Math 110: Discovering in Mathematics

Number A Day from the Mathematical Association of America (changes each weekday). Check it out for interesting and odd facts about numbers.

Week 15

Journal Homework for Class Tuesday, May 4:

Review all of Section 5.4: Feeling Edgy. This may be different in the new edition of the text. Review the graph theory handouts from the last classes.
You should be able to define and give examples of the following concepts from our recent work.

loop
path and Euler path (what's the difference?)
circuit and Euler circuit (what's the difference?)--how is a path different from a circuit?
degree of a vertex
connected graph
regular graph

You should be able to state and use Euler's four theorems when working with graphs:

Euler's Characteristic Theorem: You should be able to work through the proof as on this week's homework.
Euler's Circuit Theorem: What's the key idea in the proof?
Euler's Path Theorem
Euler's Degree Sum Theorem: What was the key idea in the proof?
The number of odd degree vertices in a graph is even. What was the key idea?

From your text (p. 407-408) work Mindscapes 12 (Euler Circuit), 18, and 20 (Euler Paths).
Download this worksheet and do the three problems.

Week 14

Journal Homework for Class Tuesday, April 27:

Read all of Section 5.4: Feeling Edgy. This may be different in the new edition of the text.
Review the handout from Thursday's class. You should feel confident about proving the Euler characteristic of a plane connected graph is 2.
From your text (p. 419-420) work Mindscapes 1, 2, 5, 7 (pick any two figures), 13 (Hint: Use the Euler characteristic--you don't need the exact numbers of edges and vertices, just how many more edges than vertices), and 15.

Journal Homework for Class Thursday, April 29:

Read Section 5.3: Circuit Training. This may be different in the new edition of the text.
Review the handout from Tuesday's class. Keep working on the next few problems in preparation for class.
From your text (p. 405-408) work Mindscapes 1, 3, 6, 7, and 19.

Collected Homework Due Friday, April 30, 2:00 PM. Note the early time!

Download this worksheet on the Euler Characteristic and do the problems on it.
Added on Tuesday Download this worksheet on Euler circuits and do the problems.
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Week 13

Journal Homework for Class Tuesday, April 20:

Read the handout: An Introduction to the Mathematics of Voting. Pay attention to the final section on Fairness. You should also read the second half of Chapter 9.4 in our text more carefully. Concentrate on what Arrow's Theorem says.
From last Thursday in the Voting Handout (if you have not already done so): In Section 1.11 in the Homework section (p. 14-15), try Mindscape #2 and 4.
From the handout An Introduction to the Mathematics of Voting, work the Mindscapes in the text: #1.7 (p. 7) and 1.8 (p. 8). Then work the Mindscapes in the Homework section (p. 15-16) #4, 5 (c,d,f). Finally, from your text (p. 865) work Mindscapes 7, 8, and 9.

Journal Homework for Class Thursday, April 22:

Review the handout from today's class on range voting. Review the four fairness criteria and the examples at the end of An Introduction to the Mathematics of Voting. You should also review the second half of Chapter 9.4 in our text more carefully. Concentrate on what Arrow's Theorem says.
Download this worksheet on voting methods and do the four problems on it in your journal.
New Material: In your text, read pages 410 through 413 in Section 5.4 "Feeling Edgy." Our last topic of the term will be graph theory.

Collected Homework Due Friday, April 23, 3:00 PM:

On page 11 of An Introduction to the Mathematics of Voting work Mindscapes #1.9.
On pages 15-16 of An Introduction to the Mathematics of Voting work Mindscape #3 and 9(b).
Download this worksheet on voting methods and do the problems on it. After Tuesday you should be able to do all parts of the problem.
Added Tuesday: Download this worksheet on voting methods and do the problems on it.
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Week 12

Journal Homework for Class Tuesday, April 13:

Read the handout: An Introduction to the Mathematics of Voting. Read through Section 1.9 (at the top of page 11). There are lots of different voting methods! You should also read the first half of Chapter 9.4 in our text.
Review pages 213-219 on geometric correspondences. You are invited to read the rest of the chapter, but it is harder material.
Make sure that you have done all the Mindscapes from last week.
At the end of Section 3.5 (p. 225-226): Work Mindscapes #3, 4, 5, 8, and 9. Use drawings for all of these.
Extra Credit: At the end of Section 3.5 Work Mindscapes #20. Make a nice drawing.

