Fall 2021 - MATH 340 D100
Algebra II: Rings and Fields (3)
Class Number: 1223
Delivery Method: Remote
Course Times + Location:
Mo, We, Fr 11:30 AM – 12:20 PM
REMOTE LEARNING, Burnaby
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.
This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.
You will need a camera to take photographs of your work. A phone is acceptable.
TopicsIntegers 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
- Lecture: synchronous- lectures will be held at fixed times, on-line
- Midterm(s): synchronous; date: TBA
- Final exam: synchronous; date: TBA
- Quizzes 15%
- Weekly Assignments 25%
- Final Exam 60%
- Access to strong and reliable internet.
- Ability to scan documents (phone app acceptable)
- Access to webcam and microphone (embedded in computer sufficient)
A First Course in Abstract Algebra: Rings, Groups, and Fields
Marlow Anderson and Todd Feil
3E/2014 CRC Press LLC
Dummit and Foote
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TEACHING AT SFU IN FALL 2021
Teaching at SFU in fall 2021 will involve primarily in-person instruction, with approximately 70 to 80 per cent of classes in person/on campus, with safety plans in place. Whether your course will be in-person or through remote methods will be clearly identified in the schedule of classes. You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).
Enrolling in a course acknowledges that you are able to attend in whatever format is required. You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.
Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (firstname.lastname@example.org or 778-782-3112) as early as possible in order to prepare for the fall 2021 term.