Lecture notes | Czech | English |
---|---|---|
Algebra 1 | alg1_cz | alg1_en |
Algebra 2 | alg1_cz | alg2_en |
Date | Topics | Lecture notes | Homework |
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13/02 | Group homomorphisms and isomorphisms, invariants, classifications Ex: Examples | Section 1 | |
20/02 | Normal subgroups, quotient groups, homomophism theorem, 1st isomorphism theorem | Section 2 | |
27/02 | Ideals and divisibility, PIDs, ideals in fields Ex: quotient groups, intersection and sum of ideals | Section 3 | |
06/03 | Quotient rings, homomorphism theorem, 1st and 2nd isomorphism theorem for rings | Section 4.1,4.2 | |
13/03 | prime and maximal ideals; Ring and field extensions, degree Ex:quotient rings, ring and field extensions | Sections 4.3, 5 | 1st HW due 27.3 |
20/03 | Algebraic and transcendental numbers Minimal polynomials of algebraic numbers | Section 6 | |
27/03 | Extensions by more than one element, constructability, ruler-and-circle constructions Ex: minimal polynomials and algebraic numbers | Section 6.3, 7 | |
03/04 | Uniqueness of splitting fields (up to isomorphism), Classification of finite fields | Sections 8, 9 | |
Easter Monday | |||
17/04 | Modular representations of rings, Fast Fourier Transformation | Section 10 | |
24/04 | Fast polynomial multiplication and division, formal power series Ex: general field extensions and their degree | Section 11 | |
International Workers' Day | |||
V-Day | 2nd HW due 24.5 |
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15/05 | Square-free factorizations of polynomials Berlekamp's algorithm for decomposition into irreducibles | Section 12 | |
22/05 | Berlekamp's algorithm; algebraic structures, substructures, homomorphisms Ex: ordered sets, lattices and Boolean algebras | Sections 12, 13 |