bCourses Site

Piazza site

GSI: Benjamin Castle, 961 Evans, Mon 1–3, Tue 2–5, Wed 12–2, Thu 12–3

DSP students should speak to the instructor as soon as possible, even if you don't have a letter yet.

Guidelines on what to do if you think you may have a conflict between this class and your extracurricular activities. In particular, you must speak to the instructor before the end of the second week of classes.

Academic honesty in mathematics courses: A statement on cheating and plagiarism, courtesy of Michael Hutchings.

How to get an A in this class, courtesy of Kathryn Mann.

January 21:Introduction to group theory Reading: Know material in Section 2.7 of Artin, Chapter 1 of Judson Reading (today's material): Artin Sections 2.1–2.2, Fraleigh, pages 41–42January 23:Examples of groups, subgroups Reading: Artin Sections 1.5, 2.2–2.3, 2.9, Judson Section 5.1January 28:primes in ℤ, cyclic (sub)groups Reading: Artin Sections 2.3–2.4 * Homework 1 (due on Tuesday, February 4): click hereJanuary 30:homomorphisms and isomorphisms, cosets Reading: Artin Sections 2.5–2.6 and 2.8February 4:cosets, normal subgroups, quotient groups Reading: Artin Sections 2.8, 2.12 * Homework 2 (due on Tuesday, February 11): click hereFebruary 6:first isomorphism theorem, (semi)direct products Reading: Artin Sections 2.11–2.12 Reading: Dummit and Foote, pages 175–180 on semidirect productFebruary 11:group extensions, dihedral groups, group actions Reading: Wikipedia page on group extensions Reading: Artin Sections 6.4 (dihedral groups), 6.7 * Homework 3 (due on Tuesday, February 18): click hereFebruary 13:group actions Reading: Artin Sections 6.7–6.11, 7.1February 18:class equation,p–groups Reading: Artin Sections 7.2–7.3, 7.5 * Homework 4 (due on Tuesday, February 25): click hereFebruary 20:Sylow theorems Reading: Artin Sections 7.6–7.7February 25:solvable and simple groups Reading: Artin Section 7.4 Reading: Dummit and Foote, pages 105, 194–196 on solvable groups Reading: Proof that A_{n}is simple for n≥5 Recommended (but optional) reading: Artin Sections 7.9–7.10 on group presentationsFebruary 27:rings Reading: Artin Sections 11.1–11.2March 3:homomorphisms, ideals Reading: Artin Sections 11.3 * Homework 5 (due on Thursday, March 12): click hereMarch 5:Midterm (in class) Material: everything up to the end of Feb 25 class, all homework questions but not: semigroups; monoids; things covered in the textbook that we didn't talk about in class Closed book (ie. no notes, textbook, or any other material allowed) Practice problems on material not covered by the homework: Artin Section 7: 4.7, 4.8, 4.9, 5.2, 5.12, 7.3, 7.4, 7.9, 8.4, 8.5 Prove that every p–group is solvable; that a p–group has a normal subgroup of every possible index; that if |G| = p^{e}m, then G has a subgroup of order p^{i}for each i = 1, ..., e I will not ask you to reprove anything we did in class, but you should understand the techniques that go into the proofs, and how to use them You might need to give definitions of terms from classMarch 10:no class!March 12:quotient rings, product rings Video: on bCourses; 5:10 quotient rings, 23:10 example 1, 26:30 example 2, 43:30 example 3, 1:03:20 product rings, 1:06:50 some category theory (optional), 1:20:40 final questions Reading: Artin Sections 11.4, 11.6March 17:product rings, idempotents, adjoining elements, fractions, primes and irreducibles Video: on bCourses Reading: Artin Sections 11.6–11.7, 12.2 * Homework 6 (due on Tuesday, March 31): click hereMarch 19:primes and irreducibles, Euclidean domains, principal ideal domains, unique factorisation domains Video: on bCourses Reading: Artin Section 12.2March 31:unique factorisation domains,Z[x] is a UFD, factoring inZ[x] Video: on bCourses Reading: Artin Sections 12.2, 12.4 * Homework 7 (due on Tuesday, April 7): click hereApril 2:fields, algebraic/transcendetal elements, degree of extensions, splitting fields Reading: Artin Sections 15.1–15.4, 15.6April 7:finite fields, more on splitting fields, Galois theory introduction Reading: Artin Sections 15.7, 16.3–16.4 * Homework 8 (due on Tuesday, April 14): click hereApril 9:characteristic 0 fields and primitive elements, fixed fields, splitting fields = Galois extensions Reading: Artin Sections 15.8, 16.5–16.6April 14:fundamental theorem of Galois theory, solvability by radicals Reading: Artin Section 16.7, Judson Section 23.3 * Homework 9 (due on Tuesday, April 21): click hereApril 21:solvability by radicals (converse), symmetric functions, solving cubics/quartics Reading: Artin Sections 16.8–16.8, Stewart Sections 18.4–18.5, Lemma 10.1 * Homework 10 (due on Tuesday, April 28): click hereApril 28:straightedge and compass constructibility, regular n–gons Reading: Artin Section 15.5, Judson Section 21.3, and notes here

Back