Math 351 - Modern Algebra 1

Spring 2020

Professor Ballantine 

Suggested Topics for the Final Project

Choose a topic by April 17 and inform me about your choice. 

Suggested topics: 

1)  (taken) Chapter 24 of the textbook (include 3-4 exercises). This is an excellent project if you consider further study of abstract algebra. 

2)  Theorem 7.2 (detailed proof, examples, exercises).

3)  (taken) Chapters 12 and 13 (rings and fields). This is an excellent project if some of the members of the group are a seniors and don't have a chance to take Modern Algebra 2. 

4)  Groups of units modulo $n$. When are they cyclic. (Suggested reading at the end of chapter 8, especially the last article). The articles can be accessed through the e-journals link on the library website (I can also help with obtaining the articles). 

5)  (taken) Applications at the end of chapter 8 (pg. 161-167.)

6)  The last suggested reading at the end of chapter 2 (Introduction to group theory for chemists). Choose this project  if you are interested in chemistry. 

7)  (taken) The second suggested reading at the end of chapter 2 (An application of elementary group theory to central solitaire). If you are interested in group theory applied to games, you can investigate this article and also the last suggested reading at the end of chapter 3 (Perfect shuffles and their relation to math)

8) (taken) Suggested reading at the end of Chapter 5: Invariants under actions to impress your friends. 

9)  (taken) Suggested reading at the end of Chapter 5: The magic cube's cubies are twiddled by cubists and solved solved by cubemeisters.

10)  (taken) Suggested reading at the end of Chapter 5: The hunting group