Category Archives: Assignments

OpenLab #5: Advice for the Future

Assignment (due Tuesday, December 17).  Imagine that you are invited to speak on the first day of MAT 2070, to give advice to entering students.  Write at least three sentences responding to at least one of the following, describing what you would tell them.

  1. What do you wish that you had been told at the start of this class, to help you succeed?
  2. Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.
  3. What is the most important prior knowledge (not taught in the class) that you need in order to succeed?  Why is it important?

Extra Credit.¬† Respond to someone else’s comment. ¬†Do you agree? disagree? Have anything to add?

Homework Week 13

Homework Week 13
Written work РSection 11.2 p185: 1,2,7.  In addition, complete Example 11.8 at the top of p180. Section 12.1 p198: 1,3,9,11.  (Due Tuesday 12/3)
WeBWorK Р none
OpenLab Рnone

Homework Week 12

Homework Week 12
Written work РChapter 10 p167: 25, 28 (problem 30 is extra credit),  Section 11.0 p176: 3,4 (Due Tues 11/19)
WeBWorK РAssignment6-Sec11.1 (Due Tuesday 11/19 at midnight)
OpenLab¬†–¬†(reminder: OpenLab #4, ‚ÄúThe MIU puzzle continued,‚ÄĚ is due Thursday 11/14. Submit your answer between Tuesday, 11/12 and Thursday, 11/14. )

Homework Week 11

Homework Week 11
Written work¬†–¬†Chapter 10 p167: 1, 2, 10, 15 (Due Tuesday 11/12)
WeBWorK Рnone
OpenLab¬†(reminder: OpenLab #4, “The MIU puzzle continued,” is due Thursday 11/14. Submit your answer between Tuesday, 11/12 and Thursday, 11/14. )

OpenLab #4: The MIU puzzle, continued

UPDATE: See the “Assignment Version 2” added below.

This assignment is a continuation of OpenLab #3, on the MIU puzzle.  Your assignment this time is a little different.  Consider the following conjecture about the MIU puzzle:

Conjecture. ¬†Any goal word (any word with first letter M, followed by a combination of U’s and I’s) can be obtained from the starting word MI using the rules of the MIU puzzle.

Assignment (Due Thursday 11/14.  Submit your answer between Tuesday, 11/12 and Thursday, 11/14). Is the conjecture above true?  If so, prove this fact.  If not, provide an example of a goal word that cannot be obtained, and prove that it is impossible for your word to be obtained.

IMPORTANT: Because of the nature of this assignment, DO NOT SUBMIT YOUR ANSWER BEFORE  TUESDAY 11/12. However, I strongly recommend getting started on this problem well before that date!

ASSIGNMENT VERSION 2

If you wish, you can respond to the assignment below INSTEAD of completing the assignment above.  In the assignment below, you will be writing about your experience working on the MIU puzzle above.  Be sure to respond to EACH PART Рdetailed answers to part 2 and 3 below will gain the MOST credit.

  1. Write down what you think the answer is Рno proof necessary.
  2. Describe in as much detail as you can the process of working on the assignment.  What did you think in the beginning? What are the different things you tried in order to solve the problem?  Describe each one, in the order that you tried them.
  3. Give a detailed list of the resources you used, and how you used each one (these could include anything – your brain, pen & paper, a computer (what applications did you use), the internet, other people, and so on).
  4. What activity or resource do you feel was most effective for you in working on the assignment (what helped you the most in understanding the assignment and figuring out an answer)?

Extra Credit. ¬†Respond to one of your classmates’ submissions.

 

Homework Week 10

Homework Week 10
Written work¬†–¬†Chapter 8 p143: 3, 8, 18, 19, ¬† ¬†Chapter 9 p150: 3, 4, 5 (Due Tuesday 11/5)
WeBWorK Рnone
OpenLab РOpenLab #4, The MIU puzzle continued, is due Thursday 11/14. Submit your answer between Tuesday, 11/12 and Thursday, 11/14.  (The assignment will be posted after class on Tuesday 10/29.)

Homework Week 9

Homework Week 9
Written work РChapter 7: One odd-numbered problem and one even-numbered problem of your choice from Chapter 7, p127.
WeBWorK Рnone
OpenLab Р(reminder: OpenLab #3, assigned last week,  is due Tuesday 10/29).

OpenLab #3: The MIU puzzle

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. The MIU game asks one to 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

WARM UP.  In each example, start with the axiomatic word MI and show, step-by-step, how to obtain the goal word (in each step, state which of the rules you used). These are just for practice (you do NOT need to submit your answers).

Example 1: Goal word MIU
Example 2: Goal word MIIU
Example 3: Goal word MIIUIIU
Example 4: Goal word MUUII
Example 5: Goal word MUUIIUIIU

Here is a sample solution to Example 2:
MI to MII (rule 1)
MII to MIIU (rule 2)

Assignment (due Tuesday, 10/29): Your assignment has three parts.

PART 1. ¬†First, create an MIU puzzle — that is, make up a goal word, and post it in the comments. ¬†Try to create a goal word that balances the following two requirements:

  1. The goal word should not be too long – definitely not more than 10 letters (but the shorter the better).
  2. The goal word should be tricky to reach, requiring at least four steps to reach (but the more the better).  See if you can find a clever use of the rules!

PART 2. ¬†The second part of your assignment is to solve someone else’s puzzle. ¬† Type your solution step-by-step, indicating which rule you used at each step. ¬†Leave your comment as a response to their puzzle. ¬†Only one solution per puzzle!

PART 3.  The third part of your assignment is to write a short paragraph (at least 3 sentences) responding to the following prompt.  Be sure to respond to each part:

Writing Prompt, MIU puzzle: ¬†Did you enjoy this assignment? Why or why not? ¬†Describe a connection between this assignment and our work in the class. ¬†(If you don’t believe there is a connection, try to imagine why we are doing this). ¬†Leave your response in the comments.

Homework Week 8

Homework Week 8
Written work РChapter 6 p. 116 #5, 8 (due next Tuesday, 10/22)
WeBWorK Рnone
OpenLab РOpenLab #3, due Tuesday 10/29.

NOTE: Exam #2 will take place on Thursday, 10/24.

 

Homework Week 7

Homework Week 7
Written work РChapter 4 p.98 #1, 6, 15, 16,  Chapter 5 p.108 #1, 4, 20 (due next Thursday, 10/17 РNOTE that Tuesday 10/15 is a Monday schedule, so our class does not meet)
WeBWorK Рnone
OpenLab Рnone

KEEP IN MIND: For written work, the odd-numbered problems have complete solutions in the back of the book.  USE THIS RESOURCE.  You should try the problem on your own first, but when you are done read the solution carefully, and adjust your answer accordingly!  Let these examples be your guide on how to approach a proof.