MATH 335 Modern Algebra Spring 2016 |
Lecture | MWF 9:10-10:00 a.m. (TH 325) |
Prerequisites: | MATH 301 & MATH 325 with grades of C or better |
Instructor | Dr. Matthias Beck |
Office | Thornton Hall 933 |
Office hours | Mondays 12-2, Wednesdays & Fridays 11-12, and by appointment |
Course objectives. Algebra studies the structure of sets with operations, such as integers with addition and multiplication, or vector spaces with linear maps. The abstract point of view, based on an axiomatic approach, reveals many deep ideas behind seemingly innocent structures--such as the arithmetic of counting numbers--and serves as an elegant organizing tool for the vast universe of modern algebra. Generations of brilliant minds have crystallized these ideas in the ideas in the concept of groups, rings, fields, modules, and their quotient structures and homomorphisms--the topics of MATH 335 & 435. Our main goal in MATH 335 is the study of groups and rings. We will not strive for the maximal possible generality but rather work out as many concrete examples/incarnations of theoretical concepts as possible. Another goal of this course is to make the students immerse in communicating mathematical thoughts (proofs, examples, counterexamples) in a written form.
Syllabus. Topics in this course will include:
- Integers & the Euclidean algorithm
- Complex numbers, roots of unity & Cardano's formula
- Modular arithmetic & commutative rings
- Polynomials, power series & integral domains
- Permutations & groups
Textbooks.
- Al Cuoco & Joseph J. Rotman, Learning Modern Algebra, MAA Textbooks, 2013.
- Frederick M. Goodman, Algebra: Abstract and Concrete, edition 2.6.
Participation. About half of the material covered in this class will be worked out in small groups during class sessions; this philosophy is sometimes called inquiry-based learning. It will thus be essential that every student participates actively in every class. If you have to miss a class due to a medical or family emergency, please let me know before the class; otherwise, I expect you to be in class and actively engaged.
Homework. I will assign homework problems as we go through the material. We can discuss the homework problems at any time during class. All homework assignments of a given week have to be handed in by the start of the Wednesday class of the following week. (If you type your solutions, you may email me a pdf copy before the Wednesday class.) You may hand in some of your problems early to be able to correct your mistakes. Although you may (and should) work together with your class mates, the solutions you hand in have to be your own.
Quizzes. I will frequently check your progress through unannounced quizzes given at the beginning of class. A quiz will typically test your concept of a certain definition or statement. There will be no make-up quizzes. At the end of the semester, I will drop the lowest of your quiz grades.
Grading system.
Participation & quizzes | 10% |
Homework | 50% |
Midterm exam (March 18) | 20% |
Final exam (May 20, 8 a.m.) | 20% |
I want to ensure that each of you accomplishes the goals of this course as comfortably and successfully as possible. At any time you feel overwhelmed or lost, please come and talk with me.
The math. The way to learn math is through doing math. It is vital and expected that you attend every class meeting. You will get a good feel for the math from there, but it is even more crucial that you do the homework. Working in groups is not only allowed but strongly recommended. The iLearn system allows you to send emails to anybody in your class. While I strongly encourage you to work together, the solutions you hand in must be your own.
Fine print.
SFSU academic calender
BS rule
Academic Integrity and Plagiarism
Tutoring
CR/NCR grading
Incomplete grades
Late and retroactive withdrawals
Student disclosures of sexual violence
Students with disabilities
Religious holidays
This syllabus is subject to change. All assignments, as well as other announcements on tests, policies, etc., are given in class. If you miss a class, it is your responsibility to find out what's going on. I will try to keep this course web page as updated as possible, however, the most recent information will always be given in class. Always ask lots of questions in class; my courses are interactive. You are always encouraged to see me in my office.