The course described on this page

ended December 18, 2008

## Math 110: Discovering in Mathematics,

Section 2Department of Mathematics and Computer Science Hobart and William Smith Colleges Fall 2008. Instructor: David J. Eck. Monday, Wednesday, Friday, 3:00 to 3:55 PM. Room Eaton 110. Course handout: http://math.hws.edu/eck/courses/math110_f08.html

## Final Exam: December 18

The final exam for this course takes place at 8:30 AM on Thursday, December 18. An information sheet is available.

## Fifteenth Week: December 8, 10, and 12

The final reading from

Symmetry, Shape, and Spaceis Sections 7.1 and 7.2, excluding the part about Volume Formulae on pages 212 to 214. We will be working on this material in class on Monday and Wednesday, with a handout on Monday.For Friday's class, you should read and be prepared to discuss the last two chapters in

The Math Instinct, Chapters 12 and 13, pages 239 to 264.The final homework, a short assignment on mathematical infinity, is due in class on Wednesday.

## Fourteenth Week: December 1, 3, and 5

Once again, I am changing the schedule. For the last two weeks of class, we will start by looking at the concept of infinity for two days. A short homework on this topic will be handed out on Wednesday. After that, we will work on Sections 7.1 and 7.2, with an in-class group assignment from those sections some time next week.

For Wednesday of this week, you should read Chapter 5 in

ZERO: The Biography of a Dangerous Idea. This is the final reading from that book.Don't forget that the pictures from Assignment 11 are due by Wednesday. If you have not already sent them to me by email or put them in my drop box, do so by then. Also, the outline of your final project is due on Friday.

Here are some of the images turned in by students for Assignment 11:

## Thirteenth Week: November 24

Previously planned:

~~On Monday, we will look at some of the mathematics of~~perspective. This is mentioned in Chapter 4 ofZEROand is covered in Section 10.1 ofSymmetry, Shape, and Space. You should read Section 10.1 (although you won't be responsible for all the details of perspective drawing).What we will actually do: On Monday, we will go over Assignment 10, and we will talk some more about fractals, fractional dimension, and the programs that were used in class last Friday.

Assignment 12, which asks you to prepare an outline of your final project, will be due on Friday, December 5. (The project itself will be due at the final exam period.)

There is no class on Monday or Wednesday because of the holiday. Happy Thanksgiving!

## Twelfth Week: November 17, 19, and 21

On Monday, we will continue talking about the fourth dimension and about dimensions in general. The homework on this material, Assignment 10, is due on Friday. As part of this assignment, you should read Sections 6.1 and 6.2 of

Symmetry, Shape, and Space.The reading for Wednesday is Chapter 4 from

ZERO: The Biography of a Dangerous Idea. On Wednesday, we will discuss this chapter in class, and we will prepare for Friday's class.Class on Friday will be a computer lab. For this lab, we will meet in Gulick 208, the computer lab on the second floor of Gulick Hall. During the lab, you will start and possibly finish Assignment 11.

Here is a link to the Rubik's Tesseract applet that we looked at in class.

## Eleventh Week: November 10, 12, and 14

The test that was scheduled for last Friday, November 7, has been moved to Monday, November 10.

On Wednesday, we will view a 35-minute video adaptation of

Flatland, a 19-th century novel about a two-dimensional world. The reading for the week (and into the beginning of next week) is Sections 6.1 and 6.2 ofSymmetry, Shape, and Space, with deal with the idea of two, four, and higher dimensional worlds.There is no assignment due this week, and there is no reading from

ZERO.

## Tenth Week: November 3, 5, and 7

There is a test this week, on Friday, November 7. An information sheet is available.

Assignment 9 is due on Wednesday.

: We have departed somewhat from the original tentative syllabus for the course. Here is a revised schedule (still somewhat tentative) of what we will be doing for the rest of the semester:Revised Schedule

November 3, 5, 7:Finish up voting and symmetry. Test on Friday, November 7.November 10, 12, 14:Sections 6.1 ("Flatlands") and 6.2 ("The Fourth Dimension") fromSymmetry, Shape, and Space. View the DVD of "Flatland" in class on Wednesday.November 17, 19, 21:Section 10.1 ("Perspective") fromSymmetry, Shape, and Space. Reading for Wednesday:ZERO, Chapter 4. Computer lab on Friday in Gulick 208.November 24:Section 10.2 ("Optical Illusion") fromSymmetry, Shape, and Space. Thanksgiving break; no class on Wednesday or Friday.December 1, 3, 5:Section 11.1 ("Non-Euclidean Geometry") fromSymmetry, Shape, and Space, or other reading. Reading for Friday: Chapter 5 ofZERO.December 8, 10, 12:Sections 7.1 and 7.2 fromSymmetry, Shape, and Space, or other reading. Reading for Friday: Chapters 12 and 13 ofThe Math Instinct.December 18:Final exam, 8:30 AM.

## Ninth Week: October 27, 29, and 31

This week we take a break from other topics to talk about the mathematics of voting. The reading consists of a handout and a number of pages from the book

Gaming the Vote: Why Elections are not Fair, by William Poundstone. The schedule of readings is:For Monday: The handout and Chapter TWO of

Gaming the Vote, pages 45 to 51.For Wednesday: Chapter SEVEN of

Gaming the Vote, pages 133 to 148.For Friday: Chapter FOURTEEN of

Gaming the Vote, pages 231 to 241.Assignment 9 is on this material and is due next Wednesday, November 5. The due date for Assignment 8 has been extended to this Wednesday, October 29. Don't forget that there is a test coming up next week on Friday, November 7.

