# Modern Algebra I - MA 541

Fall 2017 Semester

## Tu-Th3:30 PM - 5:00 PM

### Instructor:Timothy Kohl

Office:                         MCS 235

Telephone:                   617-353-8203

E-mail:                        tkohl@math.bu.edu (I read my e-mail throughout the day!)

Office Hours:               M, W 4-5

Text:    A First Couse in Abstract Algebra (7th Ed.) – John B. Frahleigh (Addison Wesley) 200.

Remarks:   The main prerequisites for this course are some basic set theory and number theory, which we will review. The content of this course is exclusively group theory. Groups are examples of algebraic systems that are rather different from the integers, rationals, or real numbers which you’ve worked with in other classes. Groups, especially finite groups, are self-contained systems with their own ‘arithmetic’ that is often quite different than what one is familiar with from say calculus or basic algebra. At a deeper level, groups are a means of encoding the notion of ‘symmetry’ in a concise form. This has ramifications across many mathematical disciplines. As you will see if you take MA 542, symmetry is important, for example, in the study of the solutions of polynomial equations. In fact, questions regarding whether such equations have solutions can be decided based on group theoretic criteria. Also, group theory problems are an excellent means of learning how to write good mathematical arguments. Some of the questions themselves will seem simple, but they can be highly instructive, and are an excellent means of learning how to reason abstractly.

Outline of topics to be covered:

(Note: Not all sections in a given chapter are covered.)

Part I                Groups and Subgroups                                      -           Chapters 1 - 7

Part II               Permutation Groups, Cosets, Direct Products     -            Chapters 8 - 11

Part III             Homomorphism and Factor Groups                   -           Chapters 13, 14, 16

Exams:  During the semester, there will be a take-home mid-term exam worth 100 points, as well as an in-class final exam worth 200 points. The schedule for these exams is given on the next page.

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Homework:   During the semester, I will generally assign homework on a daily basis. This homework is your primary means of learning the material, even more so than the lectures. Indeed, it is only by actually working out the solutions to problems that one really learns this material. Not doing homework is a bad idea and will result in a poor performance in the course.

Additionally, there will be, throughout the course of the semester, 10 turn-in homework assignments, each worth 20 points, for a total possible maximum of 200 points if you complete each perfectly. Each turn-in assignment will be due by the next class meeting after it was assigned.

[Note: On the homework, you may discuss the material with each other, but plagiarism is not acceptable. Your written answers must be your own. I do not wish to see identically worded answers on the exams or homework.]

Grading:   Your grade in the course will be based on the combined sum of the midterm, the 10 turn-ins, and the final exam, out of a possible total of 500 points.

Cheating:   I consider cheating to be a very serious offense and any cases of it will merit action by the University Academic Standards Committee.

Important Dates:

No class on Tuesday October 10th due to substitute Monday schedule

Thanksgiving break – Thursday November 23th

Midterm Exam – Assigned Thursday October 12 (due Thursday October 17)

Final     – Tuesday December 19 3PM – 5PM

The last day of class will be Tuesday, December 12.

Web Page:       There is a web page for the course where you can find the homework assignment listings, as well as the syllabus and other materials that will be made available during the course.

The URL is:

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