MATH 493 - Honors Algebra I
Fall 2013, Section 001
Instruction Mode: Section 001 is (see other Sections below)
Subject: Mathematics (MATH)
Department: LSA Mathematics
See additional student enrollment and course instructor information to guide you in your decision making.


Requirements & Distribution:
Waitlist Capacity:
Advisory Prerequisites:
MATH 296, 412, or 451.
This course counts toward the 60 credits of math/science required for a Bachelor of Science degree.
May not be repeated for credit.
Primary Instructor:


Background and Goals: This is one of the more abstract and difficult courses in the undergraduate program. It is frequently elected by students who have completed the 295--396 sequence. Its goal is to introduce students to the basic structures of modern abstract algebra (groups, rings, and fields) in a rigorous way. Emphasis is on concepts and proofs; calculations are used to illustrate the general theory. Exercises tend to be quite challenging. Students should have some previous exposure to rigorous proof-oriented mathematics and be prepared to work hard. Students from Math 285 are strongly advised to take some 400-500 level course first, for example, Math 513. Some background in linear algebra is strongly recommended Content: The course covers basic definitions and properties of groups, rings, and fields, including homomorphisms, isomorphisms, and simplicity. Further topics are selected from (1) Group Theory: Sylow theorems, Structure Theorem for finitely-generated Abelian groups, permutation representations, the symmetric and alternating groups (2) Ring Theory: Euclidean, principal ideal, and unique factorization domains, polynomial rings in one and several variables, algebraic varieties, ideals, and (3) Field Theory: statement of the Fundamental Theorem of Galois Theory, Nullstellensatz, subfields of the complex numbers and the integers mod p. Alternatives: Math 412 (Introduction to Modern Algebra) is a substantially lower level course covering about half of the material of Math 512. The sequence Math 593--594 covers about twice as much Group and Field Theory as well as several other topics and presupposes that students have had a previous introduction to these concepts at least at the level of Math 412. Subsequent Courses: Together with Math 513, this course is excellent preparation for the sequence Math 593--594.


MATH 493 - Honors Algebra I
Schedule Listing
001 (LEC)
 In Person
MWF 2:00PM - 3:00PM
Note: Students with the prereq (395) should add to the wait list in order to receive an override. Other students please visit the office-- 2084 East Hall.

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Syllabi are available to current LSA students. IMPORTANT: These syllabi are provided to give students a general idea about the courses, as offered by LSA departments and programs in prior academic terms. The syllabi do not necessarily reflect the assignments, sequence of course materials, and/or course expectations that the faculty and departments/programs have for these same courses in the current and/or future terms.

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