## Eighth Week: October 20, 22, and 24

We will spend the week finishing up symmetry groups, Sections 5.2, 5.3, and 5.4. The reading for Friday is Chapter 3 of

ZERO. Other than that, there is no homework due this week. The next homework, Assignment 8, is due next Monday, October 27.Here are some of the images produced by students in this course for Assignment 7:

## Seventh Week: October 15 and 17

There is no class on Monday because of Spring break. On Wednesday and Friday, we will continue our survey of planar symmetry groups. Over the course of this week and next, we will finish Sections 5.2, 5.3, and 5.4. The next homework, Assignment 8, covers this material and is due on Monday, October 27. That assignment also has one part that will get you thinking about your final project for the course.

The reading for Friday's class is Chapter 2 of

ZERO: The Biography of a Dangerous Idea. You should be prepared to discuss it in class, and you should also be prepared for a quiz. Assignment 7 is also due on Friday.

## Sixth Week: October 6, 8, and 10

This week, we begin a series of sections from the textbook on symmetry groups in the plane. The reading for the week is Section 5.2, which introduces the "rosette" groups. Over the next two weeks, we will do the next two sections, which cover the "frieze" groups and the "wallpaper" groups.

Wednesday's class this week will be held in the Multimedia Computer Lab in the Library to work with a pair of programs that do symmetries. Assignment 7 is based on those programs.

Assignment 6 is due on Wednesday. (The handout version of Assignment 6 had some images that are omitted from the web page.)

We also begin reading a new book this week. The reading for Friday's class is Chapters 0 and 1 of

ZERO: The Biography of a Dangerous Idea.

## Fifth Week: September 29; October 1 and 3

There is a test on Friday of this week. In class, we will be starting Section 5.1. Material that we cover on Monday might be on the test, but nothing that we do on Wednesday. Because of the test, there is of course no reading for Friday's class.

Here is the an information sheet about the test, to be handed out in class on Monday.

Assignment 5 is due on Wednesday. (For Part 1 of this assignment, you can make a table of the 15 answers, and then just explain how you got some representative sample of those answers.)

## Fourth Week: September 22, 24, and 26

In class on Wednesday and possibly on Friday, you will be working on "irregular tilings," Section 4.2 in

Symmetry, Shape, and Space. On Monday, I will lecture on number systems, and there is a handout on that topic for you to read. The reading for Friday's class is Chapter 11 ofThe Math Instinct. You will find that part of this section is related to the number systems handout.Assignment 4 is due on Wednesday of this week (September 24). This assignment is based on group work from Section 4.1 on semi-regular tilings of the plane. There is no handout for this assignment. Each group should turn in a folder with:

- The name of each person in the group.
- A list of the possible vertex configurations (from the table on page 88).
- A short essay discussing how your group found the possible configurations and how you determined that some of them cannot be used to tile the entire plane.
- Drawings on tracing paper of the 8 semi-regular tilings (or at least as many of them as your group can find).

## Third Week: September 15, 17, and 19

Here is Assignment 3, based on last week's work, which is due this Wednesday:

Assignment 3, Due Wednesday, September 17We will be working on Section 4.1 this week. This section is about "tilings" of the plane. We will look at the so-called "regular" and "semi-regular" tilings. Your goal will be to find the eight semi-regular tilings.

The reading for Friday is Chapter 10 of

The Math Instinct. (Note that we skipping Chapters 4 through 9.) You should read thisbeforeclass on Friday and be prepared to discuss it. (You should also, of course, be prepared for the possibility of a quiz on this reading.)

## Second Week: September 8, 10, and 12

The following assignment was handed out on Friday, September 5, and is due in class this Wednesday, September 8:

During the second week of the course, we will be working on Chapter 2 from

Symmetry, Shape, and Space. You will be doing exercises from both Section 2.1 and Section 2.2; some of them will be collected as homework next week. You should bring the textbook to class, since you will be working on some of the exercises in class. You should also bring a ruler, a pen, and a pencil. The book also asks for tracing paper and graph paper, but these will be provided to you; you do not have to bring them yourself.The reading for Friday's class is Chapters 2 and 3 of

The Math Instinct. Remember that you should do this readingbeforeclass on Friday, so that you will be ready to discuss it in class.

Note added Wednesday: It looks like the exercises from Section 2.1 that will be part of the next homework are exercises number 2, 3, 4, 5, 6, 9, 10, 11, 12. However, I won't be asking you simply to answer each exercise; instead, I'll ask several questions based on these exercises. I'll also ask you to draw a couple of Celtic knots like those in Section 2.2, but we won't be doing a lot from that section. The actual assignment will be handed out in class on Friday.

## First Week: September 1, 3, and 5

The first assignment is a short survey that will be handed out on the first day of class, and that will be collected at the next class on Wednesday, September 3. You will get five homework points for turning in the survey. If you enter the course late, you should still fill out the survey and turn it in by the second day that you attend the class.

For the first two days of the course, we will discuss some background material from Chapter 1 of

Symmetry, Shape, and Space. We will work on a few of the exercises from this chapter in class, and I will assign a few exercises as homework to be collected next week. However, you do not necessarily have to read the chapter, since we will cover the material that I think is important in class.

Beforeclass on Friday, you should read Chapter 1 ofThe Math Instinct, and you should be prepared to discuss it in class on Friday.