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SPACE 2016
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Course URL: http://www.math.umn.edu/~math-sa-sara0050/teaching/08s/

Office: 109A / 4 Vincent Hall, Phone: (612) 625 - 2004

Office Hours: MW 12:05pm - 1:00pm or by appointment

Office: 524 Vincent Hall, Phone: (612) 624 - 0284

Office Hours: TTh: 01:25pm - 02:15pm or by appointment

- Announcements
**(05/05)** - Syllabus
- Lecture Schedule
- HOMEWORK PROBLEMS
- Exams and their Solutions
- Gradebook
- Useful Links

**05/05:**- Here are a few word problems for review for Exam 4: Page 1 and Page 2.
**05/02:**- Review for Exam 4 is posted.
**04/21:**- The second writing assignment (due on Monday May 5) is posted.
**04/15:**- Extra Review for Exam 3 is posted.
**04/10:**- Review for Exam 3 is posted.
**04/10:**- The distribution of scores for Exam 2 was as follows:

**49.0, 47.5, 47.5, 47.0, 47.0, 46.5, 46.5, 45.0, 45.0, 45.0, 44.5, 44.5, 44.0, 43.0, 41.5, 41.0, 40.0, 39.5, 39.5, 38.5, 36.5, 36.5, 36.0, 34.0, 30.0, 27.5, 26.5, 26.0, 16.5** **03/10:**- The Monday (March 24) after spring break is study day for the first writing assignment which is due on Wednesday March 26.
**03/05:**- Review for Exam 2 is posted.
**03/03:**- Solutions for Week 6 Homework (i) and (ii) are posted.
**02/19:**- The distribution of scores for Exam 1 was as follows:

**47.5, 47.5, 47.5, 47, 46.5, 46.5, 46, 45.5, 45, 45, 45, 44.5, 44, 44, 42.5, 42, 42, 42, 41.5, 40.5, 40.5, 40, 40, 39, 38, 36, 36, 32, 30, 24.5, 24.5, 21** **02/06:**- Review for Exam 1 is posted.
**02/06:**- Late homework submission policy: The homework can be turned in 1 class late for half credit.
**01/31:**- The office hours for me have changed to 01:25pm - 02:15pm on Tuesdays and Thursdays.
**01/30:**- Welcome to MATH 3118: Spring 2008.

The homeworks will be due at the beginning of the class. As an alternative, you may hand them in my mailbox (Vincent 107) by 10.00am of the due date. The homework can be turned in 1 class late for half credit. Ideally, students should do the homework problems assigned for the previous classes before coming to the class.

**Note:**

I will grade *only* three problems per week. (3 marks for each problem plus 1 mark for neatness etc. making a total of 10 points per week for homework.)

**Week 15 Homework (i):**(__Due Mon 04/28__)- Please click here to print the PDF file of the last homework of the semester.
**Week 14 Homework (ii):**(__Due Wed 04/30__)- There are two parts of the HW assignment.

- Print off and complete the Island of Isometric Views sheet.
- Go to http://get.games.yahoo.com/proddesc?gamekey=qbert and play a few rounds. Write down your high score.

You can use Easy level and if you want to have more fun you can use Normal level. Have fun!

**Week 14 Homework (i):**(__Due Mon 04/28__)- Please click here to print the PDF file of the next homework.
**Writing Assignment II:**(__Due Mon 05/05__)- Please click here to print the PDF file of the second writing assignment.
**Week 13 Homework (ii):**(__Due Wed 04/23__)- Please click here to print the PDF file of the next homework.
**Week 12 Homework (i):**(__Due Mon 04/14__)- Please click here to print the PDF file of the next homework.
**Week 11 Homework (ii):**(__Due Wed 04/09__)- Please click here to print the PDF file of the next homework.
**Week 11 Homework (i):**(__Due Mon 03/07__)- Please click here to print the PDF file of the next homework.
**Week 10 Homework (ii):**(__Due Wed 04/02__)- Please click here to print the PDF file of the next homework.
**Week 10 Homework (i):**(__Due Mon 03/31__)- Please click here to print the PDF file of the next homework.
**Writing Assignment I:**(__Due Wed 03/26__)- Please click here to print the PDF file of the first writing assignment.
**Week 8 Homework (i):**(__Due Mon 03/10__)- Please click here to print the PDF file of the next homework.
**Week 7 Homework (ii):**(__Due Wed 03/05__)- Please click here to print the PDF file of the next homework.

Please disregard #1 and #2 part D. You need not hand the solutions to these questions in. **Week 7 Homework (i):**(__Due Mon 03/03__)- Please click here to print the PDF file of the next homework.
**Week 6 Homework (ii):**(__Due Wed 02/27__)- Write the fraction (6-i)/(3+4i) in a+bi form.

**Solution.**(14/25) + (-27/25)i. - Are the complex numbers closed under division? Why or why not?

**Solution.**No. Since 1/0 is not a complex number. - Show that: . That is, show that the conjugate of the product is the product of the conjugates.
- What is the conjugate of i?