Journal Homework for Class Thursday, April 15:

Review and finish reading the handout: An Introduction to the Mathematics of Voting. You should also read the first half of Chapter 9.4 in our text to get another view of this material. (Just skim from the bottom of page 859 to the middle of 862.)
From the handout An Introduction to the Mathematics of Voting, work Mindscapes #1.1 (p. 2), 1.3 and 1.4 (p. 5). Finally do Mindscape 1.9 (a and b) on page 11. What play is the Hare method winner? The vote-for-two winner?
Work ahead: In Section 1.11 try Mindscape #2 and 4. (You will have to read about Borda and Approval Election Methods which we will discuss in detail on Thursday.)

Collected Homework Due Friday, April 16, 3:00 PM:

At the end of Section 3.5 (p. 226-227): Work Mindscapes #7, 10
Added on Tuesday: At the end of Section 9.4 (p. 864): Work Mindscape #1. Your answer should be in the form of a paragraph or two. It should be neatly and carefully written or typed. Clearly indicate your sources.
Download this worksheet on voting methods and do the problems on it.
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Week 11

None of these problems need to be handed in at Exam 2, but if they are, you will receive extra credit.

Journal Homework for Class Tuesday, April 6:

Review Section 3.4 on power sets and various sizes of infinity. Make sure that you understand the rule used to poduce the MYSTERY set that is used in the proof of Cantor's Power Set Theorem (p. 202-204).
Review the Subset Counting Theorem on page 199. You should be comfortable with power sets and their notation.
Review the Continuum Hypothesis on page 206. What makes it so interesting?
Review the handount of materials concerning the second exam. Come to class with questions.
At the end of Section 3.4 (p. 209-210): Work Mindscapes #13, 16, and 17.
Give an example of a set S such that its power set P(S) has 9 elements or explain why this is not possible.

No Collected Homework This Week: Exam 2 on Thursday, April 9. Bring your journal to the exam.

Week 10

Journal Homework for Class Tuesday, March 30:

Read Section 3.3 which shows why the real numbers and the natural numbers have different cardinalities. You should be able to construct Cantor's diagonalization proof of this idea. It is very similar to what we did to show that the set of all sequences of 0's and 1's has a different cardinality than N. A diagonalization proof is sure to appear on the next exam.
Make sure that you have done all the Mindscapes from last week.
At the end of Section 3.4 (p. 191-192): Work Mindscapes #5, 11.

Journal Homework for Class Thursday, April 1:

Review the proof that N and R have different cardinalities. It will be helpful on one of the hand in problems and there is certain to be a similar question on the next exam.
Read Section 3.4 through page 200. This is the material we covered on Tuesday. Look ahead to the rest of the section. The power set theorem will answe our question about sizes of infinity (infinite cardinals).
At the end of Section 3.4 (p. 208-209): Work Mindscapes #1, 3, 6, and 10.

Collected Homework Due Friday, April 2, 3:00 PM:

At the end of Section 3.1 (p. 164): Work Mindscape #18.
At the end of Section 3.2 (p. 178-179): Work Mindscapes #11, 14, and 16. (Describe the pairings with formulas when possible.)
At the end of Section 3.3 (p. 191-192): Work Mindscapes #4, 10, and 14 (Hint: Think about the sequences of 0's and 1's.
Added Tuesday t the end of Section 3.4 (p. 208-209): Work Mindscapes #7 (explain) and 8 (solutionin back).
Extra Credit: At the end of Section 3.2 (p. 181): #26.
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Week 9 (after Break)

Work on your projects. Come see me if necessary.

For fun: This website gives you access to the first 200,000,000 digits of pi. Among other things, you can search the digits of pi for your birthday, graduation, or favoirte string of numbers, like the first several digits of the golden ratio, phi (1.6180339).

Journal Homework for Class Tuesday, March 23:

Read Section 3.2 through page 174. You should have lots of questions about the ping-pong ball conundrum (see page 171.) I will be asking you about that in class when you return. Make sure you can define finite and infinite sets and that you understand when two sets have the same cardinality. These terms are all likely to appear on the next exam as well as in homework problems.
Review the proof that the natural numbers N are infinite.
Review Section 3.1. Make sure you know the definition of a one-to-one correspondence.
At the end of Section 3.1 (p. 163-164): Work Mindscapes #4, 7, 9, and 10.
At the end of Section 3.2 (p. 178-179): Work Mindscapes #3 (this is just asking you to use bracket notation { } as in problem 9, 4 (no proofs needed), 6, 7, 9, and 13.

Journal Homework for Class Thursday, March 25:

Read the rest of Section 3.2. Pay careful attention to the material on correspondences between the natural numbers and all of the integers and between the natural numbers and the rationals. These correspondences show that all three sets have the same cardinality, which is surprising! You should be able to show how these correspondence are formed.
Exercises: Work these Mindscapes at the end of Section 3.2: 17, 30, 32 (BIG HINT: Each intersection is a pair of natural numbers such as 3rd St and 5 Fifth Ave or 3/5. Think about the correspondence between N and the rationals.

CODE PROJECT Due Friday, March 26, 2:00 PM.

NO Collected Homework this week: I will omit collecting these problems this week so that you can finish your projects. But I may collect some of these next week or put some of these on the next exam. So make sure to do them.

At the end of Section 3.1 (p. 163-164): Work Mindscapes #12 and 18.
At the end of Section 3.2 (p. 178-179): Work Mindscapes #9 and 14.
Added Tuesday: At the end of Section 3.2 (p. 178-179): Work Mindscapes #11, 16, and 26.
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Week 7.999999.....

Work on your projects. Come see me if necessary.

Journal Homework for Class Tuesday, March 9:

Review Section 2.6. Make sure you know the definition of a rational number. Begin reading Section 2.7.
At the end of Section 2.6 (p. 139-140): Work Mindscapes #15, 16, 19, 22, and 23.
At the end of Section 2.7 (p. 155): Work Mindscapes #17 and 23 (similar to what we did at the end of class).

Journal Homework for Class Thursday, March 11:

Read the Introduction to Chapter 3 and then Section 3.1 on infinity. Pay careful attention to the material on correspondences on page 162.
Review Section 2.7 on the real numbers. Make sure you can define terminating, non-terminating, and periodic decimals. Which types are rational numbers?
Exercises: Work these Mindscapes at the end of Section 2.7: 2, 6, 13, 18, 20, and 24.

Collected Homework Due Friday, March 12, 3:00 PM:

In one of your earlier journal problems you showed that the square root of 5 is irrational. (You can assume this.) Is the Golden Ratio phi rational? Use the exact value of phi (which involves the square root of 5), not a decimal approximation. Give a careful argument. (See notes from Thursday and the answers to the last assignment.)
Is the square root of 14 rational? Give a careful argument. (See your class notes about the square root of 6 and the answers to the last assignment.)
Carefully work out these Mindscapes at the end of Section 2.6 on Irrationals:

#18. See notes from Thursday's class.
#29. Easy: Remember how exponents work.

Carefully work out these Mindscapes at the end of Section 2.7 on Real Numbers:

#7.
#10. See the hint!
Express 563.121212... as a rational number. Then do
#22.

Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Week 7

Review your tests. Come see me if necessary.

Journal Homework for Class Tuesday, March 2:

Review the Answers to the first exam (see email). Come see me if necessary.
Read the first three pages of Section 2.6. Make sure you know the definition of a rational number.
Review Exercises: These both use Fermat's Little Theorem. At the end of Section 2.5 (p. 126-127): Work Mindscapes #7 (use Fermat's Little Theorem, and also just work it out) and #17 (Hint: 668 = 666 + 2).

Journal Homework for Class Thursday, March 4:

Choose two partners (groups of three) for your coding project. I will be handing it out on Thursday and will need to know your partners.

Read Section 2.6 on Irrational Numbers of the text. Make sure you know the definition of a rational number.
Review the proof that the square root of 2 and the square root of 3 are irrational. Make sure you can do this type of argument. Try a few more examples for different primes. (Example, try showing the square roots of p = 5 or 7 are irrational.
We will discuss irrational powers next time. See if you can figure them out on page 136.
Exercises: Work these Mindscapes at the end of Section 2.6: 2, 4, 6 (3 square roots of 2 divided by 5 square roots of 2), 7, and 10. These are good practice for the next exam! Come for help if you get stuck.

Collected Homework Due Friday, March 5, 3:00 PM:

Carefully work out this Mindscape at the end of Section 2.5 on Codes: #16 (Hint: This uses Fermat's Little Theorem. Rewrite the first exponent as 6 x 100. How will you rewrite the exponent in the second part?
Exercises
Carefully work out these Mindscapes at the end of Section 2.6 on Irrationals:

#3
#8
#12
#11. Hint: Assume it is rational: a/b. Then solve for the square root of 3. What happens? But what do we know about the square root of 3 from class and the text?

Super Extra Credit: If p is prime, prove that the square root of p is irrational.
Super Extra Credit: Present to our class that a proof that the square root of 6 is irrational.
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Week 6

Test 1 Thursday. Don't forget your Journal!

Download this Practice Worksheet for Test 1. We will discuss some of these in class Tuesday.

Download this Additional Review Worksheet for Test 1. We will discuss some of these in class Tuesday.

Journal Homework for Class Tuesday, February 23:

Reread Section 2.4 of the text.
Read the beginning of Section 2.5 on codes through page 114. Then carefully read the "The Basic Theme of the Public Aspect of the RSA Coding Scheme in 10 Sentences" at the top of page 115. I won't kid you, the mathematics of RSA coding is complicated and we will not cover it in any detail. If you understand the ideas in this paragraph that will suffice. Finally, read about Fermat's Little Theorem on page 117. Try a few examples for different n and p to see what it means. (Example, try p = 7 and n = 3, 4, and 5.
Exercises: Work these Mindscapes at the end of Section 2.4 on modular arithmetic and UPC codes (p. 106-108): 2, 5, 7, 8, 9, 13, 16, and 38. These are good practice for the exam! Come for help if you get stuck.
Try: the additional modular arithmetic and product code problems on the handout for Thursday's class. These do not have to be done in your journal. Hand in the [Challenge] problem on Tuesday for extra credit.
Prepare for the exam: Consult the review sheet and try a few of the problems on the back.

No Collected Homework this week. Remember Journals are due at the Exam.

Week 5

Sieve of Eratosthenes: algorithm steps for primes below 120 (including optimisation of starting at squares)

(From Wikipedia)

Journal Homework for Class Tuesday, February 16:

Reread Section 2.3 of the text. Concentrate on the last few sections. What is the chart on page 87 trying to tell us? What is Fermat's Last Theorem?
Read the beginning of Section 2.4 on modular (clock) arithmetic. Your project will require a good understanding of this material. Modular arithmetic is used in lots of codes (UPC, ISBN, driver's licenses, etc.).
Read the back of the green handout from class on Thursday. Following the directions can you find all the primes less than 200? Come to class prepared to ask questions!
Exercises: Work these Mindscapes at the end of Section 2.3 (p. 92-94): 1, 2, 3, 8, 11, 22 (and the same question for four distinct primes), 24, and 27. Come for help if you get stuck.

Journal Homework for Class Thursday, February 18:

Review the end of Section 2.3. What is Fermat's Last Theorem? What are the Twin Prime and Goldbach questions? It's pretty amazing that such simple sounding problems don't have solutions!
Read Section 2.4 on modular (clock) arithmetic. Class on Thursday will prepare you for your projecet on UPC's and ISBN codes. This is a neat and important use of mathematics.
Bring: brig an item with a UPC (barcode) to class on Thursday (not a book with an ISBN, that is a different code.)
Exercises: Work these Mindscapes at the end of Section 2.3 (p. 93-95): 15, 17 (from your sieve, what can you say about the first two numbers, so start working on the third), and 32. Come for help if you get stuck.

Collected Homework Due Friday, February 19, 3:00 PM:

Carefully work out these Mindscapes at the end of Section 2.3 (p. 92-93):

#5 (think about your sieve on the green sheet if you are stuck)
#7 (Try different values for n starting at n = 1 until you find a non-prime.)
#12
#23
#25 (see your class notes from Thursday!)
Added Tuesday: #14
Added Tuesday: If p is prime and p > 2, carefully explain why p + 3 is NEVER prime.
Added Tuesday: Your watch reads 9:37. What time will it be in 93 hours? In 1111 hours?
Added Tuesday: Section 2.4, Page 106 #3. Mod 7 means you have a clockface with 7 hours going from 0 to 6.

