# Spring 2017 MATH 113 001 LEC

Section | Days/Times | Location | Instructor | Class |
---|---|---|---|---|

001 LEC | MoWeFr 10:00AM - 10:59AM | Evans 740 | Virginia Harrison | 18239 |

Units | Enrollment Status |
---|---|

4 | Wait List |

**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.

**Course Webpage:**