### Algebra (MAT 311)

LECTURER: E Andriantiana

### Description

Algebra is one of the main areas of mathematics with a rich history. Algebraic structures pervade all modern mathematics. This course introduces students to the algebraic structure of groups, rings and fields. Algebra is a fundamental course for any further study in mathematics.

### Topics

Sets, equivalence relations, groups, rings, fields, integral domains, homorphisms, isomorphisms, and their elementary properties.

### Possible resources

• Lecture notes will be provided: an electronic version uploaded on RUconnected and a printed version provided in class.
• The main book followed is John R. Durbin, Modern algebra : an introduction, New York : John Wiley, 1992.

### Assumption of prior learning

Prior to the MAT311 course, students are expected to be able to:

• compute intersection, union, difference of two given sets,
• compute composition of mappings, understand the meaning of injective, surjective or bijective mappings,
• recognize basic proof techniques such as induction, reasoning by contradiction or contraposition.

### Course Organisation

• Lectures: This course has three one-period lectures each week.

• Tutorials: Every week, there will be a one hour tutorial. Tutorial questions will be uploaded in the RUconnected a few days in advance. You are expected to have prepared those questions, so that the one hour tutorial can be used for discussing specific questions that you found challenging. Solutions to tutorial problems will be provided on the due date. Note that solving the problems specified in the tutorial is one of our goals, but understanding the claims in each problem and its solution is another important objective. In this course, tutorial problems often deal with more properties that are good to know but we did not have time for during lectures. Students are advised to look for more exercises (any exercises on the topics treated in class) in the many books of algebra in the library.

• Assignment: Every week, selected questions from the tutorial will be chosen to be assignment. The assignments will be marked.

• Class tests: The course has one class test in each term.