Prerequisites: Senior standing as mathematics major and the completion of at least two ?300-level mathematics courses
Texts: 1. Excursions in Calculus - An Interplay of the Continuous and the Discrete, by Robert M.
Young. The Mathematical Association of America (MAA)

2. The Mathematical Experience, by Hersch and Davis

Grading: Class attendance and participation in discussions …………………………… 15%
(Attendance is expected and will be
explicitly noted)

Written assignments and presentations in class……….……………………... 25%

Successful completion of assessment test project ………………………………. 10%
Final paper & oral presentation ……………………………………………..... 50%

Remark 1. Class participation involves actively following and contributing to classroom discussions,
presenting solutions to problems, and interacting with other students in group sessions.

Remark 2. Among the writing assignments will be detailed solutions to problems (GRE and other), proofs
of theorems discussed in class, a mathematical autobiography, a review/assessment of an
article from a mathematics journal, an evaluation of another student’s work, and other
assignments developed with your help during the semester.

Remark 3. Some writing assignments may be given as class work.

IMPORTANT:Remark 4. All written work will be submitted again as a portfolio at the end of the semester.

Some Course Goals:
• To help students assess their knowledge of mathematics and their ability to apply that knowledge to solve problems
• To encourage students to integrate the mathematical knowledge they have acquired during their coursework and to make them aware of how they can use this knowledge to solve pure and applied mathematics problems
• To provide an opportunity for each student to further develop an ability for self activated study in mathematics through independent research and the writing of an substantial and polished expository paper
• To help students become aware of the extent and nature of the national and international mathematical community and how contact with this community can further their professional goals
• To help students develop an awareness of the extent and nature of the diverse branches of mathematics.
• To give students a writing intensive experience in mathematics.

Here are some of the important assignments for this course:

FIRST WRITTEN ASSIGNMENT (Due Monday, Jan. 22) Read Is Mathematics Necessary? by Underwood Dudley. Read the Preface and Introduction to The Mathematical Experience. Find out who Gian-Carlo Rota was. Find out what the Glasperlenspiel is. Who thought it up? Hand in a summary of the main points made in Is Mathematics Necessary?.

SECOND WRITTEN ASSIGNMENT (Due 1/24):
One of the goals for you in this course is for you to assess your mathematical progress and to reflect upon the next steps you will be taking towards starting your professional career. The first assignment asks you to write a "mathematical autobiography" in which you describe your experiences learning mathematics.
You should make references to the article Is Mathematics Necessary by Underwood Dudley and the sections in The Mathematical Experience entitled “The Ideal Mathematician” and “A Physicist Looks at Mathematics”, both in chapter 2. Other things may be included, such as your plans for involvement with mathematics in the future.

ARTICLE REVIEW AND SUMMARY: (Due February 7
You are to select with my help, study, summarize and review an article from a mathematical journal. Details about this assignment will be discussed later. Ideally the area of the article you choose might be related to your research topic.

FINAL PAPER AND PRESENTATION
The final paper and presentation must be developed throughout the semester must be on a topic about which you do extensive new research and study during this semester. You MAY develop the paper while working with a group studying a particular area of mathematics, or you can work independently. Members of a group will eventually focus on a different aspect of the topic and your final paper and presentation will be organized around the overall responsibilities of the group to give a thorough and understandable presentation of the topic to the class. Your paper will be your own work written by you. You must do independent research, write well, and write about and orally present appropriate mathematical content.
The purpose of this project is to show you that you know how to learn new mathematics on your own and in groups and how to communicate effectively with others about your learning. You will find that you will learn from your own efforts and the work of others.