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Course Policies Math 301 Real Analysis, Fall 2021

Overview

We will delve into the wonders of the real line and explore some of the surprising ways that our intuition can lead us astray when considering properties of the real numbers and continuous and differentiable functions. We will focus not only on the amazing, rich content of analysis but also on understanding the need for rigorous, precise mathematical exposition.

I also want you to think deeply about how some of the ideas and approaches from this class are applicable to the non-mathematical parts of your life. In other words, I think there are some worthwhile life lessons to learn from Real Analysis. We will discuss this throughout the semester. This is going to be a really fun fall!

The plan is that this will be more of a "normal" semester than last year, but there are still a lot of unknowns about exactly how things will play out, both for the campus overall and for each of us individually. We'll need to be flexible, and we might have to make some adjustments as the semester goes along.

Let's all be kind to each other, and we'll figure it out.

Goals for a 300-level Mathematics Course

Real Analysis plays an important role in your mathematical development and in the math curriculum at Wheaton. There are several primary objectives of any upper-level math course at Wheaton. In particular, by the end of this semester you should:

Goals Specific to Real Analysis

Much of the mathematical content we will study this semester can be motivated by:

How do we take intuitive ideas that we understand very well and make them more precise and rigorous?

Specifically, you should gain a deeper understanding of:

Expectations

Mathematics is a very active discipline that is best learned by doing rather than by observing. One of the features that makes your Wheaton education so special is that we have time in small classes to explore material together. The class meetings are not intended to be a complete encapsulation of the course material, but instead will focus on the major concepts from the Pre-Class Assignments and clarifying the more subtle ideas in the course.

You should expect to put in approximately 3 hours outside of class for each scheduled hour of class. In other words, expect to spend a roughly 9 hours per week on Real Analysis outside of the scheduled class meetings. There will be some weeks where you spend more time, and there may be some weeks where you spend slightly less.

The Honor Code

We operate under the Wheaton Honor Code for all of your academic work at Wheaton. This carries certain freedoms and responsibilities for both you as a student and me as a professor. I take this quite seriously.

Most likely, no Honor Code issues will arise this semester. If you are uncertain about whether a particular situation falls under the Honor Code, then please consult with me. However, if an Honor Code issue does come up, I will assume that you are prepared for the full consequences. Remember that you should write out, and sign, the following statement on all course work:

"I have abided by the Wheaton College Honor Code in this work."

Evaluation

Your final grade will be determined by

Pre-Class Forum Posts 5%
Class Engagement/Participation 10%
Problem Sets 30%
Three Take-home Exams 50%
Book Review 5%

Pre-Class Forum Posts

The purpose of reading the text before class is that if you are familiar with the basic concepts and definitions, then the class meetings can be devoted to the major ideas and subtleties of the material. Mathematical understanding is built in stages, and you will absorb the material more quickly if the class meetings are your second exposure to the fundamental ideas.

The Pre-Class Assignments include details of which secion(s) of the text you should read for the week. Analysis has some difficult, but beautiful, concepts that will take some time for you to process and to build your own understanding. I think you can learn a significant amount by asking questions and seeing what questions your peers ask. Most weeks, you will submit at least one comment/question about the reading to an onCourse forum by Monday at midnight, and reply to at least one comment by one of your peers by Wednesday at midnight.

I will grade your forum posts using a binary scale: If you make a serious attempt, you will get full credit. The purpose of these posts is to encourage you to engage with the material before class and to see what your peers are thinking. These posts will also give me insight into where the class is.

Class Engagement/Participation

A significant part of the class meetings will be devoted to working in small groups on problems that delve more deeply into the content from the readings and discussed at the beginning of class. A substantial amount of your learning will happen during these collaborative sessions by bouncing ideas off of other students and seeing how other groups approach the problems. I will also determine your Engagement/Participation grade for each class meeting using a binary scale: You were present and engaged with your peers or you weren't.

However, I also know that there may be times when you have a valid reason for missing class, especially this semester when there is so much uncertainty and we're taking extra precautions to keep each other safe. I'll be really flexible, so if you need to miss class, please let me know. Let's just keep the lines of communication open.

Problem Sets

You will have a Problem Set due most Thursdays at midnight. I firmly believe that one of the best ways to build your understanding of mathematics is to explore the ideas with other students. Therefore, you will work on the Problem Sets in groups of two, or possibly three, and each group will turn in a single set of solutions. I will randomly assign new groups for every problem set. Depending on the timing around exams and breaks, a few of the Problem Sets may be individual assignments instead. There are more details about the logistics and expectations for your write-ups of the Problem Sets on the course webpage.

Take-home Exams

The purpose of the exams is for you to demonstrate your understanding of the course material and, just as importantly, to give you feedback on where your understanding is strong and where you may need more work. The exams will be open-note take-home exams where you will have several days to work on them. See the Tentative Daily Syllabus for dates of the exams. I will provide more details about the structure of the exams as the time gets closer.

I know that exams can be stressful, especially with the other academic, extracurricular, and family commitments that you may have. To try to reduce some of this stress concerning your grade, I will weight your exam scores by differing amounts: Your lowest exam score will count 20% of your exam grade, the second lowest will count 30%, and the highest will count 50% of your exam grade. For example, if your four exam scores are 71, 82, and 93, then your overall exam average will be 85.3.

Book Review

The motivation for this assignment is that there are a lot of really interesting expository books about mathematics, and as part of your general education, you should develop the habit of reading them. This is an opportunity to learn about a mathematician or area of mathematics that you might not be exposed to otherwise. I’ll give you more details about the assignment a few weeks into the semester.

Getting Help with Real Analysis

Please come see me during my drop-in office hours! No appointment necessary! If you have a conflict and cannot make my office hours, please email me and we can set up an appointment for another time.

Remember that the goal of the course is to help you learn Real Analysis and develop as a mathematician! If there's any point where you feel that the structure of the class isn't working for you, please come by and we can figure out some possible strategies.

Having difficulty purchasing required materials?

Support is available for students having trouble purchasing required materials for classes. Students can contact Karen McCormack (mccormack_karen@wheatoncollege.edu) in the Office of the Provost for help finding support for required materials.

Accessibility at Wheaton

Wheaton is committed to ensuring equitable access to programs and services and to prohibit discrimination in the recruitment, admission, and education of students with disabilities. Individuals with disabilities requiring accommodations or information on accessibility should contact Autumn Grant - Associate Director for Accessibility Services at the Filene Center for Academic Advising and Career Services. ~ accessibility@wheatoncollege.edu or (508) 286-8215

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