Spring 2017 MATH 113 001 LEC

Introduction to Abstract Algebra
001 LECMoWeFr 10:00AM - 10:59AMEvans 740Virginia Harrison18239
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Additional Information: 

Prerequisites: 54 or a course with equivalent linear algebra content. Ambitious students may take this course without lower division prerequisites by permission of the professor.

Description: This will be an unusual version of Math 113. We shall cover the basic syllabus as seen in Herstein, including

  • Sets and relations.
  • The integers, congruences, and the Fundamental Theorem of Arithmetic. Groups and their factor groups.
  • Commutative rings, ideals, and quotient fields.
  • The theory of polynomials: Euclidean algorithm and unique factorizations.The Fundamental Theorem of Algebra.
  • Fields and field extensions.
  • Vector spaces

We will also develop basic concepts of category theory, emphasizing universal properties of various structures we encounter.  Our main text will be J. Harrison's highy regarded "Universal linear algebra for students of math and physics" which will be modified to cover the syllabus of 113. This course will begin with the basics of set theory and systematically develop basic algebraic structures. It is essentially self-contained. The course will require steady hard work throughout the semester but will have a big payoff by the end for those who do the work. 

Office: 829 Evans Hall

Office Hours: MWF 11-12

Required Text:  Abstract Algebra 3rd Edition by I.N. Herstein
 and Universal Linear Algebra for Students of Math and Physics by J. Harrison (a draft pdf will be provided)

Recommended Reading: 

Grading: tba

Homework: There will be 5-10 mins devoted to weekly homework assignments at the end of each lecture.

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