**Solution.**-i. - The ^ notation means "raised to". Simplify i^2, i^3, i^4, i^38.

**Solution.**i^2 = -1, i^3 = -i, i^4 = 1, i^38 = -1.

- Write the fraction (6-i)/(3+4i) in a+bi form.
**Week 6 Homework (i):**(__Due Mon 02/25__)- Prove that the rationals are closed under multiplication.
- Prove that the complex numbers are closed under subtraction.
- Density Theorem for the Rationals: Between any two rationals there exists another rational.
- Is this true for the integers? Example?

**Solution.**No. There is no integer between any two consecutive integers. - Find a rational between 3/4 and (3/4 + 1/1000000000000).

**Solution.**3/4 + 1/2000000000000 - Prove the Density Theorem. Hint: Do it for two general numbers. How can you guarantee that you are between two numbers? Double Secret Hint: Use something we discussed in statistics.

**Solution.**For any two rationals, r < s, q=(r+s)/2 is a rational such that r < q < s. - Do this product: (2-4i)*(3+2i). Your answer should be in a+bi form. (If you are stuck, pretend i = x, and pretend you are back in college algebra again). And remember that i^2 = -1

**Solution.**14 + (-8)i.

**Week 5 Homework:**(__Due Wed 02/20__)- Monday's assignment in class consisted of a number systems diagram and a table to complete. This is not found anywhere in digital form so you should contact a classmate for the details if you were not in class. WARNING: There may be more assignments which are not easily put on the website in the coming weeks, as we use the green book less frequently. So if you miss class you will need to contact a classmate for the assignment before it is due or else turn the assignment in late, and receive half credit. So make buddies now with someone who does come to class if you are a frequent skipper. Or just come to class, where you will receive a strong sense of satisfaction in learning mathematics, support from your peers, not to mention 4 attendance/participation points, AND the assignment first-hand.
**Week 4 Homework:**(__Due Mon 02/11__)- You should memorize a Data Analysis benchmark from the MN Math Standards (the packet you got in class) at the grade level you think you will be teaching. You should also include the 4 digit ID number in your memory. Each benchmark has a 4 digit ID number, such as 5.4.1.1 This would be a fifth grade, fourth strand (Data Analysis strand), first standard, first benchmark.
**Week 3 Homework (ii):**(__Due Wed 02/06__)-
- A high school counselor collects income data on recent graduates.
The following is the data for 10 randomly selected graduates.
- Make a scatterplot for the data, labeling appropriately.
- Sketch the regression line, keeping in mind that this line should have a balance of data points that are above it and below it.
- Describe the overall relationship represented by the regression line between years of ed. and income.

Years of education beyond high school Income 2 27 5 33 0 22 2 25 7 48 4 35 0 28 6 32 4 22 5 30 - John wants to make a circle graph of his monthly expenses. He sees that 30% of his expenses is spent on rent. What central angle should he make for rent in his circle chart?

- A high school counselor collects income data on recent graduates.
The following is the data for 10 randomly selected graduates.
**Week 3 Homework (i):**(__Due Mon 02/04__)- 7.3.4, 7.3.6, 7.3.10 and two additional problems:
- A local menu offers choices from eight entrees, three varieties of potatoes, either salad or soup, and five beverages.
- What is the probability that a patron has a meal with soup?
- What is the probability that a patron has a meal with French fries and cola to drink?

- Let's think about tennis. Roger Federer has a 5 wins to 2 losses record against Novak Djokovic. So assume that Federer has a probability of 5/7 to win any one set against Djokovic. (In tennis, each time 2 players compete, they play a 'match'. Each match is decided by who wins the majority of 'sets' in the match.?
- What is the probability that Federer will win a 'best two out of three sets' match against Djokovic?
- What is the probability that Federer will win a 'best three out of five sets' match against Djokovic?
- Who do you feel will win? Why?

- A local menu offers choices from eight entrees, three varieties of potatoes, either salad or soup, and five beverages.
**Week 2 Homework (ii):**(__Due Wed 01/30__)- 7.3.1 (i), 7.3.2
**Week 2 Homework (i):**(__Due Mon 01/28__)- 7.1.3, 7.1.5, 7.1.7, 7.1.8, 7.1.11

The fourth and final exam will be on Wednesday, May 7th. Here is a review.

The third exam will be on Wednesday, April 16th. Here is a review.

The second exam will be on Wednesday, March 12th. Here is a review.

The first exam will be on Wednesday, February 13th. Here is a review.

This sheet is not comprehensive. You should look over your notes as well, and review relevant homework problems.

**Probability:**- You should be able to:
- Describe the sample space for simple examples such as rolling dice, flipping coins, etc.
- Give the probability for the entire sample space, for an empty set.
- Compute probabilities for simple experiments.
- Understand when to multiply and when to add probabilities.
- Understand how and when to use the Binomial Model.
- Determine whether events are independent by verifying computationally.
- Understand how and when to use tree diagrams.

**Statistics:**- Create and interpret the following: stem and leaf display, histogram, line plot, bar graph, line graph, circle graph, scatterplot, regression line.
- Compute and interpret: mode, median, mean, quartiles, range, box and whisker plot, standard deviation, variance, z-score.
- Provide examples of the measures of central tendency, and measures of dispersion.
- Critique questionable statistics used in justifying ridiculous claims.
- Create lists of data to satisfy requirements about the measures of central tendency and the measures of dispersion.

**Additional:**- Provide an example of at least one benchmark (any grade level K-8) from the current Minnesota math standards.