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Berkeley MATH 104 - Syllabus

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1 University of California, Berkeley Department of Mathematics Mathematics 104: Introduction to Analysis Bob Anderson Spring 2005 [email protected] Tuesday, Thursday 11:00-12:30, 71 Evans 510-642-5248 Text: Kenneth A Ross, Elementary Analysis: The Theory of Calculus 501 Evans Graduate Student Instructor: Aubrey Clayton, [email protected], 891 Evans Aubrey will be working with students in all five sections of Math 104 this semester. He will hold workshops and office hours on Mondays and Tuesdays, times TBA Purpose: The principal purpose of this course is to train students to create and write proofs on their own. We will give a rigorous development of the theory of calculus. Prerequisites: Math 53 and 54. Course Requirements: 20% Weekly Homework Assignments, due in class each Tuesday (except Tuesday March 15). I will count the best 12 of 15 problem sets 30% Midterm Test Thursday March 10 5:00-8:00pm (location TBA) 50% Final Exam Wednesday May 18 8:00-11:00am (location TBA) Office Hours: Bob Anderson: Wednesday 1-3 in 501 Evans, or at other times by appointment. The best way to reach me outside of class is via e-mail: [email protected]. All E-mail from students in the class will be answered. Aubrey Clayton’s office hours will be on Mondays and Tuesdays, times TBA. Class Web Site: All class assignments, announcements, and problem set solutions will be posted at http://emlab.berkeley.edu/users/anderson/Math104/104index.html. This will be the most convenient way for you to access course materials, and it is strongly recommended that you use it. You can access this site from either Netscape or Internet Explorer. Homework Assignments: The homework assignments are the most important part of the course. You can only learn mathematics by doing it yourself; you only really understand mathematics well when you can explain it to others. You are encouraged to work with others on the homework assignments, but you should not copy someone else’s solution, since that defeats the whole purpose of doing2 the homework. If you work with others on a homework problem, the best way to ensure you really understand the solution you arrive at jointly is to write out the solution on your own. Curve: I don’t adhere to a rigid predetermined grade distribution when assembling the final letter grades. I have in mind a particular standard for what constitutes an A, a B, and so on. In principle, I would be willing to award all A’s, or all F’s, if the performance of the class justified it; accordingly, you should not feel that you are in competition with other students, or that if someone else does well, that will hurt your grade. In practice, there are likely to be lots of A’s, B’s and C’s, and possibly some D’s and F’s. If you want an A in this class, you will need ability and hard work—likely 20 hours per week.3 Course Outline: This outline is an approximate indication of the timing of presentation of the course material; we may run slightly ahead of or behind schedule. The lectures will follow the proofs in the text quite closely; hence, it makes sense for you to focus on listening and understanding during the lecture, even if it means your notes are incomplete. Lecture Date Section 1 T 1/18 4 2 Th 1/20 4,5,7 3 T 1/25 7,8 4 Th 1/27 9 5 T 2/1 9,10 6 Th 2/3 10 7 T 2/8 10 8 Th 2/10 11 9 T 2/15 11,12 + handout on Lim Sups and Lim Infs 10 Th 2/17 12,13 11 T 2/22 13 12 Th 2/24 13 + handout on Contraction Mapping Theorem 13 T 3/1 13,14 14 Th 3/3 14,15 15 T 3/8 Question and Answer Session 16 Th 3/10 No class at 11:00; Midterm Test 5:00-8:00pm, location TBA, covers material through section 14 17 T 3/15 15 No problem set due this week 18 Th 3/17 17 T 3/22 Spring Break Th 3/24 Spring Break 19 T 3/29 17,18 20 Th 3/31 18 21 T 4/5 19 22 Th 4/7 20 23 T 4/12 21 24 Th 4/14 23,24 25 T 4/19 25,28 26 Th 4/21 28,29 27 T 4/26 29,32 28 Th 4/28 32,33 29 T 5/3 33 30 Th 5/5 34 31 T 5/10 Question and Answer Session W 5/18 Final Exam 8:00am-11:00am, location


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