Description of course: Abstract Algebra is the study of mathematical structures carrying notions of "multiplication" and/or "addition." Though the rules governing these structures seem familiar from our previous middle and high school training in algebra, they can manifest themselves in a beautiful variety of different ways. The notion of a group, a structure carrying only multiplication, has its origins in the classical study of roots of polynomial equations and in the study of symmetries of geometrical objects like platonic solids. Today, group theory plays a role in almost all aspects of higher mathematics and has important applications in chemistry, computer science, materials science, physics, and in the modern theory of communications security.
The main topics covered will be (finite) group theory, homomorphisms and isomorphism theorems, subgroups and quotient groups, group actions, the Sylow theorems, ring theory, ideals and quotient rings, Euclidean domains, principle ideal domains, unique factorization domains, module theory, and vector space theory. Time permitting, we will investigate topics such as public key cryptography systems such as RSA. This will be a heavily proof-based course with homework requiring a significant investment of time and thought. The course is a must for all students planning to study higher mathematics, and would be helpful for those considering entering subjects such as computer science and theoretical physics.
Expected background: The official prerequisite is linear algebra, either Math 222 or 225, in in reality, all that is required is a mature mathematical mind, some experience with writing proofs, and the desire to work incredibly hard.
Work with anyone on solving your homework problems,Writing up the final draft is as important a process as figuring out the problems on scratch paper with your friends, see the guidelines below. Mathematical writing is very idiosyncratic -- we will be able to tell if papers have been copied -- just don't do it! You will not learn by copying solutions from others or from the internet! Also, if you work with people on a particular assignment, you must list your collaborators on the top of the first page. This makes the process fun, transparent, and honest.
Policies(or otherwise the small print)
Homework: Weekly homework will be due at the start of class on Friday. Each assignment will be posted on the syllabus page the week before it's due.
Late or improperly submitted homework will not be accepted. If you know in advance that you will be unable to submit your homework at the correct time and place, you must make special arrangements ahead of time. Under extraordinary circumstances, late homework may be accepted with a dean's excuse.
Your homework must be stapled, with your name clearly written on the top. Consider the pieces of paper you turn in as a final copy: written neatly and straight across the page, on clean paper, with nice margins and lots of space, and well organized.
No homework will be due during the week of the midterm exam.
Your lowest homework score from the semester will be dropped.
Exams/quizzes: The quizzes will be announced at least a week ahead of time. The midterm exam will take place in-class on Monday 16 October. The final exam will take place 02:00 pm - 05:30 pm on Tuesday, December 19, 2017 in ML 211.
Make-up quizzes and exams will only be allowed with a dean's excuse.
The use of electronic devices of any kind during exams is strictly forbidden and would be pointless anyway.
Homework guidelines: Generally, a homework problem in any math course will consist of two parts: the creative part and the write-up.
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