# Week 9 Assignments

Written work, Due Tuesday, November 4th, in class:
Chapter 7 p129: 5, 9, 10, 12
**Chapter 8 p143: 3, 7, 18, 19
**Chapter 8 has been extended to Tuesday, November 11th
WeBWorK – none
OpenLab – OpenLab #8 due Thursday, November 6th at the start of class

Class work: There will be group & individual work completed & submitted in class on Thursday 10/30/14, which will count towards your “Project” grade.

# Midsemester Grades are posted

You can find your midsemester grades on the GRADES page.  Let me know if you have any questions.

A note about grading of written assignments.  These assignments are a mix of odd and even numbered problems in the book – the odd numbered problems have solutions in the back.  Unless otherwise stated, odd problems will be worth 4 points each and even problems worth 8 points.

Best regards,
Prof. Reitz

# Week 7 Assignments

Written work, Due Tuesday, October 21st, in class:
– Chapter 4 p.100: 1, 6, 15, 16
– Chapter 5 p.110: 1, 4, 20
GRADING: Odd problems are worth 4 points each, even problems worth 8 points each.
WeBWorK
– none
OpenLab – OpenLab #7 will be posted on Friday, 10/17, and will be due TUESDAY 10/28 (the class following the exam).

Exam #2 will take place on Thursday, 10/23.

# OpenLab #6: Choose a game!

What is it that mathematicians really do?  They prove theorems, it’s true – but that’s just the end result.  Along the way comes the fun part – playing around with a problem, trying to see if you can understand the rules of the game, and find some kind of pattern that “makes the whole thing make sense”.  Over the next few weeks, you will be working individually and in groups on a puzzle or game.  Of all the things you do in this class, this work will be most similar to the work that real mathematicians do.

OpenLab #6: Due this Thursday 10/16

Read through the descriptions of the three puzzles below.  Then respond to this comment, ranking them in order of preference.  That’s all you have to do.

For example, you might respond like this:

First choice: Mutilated Checkerboards
Second choice: Bridges and Walking Tours
Third choice: MIU Game

NOTE: This project is about the process of playing around with a problem when you do not know what the answer is (or even what the problem is, really).  BUT all of these puzzles are well-documented on the internet.  I request that you do not Google them, or look at any other resources related to them, until this project is over.

RULES:

• Read the puzzle descriptions below.  Do NOT Google these topics for more information.
• If you are already familiar with one of these puzzles, pick another one as your first choice.
• Puzzles will be assigned next week, with more information and specific instructions.
• You do NOT need to solve these puzzles for now.

## The Puzzles

### Puzzle 1: The MIU Game

We are going to play a game with strings of symbols.  This game was invented by a man named Douglas Hofstadter and found in his book Gödel, Escher, Bach. Here are the rules:

Suppose there are the symbols ‘M’, ‘I’, and ‘U’, which can be combined to produce strings of symbols called “words”, like MUI or MIUUU. In the MIU game, we always start with the “axiomatic” word MI, and transform it using the following four rules, to obtain some “goal” word.  The rules state that you may:

1. Add a U to the end of any string ending in I. For example: MI to MIU, or MUUII to MUUIIU.
2. Double any string after the M (that is, change Mx, to Mxx, where ‘x’ represents any string of symbols). For example: MIU to MIUIU
3. Replace any III with a U. For example: MUIIIU to MUUU
4. Remove any UU. For example: MUUU to MU

EXAMPLE 1
Goal Word: MIIU
Solution:

Start with MI (axiomatic word)
MI to MII (rule 1)
MII to MIIU (rule 2)

EXAMPLE 2
Goal Word: MIIIIIIU

### Puzzle 2: Mutilated Checkerboards

We are going to play a game with checkerboards and dominos.  So that we all have the same picture in our heads, a checkerboard is an 8×8 grid of squares (64 squares total), colored alternatingly black and white:

A domino is a 1×2 block, which is exactly the size of two squares on the checkerboard (the dots on the domino do not mean anything in this game):

Your goal is to cover the checkerboard with dominos, according to the following rules:

1. You can use as many dominos as you wish.
2. Dominos can be arranged horizontally or vertically, as long as each domino covers exactly two squares on the checkerboard.
3. Dominos cannot overlap each other, and cannot extend off the edge of the board.

EXAMPLE 1:  Can you cover the checkerboard with dominos?

EXAMPLE 2: What if we remove one of the corner squares from the checkerboard (a “mutilated checkerboard”) – now can you cover it with dominos?

### Puzzle 3: Bridges and Walking Tours

We are going to play a game creating walking tours of cities with bridges.  We begin in the city of King’s Mountain, which is built on four land masses – both shores of a river and two islands in midstream – connected by a total of seven bridges (shown in green).

EXAMPLE 1:  Can you create a walking tour of the city that crosses every bridge exactly once?  You can begin anywhere you like, and end anywhere you like, as long as you cross each bridge just once.

