This course ended May 10, 2008

Math 110: Discovering in Mathematics, Section 1

   Department of Mathematics and Computer Science
   Hobart and William Smith Colleges

   Spring 2008.

   Instructor:  David J. Eck.

   Monday, Wednesday, Friday, 9:05 to 10:00 AM.
   Room Napier 201.
   
   Course handout:  http://math.hws.edu/eck/courses/math110_s08.html

Fiftheenth Week and End of Term: May 5 and May 10

Monday, May 5 is the last day of class. Final papers will be returned, and we will wrap up the course with an overview of what has been covered throughout the term.

The final exam is on Saturday, May 10, at 1:30 PM, in our regular classroom. An information sheet about the exam is available.

Fourteenth Week: April 28 and 30; May 2

The final project paper is due on Wednesday. This is the final assignment for the course. There is no reading assignment this week, but I will be summarizing some ideas from the rest of The Poincaré Conjecture in class.

Thirteenth Week: April 21, 23, and 25

Our main goals for the week are to understand the statement of the Poincaré Conjecture and to begin a study of non-Euclidean geometry that will get us to a point where we can discuss how the Poincaré Conjecture was proved (if only in very general terms).

The reading for the week in Chapters 6, 7, and 8 of The Poincaré Conjecture. These chapters are largely historical. I don't expect you to remember all the people in the history, but you should get a general idea of the history of non-Euclidean geometry. (Note that the reading is different from the reading that was originally listed on the Syllabus.)

Twelfth Week: April 14, 16, and 18

On Monday, we will continue our discussion of the first three chapters of The Poincaré Conjecture. For Friday, you should read Chapters 4 and 5 of that book (and expect a quiz).

For Wednesday, the class will work in groups on part of Assignment 10. The two parts of the assignment that you will work on are based on (1) the discussion of surfaces from class and The Poincaré Conjecture and (2) a handout on symmetry groups of the plane.

The third part of Assignment 10 is to write an outline for your final project paper. The paper will be due on the last Wednesday of the term, April 30. Assignment 10 and the final project are the last assignments of the term.

Here are some of the pictures that people in the class made for Assignment 9 The pictures in each group are in no particular order. Exercise 1 was to make a tiling using a small number of polygons. Exercise 2 was to make a similar pattern, but then to color in the shapes. Exercise 3 was to make any interesting pattern with the Escher Sketch program:

Exercise 1Exercise 2Exercise 3
Brian
Erin
Maureen
Rebecca
Gabrielle
Alyson
Jessica
Tom
Courtney
Deana
Jeremy 		Adrienne
Amanda
Emily
Willy
Gabrielle
Joe
Katy
Ned
Sarah
Deana
Alyson 		Ben
Rebecca
Willy
Blair
Maureen
Graham
Karin
Katy
Jessica
Sarah
Paul
Victoria

Eleventh Week: April 7, 9, and 11

We start a new book this week. The reading for Friday is Chapters 1, 2, and 3 of The Poincaré Conjecture. Please make sure that you have read this material before class on Friday and that you are prepared to disuses it.

A change of pace for Monday and Wednesday of this week: On Monday, we view the animated movie version of Flatland, and the on Wednesday will be a computer lab in room Gulick 208. The handout for the lab is

http://math.hws.edu/eck/math110/assg9.html

The lab worksheet includes Assignment 9, which is due next Wednesday, April 16.

Tenth Week: March 31; April 2 and 4

There is a test on Friday, April 4. An information sheet is available. (It's mainly an overview of the material that has been covered since the previous test.)

On Monday, as an introduction to the next section of the course, we will view a 35-minute film version of the book Flatland, about a two-dimensional world, the beings that inhabit it, and their encounter with the mysterious third dimension.

Aside from that, on Monday and Wednesday, we will discuss "The Book of Sand" and will finish up our excursion into cryptography.

Ninth Week: March 24, 26, and 28

There is no assignment due this week. Assignment 8 is due next Wednesday, April 2. Remember that there is a test coming up next Friday, April 4.

It's time to start thinking about final projects. A list of possible topics will be handed out in class on Monday. Part of Assignment 8 asks you to pick two possible topics and do a bit of preliminary research on them.

On Monday, we will spend a little more time on number bases, and then move on to a brief look at modular arithmetic and cryptography. A very short introduction to cryptography will be handed out in class. You should read this handout before class on Wednesday.

For Friday's class, you should read Chapter 6 of ZERO: The Biography of a Dangerous Idea. You might find this chapter to be a little more bewildering than our usual reading. I am mainly interested in some of the ideas about infinity that are presented in this chapter. We will discuss them in class on Friday.

