Course Description

MAT 290 really has three goals in aspiring to this grand vision:

• to be a ``transition'' course in mathematics, helping to lead students from courses in the calculus sequence to theoretical upper-level mathematics courses;
• to be a ``survey'' course in mathematics, describing the intriguing questions and insights fundamental to many diverse areas of mathematics;
• to be a ``fun'' course in mathematics, blending play and challenge, joy and frustration in the quest for understanding, truth, and beauty.

The official Centre College Catalog description for MAT 290 is:
This course develops the abstract thinking and the writing skills necessary for proof-oriented mathematics courses and surveys various areas of mathematics. Fundamental concepts and questions are studied from mathematical logic, abstract algebra, number theory, and real analysis. Further topics include complex analysis, statistics, graph theory, and/or other areas of mathematics according to the interests of instructor and students. Prerequisite: MAT 171.

Class Schedule

Section	Meeting Time	Meeting Place
A	MWF 10:20 - 11:20	Olin 107

Your Professor

Your Textbook

Your Grade

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

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 two elements of my practices in testing and grading. First, 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. Second, I expect you to articulately express focused and complete solutions to the questions you are answering. 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. In my experience, this combination of challenging questions and thorough responses 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 23 - 25 of the Centre College 2007 - 2008 Student Handbook.

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 Class Attendance. 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.

During the term, you will create a ``proof portfolio.'' For 10 of the 13 weeks of the term you will be assigned one proof that you need to develop entirely on your own in consultation with your professor. The portfolio should contain all your scratch work leading up to drafts of proofs that I will comment on and a final polished product that will impress any mathematician -- including yourself! You'll gather all this information together into a single notebook or binder to create a complete proof portfolio by the end of the term. Grades for each of the 10 proofs will be recorded on a 5 point scale -- so each is worth about 1% of your final grade. More details will become available on the Homework Schedule webpage.

Quizzes are taken every day at the end of class; there are no make-up quizzes. The quizzes will cover the material we studied the previous class. While taking the quiz you are free to consult the homework you will submit with your quiz that day. On the other hand, you may not consult the textbook nor your in-class notes. 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.

Homework is an essential daily 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 assignments are found on the Homework Schedule webpage.

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. 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.

Homework is assigned daily 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. When your quiz/exercise/reading paper is returned, you will find the grade reported on a 15 point scale - 5 for quizzes, 9 for a subset of the exercises, and 1 for reading. At the end of the term, the lowest grade is dropped, the remaining grades summed, and the result normed to the 90 points of your Class Participation grade for the daily quizzes, homework exercises and reading assignments.

Exams

Exam	Date	Time
Midterm Exam 1	February 27th	one hour in-class
Midterm Exam 2	March 28th	one hour in-class
Midterm Exam 3	April 23rd	one hour in-class
Final Exam	May 12th	8:30 - 11:30

Class Attendance

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 reason, 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 19 - 20 of the Centre College 2007 - 2008 Student Handbook.

In the past, some of my 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.

Study Sessions

Some Thoughts on Exercises and Proofs

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 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 mathematics improve each week of this term. And more importantly, you will experience a positive change in how you think, and explore ideas, and express your insights into our world.

Basic 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 and help 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 for other classes and organizing calendars are not mathematics),
• reading during class is encouraged, provided that it is primarily devoted to mathematics (most newspapers and humanities textbooks do not contain mathematics),
• 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 so we can make the best use of our time together.

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 page 61 of the Centre College 2007 - 2008 Student Handbook.

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. Before you leave the first class, you should know how to be in touch with at least two of your classmates.

In many ways, mathematics is really about asking questions and then searching for, and hopefuly finding, truths in answer to our questions.

Some Final Thoughts

We are an intelligent species and the use of our intelligence quite properly gives us pleasure. In this respect, our brain is like a muscle...when it is in use, we feel very good. Understanding is joyous! Carl Sagan

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