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01:640:351 - Introduction to Abstract Algebra I

  • Course Code: 01:640:351
  • Semester(s) Offered: Fall, Spring
  • Credits: 4
  • Counts toward math major/minor?: Yes
  • Prerequisites: Math 250 and Calc III and a C or better in Math 300

General Information

Math 351 is one of two courses most mathematics majors may take to satisfy the algebra requirement. The other is Math 350.
Math 351 was originally part of a two-course sequence, Math 351-352. The continuation, Math 352, is no longer offered.

Catalog Description

01:640:351-352 Introduction to Abstract Algebra I, II (4,3)
Abstract algrebraic systems, including groups, rings, fields, polynomials, and some Galois theory.
Prerequisites: CALC3; 01:640:250; and a C or better in 300 or permission of department.

Textbook

For current textbook please refer to our Master Textbook List page

 

Topics, in approximate order

Division
Primes and unique factorization
Congruence
Modular arithmetic
Rings
Properties of rings
Isomorphisms and homomorphisms
Division in F[x]
Irreducibles and unique factorization
Roots and reducibility
Congruence in F[x]
Congruence and Ideals
Ring isomorphism theorems, prime and maximal ideals
Groups
Properties of groups
Subgroups
Group isomorphisms and homomorphisms
Symmetric and alternating groups
Lagrange’s Theorem
Conjugacy classes
Normal subgroups
Quotient groups
Center and commutator subgroups
Group isomorphism theorems
Simplicity of alternating groups
Classification of finite abelian groups

 

Sample Course Page

Spring 2022: Prof. Borisov

Disclaimer: Posted for informational purposes only

This material is posted by the faculty of the Mathematics Department at Rutgers New Brunswick for informational purposes. While we try to maintain it, information may not be current or may not apply to individual sections. The authority for content, textbook, syllabus, and grading policy lies with the current instructor.

Information posted prior to the beginning of the semester is frequently tentative, or based on previous semesters. Textbooks should not be purchased until confirmed with the instructor. For generally reliable textbook information—with the exception of sections with an alphabetic code like H1 or T1, and topics courses (197,395,495)—see the textbook list.