Description:
Brief description of the course:
1. Language of mathematics and Set theory: Boolean algebra: logical operators, truth tables, logic laws. Set theory: sets, set operations. number sets
2. Functions: mappings between sets, injection, surjection, bijection, computability and big O notation.
3. Probability theory: Elementary counting principles, permutations, combinations, events and probabilities, random variables and distributions.
4. Number theory: Divisibility, GCD, Euclidean algorithm, Bezout identity, prime numbers, congruences, Euler φ- function,
Chinese Remainder Theorem
5. Group theory: Groups basic definitions and properties, types of groups (cyclic, dihedral, symmetric), subgroups, homomorphism, isomorphism, Lagrange theorem, quotient groups, product groups.
6. Ring theory: Rings basic definitions and properties, polynomial rings, ring homomorphism, ideals, quotient rings, fields
Learning outcomes:
After completing this course, the student:
- understands mathematical texts at undergraduate level;
- uses standard mathematical notation and terminology in academical writing;
- writew and evaluatew correct, clear and precise mathematical proofs in an applicable level of detail;
- recalls definitions and theorems in mathematical areas, which are covered in the course.
