Instructor: Margaret Robinson
Meetings: Monday, Wednesday 1:15-2:30 and Friday 1:15-2:05 in Clapp 422.
Text: Abstract Algebra, Thomas W. Hungerford, second edition published 1997.
Homework: Homework will be assigned weekly to be due the following week. Graded homework can be picked up from the envelope outside my office or in class. Homework can be redone and handed in again, if done promptly (i.e. within a week of getting it back). I reserve the right not to accept redone homework that is too late. You may want to set up a weekly homework session to work on the problem sets in the evening as a group. I will try to come to some of them.
Tests and Quizzes: On most Fridays, we will have book work quizzes on the most important theorems of the last week. There will be two tests, and a self-scheduled or take-home final examination. If you are unable to take a test for any reason, you should contact me before the test. (You can email me at robinson any time of the day or night.)
Grading: The homework, quizzes, and class participation make up 25% of your grade, each test is 25%, and the final examination is 25%.
Mid-term examinations are tentatively scheduled for the early part of October (The Monday or Wednesday - Oct. 1 or 3 - right before October break or the Friday following October break - Oct. 12) and early to mid-November.
Introduction to the class: What is meant by 'abstract mathematics'? Abstract means 'drawn from' reality (from the Latin, abstractus). An abstraction is by definition one thing concentrating in itself the virtues of many.
We will be working with the following process:
This technique revolutionized mathematics in the 20th century and supplied the link between branches of the subject which had previously appeared unrelated. Simple proofs of what had been very difficult problems have emerged as obvious corrollaries to abstract results. Emmy Noether (1882-1933), among the greatest of modern mathematicians, originated the algebraic way of thinking.
The terminology and methodology of abstract algebra are widely used in computer science, physics, chemistry, and data communications, cryptology, crystallography, art, algebraic coding theory, electric circuits, the solvability of polynomials as well as in all areas of mathematics.
The most important thing to learn from this course is to like the process of grasping new concepts and objects and making them real to yourself. Of course, it is also important to learn to use them to read and write mathematical proofs.
Books for you to look at:
Web sites to become familiar with: