Course Description

An introduction to abstract algebra. Course begins with arithmetic and congruence in the integers, and introduces modular arithmetic. Course then moves to the more general setting of rings, and extends concepts from the integers to polynomial rings and other rings. The concepts of ideals and quotient rings are introduced. Groups are introduced, and normal subgroups and quotient groups appear as the analogues of ring-theoretic concepts.

Additional Requirements for Graduate Students:
Extra problems on weekly homework.

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Athena Title

Modern Algebra I

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Equivalent Courses

Not open to students with credit in MATH 4000E or MATH 6000E

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Prerequisite

(MATH 3000 or MATH 3300 or MATH 3300E or MATH 3300H or MATH 3500 or MATH 3500H) and (MATH 3200 or MATH 3200W or CSCI 2610 or CSCI 2610E)

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Semester Course Offered

Offered fall, spring and summer

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Grading System

A - F (Traditional)

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Student learning Outcomes

• Students will acquire computational skills with modular arithmetic and polynomials, as well as with concrete examples of rings and groups.
• Students will master basic definitions related to abstract algebraic structures such as rings, fields, groups, ideals, and quotients.
• Students will develop their abstract reasoning and proof-writing skills, enabling them to write rigorous proofs about rings and groups in both general and concrete settings.

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Topical Outline

• Arithmetic in Z (the integers)
• Congruence in Z and modular arithmetic
• Rings
• Congruence in F[x] and congruence-class arithmetic
• Ideals and quotient rings
• Groups
• Normal subgroups and quotient groups

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Institutional Competencies Learning Outcomes

Analytical Thinking

The ability to reason, interpret, analyze, and solve problems from a wide array of authentic contexts.

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Syllabus

Select Faculty / Instructor to download syllabus:   Collins, Brett   Pollack, Paul

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Public CV

Select a file to download:   MATH4000_Collins_CV.pdf   MATH40006000_POLLACK_CV.pdf

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