|
Lecturer(s)
|
-
Dofková Radka, doc. PhDr. Ph.D.
-
Zdráhal Tomáš, doc. RNDr. CSc.
|
|
Course content
|
1. **Introduction** - Construction of sets - Universe of sets - Importance of set theory for mathematics 2. **Class Theory** - Language of class theory - Equality of classes - Representation of formulas by classes - Other operations on classes - Relations and orderings - Mappings - Equivalence and subvalence of classes 3. **Set Theory** - Basic axioms for sets - Equivalence and isomorphism of sets - Finite sets - Theory of finite sets - Well-ordered sets 4. **Additional Axioms of Set Theory** - Axiom of choice - Zermelo's theorem - Continuum hypothesis
|
|
Learning activities and teaching methods
|
Lecture
- Homework for Teaching
- 50 hours per semester
|
|
Learning outcomes
|
The goal of the course "Introduction to Set Theory" is for students to understand the basic concepts of set construction, the universe of sets, and the importance of set theory for mathematics. They will learn the language of class theory, class equality, the representation of formulas by classes, and other operations on classes, including relations, orderings, and mappings. Students will gain knowledge of the basic axioms for sets, the equivalence and isomorphism of sets, the theory of finite and well-ordered sets. Additionally, they will become familiar with the axiom of choice, Zermelo's theorem, and the continuum hypothesis. From this course, students will take away fundamental knowledge of the construction and properties of sets and classes, the ability to apply set and class theory to various mathematical problems, skills in analyzing and solving problems using axiomatic systems, and an understanding of advanced concepts in set theory that are foundational for further studies in mathematics.
Understanding of the set-theoretical concepts of mathematics.
|
|
Prerequisites
|
For the course "Introduction to Set Theory," students should have a solid foundation in the following areas of mathematics: 1. **Basic Mathematical Logic**: Understanding logical operations, quantifiers, and fundamental principles of proofs. 2. **Algebra**: Knowledge of basic algebraic structures such as groups, rings, and fields. 3. **Number Theory**: Basic concepts and operations with natural, integer, and rational numbers. 4. **Analytic Geometry**: Basic knowledge of planes, lines, and curves. 5. **Mathematical Analysis**: Fundamental concepts of limits, derivatives, and integrals. These prerequisites will ensure that students have the necessary skills and knowledge to successfully grasp set and class theory.
|
|
Assessment methods and criteria
|
Student performance, Dialog
Active knowledge of the subject matter. Specific requirements (including individual assignments for term papers) are provided in the relevant team on MS Teams. Regarding active physical attendance, students in both full-time and part-time programs are required to attend at least 49% of classes, while students studying under an Individual Study Plan (ISP) must attend at least 20%. (The exact requirements for ISP students need to be discussed with the instructor in person at the beginning of the semester.)
|
|
Recommended literature
|
-
BLAŽEK J., VOJTÁŠKOVÁ B. (1994). Teorie množin. Ústí nad Labem.
-
KOPECKÝ, M. (1996). Úvod do teorie množin. Lomouc.
|