Math-113 Introduction to Abstrac Algebra, Fall 2019 Section 3

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

Syllabus

GSI: To be assigned in September

Homework Assignments

Reading Assignments

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