#
FI:MB101 Mathematics I - Course Information

## MB101 Mathematics I

**Faculty of Informatics**

Spring 2018

**Extent and Intensity**- 2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
**Teacher(s)**- doc. Mgr. Ondřej Klíma, Ph.D. (lecturer)

doc. Mgr. Josef Šilhan, Ph.D. (lecturer)

Mgr. David Kruml, Ph.D. (seminar tutor)

doc. RNDr. Martin Čadek, CSc. (assistant)

RNDr. Jiří Glozar (assistant) **Guaranteed by**- prof. RNDr. Jan Slovák, DrSc.

Faculty of Informatics

Supplier department: Faculty of Science **Timetable**- Wed 8:00–9:50 D3, except Wed 16. 5.
- Timetable of Seminar Groups:

*J. Šilhan*

MB101/02: Thu 10:00–11:50 A320,*J. Šilhan*

MB101/03: Thu 12:00–13:50 A320,*D. Kruml*

MB101/04: Thu 16:00–17:50 A320,*D. Kruml* **Prerequisites**(in Czech)- !
**MB005**Foundations of mathematics && !**MB201**Linear models B **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 16 fields of study the course is directly associated with, display
**Course objectives**- 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; apply these concepts to iterated linear processes; solve basic problems in analytical geometry.
**Syllabus**- The course is the first part of the four semester block of Mathematics. In the entire course, the fundamentals of general algebra and number theory, linear algebra, mathematical analysis, numerical methods, combinatorics, as well as probability and statistics are presented. Content of the course Linear models:
- 1. Warm up (4 weeks) -- scalars, scalar functions, combinatorial examples and identities, finite probability, geometric probability, geometry of the plane, relations and mappings, equivalences and orderings.
- 2. Vectors and matrices (3 weeks) -- vectors, vector space, linear independence, basis, linear mappings, matrices, matrix calculus and determinants, orthogonality, eigenvalues and eigenvectors.
- 3. Linear models (3 weeks) -- systems of linear (in)equalities, linear programming problem, linear difference equations, iterated linear processes (population models) and Markov chains.
- 4. Analytical geometry (2 weeks) -- geometrical applications: line, plane, parametric versus non-parametric descriptions, positioning of planes and lines, projective space extension, angle, length, volume, elementary 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 - 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 - J. Slovák, M. Panák a kolektiv, Matematika drsně a svižně, učebnice v přípravě

*recommended literature*- MOTL, Luboš and Miloš ZAHRADNÍK.
**Bookmarks**- https://is.muni.cz/ln/tag/FI:MB101!
**Teaching methods**- Two hours of lectures, two hours of tutorial. Lecture covering the theory with illustrative solved problems. Tutorials devoted to solving numerical problems.
**Assessment methods**- During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are 5 tests during the semester. The seminars are evaluated in total by max 5 points. Students, who collect during the semester (i.e., from tests and mid-term exams) less than 8 points, are graded as X and they do not proceed to the final examination. The final exam is two hours long and written for max 20 points. For successful examination (the grade at least E) the student needs in total 22 points or more.
**Language of instruction**- Czech
**Follow-Up Courses****Further comments (probably available only in Czech)**- Study Materials

The course is taught annually.

Information on course enrolment limitations: Přednostně určen pro neúspěšné z podzimu 2006 **Listed among pre-requisites of other courses****MA007**Mathematical Logic

MB005 || MB101|| MB201|| PřF:M1120 || PřF:M1125**MA015**Graph Algorithms

MB005||(MB101&&MB102)||(MB201&&MB102)||(MB101&&MB202)||(MB201&&MB202)||(PřF:M1120)||PROGRAM(N-IN)||PROGRAM(N-AP)**MB141**Linear algebra and discrete mathematics

!NOW(MB151) && ( !MB151 || !MB154 ) && ( !MB101 || !MB104 )**MB143**Design and analysis of statistical experiments

MB141 || MB142 || MB101 || MB201 || MB102 || MB202**MB151**Linear models

!MB101 && !MB201**MB153**Statistics I

( MB151 || MB101 || MB201 || MB152 || MB102 || MB202 ) && ( !MB103 && !MB203 && !MV011 )**MB154**Discrete mathematics

!MB104 && !MB204 && ( MB101 || MB201 || MB151 || MB102 || MB202 || MB152 )**MV008**Algebra I

(MB005||MB101||MB201) && !MB008**PV275**Introduction to Quantum Computer Programming

( MB141 || MB151 || MB101 || MB201 ) && IB111

- Enrolment Statistics (Spring 2018, recent)
- Permalink: https://is.muni.cz/course/fi/spring2018/MB101