# Introduction to Algebra II (MATH 30b, Spring 2013)

 Day & Time: Tuesday and Friday 12:10 — 1:25pm Location: Goldsmith 226 Instructor: Joel Bellaiche Office Hours: Tuesday 2:30pm-4:30pm and by appointment Teaching assistant: John Bergdall Textbook: John B. Fraleigh First Course in Abstract Algebra seventh edition, Adison-Wesley , 2003. ISBN 0201763907. Prerequisites: Introduction to Algebra I or the equivalent. Examinations: There will be one in class midterm and one final exam.

Assessment: The course grades will be computed as follows:
25% Homework
25% Midterm
50% Final exam

Tests and Exams: There are no makeups for missed tests. You must take the final examination at the time scheduled by the university; no final exams will be given earlier.

Homework: There will be two kinds of homework:

• Exercises give you a chance to practice and check that you have understood the material. They will not be collected.
• Graded homework: There will be six graded homework, about one every other weeks, at dates to be annouced in class and on this web page. The lower grade will be dropped. Each of the other five is worth 5% of the final garde.

Help: Help is available if you have trouble with homework or lecture material. My office hours are a good place to start. Discussions with your classmates can also be very helpful and are strongly encouraged.

## Schedule of Lectures

 Class Topic Read Suggested Exercises Due Jan 15 Introduction. Group acting on a set. §16 Jan 18 Group acting on a set. §16 16:4,5,6,7,8,11,13,16 Jan 22 Group acting on a set §16 Jan 25 Isomorphism Theorems §34 34:1,2,7,8,9 Jan 29 Series of groups §35 35: 1,5,7 Feb 1 Series of groups §35 35:15,16,17,23 Problems set 1 Feb 5 Series of Groups. Solvable and nilpotent groups. §35,36 Feb 8 No class because of Snow storm Feb 12 Sylow's theorems §36 36:1,2,7,8,9,10,11,17,20 Feb 15 Applications of Sylow's theorems §37 37:3,4,5,6,7 Problems set 2 Feb 26 Free abelian groups and finitely generated abelian group §38 38:2,3,11,16 Match 1 Free Group §39 39:1,2,3,4,5,6 March 5 Group Presentations. Review of rings. § 40. § 18,19,26,27 Match 8 The field of quotients of an integral domain § 21 Problems set 3 Solutions to exercise 4 March 12 Ring of Polynomials § 22 March 15 Factorization of Polynomials § 22 March 19 Factorization of Polynomials, Fraction ringd/td> § 22,23 March 22 Midterm April 5 Geometric Construction § 32 Problems set 4 April 9 Finite fields § 33 April 12 Automorphisms of fields § 48 April 16 The isomorphism extension theorem § 49 April 19 Splitting fields § 50 April 23 Separable extensions § 51 Problems set 5 April 26 Galois Theory § 53 April 30 Galois Theory § 54,55,56 May 3 Galois Theory § 54,55,56 Problems set 6