Department of Mathematics

SUNY at Stony Brook

**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.

**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.

**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.

**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.

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

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

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

**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)

Final: Thursday, December 19, 11:00-1:30 pm

*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.