Branch programme/details

The goal of the study is to provide graduates with complete master education which will prepare them for the profession of a mathematics teacher at the lower and upper secondary schools of all types. The study is based on the balance of cognitive, didactic and pedagogic-psychological parts of teacher education. An emphasis is put on the use of didactic innovations in the teaching of mathematics with regard to the up-to-date didactic conceptions. The graduates will be prepared for the construction of school educational programmes with the focus on the integration of various areas of mathematics (arithmetic, algebra, geometry, statistics, financial mathematics, etc.) and various educational fields. The graduates will acquire sufficient amount of knowledge and skills to work in a differentiated way with pupils talented for mathematics.

See study plan on http://studium.pedf.cuni.cz/karolinka/

1. Oral exam. Maximum number of points is 30 (2 questions, 15 points each). 
    The oral examination consists of problem solving and a theoretical part.
    The applicant is asked to bring a list of completed mathematical courses with brief syllabuses from the previous university study.

2. Oral exam – assessing the applicants’ general awareness of pedagogy and psychology, and their motivation to study the chosen subjects – a maximum score of 30 points.

Total score – 60 points maximum.

1. Mathematics

Topics: 
Basics of mathematics (mathematical logic, sets); positional systems, divisibility tests, Diophantine equations, Euclidean algorithm, congruence; linear algebra (matrices, determinants, systems of linear equations, vector spaces, linear mappings); relational structures (order, equivalence); polynomials (algebraic and functional definitions of the polynomial, divisibility, algebraic and numerical solutions to equations); vectors, shapes in E2, E3, E4 and their incidence relationships studied via vectors; coordinate systems, basis; algebraic structures (group, field, ring, homomorphism, isomorphism); geometric transformations in a synthetic and analytic ways in E2: congruencies in plane (combination, classification, group of congruence); similar transformations in plane (classification, group of similarities); homothety (Monge theorem, Menelaus theorem); affine transformations in A2 (classification, synthetic and analytic descriptions, group of affine transformations); circle inversion, problems of  Appolonius; conics (affine and metric properties); elementary functions; calculus (continuity, limit and derivative – definition, properties, calculation; properties of functions continuous on an interval; mean value theorem; maximum and minimum; properties of a function and the construction of its graph); integrals (primitive function and definite integral – definition, properties, calculation; use in geometry, improper integral); differential equations (simple equations with independent variables, linear differential equations of the first order; linear differential equations of the second order with constant variables – general solution and solution with an initial condition); number sequences and series (number sequences – properties, limit of a sequence and its calculation; number series – properties, convergence criteria for series with non-negative terms, alternating series, absolute and non-absolute convergence).

2. Pedagogy and Psychology

Oral exam – assessing the applicants’ general awareness of pedagogy and psychology, and their motivation to study the chosen subjects – a maximum score of 30 points.

Admission to Master's studies is conditioned by completed secondary education confirmed by a school-leaving certificate. Admission to Post-Bachelor studies (Master's programme) is likewise conditioned by completed education in any type of study programme.

Verification method:	entrance exam
Confirmation date (of entrance exam) from:	08.06.2020	Until:	16.06.2020
Alternative date (of entrance exam):	24.06.2020	Until:	25.06.2020

University textbooks with the topics given above. For example:

Coxeter, H.S.M. Introduction to Geometry. John Wiley & Sons, USA 1989

Gans, D. Transformations and geometries. New York, Appleton-Century-Crofts, Meredith Corporation, 1969.

Brannan, D.A., Esplen, M.F. Gray, J.J. Geometry. Cambridge, UK, Cambridge University Press, 2000.

Cameron, P.J.: Introduction to Algebra. Oxford University Press, 2001.

Ross, K.A.:Elementary Analysis: The Tudory of Calculus. Undergraduate texts in Mathematics, Springer Verlag New York-Heidelberg-Berlin 1980

Fischer, E.: Intermediate Real Analisis. Undergraduate Texts in Mathematics, Springer Verlag NewYork-Heidelberg-Berlin 1983

Ross, K. A.:Elementary Analysis: The Tudory of Calculus. Undergraduate texts in Mathematics, Springer Verlag New York-Heidelberg-Berlin 1980

Kra, I. Abstract algebra with applications. Online textbook: http://www.math.sunysb.edu/~irwin/algbk.pdf

Brin, M. G. Modern algebra. Online textbook: http://www.math.binghamton.edu/matt/m402/pack402.pdf