Courses for exchange students in the academic year 2016/2017:

Winter term:

KMT/ ECAL1  Calculus 1  

 

Number of ECTS credits:

6

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Jitka Laitochova

Semester in which the course is taught:

winter

Description:

Differential calculus of real functions of a real variable and its applications. It is focused at basic terms of the theory like real functions of a real variable, limits, continuity, derivatives, maxima and minima and graph sketching. 
Content: Basic terms and concepts; limits; derivatives; transcendental functions; application of derivatives; curve sketching with derivatives; approximations of functions (differentials, Taylor's theorem); derivatives of implicit functions; sequences.

 

 

KMT/ ECAL3  Calculus 3

 

Number of ECTS credits:

6

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Jitka Laitochova

Semester in which the course is taught:

winter

Description:

Differential calculus of functions of two or more variables. Applications of partial derivatives are demonstrated.

Main topics: 
n-dimensional space, metric space, Euclidean space. Neighbourhood of n-dimensional space. 
Function of several variables. Domain and range. Geometric meaning of the function z = f (x, y). 
Limit of a function of several variables. Improper limit. 
Continuity of functions of several variables. Composite functions of several variables. Theorem on the continuity of composite functions. 
Partial derivatives of functions of several variables. Geometrical meaning of partial derivative of a function f (x, y). Higher partial derivatives. Schwarz theorem. 
Differentiable function. Complete differential. Geometrical meaning of the complete differential df(x, y). Complete differentials of higher orders. 
Partial derivatives of composite functions. Higher derivatives of a composite function. 
Taylor and Maclaurin's formula. 
Maxima, Minima, and Saddle Points. Fermat's theorem 
Sufficient conditions for local extrema. 
Implicit functions and their derivatives. Theorems on the existence of a derivative of an implicit function expressed by the equation F (x, y) = 0 and the equation F (x, y, z) = 0 

 

KMT/EAG1B  Algebra course 1  

 

Number of ECTS credits:

6

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Tomáš Zdráhal

Semester in which the course is taught:

winter

Description:

The course main objective is an active understanding of basic algebraic concepts necessary for further study of algebra and other mathematical disciplines. 

Introduction to propositional and predicate logic. Algebraic structures with one or two operations. Vector spaces - linear dependency, basis, dimensions, orthogonality. Linear algebra. 

 

 

KMT/EAG3B  Algebra course 3  

 

Number of ECTS credits:

6

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Tomáš Zdráhal

Semester in which the course is taught:

winter

Description:

The aim is understanding of algebraic solvability of algebraic equations. 

Polynomials 
Decomposition of polynomials of one indeterminate over the field of complex and field of real numbers. Symmetric polynomials 
The main theorem on symmetric polynomials, using symmetric polynomials. 
Algebraic solutions of algebraic equations 
Binomial equations, algebraic solvability of algebraic equations of the second, third and fourth degrees. 

 

 

 

KMT/EIAMB  ICT application in Mathematics

 

Number of ECTS credits:

4

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

David Nocar

Semester in which the course is taught:

winter

Description:

The subject is focused on introducing to students the possibilities of mathematical software, both applying MS Office (Microsoft Equation, MathType) and specific mathematical applications used in mathematics teaching at elementary schools. It meets the requirements of educating future mathematics teachers within the state informational politics and of informational literacy of all teachers.    

It works with basic types of mathematical instructional environment (dynamic geometry, spreadsheets, computer algebraic systems). Individual systems are demonstrated by Cabri Geometrie (or: CaR Geogebra, GEONExT), MS Excel (or: OpenOffice Calc and Google Spreadsheets), Imagine Logo (or: Comenius Logo) and Derive. 

 

 

 

 KMT/EETM  English Terminology in Mathematics 

 

 

Number of ECTS credits:

4

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Jitka Laitochova

Semester in which the course is taught:

winter

Description:

The subject consists of three independent units Algebra, Geometry and Calculus. Each of these units deals with basic terms, assertions and problems focusing on applications of mathematics at elementary schools. The subject is taught in English. 

 

 

KMT/EKGE  Construction Geometry for Teachers of Mathematics

 

Number of ECTS credits:

4

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work,

the student elaborates and passes on 2 drawn problems.

 

Lecturer:

Jitka Hodaňová

Semester in which the course is taught:

winter

Description:

Focal properties of conic sections. Orthogonal projection. Free parallel projection.  Monge's projection, axonometric projection and its application (Projective method of choice).

 

KMT/EIDMA The Introduction to Didactics of Mathematics A

 

Number of ECTS credits:

5

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Radka Dofková

Semester in which the course is taught:

winter

Description:

The purpose of this seminar is to introduce students to basic points from didactics of mathematics in prospective mathematics teachers training. The course will be structured to present main didactical principles of mathematical teaching and to practice various activities which are supposed to increase pupils´ motivation in mathematics.

 

  

KMT/EDMA Development of Mathematical Abilities             (KMT/ABILI)

 

Number of ECTS credits:

4

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Martina Uhlířová

Semester in which the course is taught:

winter

Description:

The course is designed for students of primary school teacher training. The aim of the course is: to familiarize the students with methods and means of developing mathematical abilities of young children, i. e. to provide them with activities aiming at the development of spatial imagination, with some ideas for solving word problems, and with number tasks, to explain the basic terms and concepts.