Download and complete this Worksheet based on Tuesday's class. Make sure your work is neat.
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Week 4

Journal Homework for Class Tuesday, February 9:

Reread Section 2.2 of the text. Concentrate on the last few sections, including the game Fibonacci Nim.
Read the beginning of Section 2.3 on primes.
Exercises:

Journal Homework for Class Thursday, February 11:

Read Section 2.3 on prime numbers. The Division Algorithm and Prime Factorization will be familiar from your earlier mathematical experiences.
Review the proof that every number is interesting at the end of Section 2.1 (p. 56-57). Induction allows us to prove an infinite number of statements (one for each natural number) all at once! What a great thing.
Exercises: These are relatively short: At the end of Section 2.2 (p. 73): Work Mindscapes 17, 19, 22 and 24.
Exercises: Looking ahead. These are also short and will get you thinking about prime numbers after reading about them. At the end of Section 2.3 (p. 92): Work Mindscapes 1, 2, and 3.

Collected Homework Due Friday, February 12, 3:00 PM:

Download the Mindscape Worksheet based on Thursday's class. You must work with a partner on this. Hand in only one good copy for you both. Be sure to keep a copy for yourself.
At the end of Section 2.2 (p. 74): Write up solutions to Mindscapes 20 and 23. Explain your answer.
Write 365 as a sum of different non-consecutive Fibonacci numbers.
Suppose that the sum of different non-consecutive Fibonacci numbers for a natural number n starts with n = 144 + . . . . . What is the largest possible value for n? (There are at least two different ways to think about this problem. Bonus if you solve it more than one way.)
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Week 3

Graphic: Justin Thyme, NYT

This treasure map has two infinite mathematical expressions on the left that look daunting.
But fear not, our cowboy-booted heroine Penny will show you that these are nothing but
the same as the simple equations on the right. (Recently appeared in NYT.)

Journal Homework for Class Tuesday, February 2:

Reread Section 2.1 of the text. Concentrate on the Pigeonhole Principle.
Read Section 2.2 of the text.
Exercises: At the end of Section 2.1: Work Mindscapes 8, 10 and 11 in your journal. (A calculator is needed for 8 and 11. For 11, justify your estimate!)
Buy: Buy a pineapple (over the weekend) and bring it to class on next Tuesday. Both Wegmans and Tops have them in stock. If you would like to pair up with someone else in the class and bring one pineapple between the two of you, that will be sufficient, but at least half the class should have pineapples.

Journal Homework for Class Thursday, February 4:

Read Section 2.2 of the text. Concentrate on the "Converging Quotients" and the "Golden Ratio" sections. We will the former at length in class.
Here are two nice sites on the Fibonacci Numbers: Fibonacci Numbers and the Golden Section and Fibonacci Numbers in Nature. The second includes some nice pictures, as well as diagrams illustrating the different spirals. It also discusses how plant and tree growth exibit Fibonacci numbers through branching. Really neat!!
Here's a youtube video that discusses the use of the The Fibonacci in Lateralus. (Thanks Dan W.)
Exercises: At the end of Section 2.2: Work Mindscapes 5 (will help for class!), 6, 10 (will help for class Thursday), and 12 (do 10 first) in your journal. If you know how to use a spreadsheet that can simplify some of these.

Collected Homework Due Friday, February 5, 3:00 PM:

At the end of Section 2.1: Write up solutions to Mindscapes 4, 14, and 16. We will have more to say about these problems in class on Tuesday.
Added on Tuesday: Thirty buses are to be used to transport all 2000 HWS students to NYC to go to the MOMA. There 80 seats per bus.
1. Explain why one of the buses will have at least 67 students.
2. Explain why one of the buses will have at least 14 empty seats.
Added on Tuesday: At the end of Section 2.2: Mindscapes 4, 8 (Hint: If stuck, take a look at the #7 which is solved in your text.)
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Week 2

Note: I have relisted some of the assignments from last week... it will make sense for our weeks to run from Monday through Friday (rather than Thursday through Tuesday). There are also new Journal assignments.

Relisted Journal Homework for Class Tuesday, January 26:

Exercises: In your Journal work on stories 2, 3, 5, 6, 7, and 10, pages 3-14. Story 10 is on the back of your syllabus (not the one in the text) and can also be downloaded here. Concentrate on the story your group was assigned, but work on all the listed problems. Think about the techniques and ideas we discussed in class about approaching a new problem.
Play Let's Make a Deal in this online Science article in the New York Times and use this to explore the "Monty Hall" problem in Story 7. Try each strategy (Switch or Stay) at least 20 times in a row. Which strategy is best? Does it matter? Include your results in your Journal.

