Mathematics 250A
Algebra

Fall, 2015
TuTh 2:10-3:30PM
247 Cory

Group theory, including the Jordan-Hölder theorem and the Sylow theorems. Basic theory of rings and their ideals. Unique factorization domains and principal ideal domains. Modules. Chain conditions. Fields, including fundamental theorem of Galois theory, theory of finite fields, and transcendence degree.
Professor Kenneth A. Ribet
email:
Telephone: 510 642 0648
Fax: (510) 642-8204
Office hours (885 Evans Hall)
Ribet lecturing last
semester

Graduate Student Instructor

George Melvin will be the GSI for this course. See his math 250A page for contact information and resources relevant to this course.

Textbook

cover of Lang book decorated forward page to Ribet's old copy of the book
Algebra by Serge Lang

Homework

Homework will be due on Thursdays, with the first assignment due on September 3 and the last on December 10 (RRR week). There will be perturbations because of the midterms and because of Thanksgiving.
  1. Assignment due September 3: Lang, Chapter I, exercises 4. 7, 9, 15-19
  2. Assignment due on September 10: Lang, Chapter I, exercises 23, 24, 25, 26, 27
  3. Assignment due on September 17: Lang, Chapter I, exercises 28, 29, 32, 33, 39, 40, 44, 45
  4. Assignment due on September 25
  5. Assignment due on October 1: Lang, Chapter II, exercises 9 (ask for a hint), 10, 12, 1, 2
  6. Assignment due on October 8: Lang, Chapter II exercises 3-6 and Chapter III exercises 3-6. (Solution to problem 4a by George Melvin.)
  7. Assignment due on October 15: Lang, Chapter II, exercises 13-19
  8. Assignment due on October 27:
  9. Assignment due November 5: Lang, Chapter IV, exercises 5ac, 7, 8, 9, 10
  10. Assignment due November 12: Lang, Chapter IV, exercise 18 and Chapter V, exercises 1-7
  11. Assignment due November 19: Lang, Chapter V, exercises 8-13
  12. Assignment due December 2 at 4PM: Lang, Chapter V, exercises 14-19
  13. Assignment due December 10 (RRR week): Lang, Chapter VI, exercises 1 (a, b, c, d, e, i, k), 4, 7, 9

Examinations

Please do not plan travel on the dates of these exams. If you believe that you have a conflicting obligation because of an intercollegiate sport or other extracurricular activity, please read these guidelines immediately.

Grading

I compute letter grades by calculating a "composite grade" for each student after the final exam papers have been graded. The composite grade will attempt to reflect the following weights: Homework 35%, midterm exams 15% each, final exam 35%.

Class schedule

This table will record themes that we touched on during each class meeting and project ahead to future class meetings. For a view of this class as taught by Elena Fuchs, see the 2012 class schedule.

DateThemes Sections
Aug. 27
Intro to the course
Group actions
§§ 1.1-1.5
Sept. 1
Group actions
Sylow's theorems
§§ 1.5-1.6
Sept. 3 Sylow's theorems § 1.6
Sept. 8
More about Sylow
Jordan-Hölder
§ 1.3
Sept. 10
Jordan-Hölder
Abelian groups
§1.3, §§1.7-1.8
Sept. 15 Finitely gen. ab. groups § 1.8
Sept. 17 Elementary divisors §§ 3.4, 3.7
Sept. 22 Rings §§ 2.1-2.2, A.2
Sept. 24 First Midterm Exam
Sept. 29 Commutative rings §§ 2.2-2.4
Oct. 1 UFDs, PIDs §§ 2.5, 3.1
Oct. 6 Modules §§ 3.1-3.4
Oct. 8 Projective modules, categories,... §§ 1.11, 3.4
Oct. 13 Representable functors, tensor products §§ 16.1-16.3
Oct. 15 Representable functors, tensor products §§ 16.1-16.3
Oct. 20 Mostly flat modules §§ 16.1-16.3
Oct. 22 Flat modules and polynomials §§ 16.1-16.3, 4.1
Oct. 27 Polynomials §§ 4.1-4.3
Oct. 29 Second Midterm Exam
Nov. 3 Yet more on polynomials §§ 4.1-4.4
Nov. 5 Polynomials, field extensions §§ 4.3, 4.4, 5.1
Nov. 10 Algebraic extensions, algebraic closure § 5.2
Nov. 12 Algebraic extensions §§ 5.1-5.2
Nov. 17 Normal extensions, separable degree §§ 5.3-1.4
Nov. 19 Finite fields § 5.5
Nov. 24 Primitive element theorem, Galois stuff §§ 5.4, 6.1
Dec. 1 Galois theory, fundamental theorem of algebra §§ 6.1-6.2
Dec. 3 Galois theory: examples and applications §§ 6.2-6.3
Dec. 8 Review
Dec. 10 Questions
Dec. 15 Final Exam, 8AM-11AM

Practice and old exams

Random Links

Last Updated:

Valid HTML 4.01!