MA 361 - Elementary Modern Algebra I (Fall 2007)

Overview

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

Basic Information

Time and Place: 10:00-10:50  MWF, CB 341

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: 11:00-11:50  MWF in POT 763, or by appointment.
You can also consult me by email.

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

• Exam 1 (CB 341, Sept 26, 10:00-10:50 am)
  
• Exam 2 (CB 341, Nov 7, 10:00-10:50 am)
• Final exam (CB 341, Dec 12, 8:00-10:00 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 including methods for digital signatures.
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 0 - 4 of the textbook.

CONTENTS:

  1. Sets and maps
  2. Properties of the integers
  3. The definition and examples of groups
  4. Subgroups
  5. Cyclic groups
  6. Permutations
  7. Cosets and the theorem of Lagrange
  8. The RSA cryptosystem
  9. Group homomorphisms
  10. Normal subgroups
  11. Factor groups
  12. Direct products
  13. Simple groups
  14. The definition and examples of rings
  15. Integral domains
  16. Fields
  17. Ring homomorphisms
  18. Fields of quotients





Homework and Quizzes

A short quiz will be given during the last 10 minutes of each Friday lecture beginning September, 3. Make-up quizzes will not be given without an excused absence.

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-f07/el-a-f07.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)




Practice exams

Try to solve the exams on your own before you discuss the solutions.
• For the first midterm:   Test (pdf-file) ;   Selected solutions (pdf-file)
• For the second midterm:   Test (pdf-file);   Solutions (pdf-file)
• For the final exam:   Test (pdf-file);   Selected solutions (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.