 

 

 

Summer term

KMT/ ECAL2  Calculus 2      

 

Number of ECTS credits:

6

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Jitka Laitochova

Semester in which the course is taught:

summer

Description:

Integral calculus of real functions of a real variable. Main topics are indefinite integral, definite integral and applications of definite integral.

 

 

KMT/ ECAL4  Calculus 4  

 

Number of ECTS credits:

6

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Jitka Laitochova

Semester in which the course is taught:

summer

Description:

Infinite sequences and infinite series of constants and functions. Basic theory of infinite series. Applications of power series. 
Main topics: 
Infinite sequences of numbers. 
Infinite series of numbers - basic terms and concepts. 
Series with non-negative members. 
Absolute convergence. 
Sequences and series of functions. 
Power series and their applications. 

 

 

 

KMT/EAG2B  Algebra course 2 

 

Number of ECTS credits:

6

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Tomáš Zdráhal

Semester in which the course is taught:

summer

Description:

The course focuses on exploring the algebraic properties of the structure of polynomials over a general range, respectively. field integrity. The main differences algebraic and functional approach to polynomials. Students will also address the divisibility of polynomials over a general body and some methods of finding the roots of polynomials. 

 

 

KMT/EAG4B  Algebra course 4  

 

Number of ECTS credits:

6

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Tomáš Zdráhal

Semester in which the course is taught:

summer

Description:

The course aims to fully understand to the theory of algebraic structures with several operations.

Properties of groups. Lagrange's theorem in the group theory. Factor groups. Group homomorphism. Lattices and lattices homorphism. Boolean algebra. Application of lattices and Boolean algebras. 

 

 

KMT/EIDMB The Introduction to Didactics of Mathematics B

 

Number of ECTS credits:

5

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Radka Dofková

Semester in which the course is taught:

summer

Description:

This seminar follows on The Introduction to Didactics of Mathematics A from summer semester. There will be more special technics which could be useful in mathematics teaching at primary school.

There  will be focus on students´ active involvement into course and on practical teachings methods.

  

KMT/EITME   ICT in Mathematics Education

Number of ECTS credits:

4

Course completion:

Exam

Completion requirements:

50 % attendance, tutorial work

Lecturer:

Jan Wossala

Semester in which the course is taught:

summer

Description:

The purpose of the course is to familiarize students with current possibilities of using ICT in the teaching of mathematics at lower primary schools. Great attention will be paid to possible applications of computers as a support for teachers, the education process, and the pupil`s individual work.

Students should acquire the skills needed in order to effectively incorporate the computer technology into the teacher preparation, to involve the computer technology in the teaching of mathematics, and to employ computers for the purposes of the primary school pupils` individual work and homework.

 

KMT/EPRST Introduction to probability theory and mathematical statistics

 

Number of ECTS credits:

6

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Kamila Fačevicová

Semester in which the course is taught:

summer

Description:

The aim of the course is to introduce the basics of the probability theory and mathematical statistics. The course is focused on probability of a random event occurance, basic characteristics of random variables and analysis of dependency between two random variables. Also some descriptive statistical tools are explained.

 

 

KMT/EAMS Applications of mathematical statistics

 

Number of ECTS credits:

4

Course completion:

Exam

Completion requirements:

 

50 % attendance, tutorial work

Lecturer:

Kamila Fačevicová

Semester in which the course is taught:

summer

Description:

The aim of the course is to serve a basic knowledge about statistical hypothesis testing. Students are supposed to learn how to analyse their own datasets. Particularly, how to state the statistical hypothesis, choose the proper method and proceed the analysis using R software. One of the main part of the course is dedicated to the interpretation of the results.

 

 

 


Didaktický seminář
10. 10. 2017

Ve čtvrtek 14. prosince 2017 ve 14:00 se bude konat v "Malé" aule didaktický seminář na téma "Matematika pro rozvoj myšlení a představivosti". Přednášející Mgr. Jitka Hodaňová, Ph.D., Katedra...

Jan Wossala

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Didaktický seminář
10. 10. 2017

úterý 28. listopadu 2017 ve 13:15 se bude konat na učebně P28 didaktický seminář na téma "Eight-thousanders of Number Theory". Přednášející doc. RNDr. Miroslav Haviar, CSc., Katedra matematiky,...

Jan Wossala

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Didaktický seminář
10. 10. 2017

pondělí 20. listopadu 2017 ve 13:30 se bude konat na učebně N24 didaktický seminář na téma "Badatelské úlohy a jejich využití ve výuce matematiky". Přednášející RNDr. Libuše Samková, Ph.D.,...

Jan Wossala

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Konference ODAM 2017
19. 05. 2017

Katedra matematiky PdF UP v Olomouci Vás zve na konferenci ODAM 2017 pořádanou ve dnech 31. 5. - 2. 6. 2017 v prostorách Pedagogické fakulty Univerzity Palackého v Olomouci.  

Jan Wossala

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Přednáška "Práce s chybou v matematice"
02. 05. 2017

V rámci akce "Noc vzdělávání" proběhne dne 9. 5. 2017 přednáška Práce s chybou v matematice. Místo konání: učebna N24 Datum a čas: 9. 5. 2017 od 20:15 do 21:00 Přednášející: PhDr. Radka Dofková,...

Jan Wossala

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