Math 541 - Modern Algebra

• Prerequisites: Math 320 or 340, or consent of instructor.
• Frequency: Fall (I), Spring (II)
• Student Body: Math majors and graduate student in related areas
• Credits: 3. (N-A)
• Recent Texts: M. Artin, Algebra, Prentice-Hall 1991
  Bhattacharya, Jain and Nagpaul, Basic Abstract Algebra, Cambridge Univ. Press, 1994
• Course Coordinator: Arun Ram, Steven Bauman
• Background and Goals: This is the first semester of an introduction to basic abstract algebra. It is recomended for math majors and it is essential for students preparing for graduate studies in mathematics and in some related fields.
• Alternatives: Math 441 is a less theoretical version of Math 541
• Subsequent Courses: Math 542.

Content coverage:

• How to do proofs; Sets and functions: unions, intersections, products, injections, surjections, bijections, inverse functions, equivalence relations
• Groups: subgroups, normal subgroups, homomorphisms and quotients
• Rings: subgroups, ideals, homomorphisms, and quotients
• Commutative rings: fields, integral domains, prime ideals, maximal ideals, PIDs and Euclidean domains