Math 46
Fall 2009 Home Page
Green Sheet

Class 21, Th., Dec. 3, 2009
We reviewed! Please bring a scantron for the exam (the half-page, brown or green kind). I am currently planning that your exam will have 20 multiple choice questions and 3 explanation questions, the latter focused on fractions.

Bring your portfolio, and any homework I have not yet checked, as well as any handouts not yet collected.

Class 20, Tue., Dec. 1, 2009
We went over the musical scales handout. We also went over exam 2. Bring homework for next chapter Thursday, also questions for review. Turn in the musical scales handout.
The California Math Counci's yearly Asilomar conference is this coming weekend, registration is $75 for students. It is a wonderful conference, and if you do begin teaching, you may want to try to get your school to fund your attendance (Asilomar is also a beautiful site, right on the ocean.)

Class 19, Tue., Nov. 24, 2009
We did the Barbie and proportion activity. You also received several handouts which you should be working on to turn in Tuesday.
Do homework through the end of section 8.2.

Class 18, Thu., Nov. 19, 2009
Here is the link to the Math 46 google group.
You are all members already under the email address which I have for you. But you must still register with Google. Go to the group site and they will ask you to register, if you have not already. Please use it to work on the take-home exam.
We worked on the take-home exam.
We also examined the exponential function you obtain when folding a sheet of paper in half multiple times.
Do homework through section 8.1.

Class 17, Tue., Nov. 17, 2009
We went over fractions, decimals, the take-home exam.
Here are some links mentioned in class:
George Vaccaro and Verizon math.
Million Digits of Pi.
Memorization of digits of pi.
I don't believe I've taken up chapter 4 homework and the Poinsot stars handout yet, will do that Thursday!
Do HW through section 7.4.

 Class 16, Th., Nov. 12, 2009
We went over more material on fractions and decimals.
I emailed your take-home exam to your email address. Let me know if you did not receive it.
I also set up a discussion site for the class.
Complete section 6.3 and 7.1 homework.

Class 15, Tue., Nov. 10, 2009
We talked about perfect numbers and numbers of factors.
Here's the BOINC main page, for using your computer to contribute to scientific projects.
Here is the GIMPS home page, which is the site that looks for large Mersenne primes, used to discover new perfect numbers.
We went over new material on fractions.
Do homework for sections 5.4, 6.1 and 6.2.

Class 14, Thu., Nov. 5, 2009
We went over material from sections 5.1 through 5.4
Please hand in chapter 4 homework and the Poinsot Stars handout on Tuesday.
Do homework for sections 5.1 through 5.3.

Class 13, Tue., Nov. 3, 2009
We went over group problems.
We will move into chapter 5 on Thursday.

Class 12, Thu., Oct. 29, 2009
We heard reports, also spent some time on group problems. We'll work on group problems again on Tuesday. Also, will finally take up Ch. 3 homework on Tuesday.

Class 11, Tue., Oct. 27, 2009
We went over the modular arithmetic handout. Complete the Poinsot Stars handout and we will look at it again on Thursday.
Please bring your PEMDAS mnemonic (memory device) on Thursday, I'll post them at this web site.
Papers due Thursday, MUST be 600 words at least, you'll need to give a short oral presentation on it.
We did the least common multiple clapping activity also, and covered section 4.3, and introduced section 4.4 on applications of modular arithmetic.
We also assigned group problems, which we'll work on Thursday.
Homework: Sections 4.3 and 4.4.

Class 10, Thu., Oct. 22, 2009
We went over the Patterns and Modular Arithmetic handout, which is due Tuesday.
We also looked at Poinsot stars. Bring the Poinsot Stars handout on Tuesday, we will start that as well.
Please work homework through section 4.2
Turn in the Chapter 3 homework on Tuesday.
Remember your papers (see below) are due next Thursday.
Group problems will be:
3.4, # 21
4.1, # 10,17 
4.1, #18,19
4.1, #25,30
4.2, #9,11
4.3, #19,20
4.4, #13,15


Class 9, Tue., Oct. 20, 2009
We went over some homework problems from chapter 2.2 relating binary notation, Hamming codes, and Venn diagrams.
We also looked at some slides about recent studies showing why people probably have difficulty memorizing certain artithmetic facts such as the multiplication table.
Then we went over section 3.5, on mental arithmetic and estimation.
Bring a calculator on Thursday, when we will go over section 3.6, on calculator use.
Again, bring to class Thursday:
Patterns and Modular Arithmetic
Modular arithmetic intro
These will be useful when we get to chapter 4, so we WILL deal with them!

You have a short paper on a subject related to the course that catches your interest due iat the end of next week (Thursday, Oct. 29) and worth 5% of your grade. Due date Thursday, Oct. 29. Here's the description of the essay:
 Report on an article or chapter from a popular book about mathematics or math education. The report will be one to two pages long, typewritten, (it must be at least 600 words), and will cover the mathematics from one to several chapters of a book from the following list; other books or sources may also be used. You must use published material, not just web sites, unless you get permission from the instructor, and you MUST cite your sources. A short oral report to the class will also be required.
You should include in what you write and talk about:
(1) why you chose this topic,
(2) what you learned, and
(3) what you think about the subject in question.

