Mutlivariate integral.
9. Representing numbers in computers, floating point arithmetic and relevant errors.
10. (2) Solving systems of linear equations, finding eigenvalues and stability of numerical algorithms.

Seminar syllabus:
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

Literature:
1. Dummit, D. S. - Foote, R. M. Abstract Algebra. Wiley, 2003. ISBN 978-0471433347.
2. Mareš, J. Algebra. Úvod do obecné algebry. Vydavatelství ČVUT, 1999. ISBN 978-8001019108.
3. Paar, Ch. - Pelzl, J. Understanding Cryptography. Springer, 2010. ISBN 978-3642041006.
4. Cheney, E. W. - Kincaid, D. R. Numerical Mathematics and Computing. Cengage Learning, 2007. ISBN
978-0495114758.
5. Higham, N. J. Accuracy and Stability of Numerical Algorithms. SIAM, 2002. ISBN 978-0898715217.
6. Marsden, J. - Weinstein, A. Calculus III. Springer, 1998. ISBN 978-0387909851.

Requirements:
linear algebra, elements of discrete mathematics, elements of calculus

Předmět je ekvivalentní s MI-MPI. Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/MI-MPI/

The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
NI-PB.2020 Computer Security PP 1
NI-ZI.2020 Knowledge Engineering PP 1
NI-SPOL.2020 Unspecified Branch/Specialisation of Study PP 1
NI-TI.2020 Computer Science PP 1
NI-TI.2023 Computer Science PP 1
NI-SP.2023 System Programming PP 1
NI-WI.2020 Web Engineering PP 1
NI-SP.2020 System Programming PP 1
NI-SI.2020 Software Engineering (in Czech) PP 1
NI-MI.2020 Managerial Informatics PP 1
NI-PSS.2020 Computer Systems and Networks PP 1
NI-NPVS.2020 Design and Programming of Embedded Systems PP 1


Page updated 28. 3. 2024, semester: Z/2023-4, L/2019-20, L/2022-3, Z/2019-20, Z/2022-3, L/2020-1, L/2023-4, Z/2020-1, Z,L/2021-2, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška