bCourses Site

Piazza site

GSI: Kentarô Yamamoto (office hours details at the link)

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.

August 28: Sets, set operations, relations, functions, binary operations Reading: Section 2.7 of Artin, Chapter 1 of JudsonAugust 30: More on relations, equivalence relations, modular arithmetic, intro to groups Reading: Sections 2.7, 2.9 of Artin, Chapter 1 of Judson Reading: Section 2.1 of ArtinSeptember 2:No class! Labour day!September 4:Groups, examples of groups, subgroups Reading: Sections 2.1–2.2 of Artin * Homework 1 (due Wednesday, September 11): Artin Chapter 2, problems 1.1, 2.1, 2.3b, 2.4, 4.3, 4.5, 4.7, 4.9, 4.10September 6:Subgroups of (Z, +), cyclic subgroups Reading: Sections 2.3–2.4 of ArtinSeptember 9:Cyclic subgroups, homomorphisms Reading: Sections 2.4–2.5 of ArtinSeptember 11:Homomorphisms, isomorphisms Reading: Sections 2.5–2.6 of Artin * Homework 2 (due Wednesday, September 18; turn in only the starred questions): Artin Chapter 2, problems *5.1, 5.5, 6.1, *6.2, 6.3, 6.4, 6.7, *6.10a, 6.10b, *9.7September 13:Group of integers mod n, symmetric group Reading: Sections 1.5, 2.9 of Artin, Section 5.1 of JudsonSeptember 16:Cosets, normal subgroups Reading: Section 2.8 of ArtinSeptember 18:Quotient groups, First Isomorphism Theorem Reading: Section 2.12 of Artin * Homework 3 (due Wednesday, September 25; turn in only the starred questions): Artin Chapter 2, problems 8.1, *8.4, *8.6, 8.9, 9.4, 11.4ab, *11.4c, 11.8, 12.1, *12.4, 12.5September 20:Product groups Reading: Section 2.11 of ArtinSeptember 23:Symmetries, isometries Reading: Sections 6.1–6.2 of ArtinSeptember 25:Isometries of R^n, orthogonal groups Reading: Sections 6.2–6.3 of ArtinSeptember 27:Group actions Reading: Sections 6.7–6.8 of ArtinSeptember 30:Midterm 1 (in class) Closed book (ie. no notes, textbook, or any other material allowed) Material: Everything we covered in class up to and including September 23 Most of the material of Artin, Chapter 2 (except 2.10) and 6.1–6.2 (modulo the material we didn't cover in class) Preparation: past midterms are on bCourses Preparation: try Artin Chapter 2, problems 2.2, 2.6, 4.1, 4.2, 4.6, 5.4, 6.9, 7.1, 8.3, 8.5, 9.1, 11.5, 12.2, M.2, M.3, M.9, M.10, and Chapter 6 (last page of PDF), problems 4.2October 2:Orbit–Stabiliser theorem Reading: Sections 6.8–6.9 and 7.3 of Artin * Homework 4 (due Wednesday, October 9; turn in only the starred questions): Artin Chapter 6, problems *3.3, 3.6, 4.1, 7.1, *7.2, 7.3, *7.10 (b means the coefficients are integers mod 5), 8.2, *9.1October 5:Conjugation action; class equation Readng: Sections 7.2–7.3 of ArtinOctober 7:Group actions on subsets, permutation representations, Cayley's theorem Reading: Sections 6.10–6.11 and 7.1 of ArtinOctober 9:No class; campus closedOctober 11:No class; campus closedOctober 14:Group presentations Reading: Sections 7.9–7.10 of ArtinOctober 16:Rings Reading: Sections 11.1–11.2 of Artin * Homework 5 (due Wednesday, October 23; turn in only the starred questions): Artin Chapter 6 (page 1 of PDF): 11.1, *11.3, 11.6 (F_{3}= Z_{3}); Chapter 7 (page 2–3 of PDF): 2.3, *2.7, 2.8, *2.14, *3.3, 3.4October 18:Polynomial rings, ring homomorphisms Reading: Sections 11.2–11.3 of ArtinOctober 21:Ring homomorphisms, ideals Reading: Section 11.3 of ArtinOctober 23:Ideals, quotient rings Reading: Sections 11.3–11.4 of Artin * Homework 6 (due Wednesday, October 30; turn in only the starred questions): Artin, Chapter 11, problems *1.3, 1.6, 1.7, 2.1, 3.2, *3.3, 3.9a, *3.12, 4.3, *4.4October 25:Quotient rings Reading: Section 11.4 of ArtinOctober 28:No class; campus closedOctober 30:Quotient rings, product rings Reading: Sections 11.4, 11.6 of Artin * Homework 7 (due Wednesday, November 6; turn in only the starred questions): Artin, Chapter 11, problems *5.1, 5.2, *5.3, 5.4, 5.7, 6.1, *6.2 (justZ/(8)), 6.5, *7.1, 7.2November 1:Adjoining elements, fractions Reading: Sections 11.5, 11.7 of ArtinNovember 4:Primes and irreducibles Reading: Sections 12.1–12.2 of ArtinNoveber 6:Euclidean domains, principal ideal domains Reading: Section 12.2 of ArtinNovember 8:Unique factorisation domains Reading: Section 12.2 of ArtinNovember 13:PID vs ED, UFD vs PID Reading: Section 12.3 of Artin * Homework 8 (due Wednesday, November 20; turn in only the starred questions: Artin, Chapter 12, problems *2.1, 2.2, *2.4, *2.6b, 2.7, *3.2, 3.6, 4.4November 15:Midterm 2 (in class) Closed book (ie. no notes, textbook, or any other material allowed) Material: Artin sections 6.7–6.9, 6.11, 7.1–7.3, 11.1–11.7 (not 11.4.2a nor 11.4.3 nor the termfaithful), 12.2 (up to the end of page 360) Preparation: past midterms/questions are on bCourses Preparation: try Artin Chapter 6: 7.6, 7.7, 8.1, 9.4, 11.2; Chapter 7: 1.1, 2.2, 2.9bcd, 2.13, 2.17; Chapter 11: 1.8, 1.9, 3.1, 3.6, 3.11, 3.13, 4.3, 5.5, 5.6, 6.4, 7.3; Chapter 12: 2.1, 2.2, 2.4November 18:Z[x] is a UFD Reading: Section 12.3 of ArtinNovember 20:Factoring integer polynomials Reading: Section 12.4 of ArtinNovember 22:Fields, algebraic/transcendental elements Reading: Section 15.1–15.2 of ArtinNovember 25:Field extensions by algebraic elements Reading: Section 15.2 of Artin * Homework 9 (due Wednesday, December 4; turn in only the starred questions: Artin, Chapter 15, problems *1.1, 2.1, *2.2, *3.6, 3.9, *3.10December 2:Degree of a field extension Reading: Section 15.3 of ArtinDecember 4:Compass and straightedge constructibility Reading: Section 15.5 of ArtinDecember 6:Compass and straightedge constructibility Reading: Section 15.5 of ArtinDecember 16:Final exam (in our classroom) Closed book (ie. no notes, textbook, or any other material allowed) Sections covered: 2.1–2.9, 2.11–2.12, 6.4 (dihedral group), 6.7–6.9, 6.11, 7.1–7.3, 11.1–11.7, 12.1–12.4, 15.1–15.3, 15.5 Whatever material in those sections that wedidn'tcover in class isnottestable! Additional helpful sections: 1.5 (permutations), 3.2–3.4 (helpful for vector spaces, bases), 11.8 (maximal ideals), 15.4 (finding minimal polynomials) Additional practice questions from Chapter 1: 5.1 Additional practice questions from Chapter 3: 2.8a, 2.11, 4.3, 4.8, M.5 Additional practice questions from Chapter 11: 8.1, 8.3 Additional practice questions from Chapter 12: 4.1, 4.2, 4.5, 4.12, M.7 Additional practice questions from Chapter 15: 3.1, 4.2b, 5.2a, M.1, M.4d (multiplicative groupF\{0}of a fieldF)

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