Model theory has numerous applications in mathematics as well as in computer science since in its study lie answers to how synactic form of axioms can be determined by properties of their models and vice versa. We will study elementary substructures and elementary chains, staturated and homogeneous models, model completeness, and omega-categoricity. The emphasis will be for the student to learn how to use these ideas and on working many problems in the text. Usually, we will cover roughly the first three chapters of the text. May be repeated.
Lie theory plays a fundamental role in many areas of mathematics.
This course gives an introduction to the fundamental concepts of this subject. The material which is devoted entirely to Lie Algebra is contained in chapters 3 and 4 of the textbook. The aim is to examine the structure of a Lie Algebra in detail. The only prerequisite is a basic course in algebra. Since they were introduced about a dozen years ago, many papers have been written in both commutative and non-commutative ring theory investigating and employing Enochs notions of covers and envelopes .