Lectures: Mon.-Wed.-Fri. 9:00AM-10:00AM (Berkeley Time) at Etcheverry 3111
Professor: Semeon Artamonov
Textbook: John B. Fraleigh, A First Course in Abstract Algebra, 7th edition
Office Hours: Mon.-Wed.-Fri. 11:30AM-12:30PM (or by Appointment) at 1055 Evans Hall
GSI: To be assigned in September
Wed, Aug. 28 | Sets and Equivalence relations | §0 |
Fri, Aug. 30 | Motivation for Abstract Algebra | §1 |
Mon, Sep. 2 | No Class, Holiday | |
Wed, Sep. 4 | Binary Operations | §2 |
Fri, Sep. 6 | Isomorphism between Binary Structures | §3 |
Mon, Sep. 9 | Groups | §4 |
Wed, Sep. 11 | Subgroups | §5 |
Fri, Sep. 13 | Cyclic Groups | §6 |
Mon, Sep. 16 | Generating sets and Cayley diagrams | §7 |
Wed, Sep. 18 | Groups of Permutations | §8 |
Fri, Sep. 20 | Cayley Theorem, Orbits, and Cycles | §8-§9 |
Mon, Sep. 23 | Even and odd permutations, Alternating Group | §9 |
Wed, Sep. 25 | Cosets and Lagrange Theorem | §10 |
Fri, Sep. 27 | Direct Product | §11 |
Mon, Sep. 30 | Finitely generated Abelian Groups | §11 |
Wed, Oct. 2 | Group of plane isometries | §12 |
Fri, Oct. 4 | Midterm I | |
Mon, Oct. 7 | Group Homomorphisms | §13 |
Wed, Oct. 9 | Class cancelled due to power outage | |
Fri, Oct. 11 | Class cancelled due to power outage | |
Mon, Oct. 14 | First Isomorphism Theorem and Factor Groups | §14 |
Wed, Oct. 16 | The Fundamental Homomorphism Theorem | §14 |
Fri, Oct. 18 | Simple Groups, Center, and Commutator Subgroups | §15 |
Mon, Oct. 21 | Group Actions | §16 |
Wed, Oct. 23 | Rings and Basic Properties | §18 |
Fri, Oct. 25 | Ring Homomorphisms and Isomorphisms | §18 |
Mon, Oct. 28 | Class cancelled due to power outage | |
Wed, Oct. 30 | Multiplicative Questions and Integral Domains | §18-§19 |
Fri, Nov. 1 | Fermat and Euler Theorems | §20 |
Mon, Nov. 4 | The Field of Fractions of an Integral Domain (construction) | §21 |
Wed, Nov. 6 | The Field of Fractions of an Integral Domain (uniqueness) | §21 |
Fri, Nov. 8 | Ring of Polynomials | §22 |
Mon, Nov. 11 | No Class, Holiday | |
Wed, Nov. 13 | Evaluation Homomorphism and Division Algorithm | §22 |
Fri, Nov. 15 | Unique Factorization Domains and Irreducible Polynomials | §23 |
Mon, Nov. 18 | Midterm II | |
Wed, Nov. 20 | Ring Homomorphisms and Factor Rings | §26 |
Fri, Nov. 22 | Fundamental Homomorphism Theorem | §26 |
Mon, Nov. 25 | Prime and Maximal Ideals | §27 |
Wed, Nov. 27 | No Class, Holiday | |
Fri, Nov. 29 | No Class, Holiday | |
Mon, Dec. 2 | Principal Ideals, Ideal structure in polynomials over a field | §27 |
Wed, Dec. 4 | Algebraic Varieties and Ideals | §28 |
Fri, Dec. 6 | Groebner Bases | §28 |