Math 101: Introduction to Analysis Office Hours: Erica Flapan T 11-12:00 Millikan 226C M, W, Th 1:15-2:15 x 18711 email@example.com Goals of the Course: 1. To learn the language of analysis. 2. To improve your ability to construct rigorous proofs. 3. To obtain a deeper understanding of the theory behind calculus. 4. To build a solid foundation for Math 131 (Principles of Real Analysis). 5. To practice presenting mathematics and learning from the presentations of others. Philosophy of the Course: If you want to become an artist, you have to begin by mastering techniques for seeing and representing reality, and only then can you move on to abstract representation. If you want to learn to speak a foreign language you must begin by mastering correct grammar and spelling, and only then can you loosen up your grammar and speak in slang. Similarly, in analysis, you must first learn how to express your arguments in a formally correct way, and only then can you begin omitting details from your proofs. In this class we learn the formal way to express analysis. We begin by discussing results that are quite familiar, in order to be able to focus on how the arguments should be written. Then we move on to some new ideas, once you have mastered the basics of the language. Course content: Properties of the real numbers, the Least Upper Bound Axiom and its consequences, sequences, subsequences, continuity, and additional topics as time allows. Homework and group problems: The only way to learn to do proofs is to do them. For this reason, the homework is the most important part of this class. I expect you to spend about 8-10 hours each week on homework. Individual homework will be due every period. In addition, there will be more challenging group problems that are due every other week, and will be presented in class. All of the homework will be graded on the basis of rigor, exposition, and completeness. All of members of the group should participate in solving the group problems and be capable of presenting the solutions in class. However, you should rotate who writes up and presents the solutions to the group problems. Writing problems on the board: Seeing the solution to a problem critiqued is an important way to learn to improve your writing. Each period 1-2 students will arrive 10- 15 minutes (or more) early to write the solution to a problem on the board. You should be finished writing on the board by the time class begins. I will correct these problems in front of the class, explaining how the solutions could be improved. The solutions on the board should be anonymous so that the authors will not be uncomfortable when I critique the solutions. You should choose to write up a problem that you are unsure of in order to learn more from my comments. If you are unsure of a group problem that has already been presented, you can choose to write that solution on the board. In addition to students assigned to write up problems on a given day, anyone else can write up problems if they wish to see a problem corrected. Group Term Project: The class will be divided into three groups for the term project. The term project involves independently learning a topic that is not covered in the course, and giving a 45 minute oral presentation on the topic at the end of the semester. I can help you find books or articles on your topic, and help with any difficulties you have learning the material. You should plan to spend a significant amount of time understanding the material for your project and preparing for your presentation. The project is a good way to raise your grade in the class, so it is worth putting in a little extra time to do a great job. For more detailed information about the project see the hand out on my website http://pages.pomona.edu/~elf04747/teaching.html Exams: There will be three 2-hour midterms and a 3-hour final exam. The midterm problems will be drawn directly from the individual and group homework problems. The best way to study for the exams is to redo the problems that were assigned to make sure you know how to do all of them. No cheat sheets or notes are allowed during the exams. The 2-hour midterm exams will be split into two 1-hour parts, taking place during two class periods. The first midterm will be on September 23 and 25, the second midterm will be on October 28 and 30, and the third midterm will be on November 20 and 23. The final exam will be at 9:00 AM on December 18. Getting Help: If you have any questions about the material, the homework, or the course you should come to my office hours and/or the mentor sessions. If you cannot make my office hours, I am happy to make an appointment with you at some other time. The mentor for our class is Dwayne Chambers, who is a math graduate student at CGU. Dwayne knows the material well and he is happy to help you. Dwayne will run mentor sessions on Tuesday, Wednesday, and Sunday evenings from 7:00 PM to 8:00 PM. Mentor sessions will be in our classroom or a nearby classroom. The mentor sessions should help you collaborate with your peers, get help on the homework and group problems, and study for the exams. Since the mentor sessions are only an hour long, you will get the most out of them if you have already worked on the problems before you go to the sessions. Grades will be computed according to the percentages: Individual homework 15% Group homework 10% Term project 10% Midterms 15% each Final exam 20% Technical Details: The text for the class is Elementary Analysis: The Theory of Calculus, by Kenneth Ross. Some of the homework will be taken from the book, and some will be my own problems. I will post the homework and group assignments on my website. http://pages.pomona.edu/~elf04747/teaching.html Unless I tell you otherwise, there is a new assignment due each period. In order to avoid having to stop students from copying homework solutions from the board during class, I require that you hand in your homework when you arrive in class. Even if you arrive late, you must hand in your homework before you sit down. If you feel that you need a copy of your homework solutions to look at while we are going over a problem, you should make a copy of your homework before class. I do not accept late homework (except under unusual circumstances). So do not tell me that you forgot your homework in your room, and do not put your homework in my mailbox or the grader’s mailbox. If you have to miss class, give your homework to another student to hand in for you. After the group problems are graded the group will rewrite them and present the solutions to the class. I am happy to meet with you to discuss my comments and to help you figure out how to fix your proofs. The rewrite should contain all of the changes that I suggest in my comments. The rewrite should be written on only one side of the paper in black ink with large neat print, leaving enough room for additional corrections to be added. Each problem should clearly state the assignment number, the group letter, and which problem it is. Your rewrite should be handed in by 9:00 AM on the class day following when the graded problems are handed back.
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