Math 351 - Introduction to Abstract Algebra 1
Description
Math 351 provides an introduction to abstract algebra, including groups, rings, polynomial rings, ideals, and more. Usually, following the textbook’s order of topics, the course will cover rings first, and cover groups later.
Math 351 is one of the courses that can be used to satisfy the math major’s algebra course requirement, with the other one being Math 350 (Linear Algebra). For students wishing to pursue the honors track in mathematics, it should be noted that Math 350 (preferably its honors section Math 350H) is recommended preparation for the honors algebra sequence. The differences in topic coverage between the regular and honors section is typically minimal.
Note that there is significant overlap between the contents of 451, 452 and 351. 351 covers many of the highlights of 451 and 452, but not with the same depth.
Topics covered
Topics covered in Math 351 usually include:
- Arithmetic with integers
- Modular arithmetic
- Rings
- Arithmetic and congruence in
- Ideals and quotient rings
- Groups
- Normal subgroups and quotient subgroups
Note that the exact list of topics may vary by instructor and semester. Additional topics may include further topics in group theory, such as group actions.
Resources
Textbook
The usual textbook for the class is Abstract Algebra: An Introduction by Thomas W. Hungerford.
Additional materials
A course webpage from when the course was taught by Lev Borisov in Spring 2022 may be found online at https://sites.math.rutgers.edu/~borisov/351/syllabus.html.