Math 446 - Real Analysis I

Inga Johnson
Assistant Professor
Department of Mathematics
Willamette University
Ford 212
ijohnson(at)willamette(dot)edu
503.370.6551

Math 446 - Real Analysis I - Syllabus
Class Meetings: MW 12:50-2:20 in Ford 224

Course Goals: At the heart of any analysis course is creating a solid and clear understanding of the limiting process. A goal of this class is understanding the limiting process for general metric spaces, and in particular for real valued functions. We will make rigorous the ideas of limits and continuity from the traditional calculus classes. We will learn about the concepts of Cauchy sequences and completeness, compactness, connectedness. Students will be able to solve problems and prove statements regarding the content and concepts listed above. Students will be able to analyze sophisticated mathematical arguments to determine validity and completeness of the argument. Students will develop the ability to read and analyze mathematical texts. Students will become effective communicators of mathematical ideas and arguments.

Textbook: Closer and Closer: Introducing Real Analysis by Carol Schumacher
Errata for this text can be found here.

Course Grades: Your course grades will be calculated as follows:
Homework, Class Participation, Class Presentations: 40%
Quizzes: 10%
Midterm Exams: 25%
Final Exam: 25%

Class Procedures: This will not be a standard lecture class. In fact, lectures will be short and infrequent. Instead of "receiving" or "listening to" lectures you will be actively creating mathematics as you learn about the area of mathematics called Real Analysis. More specifically, class time will be spent (i) working in small groups on problems from the textbook or on other learning activities, (ii) presenting solutions to previously assigned homework, and (iii) discussing the upcoming reading assignment. As the instructor of the course, my role will be to orchestrate learning opportunities. It is your role to take advantage of these opportunities and engage in the material as deeply as possible. Your active participation is required. Needless to say, as class participation is so central, attendance is expected except in cases involving illness or other extenuating circumstances.

Homework: Homework will be assigned at every class period and will include two types of problems, "presentation problems" and "notebook problems." Presentation problems are problems that you should prepare for presentation in class. You will be expected to use proper mathematical notation and English grammar in both written work and oral presentation. Notebook problems are problems that you will write up and accumulate in a notebook, but may not be discussed in class. Your presentation and notebook problems should be neatly organized and clearly labeled in your notebook. I will collect the notebooks about every two weeks and look them over. The problems will be graded on a scale of 1 to 5. (I reserve the right to assign 6 points to an exceptionally well written or elegant proof!) You should not think of the grade as representing a percentage but, rather, as delivering a message:

5 --- excellent work; no real complaints on content or on writing.
4 --- argument basically correct but missing some details/less clearly argued than I would like.
3 --- argument mostly correct, but there is a misstep in the mathematics; an especially poorly written proof might merit a 3, as well.
2 --- serious gaps in the mathematics.
1 --- some ideas in the right direction, but didn't really get there.
0 --- didn't do the problem or it was completely wrong.

I will use my reading of your notebook problems and your presentations to keep track of your progress in the course and give helpful feedback as I can. As you work on the homework problems, I encourage you to work together, come see me outside of class, etc. I expect that the problems will be written up neatly and fully. In each set of notebook problems, at least one problem must be typeset in LaTeX. Essentially this means two problems per week must be LaTeXed.

Class Presentations: I have said that most of the class will consist of students presenting work to each other. You will be expected to do your share in this. Most of the time I rely on volunteers to make presentations. This makes it possible for students to present the work about which they feel most confident. But the fact that so much of the grade depends on this participation means that all students must volunteer on something like a regular basis. Do not assume that because others volunteer, you (or your grade) are off the hook. The good news is that you probably won't end up having to get every problem assigned during the semester. If you don't get it, someone else will, and you will get to see the fruits of their labors.

The person who is presenting his or her work at the board is not the only person with responsibilities in a presentation. The students sitting at their desks have as central a role to play. Students presenting their work are not meant to replace a seasoned, polished lecture that would be given by an experienced instructor. Nor should they be made to. They are counting on their fellow students to help them by making clarifying suggestions and asking questions. I will feel free to ask questions of persons who are sitting down.

Quizzes: I will give periodic short quizzes in class in which you will be asked to reproduce a proof from the text, statements of definitions, and/or proofs from class. The purpose of these quizzes is just to make sure you that internalize a handful of very important standard proofs and definitions.

Midterm Exams, and Final Exam: Midterm and Final Exams will have two components, an in-class component testing your understanding of important definitions, examples and central ideas. You will be asked to state precise definitions, answer true/false questions and short answer questions on the in-class portion of the exam. The take-home portion of the exam will include solving problems and proving statements that you have not previously seen. I expect solutions to take-home exams to be typed using LaTeX.

Special Note: If you have a documented disability and anticipate needing accommodations in this course, please make arrangements to meet with me within the first two weeks of the semester. If your disability allows for you to have extra time on exams, you must make arrangements with me three days before the scheduled exam date. Please request that a Disability Services staff send me the appropriate forms verifying your disability and specifying the accommodation you will need.

Academic Honesty: In accordance with Willamette University CLA catalog: ``Plagiarism and cheating are offenses against the integrity of the courses in which they occur and against the College community as a whole... Ignorance of what constitutes plagiarism shall not be considered a valid defense. If students are uncertain as to what constitutes plagiarism for a particular assignment, they should consult the instructor for clarification. A faculty member may impose penalties for plagiarism and cheating ranging from a grade reduction on an assignment or an exam to failure in the course." For further information about the Willamette University academic honesty policy please refer to the CLA catalog.