Examples of books with mathematical content:
The Mathematical Tourist and Islands of Truth, by Ivars Peterson.
Any of the books of Martin Gardner on mathematics (over 15 titles).
Game, Set, Math and Does God Play Dice by Ian Stewart, or other titles on math by Stewart.
The Mathematical Experience by Davis and Hersh.
A Number For Your Thoughts and Numbers At Work and At Play by Stephen P. Richards.
Tilings and Patterns by Grunbaum and Shepard.
Mathematical Snapshots by Steinhaus.
Mathematics: The New Golden Age by Keith Devlin, or other titles by Devlin.
The Emperor's New Mind by Roger Penrose.
The Mathematics of Games by John Beasley.
Archimedes' Revenge by Paul Hoffman
What is Happening in the Mathematical Sciences, ed. by Barry Cipra, Vols 1-5 (on reserve in campus library)

Examples of books with cultural content:
Ethnomathematics by Marcia Ascher.
You can also consult this Multicultural Mathematics Bibliography. Many of the references are in our library, and the bibliography contains call numbers for those that are in the library.
A number of Martin Gardner's books are in the library.

Class 8, Thu., Oct. 15, 2009
We went over chapters 3.2, 3.3, and 3.4. Please complete homework for these sections.
We also saw part of the presentation on the Brazilian street math study.
I will take up chapter 2 homework on Tuesday.

Class 7, Tue., Oct. 13, 2009
We went over more of chapter 2.3 and 2.4, played the game of Nim, and began chapter 3.
We also learned a little about African mathematics.
Do homework from chapter 3.1
Bring to class Thursday:
Patterns and Modular Arithmetic
Modular arithmetic intro

Class 6, Tue., Oct. 8, 2009
We  went over sections 2.3 and 2.4. Please do homework for these sections. Sorry this update is late.

Class 5, Thu., Oct. 6, 2009
We have first exam on Thursday. Bring your portfolio (see instructions under class 2 below. If you don't have it properly organized, you won't get credit!)
We did the  "Where's Fido?" activity - work the other problems in this handout as part of your homework.
We also played the "Sorting Junk" game (this handout describes it.)
Look at the Set site and play the game again before class.

You should be writing several paragraph journal entry for each class.
Here are solutions to the study guide for the first exam problems.
I will check your homework for chapters 1 and 2 during the exam, as well as whether you have the portfolio in order, and also look at your journals (have one entry per class).


Class 4, Thu., Oct. 1, 2009
We went over Fibonacci numbers, and learned to count the Fibonacci numbers on pine cones.
We also went over the Pigeon Hole Principle, and its "extension."
Here are some links to Fibonacci sites, it is required that you (at least) take a look at them. The second and third have lots of pictures!
A great site about Fibonacci numbers.
Here's another Fibonacci site with lots of pictures and interactive applets.
Here's an interactive site that helps explain phyllotaxis, which is the pattern of spirals in many plants. Within the site is a short film clip that is part of the explanation as to why the Fibonacci numbers appear in plants.

Also went over Polya's problem solving techniques in Tuesday's class, here's a bio of Polya.

Here's a study guide for the first exam (next Thursday) from a previous quarter. So far, we've covered many of these topics. First exam is individual, open book, open notes, calculator but not computer allowed.

Homework:
Work problems in section 2.1 and 2.2. The list of homework problems is at the bottom of this page. I will collect homework for chapter 1.
Here is the  Fibonacci number assignment, turn in Tuesday as a "quiz." The first half of the quiz was your participation in counting the number of spirals in the pine cones; everyone in class received full credit. Make sure that the plant you choose exhibits spiral patterns, not just one of the Fibonacci numbers.
Please print out these handouts, and bring them to class on Tuesday:
Patterns and Modular Arithmetic
Modular arithmetic intro

Class 3, Tue., Sep. 29, 2009
We spent a long time working on the "domino covering" problem, and using it to introduce the Fibonacci numbers. We went over new material from the text on the pigeonhole principle also, and mentioned problems solving techniques and Polya's problem solving method.
We also worked on the take-away game.
In the pigeonhole principle "magic trick," I asked you to choose seven numbers from the list 1,2,3,...,12. The properties each of your lists had were:
(1) A pair of your numbers had a sum of 13.
(2) A pair of your numbers had a difference of 6.
(3) A pair of your numbers had a difference of 3.
(4) A pair of your numbers had the property that their only common factor was 1.
(5) A pair of your numbers had the property that one divided the other equally.
We saw how the pigeonhole principle explained why properties 1,2, and 3 are true. For Thursday, can you use the pigeonhole principle to explain property 4? Remember, it's all in how you label to (six) pigeonholes!
Property 5 is more difficult to explain; in this case the six pigeonholes have different numbers of numbers assigned to them!

