Assignments for Mathematics for Liberal Arts

Day Date Activity Assignment (due one week from assignment date, unless otherwise stated)
Tue1/10 Welcome/Fun and Games Read Probability (Idea #33 in the text -- pp. 124-127), and the birthday problem (Idea #33 in the text -- pp. 132-135) for next time, Thursday, 1/12. You might also check out my on-line explanation of the birthday problem, for comparison. Consider playing "Let's Make a Deal" (so that you better understand it -- here's a good description of the game). Both of these problems are examples of Probability problems.
Thu1/12 Fun and Games For next time:
  • Read Idea 01, Zero, pp. 4-7
  • Read Idea 09, Primes, pp. 36-39
Homework 1 (due Thu, 1/19):

Put your name at the top of the paper and label it Math 115 - Homework 1. For each problem show me how you found the answer - unsupported answers are worth nothing. Feel free to explain your reasoning and, if you wish, you may include any incorrect attempts at the problem. If you use an outside source you should reference that source!

  1. Carefully write out a solution to the problem about the genie, the gem, and the three scales. Since we have discussed this in class already this will be graded on how well you write up your answer. Be sure to explain the solution carefully and include all the possibilities. Feel free to draw diagrams if you wish.

  2. There are 5 people trapped in an elevator. Being really bored one of them bets the others that at least two of them were born on the same month of the year. What is the probability she wins this bet? ( You may assume that it is equally likely to be born on any given month. this may not be strictly true, but it is close enough that the final probability wouldn't change very much.)

  3. Flip a fair penny and a fair dime. What is the likelihood that

    a. both come up heads

    b. they come up with different results?

    Hint: If you find this difficult, you might want to list out the universe of all possible flips.

  4. Roll two standard (fair) dice. What is the probability you roll

    a. a two?

    b. a seven?

    c. a 14?
Tue1/17 Zero and Natural Numbers For next time:
  • Read Idea 03, Fractions, pp. 12-15

Homework 2: similar instructions as last time (due Tuesday, 1/24):

  1. Suppose that you're at the grand opening of a grocery store, and you and Bob (another "contestant") each choose a jar of peanut butter, at random, from a display of 10 different jars of peanut butter. Under one jar is the key to a NEW CAR! Under the others is a picture of a donkey. The owner of the store shows that under seven of the (unchosen) jars there are pictures of donkeys. You're offered the chance to switch for one of the other two jars -- Bob's jar, or the jar not taken but still unturned. Do you switch, and, if so, for which one -- Bob's or the unchoosen jar? You must carefully explain your reasoning, and give the probabilities of winning depending on the three possible choices. You might consider simulating the game and show data that supports your decision.
  2. Write the prime factorizations for
    1. 1008
    2. 1009
    3. 1010
Thu1/19 Prime and Rational Numbers For next time:
  • Please read the brief description on primitive counting (remembering that I've modified the technique a little -- to count down to 1, instead of to two or three).
  • Read Idea 02, Number Systems, pp. 8-11

Homework 3 (due Thursday, 1/26):

  1. Find two distinctly different ways to write each of the following fractions as a sum of three different fractions:
    1. 1/2
    2. 2/3

  2. Use the rules of fractions to illustrate (as indicated in our text) that

  3. Solve the following shopping problems involving fractions:

    1. An item originally costing $100 is marked down 20%; then marked down an additional 30%. What is the cost of the item? How much is it marked down from its original price?
    2. An item now costs $22. It was marked down twice: 30% the first time, and then 50% on top of that. What was its original price?

  4. Illustrate the following statements about prime numbers by showing two specific examples of each:

    1. Goldbach conjecture - Every even number (greater than two) is the sum of exactly two prime numbers. For example 18=11+7

    2. Primes of the form 4k+1 can be written a the sum of two squares in exactly one way: so for k=3,
Tue1/24 Primitive Counting  
Thu1/26 Egyptian Math Homework 4 (due Thursday, 2/2): Solve the following problems
  1. Write the prime factorizations for
    1. 3451
    2. 5223
  2. Use the method of "counting by partition" to count the following (show the entire tree, and the string of ones and zeros that results):
    • 47
    • 337
    • 1008
    • 1729
  3. Use the method of "counting by partition" backwards to report the number of sheep corresponding to the following strings:
    • 1, 0, 0, 1, 0, 1, 0
    • 1, 1, 0, 1, 0, 1
    • 1, 1
    • 1, 0, 1, 1, 0
  4. In the binary card trick (Fraudini's trick -- see this on-line description),
    • What number (from 1 to 63) is one thinking of if the only cards chosen are
      • the card with all the odds from 1 to 63, and
      • the card with all the numbers from 32 to 63?
    • If I'm thinking of the number 42, describe which cards I'll choose.
Tue1/31 Egyptian Math  
Thu2/2 Egyptian Division For next time, read this on-line introduction to bases.

Homework 5 (due 2/9):

  • Demonstrate Egyptian multiplication by multiplying:
    • 23*79
    • 81*123
  • Demonstrate Egyptian division by dividing:
    • 9/4
    • 13/7
    Try these using the same sort of "doubling/halving" table that we use for multiplication.
  • Demonstrate Egyptian division by dividing:
    • 4/9
    • 7/13
    Try these using the unit fractions table method, and Fraudini's trick (writing a number as a sum of distinct powers of 2).
Tue2/7 Bases Homework (due Tue 2/14):

  1. Rewrite the number we know as 2977 (written in base 10), only using
    • base 2
    • base 8
    • base 16
    • base 5

  2. Rewrite the following numbers in base 10:
    • 101001010012
    • 735568
    • DB92F16

  3. Show how to add 2268 and 3758 (both numbers expressed in base 8).
Thu2/9 Bases/Babylonian/Mayan Math Homework (due Tuesday, 2/21):

  1. How would the Mayans write
    • 97
    • 162
    • 360

  2. How would the Babylonians write
    • 97
    • 162
    • 360

  3. Here's another mystery for you:

    Explain how Lewis Carroll was using unusual bases to do the strange math in chapter two of Alice in Wonderland? On about the third page of chapter two (after the graphic of "Giant Alice watching Rabbit run away"), Alice starts speaking out some bizarre equations:

    "Let me see: four times five is twelve, and four times six is thirteen, and four times seven is -- oh dear! I shall never get to twenty at that rate!"

    Find some reasonable bases to make the "calculations" work out....

Tue2/14 Fibonacci Numbers  
Thu2/16 Exam I  
Tue2/21 Fibonacci Numbers  
Thu2/23 Fibonacci Spirals  
Tue2/28 Golden Rectangles  
Thu3/1 Golden Rectangles  
Tue3/6 Spring Break  
Thu3/8 Spring Break  
Tue3/13 Platonic Solids  
Thu3/15 Platonic Solids  
Tue3/20 Graphs  
Thu3/22 Graphs  
Tue3/27 Links  
Thu3/29 Knots  
Tue4/3 Exam II  
Thu4/5 Knots  
Tue4/10 Mobius Bands  
Thu4/12 Fractals  
Tue4/17 Fractals  
Thu4/19 Infinity  
Tue4/24 Infinity  
Thu4/26 Logo Day  
Tue5/1 Final 1:00-3:00 p.m.

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