FI:MB101 Mathematics I - Course Information
MB101 Mathematics IFaculty of Informatics
- Extent and Intensity
- 2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
- doc. Mgr. Ondřej Klíma, Ph.D. (lecturer)
Mgr. Eva Janoušková, Ph.D. (seminar tutor)
Mgr. David Kruml, Ph.D. (seminar tutor)
- Guaranteed by
- prof. RNDr. Jan Slovák, DrSc.
Faculty of Informatics
Supplier department: Faculty of Science
- Mon 10:00–11:50 D2
- Timetable of Seminar Groups:
MB101/01: Thu 8:00–9:50 A320, D. Kruml
MB101/02: Thu 10:00–11:50 A320, D. Kruml
MB101/03: Wed 10:00–11:50 B204, 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
- 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.
- 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.
- recommended 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
- 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 F 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
- 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
- PřF:M7190 Game Theory
M1110 || M1111 || FI:MB101 || FI:MB201 || FI:MB003
- MA007 Mathematical Logic
MB005 || MB101|| MB201|| PřF:M1120 || PřF:M1125
- MA015 Graph Algorithms
- 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||MB151) && !MB008
- PřF:M7190 Game Theory