## MIN101 Mathematics I

Faculty of Science
Autumn 2020
Extent and Intensity
4/2/0. 9 credit(s). Type of Completion: zk (examination).
Taught partially online.
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (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
Thu 10:00–11:50 M2,01021, Fri 11:00–12:50 prace doma
• Timetable of Seminar Groups:
MIN101/01: Wed 12:00–13:50 M2,01021, J. Šilhan
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
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
• SLOVÁK, Jan, Martin PANÁK and Michal BULANT. Matematika drsně a svižně (Brisk Guide to Mathematics). 1st ed. 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
not specified
• 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
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