Due Thursday: Homework problems from sections 1.4 and 1.5. They will be turned in next Tuesday along with all of chapter 1.
Also on Thursday: print out and bring to class this Modular Arithmetic Intro handout and also the handout Patterns and Modular Arithmetic


Class 2, Thu., Sep. 24 2009
We went over several of the problems in sections 1.1, 1.2, and 1.3. (See the list of homework from the text for the whole quarter at the bottom of this page.) Complete 1.1 to 1.3 for homework by Tuesday, but will take up next Thursday (you'll have other assignments to complete by Thursday also, so we need to be done with them by Tuesday.

We discussed Pascal's Triangle (this link has some of the triangle's history).
Here's the wonderful article by Brian Hayes on the history of Gauss's Trick, published in 2006.

Due Tuesday:
(1) Math Autobiography. See page 2 of the green sheet for a complete description.
(2) Homework from text:
Ch. 1.1, # 2,4,9,10,11,12,14,15
Ch. 1.2, # 5,8,10,20,24
Ch. 1.3, # 4,7-11,14
(3) Put together your portfolio, a looseleaf notebook with these sections:
(4) Write a journal entry on today's class. Reflect on what we did, what was new to you, and what was not new.



Class 1, Tue., Sep. 22, 2009
Had a substitute, Lakshmi Vanniasagaram, who played the pattern game and did the frogs on a log problem.
Assignment: Ch. 1.1 and 1.2 (see problems below).
(1) Get your textbook! (See green sheet.)
(2) We worked on the pattern game and associated problems.
(3) We also worked on the "Frogs on a log" problem, and found that with
1 frog per side it took a minimum of 3 moves to exchange places
2 frogs per side it took a minimum of 8 moves to exchange places
3 frogs per side it took a minimum of 15 moves to exchange places
You might have guessed that 4 frogs per side would require 24 moves, 5 frogs per side would require 35 moves.
Figure out how to do these exchanges also, in the minimum number of moves. (See below for more explanation.)

Three round frogs (O's) and three crossed frogs (X's)  are sitting on a log with seven spaces, and want to take each other's places. A frog can move one step to a vacant square, or jump over one neighbor to a vacant square. In class we learned that it can be done in 15 moves.
O
 O
 O
  
X
 X
 X

Two frogs on a three space log can take each other's places in three moves:
O
   
X

Four frogs on a five space log can change places in 8 moves, as we also discovered in class.

O
 O
  
X
X


Here's a complete list of the HW from the textbook:
Ch. 1.1, # 2,4,9,10,11,12,14,15
Ch. 1.2, # 5,8,10,20,24
Ch. 1.3, # 4,7-11,14
Ch. 1.3: # 20,21,24
Ch. 1.4: # 1,9,13-15,19
Ch. 1.5: # 1,3,5,6,7,9,10,12,15
Ch. 2.1 #8,9,11,14.15,16-20,25,26
Ch. 2.2 #1,9,12,13,17,22,28,31,34
Ch. 2.3 # 5,6,7,10,14,18,19,26,27,31
Ch. 2.4 # 1-5,7,9,11,15,17,26,32
Ch. 3.1: # 1-5,9-10,25
Ch. 3.2 # 1,5,10,15,16,20
Ch 3.3 # 1,3,5,9a,d,17,21,25
Ch. 3.4 # 3,17,19-24
Ch. 3.5 # 1-3,8-10,15,16,18,19,20,32
Ch. 3.6 # 1-4 (a) only, 9,18
Ch. 4.1 # 5-9 part a only, 10,13,15,17-19,21,30
Ch. 4.2 # 1-4,8,9
Ch. 4.3 # 1-5 part a only, 6-13,19
Ch. 4.4 # 10, 13,16
Ch. 5.1 # 1-3,7,8,13-16,19,20,22,24
Ch. 5.2: # 1-3 a,b,c, 13,17-22,27,31
Ch. 5.3 # 10-13
Ch. 5.4 # 1-15 part a only, 20,21
Ch. 6.1 # 1-21 odd and part a only, 26,27, 29,30,31
Ch. 6.2 #1-20, part a only.
Ch. 6.1 Also do 26,27,29-31
Ch. 6.2 Also do 28,29,31,33,34
Ch. 6.3 # 1-21, part a only, 29,34
Ch. 7.1 # 1-6 part a only,16-18
Ch. 7.2 # 1-7, part a only, 15-17,19,20,27
Ch. 7.3 #1-3,10,14-16,26
Ch. 7.4 #1-4,5-13,16-18
Ch. 8.1 # 7,8,11,20,23
Ch. 8.2 1-17,24,25,27,28
Ch. 8.3 #24-27, 31,32,34,35