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

Bibliography used during classes/laboratories/others

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

Bibliography to self-study

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
01	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
02	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

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
2	TK01	Elements of heuristics (induction, analogy, specialization, generalization, use of symmetry, use of appropriate markings, etc.)	C01-C15	MEK01
2	TK02	Mathematical induction	C03-C05	MEK02
2	TK03	Argument by contradiction	C06-C08	MEK02
2	TK04	The Pigeonhole Principle	C09-C11	MEK02
2	TK05	Other methods, eg. invariants searching, The Extremal Principle, coloring proofs	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	The final grade is the arithmetic mean of the homework and colloquium grades

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

The contents of the module are associated with the research profile: no