MDA101 Mathematics I

Faculty of Science
Autumn 2024
Extent and Intensity
0/0/0. 12 credit(s). Type of Completion: zk (examination).
Teacher(s)
Dr. Ioannis Chrysikos (lecturer)
prof. RNDr. Jan Slovák, DrSc. (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
Prerequisites
no prerequisites
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Basic introductory course of the Mathematics block of the programme. The five courses aim at the development of basic skills and knowledge in all four main approaches: algebraic, geometric, combinatorial, and infinitesimal, as well as the ability to enjoy computer-assisted solutions to problems. This course focuses on discrete tools and matrix calculus, as well as analytic geometry.
Learning outcomes
mathematical approach to deductive thinking;
proper formulation of mathematical concepts and results;
matrix calculus and linear algebra and their simple applications;
distinguishing between claims and proofs;
computer assisted approach to simple discrete modelling
Syllabus
  • overview of basic concepts of Mathematics (combinatorial, algebraic, geometric, the language of Mathematics - 4 weeks);
    elements of linear algebra and geometry (3 weeks);
    matrix calculus and applications (intro to linear programming, difference equations, iterative models, spectral matrix theory - 3 weeks);
    analytic geometry (affine, Euclidean and projective geometries, multilinear calculus - 3 weeks)
Literature
  • Jan Slovák et al, Brisk Guide to Mathematics, www.math.muni.cz/~slovak/BG.pdf, Chapters 1-4
  • Ioannis Chrysikos et al, Script Project in Sage, available online, in preparation
Teaching methods
essentially asynchronous approach, based on introductory short presentations plus homework assignments, complete pdf materials, and Sage/Matlab supported tutorials;
complemented by synchronous communication with the tutor upon agreement
Assessment methods
weekly homework assignments during the semester, including peer to peer reviews;
active presentation of some homeworks to the lecturer/tutor;
one short synchronously written assignments during the term;
one final synchronously written assignment, followed by colloquial discussions/exams in small groups
Language of instruction
English
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
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