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Lecturer(s)
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Honzík Lukáš, PhDr. Ph.D.
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Course content
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1. Basic types of proofs 2. Geometric proofs 3. Proofs by contradiction 4. Proofs of statements containing an existential quantifier 5. Unicity proofs 6. Dirichlet principle 7. Proofs by mathematical induction 8. Proofs of inequalities with natural numbers
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Learning activities and teaching methods
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Collaborative instruction, Discussion, One-to-One tutorial, Group discussion, Seminar classes, Seminar
- Contact hours
- 26 hours per semester
- Preparation for formative assessments (2-20)
- 26 hours per semester
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| prerequisite |
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| Knowledge |
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| master mathematical language and procedures at the level of the bachelor's study field Mathematics in Education |
| Skills |
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| master mathematical language and procedures at the level of the bachelor's study field Mathematics in Education |
| Competences |
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| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| distinguish basic types of proofs and explain their principles |
| Skills |
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| 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 |
| Competences |
|---|
| N/A |
| N/A |
| teaching methods |
|---|
| Knowledge |
|---|
| Seminar |
| Collaborative instruction |
| Group discussion |
| One-to-One tutorial |
| Discussion |
| Seminar classes |
| Task-based study method |
| Skills |
|---|
| Seminar |
| Collaborative instruction |
| Skills demonstration |
| Group discussion |
| Task-based study method |
| Self-study of literature |
| One-to-One tutorial |
| Seminar classes |
| Competences |
|---|
| Lecture with visual aids |
| Practicum |
| Individual study |
| assessment methods |
|---|
| Knowledge |
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| Test |
| Self-evaluation |
| Continuous assessment |
| Skills |
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| Skills demonstration during practicum |
| Individual presentation at a seminar |
| Competences |
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| Test |
| Self-evaluation |
| Continuous assessment |
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Recommended literature
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HERMAN, J., KUČERA, R., ŠIMŠA, J. Metody řešení matematických úloh I. Brno: Masarykova univerzita, 2011. ISBN 978-80-210-5636-7.
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HERMAN, J., KUČERA, R., ŠIMŠA, J. Metody řešení matematických úloh II. Brno: Masarykova univerzita, 2004. ISBN 80-210-3569-2.
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Odvárko, O. a kol. Metody řešení matematických úloh.. Praha : SPN, 1990. ISBN 80-04-20434-1.
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ODVÁRKO, O. Matematika pro střední školy. Praha: Prometheus, 2023. ISBN 978-80-7196-548-0.
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Polák, J. Středoškolská matematika v úlohách I.. Praha : Prometheus, 2006. ISBN 80-7196-337-2.
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Polster, Burkard. Q.E.D. : krása matematického důkazu. 1. vyd. v českém jazyce. Praha : Dokořán, 2014. ISBN 978-80-7363-532-9.
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