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PřF:MIN101 Mathematics I - Course Information

## MIN101 Mathematics I

**Faculty of Science**

Autumn 2019

**Extent and Intensity**- 4/2/0. 9 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- prof. RNDr. Jan Slovák, DrSc. (lecturer)

prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)

doc. Mgr. Josef Šilhan, Ph.D. (lecturer) **Guaranteed by**- prof. RNDr. Jan Slovák, DrSc.

Department of Mathematics and Statistics - Departments - Faculty of Science

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Mon 8:00–9:50 M1,01017, Tue 14:00–15:50 M1,01017
- Timetable of Seminar Groups:

**Prerequisites**- High school mathematics.
**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- there are 22 fields of study the course is directly associated with, display
**Course objectives**- The course is the first part of the four semester block of Mathematics. The entire course covers the fundamentals of general algebra and number theory, linear algebra, mathematical analysis, numerical methods, and combinatorics. The aim of the first part is understanding of basic approach to building and using mathematical concepts, objects, and models; more detailed introduction to linear algebra and analytical geometry.
**Learning outcomes**- At the end of this course, students should be able: to understand basic concepts of linear algebra and probability; to apply these concepts to iterated linear processes; to solve simple problems in analytical geometry.
**Syllabus**- 1. Warm up (4 weeks) - axiomatics of scalars, elements of combinatorics and classical finite probability, geometry and matrix calculus in the plane, formal constructions of numbers (natural, integer, rational, remainder classes)
- 2. Vectors and matrices (3 weeks) - matrix calculus and systems of linear equations, applications of determinants, abstract vector spaces, linear mappings, unitary and adjoint mappings
- 3. Linear iterated models (3 weeks) - population models and discrete Markov chains with the use of the Perron theory of positive matrices, canonical matrix forms and decompositions, pseudoinverses
- 4. Analytical geometry (3 weeks) - elementary affine and Euclidean concepts, projective extension, affine, Euclidean and projective classification of quadrics.

**Literature**- MOTL, Luboš and Miloš ZAHRADNÍK.
*Pěstujeme lineární algebru*. 3. vyd. Praha: Univerzita Karlova v Praze, nakladatelství Karolinum, 2002. 348 s. ISBN 8024604213. info - SLOVÁK, Jan, Martin PANÁK and Michal BULANT.
*Matematika drsně a svižně (Brisk Guide to Mathematics)*. 1. vyd. Brno: Masarykova univerzita, 2013. 773 pp. ISBN 978-80-210-6307-5. doi:10.5817/CZ.MUNI.O210-6308-2013.*Základní učebnice matematiky pro vysokoškolské studium*info

*recommended literature*- FUCHS, Eduard.
*Logika a teorie množin (Úvod do oboru)*. 1. vyd. Brno: Rektorát UJEP, 1978. 175 s. info - RILEY, K.F., M.P. HOBSON and S.J. BENCE.
*Mathematical Methods for Physics and Engineering*. second edition. Cambridge: Cambridge University Press, 2004. 1232 pp. ISBN 0 521 89067 5. info - HORÁK, Pavel.
*Algebra a teoretická aritmetika.*2. vyd. Brno: Masarykova univerzita, 1993. 145 s. ISBN 8021008164. info

*not specified*- MOTL, Luboš and Miloš ZAHRADNÍK.
**Teaching methods**- The lectures combining theory with problem solving will be based on material for individual learning, which should precede the lectures. Seminar groups devoted to solving computatinal/practical problems.
**Assessment methods**- Four hours of lectures, two hours of tutorial. Final written test followed by oral examination. Results of tutorials/homeworks are partially reflected in the assessment.
**Language of instruction**- Czech
**Follow-Up Courses****Further Comments**- Study Materials

The course is taught annually.

- Enrolment Statistics (Autumn 2019, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2019/MIN101