MAT 423/523 Modern Algebra I
Textbook
Suggested Reading
- A First Course in Abstract Algebra, John B. Fraleigh, 7th Edition, Pearson, 2002
- Abstract Algebra, I. N. Herstein, 3rd Edition, Wiley, 1996
- Topics in Algebra, I. N. Herstein, 2nd Edition, John Wiley & Sons, 1975
Further Reading
Topics
In this course we study Group Theory that includes the following topics:
Class Meeting Times and Class Room
Office Hours
Grading
Math Forum
If you have a question on your homework or a general math question, you may post it on my Math Forum site. This forum site is equipped with MathJax which supports LaTex, a wonderful type setting system that is really good at formatting mathematical formulas and equations. MathJax allows us to write mathematical formulas and equations in popular web platforms using LaTex code.To include LaTex code in your posts and comments, use:
Weekly Schedule
The math department's official textbook for this course is
A First Course in Abstract Algebra, Joseph J. Rotman, 3rd Edition, Prentice Hall, 2005.
It is a good book however it is not necessary for you to purchase the textbook since my lectures will not closely follow the book.
A Course in Universal Algebra, Stanley N. Burris and H. P. Shankappanavar, Graduate Texts in Mathematics, Springer-Verlag, 1981
Definitions and Examples of Groups, Subgroups, Lagrange's Theorem, Homomorphisms and Normal Subgroups, Quotient Groups, The Homomorphism Theorems, Cauchy's Theorem, Direct Products, Finite Abelian Groups, Conjugacy and Sylow's Theorem, The Symmetric Group (Cycle Decomposition, Odd and Even Permutations)
Tuesday/Thursday 1:00-2:15pm in SH 303
Tuesday/Thursday 8:55-11:00am and 2:15-5:10pm.
For students on the Gulf Coast campus, office hours may be arranged through skype by appointment. My skype id is sunglee7.
3 In-Class Exams (each of which counts 30% of your total grade) and no Final Exam. The average of two better exam grades will replace lowest exam grade at the end of the semester. You are required to participate in taking the Major Field Test and it will count 10% of your total grade.
You can view your grade (raw score) here. You can view your grade (processed and curved) including the final grade for the course here. You can identify yours by the last four digits of your student id.$your-LaTex-code-here$
You can find a list of Latex codes for math symbols here. You may practice your Latexing here.If you want to try Latex in your Windows computer, you may download it for free from MikTex Project Page. If you are using a Linux distribution, usually Latex is a part of the standard packages repository. (The package is called texlive.) To use Latex, you need an editor. Texmaker is a nice interface for using Latex. You can edit/compile/view all together in Texmaker. If you don't want to deal with commands, there is a WYSWYG (What You See is What You Get) interface for Latex called Lyx.
Click on linked topics to view/download lecture notes.
Group Theory 1: An Overview | Classes begin on 8/20 | ||||
Group Theory 2: Preliminaries (Functions) Group Theory 3: Preliminaries (Basic Number Theory) |
Homework 1 | 8/27: Last day to drop full-semester classes and receive 100% financial credit 8/27: Last day to add/drop full-semester classes without instructor permission |
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Group Theory 3: Preliminaries (Basic Number Theory) Group Theory 4: Examples of Groups |
Homework 2 | 9/1: Labor Day Holiday (day and night classes do not meet | |||
Group Theory 5: Subgroups | Homework 3 | ||||
Group Theory 6: Lagrange's Theorem | Homework 4 | ||||
Group Theory 7: Congruence Modulo \(n\) | Homework 5 | Exam 1 on Thursday 9/25. It covers up to Lagrange's Theorem. | |||
Group Theory 8: Homomorphisms | Homework 6 | ||||
Group Theory 9: Normal Subgroups | Homework 7 | ||||
Group Theory 10: Factor Groups (Quotient Groups) | 10/16-10/17: Fall Break | ||||
Group Theory 10: Factor Groups (Quotient Groups) (Continued) | Homework 8 | ||||
Group Theory 11: The Isomorphism Theorems | 10/31: Last day to withdraw from the University and receive a grade of W. | ||||
Group Theory 11: The Isomorphism Theorems (Continued) | Homework 9 | Exam 2 on Thursday 11/6. It covers up from Congruence Modulo \(n\) to Factor Groups. | |||
Group Theory 12: Direct Product | |||||
Group Theory 13: Finitely Generated Abelian Groups | |||||
Review | 11/26-11/28: Thanksgiving Holidays | ||||
Review | Exam 3 on Thursday 12/4. | 12/5: Last day of full-term classes |