Course objectives:
|
The goal of the mathematical proseminar is to practice skills from a high school and provide their extensions to the university level. This preliminary course is devoted to students before their entry to the university and among others it also highlights the Czech mathematical terminology. We try to help students with the transition to the university and to pass the initial mathematical courses.
|
Requirements on student
|
After a passing the course, the student would be able to apply high school mathematical methods to solve specific problems and effectively perform fundamental mathematical operations (e.g., simplify an expression, solving equations and inequalities). At the end of semester would be a test - the students have to gain more than 60 % of points to pass the course. The tutor can replace the test by several homeworks.
|
Content
|
The program of particular seminars would consist of chosen parts of high school mathematics. We would emphasize those parts which are necessary for passing initial mathematical courses at the university (e.g., logic, algebraic expressions, equations and inequalities, functions, analytic geometry, combinatorics). We also would like to solve some interesting untraditional problems which can help students with the transition from algorithmic repeating of known processes to individual considerations and proposing own solution methods. Last but not least, we emphasize the Czech mathematical terminology and understanding to Czech mathematical texts. Seminar form of the course allows to adapt the seminars to personal needs of present students and makes their following entry to the university easier.
|
Activities
|
|
Fields of study
|
|
Guarantors and lecturers
|
|
Literature
|
-
Basic:
Josef Polák. Přehled středoškolské matematiky. 2015. ISBN 978-80-7196-458-2.
-
Recommended:
Ivan Bušek. Řešené maturitní úlohy z matematiky. 2010. ISBN 80-7196-140-X.
-
Recommended:
Josef Polák. Středoškolská matematika v úlohách I. 2010. ISBN 80-7196-337-2.
-
Recommended:
Josef Polák. Středoškolská matematika v úlohách II. 2018. ISBN 978-80-7196-419-3.
-
On-line library catalogues
|
Time requirements
|
Full-time form of study
|
Activities
|
Time requirements for activity [h]
|
Contact hours
|
26
|
Preparation for comprehensive test (10-40)
|
26
|
Total
|
52
|
|
Prerequisites
|
Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
structural considerations and expressing |
to choose appropriate (particular) method to solve a problem |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
to simplify mathematical expresions |
to solve fundamental types of equations and inequalities |
to draw graphs of elementary functions |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
|
Learning outcomes
|
Knowledge - knowledge resulting from the course: |
the student understands Czech mathematical texts and terminology |
the student suggests a solving method which consists of several particular steps |
the student knows the importance of solving equations and inequalities and understands their detailed structure |
the student knows the importance of functions in mathematics, he analyzes their properties |
Skills - skills resulting from the course: |
the student do more complicated mathematical operations effectively |
the student solves more complicated equations and inequalitites; he uses specialized methods |
the student draws graphs of elementary functions and their simple transformations |
Competences - competences resulting from the course: |
N/A |
N/A |
N/A |
|
Assessment methods
|
Knowledge - knowledge achieved by taking this course are verified by the following means: |
Test |
Skills - skills achieved by taking this course are verified by the following means: |
Test |
Competences - competence achieved by taking this course are verified by the following means: |
Test |
|
Teaching methods
|
Knowledge - the following training methods are used to achieve the required knowledge: |
Seminar classes |
Task-based study method |
Skills - the following training methods are used to achieve the required skills: |
Practicum |
Seminar classes |
Task-based study method |
Individual study |
Competences - the following training methods are used to achieve the required competences: |
Seminar classes |
Task-based study method |
|