As an algebraic geometer, I am a firm believer in the unity among the three main brances of mathematics: algebra, analysis, and geometry. (Logic deserves a place here too.) In fact algebra seems to be the main way mathematicians express things in a way amenable to computation and precision in almost all fields.
Math 250A is meant to be the first half of a basic introduction to the main concepts and techniques used in a wide range of mathematics. The main topics are groups, rings, and fields, as well as objects on which these act, especially modules and vector spaces. I will attempt to cover much of the first six chapters of Serge Lang's classic Algebra, although I may discuss tensor products and some categorical concepts as well.
The course will be graded in a relatively serious manner, including weekly homework, midterms, and a final examination. I also want students to send weekly email questions about topics covered in class, and indeed, this is to be regarded as a course requirement.