Journal Homework for Class Thursday, January 28:

Reread Sections 1.1-1.4 of the text. What did you pick up this reading that you missed the first time?!
Read Sections 2.1 of the text. What two mathematicians' names do you recognize from the Silly Stories?
Exercises: Work Mindscapes (in Section 1.4) 3, 10 and 12 in your journal. Rework any of the Story problems from the previous Journal work in light of our discussion in class today.
Bring: a lacrosse ball to class today if you have one.
Buy: Buy a pineapple (over the weekend) and bring it to class on next Tuesday. Both Wegmans and Tops have them in stock. If you would like to pair up with someone else in the class and bring one pineapple between the two of you, that will be sufficient, but at least half the class should have pineapples.

Collected Homework Due Friday, January 29, 3:00 PM:

At the end of Section 1.4 (pages 33-36): Write up solutions to Mindscapes 6, 7, 13, and 9 (Hint: Assume one of them, say Wind, did it. Then determine who is lying and who is not. Try this with the other congressmen. Which scenario works?). Be sure to explain your answers carefully, including a short explanation of how you found them. There are hints after the Mindscapes. Try not to use them for at least awhile (it is ok if you do, but try not to). Do read the Problem-solving techniques in blue (for ALL the problems) after you finish working on the problems if not before.
Bonus: (5 points) Mindscape 15 on page 37. Work with a friend!
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Week 1: Welcome to Math 110 Discovering in Mathematics!

We will begin the course by working on some of the "silly stories" in the first chapter of The Heart of Mathematics. These are fun "puzzles" but to solve them requires just the sort of careful thinking that will be required throughout the course.

Please bring The Heart of Mathematics to class each day.

Collected Homework Due Tuesday, January 26, at the start of class:

At the end of Section 1.4 (pages 32-33): Write up solutions to Mindscapes 2 and 5. Be sure to explain your answers carefully. There are hints after the Mindscapes but try not to use them for at least awhile (it is ok if you do, but try not to). Here's one suggestion for Mindscape 2: Try it with a smaller number of politicians, say 5.
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.

Journal Homework for class Tuesday, January 26:

Read the Course Syllabus. Make sure you have read all the details especially regarding assessment. Also be sure to record the exam dates in your personal calendar. Remember that there are no make-ups.
Read the Welcome!, Surfing the book, and Sections 1.1 and 1.4 of the text (pages xi-xxv, 3-14, 31-32). Eventually you will want to read Sections 1.2 and 1.3, but first it would be best to work on 1.1 for a several days.
Exercises: In your Journal work on stories 2, 3, 5, 6, 7, and 10, pages 3-14. Story 10 is on the back of your syllabus (not the one in the text) and can also be downloaded here. Concentrate on the story your group was assigned, but work on all the listed problems. Think about the techniques and ideas we discussed in class about approaching a new problem.
Play Let's Make a Deal in this online Science article in the New York Times and use this to explore the "Monty Hall" problem in Story 7. Try each strategy (Switch or Stay) at least 20 times in a row. Which strategy is best? Does it matter? Include your results in your Journal.

Bonus Concert: Attend the Rochester Philharmonic Concert on Friday, January 22 at 8:15 at the Smith Opera House. Free with HWS Student ID.

Bonus Problem: Due Tuesday, January 26 at the Start of Class

There are nine points arranged in a square like on a tic-tac-toe board. Draw four straight line segments, without lifting your pencil from the paper, through all nine points. Explain how you solved it.
What famous saying is based on this puzzle?

Collected Homework Due Friday, January 29, 3:00 PM:

At the end of Section 1.4 (pages 33-36): Write up solutions to Mindscapes 6, 7, 13, and 9 (Hint: Assume one of them, say Wind, did it. Then determine who is lying and who is not. Try this with the other congressmen. Which scenario works?). Be sure to explain your answers carefully, including a short explanation of how you found them. There are hints after the Mindscapes. Try not to use them for at least awhile (it is ok if you do, but try not to). Do read the Problem-solving techniques in blue (for ALL the problems) after you finish working on the problems if not before.
Remember that your solutions should be typed or neatly written, stapled if more than one page, and if you discuss the Mindscapes with anyone else, they should be noted.