An Invitation

For the most part, you are free to take whatever courses you would like here at Centre College. However, once you have made the choice to be a math major, you have to take MAT 380. Why do you think this is so? I encourage you to think carefully about why you have chosen to be a math major and why this class is part of the math major. What goals do you have in taking this class? What do you expect MAT 380 to give you? And, in light of your answers to these questions, what are you willing to give to this class? What investment of your time and your energy will you make? Such an intentional approach to this class will make a profound difference in your experience of MAT 380.

You should know that my primary goal is to enable your success in learning real analysis. I love the ideas in this course. They are beautiful and rank among the deepest of all of humanity's insights into reality. They are worthy of our attention. And they will change you, if you allow and chase this change. And so, I offer you an invitation to study real analysis with me. What do you think?

Course Description

The topic of this course is the calculus: a mathematical approach to working dynamically with the concept of change. The solutions of the seemingly disparate questions of finding tangent lines and computing areas beneath curves were united by Leibniz and Newton in the 1700's, producing powerful computational tools that fundamentally altered the sciences and our world. From your freshman-sophomore level calculus courses you are familiar with the computational side of the calculus. In this course, we explore and develop the theoretical side of the calculus.

We will work our way through most of Understanding Analysis. We begin by developing a good understanding of the real numbers (Chapter 1), sequence of reals (Chapter 2) and the topology of the reals (Chapter 3). We then take up the study of the calculus - limits and continuity (Chapter 4), differentiation (Chapter 5), sequences and series of functions (Chapter 6), and integration (Chapters 7). Throughout the course, the objective will be understanding the "why" of this beautiful and powerful mathematical theory and, by the end of the course, you will have developed a thorough understanding of Leibniz's and Newton's insights in developing a mathematical approach to the concept of change.

Your Professor

Your Textbooks

If you are interested in learning real analysis, then you will want to spend time reading these books, in addition to working on the exercises at the end of each section. A great many ideas from calculus will be discussed during class, but your individual study of these texts remains invaluable. For some of my thoughts on reading mathematics texts click here.

Attending Class

Section	Meeting Time	Meeting Place
A	MWF 1:50 - 2:50	Olin 129

The college has made provisions for excused absences for official college-sponsored activities and for verified medical illness. If you will miss class for these reasons, you must follow the procedures established by the college. I would also appreciate personal contact from you, especially when we must make arrangements for submitting work. For further details concerning class attendance and absence policies, see pages 20 - 21 of the Centre College 2009 - 2010 Student Handbook.

In the past, some students have chosen to take unexcused absences from class. My observation is that this has a detrimental impact on the learning process. In order to help highlight this impact and to emphasize the importance of class attendance: after three unexcused absences, every additional absence will result in a one-third letter grade reduction of your final course grade.

Your Questions

In addition, I expect that you will spend time talking with your classmates about the ideas we are studying. Often mathematics is pursued as a solitary endeavor and there are many times when focused, individual effort is essential. But just as important is the time you spend working with your colleagues to find answers to your questions. In many ways, mathematics is really about asking questions and then searching for, and hopefully finding, truths in answer to our questions.

I really enjoy thinking about why various mathematical statements are true. Most of the time I start by looking at some examples that seem to be related. Sometimes these examples will have some common property and by looking at how that property develops in the examples, I can understand a reason why a statement is true. Such a reason will often be a main idea in an exercise or an argument for why the mathematical statement is true.

Looking at examples, crafting proofs, and solving exercises takes a lot of time. In contrast to many activities in our fast-paced society, solving the types of exercises we will consider and writing complete solutions requires focus, attention, perseverance, and effort every day. Students do not successfully cram for an exam in this class! Learning math is a lot like being a part of a sports team -- players must practice every day. Most students say that studying at least ten hours a week is a minimal requirement. You should explicitly and intentionally think about your schedule and when you can make the study time you need to succeed in this course.

As with most things that require great effort, the rewards are tremendous. I am confident that you will see your computational and theoretical abilities in calculus improve each week of this term. And more importantly, you will experience a positive change in how you think, explore ideas, and express your insights into our world.

Class Participation

There are several components to class discussion. You are expected to attend every class; unexcused absences result in the lowering of a grade as detailed under Attending Class. If you are running late, come to class as soon as you can -- we will live by the adage: "Better late than never!" During class, you are encouraged to make comments, ask questions, and hop in any time during the conversation. Finally, there are the intangibles: positive attitude, general interest and attentiveness, and a willingness to give every question some good solid effort.

Homework is an essential aspect of this course -- you must do math to learn math! In this sense, homework is assigned for your benefit; to provide important practice with the ideas and techniques we study, enabling you to achieve mastery of the calculus. Homework is assigned daily on the Homework Schedule webpage and collected at the end of the following class period; late homework is not accepted. For excused absences, you should arrange to have your homework submitted by the end of the class period in which the assignment is due.

The first part of your homework consists of various exercises assigned from the section we are currently studying. The solutions you present must be complete, coherent, and well-organized. A couple of these exercises will be presented at the beginning of each class, while a couple of them will be graded. The second part of your homework consists of a reading assignment and reading questions. You should read the appropriate section of your book before coming to class and submit your answers to the reading questions with your homework exercises. For some of my thoughts on reading mathematics texts click here.

Quizzes are taken every day for five minutes at the beginning of class; there are no make-up quizzes. The quizzes will cover the definitions and theorem statements from the previous class. If you do your homework every day and look over your notes a bit before class, then you should do fine on the quizzes, and they should ultimately help you succeed on the midterm exams.

