Math 305: Introduction to Abstract Algebra and Number Theory

01:30 - 02:45 pm MW MB 139

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Catalogue Description:

MATH 305 INTRODUCTION TO ABSTRACT ALGEBRA AND NUMBER THEORY (3-0-3). Division algorithm. Greatest common divisor and Euclidean algorithm. Solving linear modular equations, Chinese Remainder Theorem, Primitive roots, solving modular quadratic equations. Introduction to group theory: motivation, definitions and basic properties. Finite cyclic groups, permutation groups, isomorphisms, Lagrange's Theorem. PREREQ: MATH 187.

Course background:
This course is designed as an introduction to some of the fundamental concepts that are at the intersection of Abstract Algebra and Number Theory.  As organized disciplines of investigation Number Theory is the older one of the two. To a large extent Abstract Algebra arose from the realization that certain structures that occur in the investigation of numbers occur in many other important contexts, and that it is more efficient to investigate these structures themselves and then apply the findings to the contexts in which these structures arise, rather than reinventing the wheel every time we need a wheel, so to speak.  

Course objectives:
1. Increase the sophistication of the student's skill in using elementary materials in clever ways to create mathematics,
2. Enrich the student's mathematical culture by attention to historical context,
3. Prime the student's professional etiquette by giving attention to proper written presentation, exposition and attribution of mathematical work,
4. Inspire the student's taste for searching for aesthetically pleasing mathematics, 
5. Develop the student's expertise in the mathematical method.


Text Books:

The text books for the course are

U. Dudley, Elementary Number Theory: Second Edition, Dover Publications, Inc.1978
C.C. Pinter, A Book of Abstract Algebra: Second Edition, Dover Publications, Inc.1990

Evaluated work in the course:

Homework (200),
Test (150)
Final Exam (150)

Calendar:
Aug.  21:     First day of classes - Solar Eclipse 2017
Aug.  25:     Last day to add without a permission number.
Sept. 01:     Last day to add, or to drop without a "W".
Sept. 04:    Labor day - no classes.
Oct. 18:     Midterm exam
Oct. 27:     Last day to drop.
Nov. 20:    Thanksgiving Break from Nov. 20 until Nov. 26.
Dec 08:     Last day of classes.
Dec 11:     03:00 pm - 05:00 pm Final Exam.