Eighth Week: March 10 and 12

An assignment is due on Wednesday, and you should also read Chapter 5 of ZERO: The Biography of a Dangerous Idea for Wednesday. On Monday, you will have some time in class to work on the assignment.

You can browse the images produced by students for Assignment 6 in this images directory. Here are direct links to some of the nicer images:

Mandelbrot SetChaos Game
Katy
Gabrielle
Deana
Amanda
Joe
Emily
Rebecca
Tom 		Willy
Jessie
Deana
Alyson
Karin
Ned
Joe
Tom

There is no class on Friday because of Spring break. Classes resume on March 24. Have a great break!

Seventh Week: March 3, 5, and 7

The reading this week is pages 100--114 of Problem Solving Through Recreational Mathematics for Wednesday and Chapters 3 and 4 of ZERO: The Biography of a Dangerous Idea for Friday. There will be a quiz on the reading from ZERO at the beginning of class on Friday.

On Monday, we will continue our discussion of last Friday's reading from ZERO, concentrating this time on number systems. We will then look briefly at prime numbers and factoring, which you will be working with on Wednesday.

On Wednesday, you will work in groups on Assignment 7, which will be due on Wednesday of next week.

Sixth Week: February 25, 27, and 29

The reading for this Friday is Chapters 0, 1, and 2 of Zero: The Biography of a Dangerous Idea. Please do the reading before class and be ready to discuss it.

Since we are starting a book that is about infinity as well as zero, and since we should do something fun after the first test, we will look at two mathematical systems that are related to infinity. On Wednesday, the class will meet in the computer lab in room Gulick 208, and you will work on the assignment described on the following web page:

Assignment 6: Order and Chaos

Fifth Week: February 18, 20, and 22

There is a test on Friday, February 22. On Monday and Wednesday, we will do a little more work on algebra, and we will review for the test. More information about the test will be available in class.

Information about the test, along with sample solutions to Assignment 5 can be found in the following PDF file: test1info.pdf.

Fourth Week: February 11, 13, and 15

We will begin Chapter 3 of Problem Solving Through Recreational Math this week. This chapter is about problems whose solutions use algebra. On Wednesday, the class will work in groups on problems from this chapter. Click here for the assignment.

The reading for Friday's class is Chapters 12 and 13 from The Math Instinct. This is the last reading from that book. Remember that next Friday, February 22, there will be a test covering the first third of the course.

The first Math department colloquium will be given on Wednesday at 4:30 in room Napier 201 (our classroom for Math 110). Vince Cassano '91 and Kim Oaks '85 will talk about their experience working as actuaries. There will be refreshments at 4:00. Recall that you are required to attend at least one math department talk this term. There will be an attendance sheet at the talk for you to sign.

Third Week: February 4, 6, and 8

The homework assignment from Chapter 1 of Problem Solving through Recreational Mathematics is due on Wednesday.

We will spend Monday and Wednesday talking about voting and voting paradoxes. For Wednesday, you should read the article "Evaluating Voting Methods," which can be found on the web at http://theorem.ca/~mvcorks/code/voting_methods.html. A homework assignment on voting methods will be handed out on Wednesday.

For Friday, you should read Chapter 11 of The Math Instinct before class. There will be short quiz on this reading at the beginning of class.

My office hours this week a little different from usual. I will be in my office:

         Monday, Wednesday, Friday:  10:10 -- 11:05
         
         Tuesday, Thursday:          12:00 -- 3:00

There is an assignment on voting that is due next Wednesday. To read the assignment, click here.

Second Week: January 28 and 30; February 1

On Monday and Wednesday, we will start using Problem-Solving through Recreational Mathematics. You should read Chapter 1 before class on Monday and think about the sample problems and their solutions. We will go over the solutions of one or two of the end-of-chapter exercises in class, and I will assign a few of the other exercises for group work on Wednesday and for homework. We will be concentrating on "logic puzzles" similar to Sample Problems 2, 3, and 4. (Note: We will not do anything with Chapter 2 in this book.)

The assignment for Wednesday's class is available as a PDF file through this link.

For Friday, you should read Chapter 10 of The Math Instinct and be prepared to discuss it in class.

First Week: January 21, 23, and 25

Monday will be a general introdution to the course. I will discuss the design of the course and the materials that we will use.

A short assignment will be handed out on Monday and will be due on Wednesday. (Click here for a copy of the assignment.) In class on Wednesday, we will discuss the assignment and you will work in groups on problems based on a handout.

On Friday, we will discuss The Math Instinct, Chapters 1 through 3. You should read this material before class on Friday.