Course objectives:
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Providing students with an overview of school mathematics. Acquiring or broadening the basic knowledge and skills necessary for solving mathematical problems. Improvement of communicative competences and competences for solving problems. Acquiring knowledge needed for following study and exercising a profession of teacher.
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Requirements on student
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Two tests. It is necessary to gain at least 14 points out of 20 in each paper. Tests contain types of problems solved during semester. Each of two tests consists of four problems, at most five points apiece. To the points gained in this way points given for individual work can be added - correctly solved problem, its presentation and explanation to others students.
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Content
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Basic types of proofs (proofs of several well-known inequalities). Proofs of statements containing the universal and existential quantifier. Proofs of simple statements on plane figures. Proofs by mathematical induction. Inductive methods for solving problems (analogy, generalization, complete and incomplete induction). Analytic and recurrent formulas of sequences given by terms. Finite sums. Simple problems of combinatorial geometry.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Basic:
Odvárko, O. a kol. Metody řešení matematických úloh.. Praha : SPN, 1990. ISBN 80-04-20434-1.
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Recommended:
Larson, Loren C. Metódy riešenia matematických problémov. 1. vyd. Bratislava : Alfa, 1990. ISBN 80-05-00627-6.
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Recommended:
Herman, Jiří; Kučera, Radan; Šimša, Jaromír. Metody řešení matematických úloh I. 2. vyd. Brno : Masarykova univerzita, 1996. ISBN 80-210-1202-1.
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Recommended:
Herman, Jiří; Kučera, Radan; Šimša, Jaromír. Metody řešení matematických úloh. II. 2. vyd. Brno : Masarykova univerzita, Přírodovědecká fakulta, 1997. ISBN 80-210-1630-2.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for formative assessments (2-20)
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26
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Contact hours
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26
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Total
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52
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
master mathematical language and procedures at the level of the bachelor's study field Mathematical Studies |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
master mathematical language and procedures at the level of the bachelor's study field Mathematical Studies |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
distinguish basic types of proofs and explain their principles |
distinguish basic types of sequences and ways of their expression |
describe the way of transition from one expression of a sequence and a sum series to another |
Skills - skills resulting from the course: |
make a proof of simple mathematical statements |
make a proof of statements containing an existential quantifier (eg using the principle of continuity, Dirichlet's principle) |
make a proof by mathematical induction |
write the given final, resp. infinite sequence and sum series analytically and recursively |
Competences - competences resulting from the course: |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Test |
Self-evaluation |
Continuous assessment |
Skills - skills achieved by taking this course are verified by the following means: |
Skills demonstration during practicum |
Individual presentation at a seminar |
Competences - competence achieved by taking this course are verified by the following means: |
Test |
Self-evaluation |
Continuous assessment |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Seminar |
Collaborative instruction |
Group discussion |
One-to-One tutorial |
Discussion |
Seminar classes |
Task-based study method |
Skills - the following training methods are used to achieve the required skills: |
Seminar |
Collaborative instruction |
Skills demonstration |
Group discussion |
Task-based study method |
Self-study of literature |
One-to-One tutorial |
Seminar classes |
Competences - the following training methods are used to achieve the required competences: |
Lecture with visual aids |
Practicum |
Individual study |
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