During the term, you will read five or six articles on the history of mathematics and answer some questions in response to the articles. During the term, you will submit two autobiographical documents -- a resume and an automathography. These papers will provide you an opportunity to reflect on some questions relevant to your study of mathematics and your preparation for work during and after your time at Centre. You will submit hard copies of these papers to me and electronic copies to turnitin.com, the standard service used by the college for assessing the originality of student papers. More details about these papers are available on the Homework Schedule webpage.

Exam Schedule

The Midterm Exams are one hour in length and are taken during class. The Final Exam is comprehensive and is taken at the time designated by the Registrar at the end of the term. The exam schedule has already been established and is given below. If you have an excused absence for a college activity, please let me know at the beginning of the term; in addition, you must make arrangements with me for a make-up exam at least one week in advance of the actual exam. The exams will take place on the following dates and times:

'

Exam	Date
Midterm Exam 1	September 23rd
Midterm Exam 2	October 21st
Midterm Exam 3	November 18th
Final Exam	December 10th

Your Grade

Class Participation	150 points	25%
Midterm Exams (3)	300 points	50%
Final Exam	150 points	25%

The 150 points for Class Participation is split up: 110 points for daily quizzes, homework exercises, reading questions, and the response questions to the history articles; and 40 points for papers and class discussion. Quizzes, presented exercises, and reading questions are graded on a 2 point scale. The other exercises on a more variable scale - the points assigned will be clear. You will be allowed to resubmit graded exercises with a sufficiently low score before the next class period for regrading. At the end of the term, the grades are summed, and the result normed to the 110 points of your Class Participation for the daily quizzes, homework exercises and reading assignments.

My usual grading scale is A: 100-85, B: 84 - 75, C: 74 - 65, D: 64 - 55,= and U: 54 - 0. In addition, your final letter grade is influenced by class attendance; see Class Attendance below for more details. This grading scale is a result of three elements of my practices in testing and grading. First, I expect you to have a lot of mathematics right at your fingertips for the exam. For most questions you should not so much be figuring out how to go about solving them, as immediately recognizing the appropriate solution technique and then implementing that process. Second, I expect you to articulately express focused and complete solutions to the questions. When grading, I carefully consider your responses and provide the feedback you deserve in light of the effort you will take to craft your answers. Third, I often include at least one question on your exams that requires some original thought and creativity. You deserve to be asked such questions and I hope you will enjoy the challenge and the opportunity these questions present. In my experience, this combination of thorough and challenging questions and feedback helps students learn a lot of mathematics really well.

As the term progresses, I will provide a summary of your grades and announce a grading scale after each exam -- this should enable you to have a clear idea of your standing in the course throughout the term. For further details concerning grades, see pages 24 - 25 of the Centre College 2009 - 2010 Student Handbook.

Academic Honesty

Disabilities

You should be reassured that Centre College is committed to making its programs accessible to all. In the higher education setting, the student is responsible for informing the college of disabilities that require accommodations and the student must initiate the process for obtaining appropriate accommodations immediately -- accomodations for disabilities cannot always be granted at the last minute and will not be granted after the fact. For further details concerning the academic aspects of disability services, see pages 59 of the Centre College 2009 - 2010 Student Handbook.

Etiquette and Expections

• attend every class,
• prepare for class (this includes completing your homework and taking a few minutes to glance through your notes before coming to class),
• wear proper classroom attire (proper dress is a reflection of our respect for our educational endeavor),
• arrive and get settled into your seat before the bell rings so that we may begin class on time,
• if late, come to class as soon as possible; better late than never,
• if late, take a seat near the door,
• if leaving early for an excused absence, please let me know and sit near the door,
• stay awake and alert during class (naps are best taken in a bed or on a couch, which are not standard classroom furniture),
• eating and drinking should be taken care of before or after class, or at least done discreetly (many chip bags make loud crinkly noises that can be distracting),
• turn off (or choose not to bring) cell phones and other noisy electronic devices to class; we'd both prefer not to have class interrupted by beeps and/or songs,
• ask questions during class and do not let too many moments of confusion and uncertainty drift past you; class is a time to learn and your questions will be of interest to others,
• talking during class is encouraged, provided that it is primarily devoted to mathematics (making weekend plans and insulting fellow classmates are not mathematics),
• writing during class is encouraged, provided that it is primarily devoted to mathematics (completing homework and papers for other classes and organizing calendars are not mathematics),
• reading during class is encouraged, provided that it is primarily devoted to mathematics (most newspapers, text messages, and humanities textbooks do not contain mathematics),
• texting during class is discouraged; help yourself and your colleagues learn the mathematics we are studying by staying single-mindedly engaged in class;
• feel free to use the restroom during class (although daily visits to the restroom 15 minutes into class are discouraged),
• come to class and to office hours with a list of questions about specific exercises or topics; occassionally "I have no idea what is going on" is an appropriate opening statement, but most often you should take the time to identify your points of confusion to help us make the best use of our time together.

Some Final Thoughts

Whatever is true, whatever is honorable, whatever is just, whatever is pure, whatever is lovely, whatever is gracious, if there is any excellence and if there is any thing worthy praise, think about these things.
Phillipians 4:8

Here's another reason to study calculus: because calculus is among our species' deepest, richest, farthest-reaching, and most beautiful intellectual achievements.
Arnold Ostebee and Paul Zorn