Fall 2023 - MATH 340 D100
Algebra II: Rings and Fields (3)
Class Number: 2032
Delivery Method: In Person
Course Times + Location:
Sep 6 – Dec 5, 2023: Mon, Wed, Fri, 11:30 a.m.–12:20 p.m.
Oct 10, 2023: Tue, 11:30 a.m.–12:20 p.m.
Exam Times + Location:
Dec 15, 2023
Fri, 3:30–6:30 p.m.
1 778 782-9887
Prerequisites:MATH 240 with a minimum grade of C- or MATH 232 with a grade of at least B.
The integers, fundamental theorem of arithmetic. Equivalence relations, modular arithmetic. Univariate polynomials, unique factorization. Rings and fields. Units, zero divisors, integral domains. Ideals, ring homomorphisms. Quotient rings, the ring isomorphism theorem. Chinese remainder theorem. Euclidean, principal ideal, and unique factorization domains. Field extensions, minimal polynomials. Classification of finite fields. Students with credit for MATH 332 may not take this course for further credit. Quantitative.
Integers and Modular Arithmetic and Polynomials
Integer division and the Euclidean algorithm
The primes and the fundamental theorem of arithmetic
Modular arithmetic and applications
Polynomial arithmetic and factorization
Rings, Domains, and Fields
Ring and field axioms
Zero divisors, units, integral domains and fields
The complex numbers and the fundamental theorem of algebra
Ring Isomorphisms, Ideals, and Homomorphisms
Functions, equivalence relations
Ideals and Kernels
Rings of Cosets
The Isomorphism Theorem for rings
Direct Product rings
Chinese Remainder Theorem
Finite and Algebraic Extensions
Classification of Finite fields
- Assignments 15%
- Midterm 25%
- Final Exam 50%
- Participation 10%
THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting ofmarks.
Please pay careful attention to the options discussed in class at the beginning of the semester.
A First Course in Abstract Algebra: Rings, Groups, and Fields
Marlow Anderson and Todd Feil
3E/2014 CRC Press LLC
Dummit and Foote
REQUIRED READING NOTES:
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