||Professor Alexandru I. Suciu
|MATH 3175 · Group Theory
|Summer 2, 2020
||MATH 3175 · Group Theory: CRN 60442, Section 1
|Course Web Site
|Time and Place
||Mon, Tue, Wed, Th 9:50am–11:30am, on Zoom (through Canvas)
||Tuesday 12 Noon–3 pm on Zoom (through Canvas)
|Undergraduate Math Mentor
||MATH 2331, Linear Algebra and MATH 2321, Calculus 3
||Abstract Algebra, 4th Edition (2019) by John A. Beachy & William D. Blair, Waveland Press, ISBN: 1478638699
||The course introduces some of the basic ideas of Group Theory, including symmetry groups, abelian, cyclic, and permutation groups, as well as subgroups, normal subgroups, group homomorphisms, quotient groups, direct products, group actions on a set, and the Sylow theorems. The theory will be illustrated by examples from geometry, linear algebra, and combinatorics, and applications will be discussed. We will cover parts of preparatory Chapters 1 & 2 and then Chapters 3 & 7 from the textbook, emphasizing group actions on a set as a unifying theme.
||Students will understand the basic ideas and some applications of groups, and will be able to explain groups, factor groups, and their relation to symmetry. Students will recognize mathematical objects that are groups, and be able to classify them as abelian, cyclic, direct products, etc. Students will understand homomorphisms and quotients of groups, as well as group actions on a set, orbits and stabilizers, conjugacy, and be able to determine when a group has a normal subgroup. Students will be able to reason mathematically, to write simple proofs, and be able to judge whether an attempted proof in group theory is correct/complete.
||Based on homework (50%), midterm exam (20%), and final exam (30%).
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