Mathematics 104 is an introduction to `"real analysis'' in several senses: in it you will learn what real numbers really are, and also how real mathematicians work with them. After discussing the real number system, we shall study the fundamental concepts of metric spaces and topology, especially continuity and compactness. Then we shall apply these concepts for a rigorous study of differential and integral calculus. By then you should love epsilon's and delta's. An important goal of the course is for you to learn to express yourself precisely and to read and write mathematical proof. The textbook, Rudin's Principles of Mathematical Analysis, is a classic. Students will be expected to learn a great deal of the material directly from the book.
My role is to point out what I feel are the most important topics, to explain and elaborate key or unclear points in the text, and to answer questions. I can do this best if I hear from students ahead of time what may be causing them difficulty, and so I encourge them to contact me by email (ogus@math.berkeley.edu) with questions about the text, preferably before the topic is scheduled for a lecture. I have posted a syllabus, which I will update and modify as the course progresses. Be sure to consult this reguarly and to read the material in the text before the corresponding lecture.
The course will be graded in a serious manner, based on weekly homework assignments, at least one midterm, and the final exam. There may also be unannounced quizzes at random times.My grades mean the following:
This honors course will cover more material and have more difficult homework than the standard version.
