Algebra – Mathematics 1530 (CRN: 15050)
Brown University – Fall, 2013
Professor Joe Silverman

Text Algebra (Pure and Applied Undergraduate Texts),
Mark R. Sepanski
American Mathematical Society (September 22, 2010) ISBN-13: 978-0821852941
Click here for an errata list.
Office Mathematics Department, Kassar House, Room 202
Phone 863-1124
Email jhs@math.brown.edu
Web Site www.math.brown.edu/~jhs/MA0153/MA0153HomePage.html
Office Hours Monday 2:00-2:45pm (just for Math 1530) and Friday 3:00-4:00 pm (combined office hours) and by appointment (send me an email).
Course Time MWF 10:00–10:50 AM (C hour)
Course Location Barus-Holley 165
Problem Sets Note: The problem sets are challenging. Don't leave them until the last minute! We will be moving rapidly. In order to learn the material, it is very important to DO THE HOMEWORK WHEN IT IS ASSIGNED.
Late homework will NOT be accepted. There are NO exceptions to this rule.
Homework must be stapled, with your name legibly written at the upper right of the first page. It is due at the start of class.
Homework should generally be done on your own. If you occasionally work with someone else in the class, you must indicate who you worked with. Further, you are not allowed to get help from people not in the class, nor may you search or ask for solutions on the internet. Doing so is a form of plagiarism and will be treated as such. The grader and I reserve the right to do our own internet searches and compare your solutions with those that we find.
Homework on the Web The homework assignments include reading assignments, due the next class, and written assignments, generally due each Wednesday.
Click here to go to the Math 1530 Web Homework Page.

Dates to Remember: There will be two in-class hour exams and a final exam.

Hour Exam #1

Mon Oct 7

In class

Hour Exam #2

Mon Nov 11

In class

Final Exam

Fri Dec 13
Exam Group TBA

2:00–5:00pm
Room TBA

Grading: The course grade will be determined on the following basis:

Problem Sets

15%

Hour Exam 1

20%

Hour Exam 2

25%

Final Exam

40%

Brief Syllabus:

Click here for a detailed syllabus and list of homework assignments.

  1. Introduction to abstract algebra
  2. Basic properties of the integers
  3. Groups
    • Definitions, examples, and basic properties
    • Subgroups and direct products
    • Morphisms, normal subgroups, and quotients
    • Finite abelian groups / Symmetric groups
    • Group actions and the Sylow theorems
    • Simple groups
  4. Rings
    • Definitions, examples, and basic properties
    • Morphisms, ideals, and quotients
    • Polynomials, irreducibilty, and factorization
    • Principal ideal domains and Euclidean domains
  5. Fields (as time permits)
    • Finite and algebraic extensions
    • Finite fields
    • Cyclotomic fields

Go to Professor Silverman's Home Page.