Math 3310 Introduction to Abstract Algebra

Fall Semester 2015-2016

Section 01

This course meets MWF 11 in Campion Hall, Room 300.

 Homework Assignments Syllabus

Welcome to the Math 3310 course website for Prof. Friedberg's class.  This website is the primary way for you to get information about our course, including the homework assignments.  It also contains the course syllabus.

Note: Many of the documents contained herein require Adobe Acrobat Reader to view and print. If you open a document and are asked to find Acrobat Reader, there is a copy in the Eaglenet Resources folder. If you need to install a copy on your computer, you may download a free copy from the Adobe web site.

Course Description

This course is concerned with abstract algebra.  This is one of the most fundamental areas of modern mathematics.  The idea is to study mathematical structures with simple rules---so simple that they may be found in many different areas---and yet to see that these simple rules impose a rich structure upon the objects.   Much of the course will be concerned with Group Theory.  Groups are behind games such as the Rubrik's cube, and they are also behind the study of symmetries in physics and secure data transmission in computer science.  They play a central role in modern mathematics.  We will also study objects called Rings.  These objects mimic the integers, and yet may be subtly different.  Their properties will allow us to discover new facts about the integers themselves.  Finally, we will study Fields.  These are Rings with extra structure.  They are important in understanding the solutions to equations and are also used in coding theory and in cryptography.

This is a foundational upper division course covering one of the subjects which is at the center of modern mathematics.  But it is intrinsically sophisticated stuff.  You can't get by just studying right before the test.  You need to go over your notes after each lecture. Learn the definitions by heart.  Work through the examples (in both text and lecture) until you understand them thoroughly.  Then learn the proofs as well as the Theorems. If you put this off, you'll find that the lectures make use of material you have not yet worked through, and you'll get behind rapidly.  But if you keep up---and don't hesitate to ask questions in class or in office hours if you're confused by something---then the course will work well.  The material is intrinsically beautiful, and you'll be introduced to the power of modern abstract mathematics.

Please note:  This course satisfies the algebra requirement for the B.A. degree in mathematics.  Students considering the B.S. degree should take Math 3311 and not this course.

Office Hours

I am very happy to answer your questions and to help you with the homework.  My Office Hours during the semester are Monday and Friday 10-11 and Wednesday 12-1 in Maloney 523.  These times are always reserved for your questions and you do not need an appointment during them.  I am also available by appointment.  Please email me for one.  Since I am Department Chair, I find myself with a great many meetings and other scheduled events, so please give me a few possible meeting times in your email.  I am always happy to work with students, so don't hesitate to ask for an appointment!!

Exam Dates

Here are the dates of the exams.  Please note that full information about the grading policy for this course may be found in the syllabus (see link above).  In particular, no makeups or early examinations are given in this course.

Hour Exam Dates: Tentatively scheduled for Friday, October 9, 2015 and Monday, November 16, 2015.    Please note that October 9 is the day before the Columbus Day weekend.

The Final Examination is on Tuesday, December 15, 2015 at 12:30 p.m.

Important: The date and time of the final examination is fixed by the Registrar and may not be changed.  Note that you MUST attend the final examination at that time.

Do you want to typeset your homework?
Here's how.  Though it takes a while to get the hang of it, this is recommended as it will help you write mathematics clearly.   To do so, try using LaTeX.  This is the standard software in use in mathematics (and many other areas).  And it's free.

Mac OSX: Get MacTeX here. Scroll down to "Trying out Tex" for demos.

Windows: You'll need two files: The MiKTeX program, and some editor.
Download sites with full instructions and lots of examples can be found here.
Or, to obtain the files directly, get
1.   MiKTeX  and
2.  some editor, such as:  WinEdt or  TeXnicCenter.

2.  Using LaTeX:

You can google "using latex" and find many references.  One good page with lots of links is:
http://www.eng.cam.ac.uk/help/tpl/textprocessing/
(For example, there is the LaTeX Wikibook and "LaTeX for Complete Novices" (by Nicola Talbot).)

1.  The Mathematical Association of America is concerned with research in mathematics and also with university teaching.  The American Mathematical Society is the primary professional organization concerned with research in theoretical mathematics.  The Society for Industrial and Applied Mathematics is the analogous primary organization for applied math. Check out their websites!  The MAA has a helpful Careers in math page. The AMS website also has some TeX resources.

2.  The BC Career Center has a Science, Math and Tech Biweekly Career Update.

2. The Association for Women in Mathematics supports women in mathematics at all levels of study. The "AWM Resources" link connects you to many other sites with useful information.  They also sponsor an annual biography contest concerning contemporary women mathematicians.  See the website for details.  The deadline for the 2016 AWM Essay Contest is January 31, 2016.

3. The Math Forum Student Center has math resources for undergraduates (and a little for grad students).

4. Math Horizons is a magazine for students interested in mathematics that aims to expand their intellectual and career horizons.

5. Are you interested in history? Here is a website concerned with the History of Mathematics.