Textbook

There are three required books for this course:

1. Flatland, A Romance of Many Dimensions,, E. Abbot, Dover Publications,
2. Fragments of Infinity, A Kaleidoscope of Math and Art, I. Peterson, J. Wiley \& Sons,
3. Symmetry, H. Weyl, Princeton University Press.

In addition to these books, we will read various articles and some sections from other books. I will give these as handouts as the course progresses. (The bottom line is that there is no one text book that is suitable for such a course!) In addition, there are many websites which will be useful resources on different topics. I will provide links to these on the assignments page as we go along.

Pre-requisites

Students in this course should have competence in algebra and geometry, and a definite interest in analytic thinking. The course objective is to use your interest in art/nature to develop your interest in mathematics, or vice versa.

If you have any concerns about your preparation for the course, or questions about possible resources for brushing up on your algebra and geometry skills, please see me as soon as possible!

Instructor

Professor Sharon M. Frechette

Office: Swords 321

Office Hours: here

Phone: 508-793-2257 or email (preferred)

Topics

There are numerous connections between mathematics, art, and nature. Some of these we will explore together, through readings, class discussion, writing assignments, and problem sets with significant mathematical content. Others you will explore on your own in the form of a course project/paper with in-class presentation (see below). Topics will be drawn from the following:

1. Symmetry.
2. Perspective drawing.
3. The Fibonacci numbers.
4. Kaleidoscopes.
5. Tesselations of the plane (including the art of M.C. Escher).
6. Twentieth-century geometric art.
7. Mathematics in paper-folding and origami.
8. Chaos and fractals.
9. Topology of Celtic knot designs.
10. Geometry of Dahlia patterns.
11. Use of proportion in art and architecture.
12. The Platonic solids.
13. Proportion and the Golden Mean.
14. Mathematics in music and rhythm.
15. Mathematical Platonism.

Class time will include a mixture of activities. Readings for each class will be assigned in advance. It is essential that you keep up with the readings, in order to make the best use of class time. Sometimes I will lecture briefly on the mathematical content of a new topic, and then give in-class activities/exercises for you to work on in small groups. Sometimes we will have a discussion as a whole on the readings. Instead of midterm exams, we will have {\em short} weekly quizzes which will focus on the material from the past few classes. At the end of the semester, class time will be spent on student presentations of your course projects/papers. I hope this will be a rich blend, making our class time together both interesting and challenging!

Grades

Course grades will be computed according to the following percentages:

Homework & quizzes	30 %
Class participation	10 %
Writing assignments	25 %
Course project/paper	25 %
In-class presentation of course project/paper	10 %
Total	100 %

Homework & Quizzes

Homework will be assigned daily (or sometimes weekly) on the Assignments page. Homework will usually be collected weekly. (Due dates will always be listed on the assignments.) {\bf Late homework will not be accepted.} I encourage you to discuss homework problems with other students and/or with me. Most of us understand math better when we have to verbally communicate about it! However, {\em all solutions that you turn in must be written in your own words.} If you discuss homework assignments with other students or with me, you must list the names of all such "consultants" at the top of your assignment.

Quizzes will cover the mathematical skills essential to your learning in the course. Quiz questions will be similar to homework and in-class problems. Quizzes will be given at the beginning of class and will be {\em short}. I expect they will only take about 10 minutes or so to complete. There will be no makeups for missed quizzes. However, I will drop your lowest two quiz scores.

Some things to keep in mind while doing your homework assignments, for our mutual benefit:

• Please be neat! Write up the problems in order, write only on one side of the page, and staple your assignment together. Leave lots of space for me to write comments.
  
  
• For most problems, you should copy out the problem statement before giving the solution. Exceptions to this would be problems where the instructions are very lengthy. In that case, it will suffice for you to give a few phrases which clearly indicate to the reader what question you are answering.
  
  
• Show enough work so that a confused student in the class could follow your solution. Don't expect that the reader already knows how to solve the problem. Just writing the answer is almost never sufficient.
  
  
• In many problems, your answer will need to be expressed in the form of a sentence, although this may contain mathematical symbols and statements. Proofread what you have written to be sure it makes sense.
  
  
• Start the assignment early (i.e. the day it is handed out). This will allow you ample time to consult with me or your classmates if you get stuck on some problems. If you start the assignment on the day before it is due, you will probably be very unhappy!
  
  
• Start the assignment early (i.e. the day it is handed out). This will allow you ample time to consult with me or your classmates if you get stuck on some problems. If you start the assignment on the day before it is due, you will be very unhappy!
  
  
• Work on making your explanations clear and concise. Make good use of notation and diagrams wherever relevant.
  
  
• If you work with other students on homework problems, as you are encouraged to do, you {\em must} write up your final solutions independently. Plan on taking scrap notes when you work out the problem first, and then "writing it up" in a clean form {\em by yourself} afterwards.
  
  

Writing Assignments

Writing assignments of varying length will be given throughout the course. A writing assignment may be to simply give your impressions of a class discussion in a few informal paragraphs. It may be a short paper based on the readings, with specific questions on which you should focus. No writing assignment will be longer than five pages. Due dates will be appropriate to the length of the assignment.

Course Project

Instead of a final exam, you will have a final course project/paper. You will give an in-class presentation on this project towards the end of the semester. Mid-way through the semester you will submit a written abstract of your proposed topic, and we will meet to discuss your plan. The goal here is for you to take a topic covered in class and explore it more in-depth, or to weave in new material with a different topic of your choice. Your project will consist of a research paper, together with original artwork which illustrates your topic. You will present your project to the class, explaining the mathematical content and your choice of artistic rendering of it. Projects/presentations will be graded on both content, style, and originality.

Academic Integrity

The College's policy on Academic Integrity, as well as the more specific Mathematics Departmental Statement on Academic Integrity must be strictly observed. For this course, the following addenda apply:

• All quizzes will be closed-book, and no sharing of information in any way is allowed during a quiz.


• If you discuss homework assignments with other students or with me (as you are encouraged to do!), you must list the names of all such "consultants" at the top of your assignment.