Introduction to mathematics 3103-N1111-1
1. Elements of set algebra as the language, in which concepts/ notions and operations on them are formalized. 2. Relations, their taxonomy and properties. 3. Graphs and their properties along with basic applications, especially in visualisation of relations. 4. Functions and their types and operations on them. 5. Algebraic structures: semigroups, groups with applications to analysis of language, rings and fields as well as lattices and Boolean algebras. 6. Elements of propositional and predicate logic as the basis for reasoning about mathematical objects.
Consecutive lectures are devoted to:
1. Intuitions about sets and their representations;
2. Set operations;
3. Cartesian products;
4. Relations;
5. Relation properties;
6. Equivalence, tolerance;
7. Orderings;
8. Graphs, trees;
9. Functions;
10. Equipotency, finite and countable sets;
11. Algebraic structures: semigroups, groups, rings, fields;
12. Lattices, Boolean algebras;
13. Models of language: semigroups of words over an alphabet.
Type of course
Learning outcomes
On termination of the course, the student should be able tounderstand and discern among basic structures qamd learn to:
1. give correct formal definitions of learned notions
2. read formal definitions of learned notions;
3. give examples of specific learned structures and of their applications;
4. solve basic simple problems related to the learned notions.
Assessment criteria
The student is graded on the basis of tests in which they should show a knowledge of problems from an earlier given list.