Discrete Mathematics
Description
This course includes fundamentals of discrete mathematics: set theory, mathematical induction, combinatorics, the cardinality of special sets, difference operator, generating function, recurrent equations, graph theory, mathematical logic.
Aim of the course
Course aim is to provide understanding of discrete mathematics.
Prerequisites
High school mathematics knowledge.
Course content
1. Set theory
2. Mathematical induction
3. Combinatorics
4. The cardinality of special sets
5. Difference operator
6. Generating functions
7. Theory of recurrence relations
8. Graph theory
9. Mathematical logic
Assesment Criteria
1. The learner demonstrates knowledge and a deep understanding of countable sets and operations with the sets. The student recognizes and applies them to solve practical and theoretical tasks.
2. The learner demonstrates the ability to construct and prove new identities by using the principle of mathematical induction.
3. The learner demonstrates the ability to identify the problem, analyze theoretical data by using the knowledge of combinatorial analysis, and the cardinality of special sets. The learner also knows the definition of binomial coefficients and can prove the identities.
4. The learner is operating with formal mathematical symbols and terms related to the operator of difference, demonstrates the ability to prove well-known theorems and lemmas of this theory.
5. The learner demonstrates knowledge and a deep understanding of concepts and propositions of degree and exponential generating functions. The learner recognizes and applies them to solve theoretical and practical tasks.
6. The learner demonstrates knowledge and a deep understanding of the theory of recurrence relations. The learner demonstrates the ability to solve recurrence relations.
7. The learner demonstrates the ability to think logically and analytically for the solution of practical tasks by using graph theory.
8. The learner demonstrates the ability to think logically, to construct, prove, and disprove statements. The learner operates with formal mathematical symbols and terms.