# Update on Week 6 Assignments

Hi everyone,

As I was absent on Thursday, I’ve updated the Week’s assignments – take a look, and keep your eye on the OpenLab for updates.  I’m curious to hear how the class went, and I’m excited to be starting proofs with you on Tuesday.

Best regards,
Prof. Reitz

# Week 6 Assignments

Written work – None.
WeBWorK – Assignment #6, due Tuesday, October 14th, at midnight.
OpenLab – OpenLab 6: Choose a game!, due this Thursday, October 16th, at start of class.

# Week 5 Assignments

Week 5 Assignments

** EXTENSION: WeBWorK Assignment #4 (due last week) has been re-opened and extended to Tuesday, October 7th, if you wish to continue working on it  (this was done because the final problem has some material on negating statements that we will cover early this week)

Written work – none
WeBWorK – Assignments #4** and #5, due Tuesday, October 7th, at midnight.
OpenLab – OpenLab #5, due Thursday, October 9th (at start of class).

# OpenLab #4: The importance of “Why?”

### Kids love to ask “Why?”

If you’re like most people who attended public school in the U.S., most of the math you’ve done in your life has been primarily computational, or algorithmic – you learn a kind of problem, you learn a method to solve it, you practice it a few times, and you demonstrate that you’ve learned it by solving a problem on an exam.  Maybe the solution involves memorizing a formula, or a set of steps (an algorithm).  Very seldom are you asked to consider the reasons behind the method – what I call the “why” questions.  And if you ever asked these kind of questions, there is a good chance that you were not often given a very satisfying answer.

Questions you may not have spent much time on in math class:

• Why does the formula look like this, instead of something else?
• Why do we do these steps, in this order? How do we know this method actually works?  Why does it work?
• Why is this fact (“theorem”) true?  I don’t believe it – can you convince me?
• What’s the big deal about this fact (or formula)?  Why is it important?

To begin this assignment, I’d like you to spend some time thinking about the different kinds of math you’ve learned in your life.  Look at math textbooks or class notes from past and current classes.  Think about the  math skills you learned at different ages – from early experiences with counting, up through things like algebra or geometry, and on to Calculus or Linear Algebra or other recent courses.   If you still have some old math work from your high school, middle school, or elementary school years that might help too (maybe your parents kept some of your childhood work?).  If you’re in the Math Ed program, you can think about the math that you are working on in your MEDU courses.  As you consider these topics, think about the “why” questions – when you were learning this topic, did you spend time in class talking about “why?”   Did you do activities or other work that helped you understand the reasons for the formulas and methods that you learned?

Assignment (due Thursday 10/2/14). The assignment consists of two parts.  Be sure to answer each part completely (they are equally important).

1.  Describe a time that you DID learn about the “why” behind a mathematical idea (why something works, or where it came from, etc.).  Tell us about it – how old were you, what was the class (or did it happen outside of class?), what was the topic, and what did you learn?

One example that came up in a class discussion was the activity introducing the number $\pi$ by having students measure the diameter and circumference of various circular objects, and showing that the ratio was always a little more than 3.

2.  State three questions about math that you do not know the answer to (but would like to!).  For each question, tell us why you find it interesting.  The questions…

• …should involve “why” or “how”
• …should be about math topics that you are already familiar with – things you’ve studied (you need not be an expert)
• …should come from different math topics, at different levels (some examples:  arithmetic, fractions, algebra, geometry, functions, calculus, probability, … )

Some examples of “why” questions.

1. Why does $a \times b$ equal $b \times a$?
2. Why do we need a common denominator when we add fractions?
3. How do we know that $\sqrt{2}$ is irrational (not equal to a fraction)?
4. Where does the quadratic formula come from?  How do we know it always works?
5. The fundamental theorem of calculus gives us a way to evaluate an integral – for example, to find the area under a curve.  How do we know this actually works, and gives the correct answer?

# Week 4 Assignments

Week 4 Assignments

HEADS UP: Next week Tuesday 9/23 is on a Friday schedule (so we do NOT meet), and next week Thursday 9/25 there are no classes.

Written work – none
WeBWorK – Assignments #3 and #4, due Tuesday, September 23th*, at midnight.
*NOTE: we do NOT have class this day!
OpenLab – OpenLab #4, due Thursday, October 2nd (at start of class).

# Week 3 Assignments

Week 3 Assignments

UPDATE: WeBWorK #3 will be due Tuesday, September 23 (not September 16 as originally indicated)

Written work – Sec 1.8*: 3, 5, 6, 8, due Tuesday, September 16th, in class.
* GRADING: odd-numbered problems worth 3 points, even problems 5 points.

WeBWorK – Assignment #3, due Tuesday, September 23th, at midnight.
OpenLab – OpenLab #3, due Thursday, Sept 18th (at start of class).