**Lectures**

MWF 12:00-12:50pm (MTH 0101)

**Instructor**

Professor Niranjan Ramachandran (atma at math dot umd dot edu)

Office: Math Building 4115 (405-5080)

Office hours: Wednesdays 1pm - 2pm, Fridays 2pm - 3pm.

**Class web page**

http://www.math.umd.edu/~atma/math403.html

**Text**

*Contemporary Abstract
Algebra* by Joseph A. Gallian (Sixth Edition).

** Description**

This is a first course in abstract
algebra. The topics are groups, rings, and fields. We will cover most
of the material in Parts 1-3 of the text. The course is both theoretical
and example oriented. It is necessary to learn to do rigorous proofs.
In fact this is perhaps the main point of the course. This course is a good
preparation for graduate studies in mathematics.

**Prerequisites**

Math 240 and Math 241, or equivalent.
Credit will be granted for only one of Math 402 or Math 403. Although the
only formal prerequisites are Math 240, 241, students will benefit from some
prior experience with mathematical proofs such as Math 310, Math 410, Math
405, or Math 406.

**Tests**

There will be two 1 hour tests (in class) with 100 points for each test.

No make-up tests will be given.

If you have to miss a test and you have a written excuse according to the University Policies, then you will be given 50% extra credit on the final.

The final exam will be a take-home due 12/14/05 and worth 100 points).

The problems for the take-home are from the textbook. Pages 90-93: 4,36

Pages 230-232: 14,16,24,28,30,32

Pages 275-277: 22, 30

Please see the webpage Final Exam
for the official schedule.

Please see the university regulations on academic
integrity.

**Homework**

Homework problems will be
assigned every week and they are due Mondays in class.

**Grader **Ninad Jog, ninad@umd.edu, Office hours
TBA

**Grading**

Two 1 hour exams |
200 points |

Final Exam |
200 points |

Homework |
100 points |

Total |
500 points |

**Test dates (tentative)**

Test 1: Monday, 3^{rd}
October.

Test 2: Monday, 7^{th}
November

Final exam: See above for information from Testudo

**Testbank (previous final
exams) **

Homework 1 (due 9/12/2005)

Chapter 0: 4,10,14,16,28,48.

Homework 2 (due 9/19/2005)

Chapter 2: 4,6,8,14,24,26,36. Chapter 3: 8,10,12

Homework 3 (due 9/26/2005)

From pages 82-86. they are #8,12,14,20,24,30,32,36,48,54.

Homework 4 (due 10/3/2005)

Chapter 5: #4,6,10,20,22,26,28,30,38,44.

Homework 5 (due 10/10/2005)

Chapter 6: #4,10,12,18,20,24,38,40.

Homework 6 (due 10/17/2005)

1. Let (S, *) be the group of all real numbers except -1 under the operation * defined by a*b = a + b + ab. (so 5*3 = 5 + 3 + 15) (Check for yourself that this is a group!). Show that (S, *) is isomorphic to the group (R*, x) of nonzero real numbers under multiplication. Actually, define an isomorphism f: R* ---> S.

Chapter 6: 30, 42, 43. Chapter 7: 2,8,10.

Homework 8 (due 11/21/2005)

Chapter 10: #16,22,24,34,36,54.

Chapter 11: #6,10,20,26,30.

Supplementary Exercises: #30 (page 232).

Homework 9 (due 12/5/05)

Chapter 24: #4,8,12,30,44.

Chapter 12: #2,4,6,12,26,48.

Last modified: 9 December 2005