Math 104, Introduction to Real Analysis

Spring 2014

TuTh 3:30-5 PM, 6 Evans

Welcome to the course webpage for Math 104 (Section 3). Here you will find some general info about the course. This is also the place to look for homework assignments, occasional course notes, and other things that might interest you. This webpage is also available through our course page on bspace.

Textbook   Homework Policy   Exams   Homework Assignments   Material by Day   Various Notes   Back to Main Page 
ANNOUNCEMENT: Our final will be on Friday, May 16th, 7-10PM in 60 Evans. It will be a cumulative exam, covering everything we did in class except for the last week of material, corresponding roughly to Sections 1-20 and 22-34 in the book, as well as some of the scanned notes in metric spaces from Rudin on bspace (you will be responsible for what was covered in lecture). You are allowed to bring handwritten notes on three sides of 8.5 by 11 inch sheets of paper with you to the final. Here are a few practice problems for the exam. As usual, you are also welcome to browse the department's exam archives as well. We will be doing review and going over some of these problems during RRR week during usual class time, in the usual classroom. Solutions will be posted at the beginning of the week of the final. Good luck!

Course Syllabus

Professor: Elena Fuchs
Office: 851 Evans
Email: efuchs at math dot berkeley dot edu
Office hours: Tues/Thurs 2:30PM-3:30PM (Note Thursday time change!) or by appointment.

Textbook and Prerequisites:

The textbook we'll be using is Ross, Elementary Analysis (2nd edition). There are many other books you can look at for reference, for example the classic book by Rudin, Principles of Mathematical Analysis , or Lebl's book which you can download here.

The official prerequisites for this course are MAT 53 and 54. While we won't use too much of what you may have learned in these courses, the assumption is that taking them will have equipped you with the appropriate mathematical maturity needed for this class.

Homeworks, Exams, and Grading:

Your grade for the course is determined as follows: 15% for homework, 25% for each of two midterms, 55% for the final, and -20% for your lowest exam score. There will be no make up exams.

Homework (along with occasional supplementary notes) will be posted here and will be due every Tuesday at 5PM in class, or in my office by the same day/time (if you choose the office option, you can slide it under the door). The lowest two homework scores will be dropped. Therefore the policy is that no late homework will be accepted, especially since we will sometimes discuss the solutions to the homework problems in class.

The midterms will be in class on Tuesday, February 25 and Tuesday, April 8.

If you have a cold or flu, I ask you to please do yourself, your classmates, me, and my young child a huge favor by staying home and resting, rather than coming to class! If this happens I will work hard to help you catch up on notes and things you missed in class once you are healthy!

Course Outline:

Real Analysis, or the study of functions over the real numbers, is essential to not only the mathematician, but to the physicist, to the engineer, and beyond. In this course we will learn about the convergence of sequences and series, and will cover rigorously notions of continuity and differentiability of functions over the real numbers. We will also venture into topics such as integration and metric spaces. Much of this has been introduced to you in courses such as Math 1A and 1B but we will focus more on mathematical rigor than on computation, which is key to truly understanding and appreciating the subject.

For many students this course may be the first (or one of the first) course in which they are challenged to think like a mathematician: through homeworks, exams, and hopefully discussions with classmates, students will become comfortable with creating and writing rigorous mathematical proofs. This skill is essential to all upper division courses in mathematics, and to any mathematician in general.

Basic Plan:

We will try to cover sections 1-37 in our book, which are roughly structured as follows:
Detailed Plan:

The following is a rough outline of what we will be doing in lecture every day, along with the relevant sections in the book. In reality, we may move faster or slower. It will be updated on a regular basis.
Some supplementary notes:

Homework assignments:

Graded homeworks can be picked up in office hours or in class on Tuesdays. Graded midterms can be picked up in office hours.