MATH 412 - Introduction to Modern Algebra
Fall 2013, Section 002
Instruction Mode: Section 002 is (see other Sections below)
Subject: Mathematics (MATH)
Department: LSA Mathematics
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Details

Credits:
3
Requirements & Distribution:
BS
Credit Exclusions:
No credit granted to those who have completed or are enrolled in MATH 493. One credit granted to those who have completed MATH 312.
Waitlist Capacity:
10
Advisory Prerequisites:
MATH 215, 255 or 285; and 217; only 1 credit after MATH 312.
BS:
This course counts toward the 60 credits of math/science required for a Bachelor of Science degree.
Repeatability:
May not be repeated for credit.
Primary Instructor:

Description

This course is designed to serve as an introduction to the methods and concepts of abstract mathematics. A typical student entering this course has substantial experience in using complex mathematical (calculus) calculations to solve physical or geometrical problems, but is unused to analyzing carefully the content of definitions or the logical flow of ideas which underlie and justify these calculations. Although the topics discussed here are quite distinct from those of calculus, an important goal of the course is to introduce the student to this type of analysis. Much of the reading, homework exercises, and exams consists of theorems (propositions, lemmas, etc.) and their proofs. MATH 217 or equivalent required as background. The initial topics include ones common to every branch of mathematics: sets, functions (mappings), relations, and the common number systems (integers, rational numbers, real numbers, and complex numbers). These are then applied to the study of particular types of mathematical structures such as groups, rings, and fields. These structures are presented as abstractions from many examples such as the common number systems together with the operations of addition or multiplication, permutations of finite and infinite sets with function composition, sets of motions of geometric figures, and polynomials. Notions such as generator, subgroup, direct product, isomorphism, and homomorphism are defined and studied. MATH 312 is a somewhat less abstract course which substitutes material on finite automata and other topics for some of the material on rings and fields of MATH 412. MATH 512 is an Honors version of MATH 412 which treats more material in a deeper way. A student who successfully completes this course will be prepared to take a number of other courses in abstract mathematics: MATH 416, 451, 475, 575, 481, 513, and 582. All of these courses will extend and deepen the student's grasp of modern abstract mathematics.

Schedule

MATH 412 - Introduction to Modern Algebra
Schedule Listing
001 (LEC)
 In Person
12132
Open
11
 
-
MWF 9:00AM - 10:00AM
002 (LEC)
 In Person
12133
Open
9
 
-
MWF 11:00AM - 12:00PM

Textbooks/Other Materials

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Syllabi

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CourseProfile (Atlas)

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