MAT 313: Abstract Algebra

Fall 2002

Department of Mathematics SUNY at Stony Brook

Textbook: Comtemporary Abstract Algebra , 4th edition, by Joseph A. Gallian, Houghton Miflin Company, 1998, or its 5th edition. An excellent book for further reading is Algebra  by Michael Artin, Prentice Hall, 1991.

Schedule: TuTH 11:20 - 12:40 pm, ESS 181

Instructor: Leon  Takhtajan, Math Tower 5-111, Phone: 632-8287,
email: leontak@math.sunysb.edu, office hours: Tu-W, 3:00-4:00 pm.

]Grader: Luis Lopez, Math. Tower 2-122
e-mail: llopez@math.sunysb.edu

Topics covered: Ring of integers - properties of integers, mathematical induction, modular arithmetics. Group theory - groups, subgroups, homomorphisms and isomorphisms, the kernel and normal subgroups, the image and factor groups, abelian and cyclic groups, permutation groups, cosets and the Lagrange coset theorem. Ring theory - rings and subrings, the unit group of a ring, homomorphisms and isomorphisms, ideals, integral domains, polynomial rings, factorization. Field theory - fields, subfields and field extensions.

Prerequisites: MAT 310, MAT 318, MAT 312 or permission of the instructor. If you have difficulties following the first few lectures, please contact the instructor for advice and possible transfer to another class.

Howework: Homework will be assigned each week and collected in class next week.

HW1: Chapter 0, problems 2,4,7,8,13,14,16,18,19,26,28,39,40,46-48.

HW1 Solution ( pdf/ps)

HW2 (due 10/3): Chapter 1, problems 5-10 (Hint: use that rotation fixes only the center of rotation and reflection fixes the axis); Chapter 2, problems 3-5,14 (Hint: use the identity a(ba)=(ab)a), 15,17,19-20,25-26, 32,34.

HW2 Solution ( pdf/ps)

HW 3 (due 10/15): Chapter 3, problems 4-8,12,14,23,29,32,44,46,50 (Hint: use the gcd),51; Practice problems (solve and compare the answers with the book): 1,17,31,33,45,47.

HW3 Solution ( pdf/ps)

HW 4 (due 10/24): Chapter 4, problems 15,21,23,24,31,40,53,61; Practice problems (not for credit): 1,3,5,9,17,19,45.

HW4 Solution ( pdf/ps)

HW5 (due 11/14): Chapter 5, problems 3,5,7,11,15,31; Chapter 6, 1,5,22,31.

HW5 Solution ( pdf/ps)

HW6 (due 11/21): Chapter 7, problems 1,7,15,17,19,25,31,42,45)

HW6 Solution ( pdf/ps)

HW7 (due 12/05): Chapter 9, problems 1,8,11,25,37; Chapter 10, problems 5,7,19,20,29,35.

HW7 Solution ( pdf/ps)

HW8 (due 12./12): Chapter 12, problem 10; Chapter 13, problems 5,9,19; Chapter 16, problems 1,3,11,15; Chapter 20, problems 1,3,4,17.

Material covered: Chapters 0-5, Chapter 6 (no inner automorphisms), Chapter 7, Chapter 9 (no internal direct products), Chapters 10 and 12; Chapter 13, pages 240-244, Chapter 15, pages 276-277, Chapter 16 pages 283-289, Chapter 20, pages 344-349.

Exams:

• Midterm I: Thursday, October 31, 11:20-12:40 pm in class (note the change of the date!) Covers material in Chapters 0-5. Midterm Solution ( pdf/ ps)
• Midterm II (take home exam). Due Tuesday, December 3; based on material in Chapters 0-5. Exam ( pdf/ps)

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• Final:       Thursday, December 19, 11:00-1:30 pm
• Grading: Grades will be assigned on the following basis: Homework 30%, Midterm (maximum of the two exams) 30%, Final Exam 40%.

DSS advisory. If you have a physical, psychiatric, medical, or learning disability that may affect your ability to carry out the assigned course work, please contact the office of Disabled Student Services (DSS), Humanities Building, room 133, telephone 632-6748/TDD. DSS will review your concerns and determine what accommodations may be necessary and appropriate. All information and documentation of disability is confidential.