Methods of Solving Mathematical Problems
Some basic information about the module
The aim of studying and bibliography
The main aim of study:
Familiarize students with the most important problem-solving techniques typically encountered in undergraduate mathematics
The general information about the module:
The module is implemented in the second semester (30 hours of tutorials)
Bibliography required to complete the module
| 1 | G. Polya | Jak to rozwiązać? | PWN, Warszawa. | 1993 |
| 2 | L. C. Larson | Problem-Solving Through Problems | Springer-Verlag, New York-Berlin-Heydelberg-Tokyo. | 1983 |
| 1 | G. Polya | Odkrycie matematyczne | WN-T, Warszawa. | 1975 |
| 2 | R. Gelca, T. Andreescu | Putnam and Beyond | Springer Science + Business Media, New York. | 2007 |
Basic requirements in category knowledge/skills/social competences
Formal requirements:
The student satisfies the formal requirements set out in the study regulations
Basic requirements in category knowledge:
Good knowledge of the concepts defined by the high school math program
Basic requirements in category skills:
Mastering the skills defined by the high school math program
Basic requirements in category social competences:
Willingness to continue to acquire mathematical knowledge. Ability to work in a group
Module outcomes
| MEK | The student who completed the module | Types of classes / teaching methods leading to achieving a given outcome of teaching | Methods of verifying every mentioned outcome of teaching | Relationships with KEK | Relationships with PRK |
|---|---|---|---|---|---|
| MEK01 | can use heuristic methods (such as: induction, analogy, specialization, generalization, use of symmetry, use of appropriate markings, etc.) in discovering patterns leading to solving mathematical problems | classes | assessment of homework, written test |
K-W04+ K-U06+ K-U08++ K-U36+ K-K03+ |
P6S-KO P6S-KR P6S-UK P6S-UO P6S-UU P6S-UW P6S-WG P6S-WK |
| MEK02 | can, in typical situations, carry out proof that a given thesis is true (or false), using mathematical induction, the pigeonhole principle and argument by contradiction, among others | classes | assessment of homework, written test |
K-W02+++ K-W05+ K-U03++ K-U04+ K-K01+ K-K06+ |
P6S-KK P6S-UK P6S-UW P6S-WG P6S-WK |
The syllabus of the module
| Sem. | TK | The content | realized in | MEK |
|---|---|---|---|---|
| 2 | TK01 | C01-C15 | MEK01 | |
| 2 | TK02 | C03-C05 | MEK02 | |
| 2 | TK03 | C06-C08 | MEK02 | |
| 2 | TK04 | C09-C11 | MEK02 | |
| 2 | TK05 | C12-C15 | MEK02 |
The student's effort
| The type of classes | The work before classes | The participation in classes | The work after classes |
|---|---|---|---|
| Class (sem. 2) | The preparation for a Class:
15.00 hours/sem. |
contact hours:
30.00 hours/sem. |
Finishing/Studying tasks:
5.00 hours/sem. |
| Advice (sem. 2) | The participation in Advice:
1.00 hours/sem. |
||
| Credit (sem. 2) | The preparation for a Credit:
7.00 hours/sem. |
The written credit:
2.00 hours/sem. |
The way of giving the component module grades and the final grade
| The type of classes | The way of giving the final grade |
|---|---|
| Class | The final grade is the arithmetic mean of the homework and colloquium grades |
| The final grade |
Sample problems
Required during the exam/when receiving the credit
(-)
Realized during classes/laboratories/projects
(-)
Others
(-)
Can a student use any teaching aids during the exam/when receiving the credit : no