Modern Algebra I
General
Prefix
MATH
Course Number
411
Course Level
Undergraduate
Department/Unit(s)
College/School
College of Science and Engineering
Description
Groups, subgroups, cyclic groups, permutation groups, isomorphisms, Cayley's theorem, cosets, LaGrange's theorem, normal subgroups, quotient groups, homomorphisms, the first isomorphism theorem, construction of the integers and rational numbers from the natural numbers, rings, integral domains, and fields.
Prerequisites
Credits
Min
4
Max
4
Repeatable
No
Goals and Diversity
MN Goal Course
No
Cultural Diversity
No
Learning Outcomes
Outcome
Describe examples of groups, rings, and integral domains with various combinations of properties.
Outcome
Describe mathematical structures that serve as counterexamples to supposed assertions in group theory and ring theory.
Outcome
Use concepts and notation of the course in an abstract sense appropriate to their definitions rather than relying on preconceived notions.
Outcome
Perform calculations with cyclic groups, modular arithmetic, permutation groups, cosets, factor groups, orders of elements, and the Fundamental Theorem of Finite Abelian Groups.
Outcome
Determine whether a set is subgroup of a group, a normal subgroup of a group, or a subring of a ring.
Outcome
State famous and 'named' theorems of group theory and ring theory (such as the First Isomorphism Theorem).
Outcome
Apply known results, concepts, and techniques of group theory and ring theory to investigate new situations and prove other results.
Outcome
Reason mathematically and correctly.
Dependencies
Courses
MATH411
is a
prerequisite
for:
Programs
MATH411
is a
completion requirement
for: