matthias beck

MATH 335 Modern Algebra Fall 2024

Lecture	Mon/Wed/Fri 2:00-2:50 a.m. Thornton Hall 211
Prerequisites:	MATH 301 & MATH 325 with grades of C or better
Instructor	Dr. Matthias Beck
Office	Creative Arts 32
Office hours	Mondays 11-12, Wednesdays 10-11, Fridays 1-2, by appointment, and via zoom

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.
• Thomas W. Judson, Abstract Algebra: Theory and Applications.

Participation. A nontrivial part of the material covered in this class will be worked out in small groups during class sessions. 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. You may (and should) work together with your class mates. We can discuss the homework problems at any time during class, and you can hand any of your solutions for feedback. We will have a homework quiz every Monday at the beginning of class, in which you will be asked one definition and one problem given in the previous week.

Grading system.

Homework quizzes	50%
Midterm Exam (October 18, in class)	25%
Final Exam (December 16, 2:45 p.m.)	25%

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. Our class is based on Federico Ardila's Axioms:

1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
4. Every student deserves to be treated with dignity and respect.

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.