MA 362 - Elementary Modern Algebra II (Spring 2008)

Overview

• Basic Information
• Material
• Homework and Quizzes
• Practice exams
• Grades

Basic Information

Time and Place: MWF 11:00-11:50 am, FB 213

You are expected to attend all lectures.

Instructor: Uwe Nagel, POT 763, 257-6793, uwenagel@ms.uky.edu and www.ms.uky.edu/~uwenagel.

Office Hours: MWF 1:00-1:50 pm, POT 763, or by appointment.
You can also consult me by email.

Exams: There will be two midterms and one final exam.

• Exam 1 (FB 213, Feb 15, 11:00-11:50 am)
  
• Exam 2 (FB 213, Mar 28, 11:00-11:50 am)
• Final exam (FB 213, Apr 28, 10:30-12:30 am).
  

Material

Textbook: A first course in abstract algebra (7th edition) by John B. Fraleigh, ISBN 0-201-76390-7.

Algebra is the study of mathematical structures. These are sets of elements endowed with certain operations. A familiar example is the set of integers with the operations of addition and multiplication. The goal of the course is to become very familiar with fundamental concepts such as groups, rings, fields, polynomials and some of their applications, e.g., in Cryptography and Coding Theory.
Algebra is used in almost every branch of mathematics. It is often instrumental in finding connections between seemingly unrelated topics. Moreover, algebraic methods have found numerous applications in many fields outside of mathematics.
The course will cover most of Chapters 4 - 6 and parts of Chapter 10 of the textbook.

CONTENTS:

  1. Review of rings and ring homomorphisms
  2. Ideals and factor rings
  3. Prime and maximal ideals
  4. Division with remainder for polynomials
  5. Zeros of a polynomial
  6. Irreducible polynomials
  7. Factor rings of polynomial rings
  8. The Chinese Remainder Theorem
  9. The multiplicative group of a field
  10. The characteristic of a ring and prime fields
  11. Extension fields
  12. Algebraic extensions
  13. Geometric constructions
  14. Splitting fields
  15. Finite fields
  16. BCH-codes

Homework and Quizzes

Homework will be collected regularly. The homework problems will be announced in class and on the web page of the class http://www.ms.uky.edu/~uwenagel/EL-A-s08/el-a-s08.html
In order to receive credit, homework solutions must be written out neatly and handed in at the beginning of the class on the due date. Late homework will not be accepted unless the delay is due to an excused absence.
You are encouraged to discuss homework problems and the course material with each other. However, when it comes time for you to write up the solutions, I expect you to do this completely on your own. It would be the best for your understanding if you put aside your notes from the discussions with your classmates and wrote up the solutions entirely from scratch. Working together on the exams, of course, is expressly forbidden.

• Set 1 (pdf-file)
• Set 2 (pdf-file)
• Set 3 (pdf-file)
• Set 4 (pdf-file)
• Set 5 (pdf-file)
• Set 6 (pdf-file)
• Set 7 (pdf-file)
• Set 8 (pdf-file)
• Set 9 (pdf-file)
• Set 10 (pdf-file)
• Set 11 (pdf-file)
• Set 12 (pdf-file)

Practice exams

• For the first midterm:   Test (pdf-file);   Selected solutions (pdf-file)
• For the second midterm:   Test (pdf-file);   Selected solutions (pdf-file)
• For the final exam:   Test (pdf-file)

Grades

There is a total of 450 points in the course which is distributed as follows:

Attendance	25 points
Homework	50 points
Quizzes	50 points
First Midterm	100 points
Second Midterm	100 points
Final Exam	125 points

In this model an A requires at least 405 points (90% or more), B at least 360 (80% or more), C at least 315 (70% or more), D at least 270 (60% or more), E for anything else.