Math 1180

Your Host: Mark Zajac



Office Hours: Catch me before class or make an appointment for the next day. Don't be shy! Questions are very, very welcome.


Syllabus: You can download a copy of the syllabus, which gives some additional details about the course.


Fall Semester: Here is a link the the web page for the Fall 2009 semester, with all of the class notes and test solutions.


Lab Web Page: You can jump to the Lab Web Page by James Moore, which provides useful information and materials for compleeting the computer assignments.


Text Website: The text has a companion web site, which includes answers to all the odd-numbered excercises.


Section Notes Suggested Problems
5.1 notes 1, 3, 15, 17, 23, 25 Note: 15, 17, 23, and 25 were only intended as important review of differentiation, not as practice with key concepts for the test.
5.2 notes 1, 3 (don't agonize -- there will be no trigonometric functions on the test), 7, 11, 13, 15, 17 Added: 9 Note: any tricky graphs will be provided for you on the test but you should know how to interpret them.
5.3 notes 1, 3, 5, 7, 9, Optional: 17, 19 (will not appear on the test but a key concept for anybody who wants to continue in mathematical biology)
5.4 notes 1, 3, 5, 7, 9 Update The Newton's Cooling Solution (notes 185) was updated to fix a mistake (01/25/10). The corrected version introudces u in a change of variables.
5.5 notes 1, 3, 25, 27 Note: don't agonize over these or waste a lot of time on the graphs -- just look at the answers and be sure that you understand. Also, the main point of asking 25 and 27 was to have the results available for the corresponding questions in the next section.
5.6 notes 11, 15, 27, 29 Note: again, don't agonize or spend a lot of time on making graphs -- just look at the answers and convince yourself that you could do it.
5.7 notes
5.8 notes


First Test:

The class average was 40/50 points.

Hints: You might wisht to compare the hints to the test key.

Key: You can use the answer key to review the grading for mistakes.



Section Notes Suggested Problems
6.1 notes
6.2 notes Lower priority: 3, 1 (with P(A) = 0), 27 (1% => P(A) = 0.01), 23 (with P(A) = 0)
6.3 notes 1, 3, 5, 7, 9, 11
6.4 notes 1, 7, 9 (ignore "counting" part of question), 11 (ignore "counting" again) DANGER! I made two pencil-o's (like a type-o, but with a pencil) when I prepared my notes: one on page 221 and one on page 223 (both the figure and the formula). These mistakes have been fixed before posting here. All posted version are correct.
6.5 notes 1, 3, 7, 9, 11
6.6 notes 13, 15, 17.a, 25, 27
6.7 notes 1, 7, 9, 15
6.8 notes 1, 3, 9, 11 (ln(e) = 1), 13 (for expectation, see 6.7-15), 15 (the "inequality" is just that the geometric mean should always be less than the arithmetic mean, which is just the usual average), 17
6.9 notes 1 (ignore "range" and "computational formula" part), 3, 5, 9 (integrate the PDF to get the CDF, set the CDF equal to 0.25, 0.5 and 0.75 to get the quartiles) 11, 13, 15


Sectond Test:

The class average was 41/50 points.

Hints: You might wisht to compare the hints to the test key.

Key: You can use the answer key to review the grading for mistakes.



Section Notes Suggested Problems
7.1 notes 1, 5
7.2 notes 1, 5 (computational formula for average and variance only), ADDED: 17 (no graph, peak at answer), 19 (no graph)
7.3 notes 1, 5, 9 NOTE: in the on-line notes, I suggested 7.4-1 for this section when I meant to suggest 7.3-1 instead.
7.4 notes 3, 5, 9, 11, 13 (skip mode), 15, 21 (see hint in on-line notes, 267)
7.5 notes 1, 3
7.6 notes 1, 3, 5, 11, 15, 35
7.7 notes 5, 15, 33, 41, 45
7.8 notes none
7.9 notes 1, 5, 7, 9, 15 (the "continuity correction" is what makes P(H<8) approximately P(X<8+0.5) when H is binomial and X is normal -- see notes 288), 17


Third Test:

The class average was 41/50 points.

Hints: You might wisht to compare the hints to the test key.

Key: You can use the answer key to review the grading for mistakes.



Section Notes Suggested Problems
8.1 notes 9 (write down L(p) for b(k; n, p) with k = 2, n = 4, then plug in p = 0.5), 15 (notes 291--292, repeat the binomial maximum likelihood derivative for n = 6 and k = 5 to find the maximum likelihood p value, then compute E(W) = ($1)P(W = $1) + (-$6)P(W = -$6) to get the average, were random variable W represents winings from betting on the game)
8.2 notes 1, 5, 7, NOT ON EXAM
8.3 notes 1 (skip c), 5, 13, 17, OPTIONAL: 3 (skip c), 7, 15, 19
8.4 notes 1, 3, 5, 7
8.5 notes 1, 3, 5, 7, 9, 11
8.6 notes
8.7 notes 1, 3, 15, 17
8.8 NOT ON EXAM
8.9 notes 3, 5, 7, 9, 11, Optional: 1, 25, 27


Nothing to do with Coefficient of Determination:



Final:

The final examination will begin at 8:00 AM on Friday the 30th of April, in JFB 102 (the same room as for class). The final will last for two hours.

Final Examination Hints:

The exam will have one question for each of the first three chapters (5, 6 and 7) plus three more questions for the last chapter (8). You will be asked to solve only five questions, of your choice, whichever questions you like best.

  1. As you can see in this hint, the question for chapter 5 will be about phase planes. I will review this during as part of a review session during class on Wednesday, the 28th of April. UPDATE: the hints were updated at 7:11 PM on the 27th of April.

  2. Problems from chapter 6 will involve some combination of concepts from questions 4 and 5 of the second test. It will not be my intention to ask about any other topics from that test, beyond the fact that all math topics are somewhat interrelated. The relevant hints are 12, 13, 14, 15, 19 and 20 but only for the continuous case. It was simple integration that gave people the most trouble. I will be looking for people to do better in this area. A review of hint 3.b from the first test is advisable.

  3. Problems from chapter 7 will involve some combination of concepts from questions 3, 4 and 5 of the third test so hints 4, 5 and 7 are relevant. Since question 4 saw no love the first time, it is the most likely candidate for recycling but it's not that hard. Check the key. Though not tested directly, the rules for adding expectations and variance might prove indirectly useful.

  4. Here are the hints for final chapter of the book. I do not promise that the hints cover every minor topic explicitly but major topics not covered in the hints will not be on the final examination. UPDATE: The wording of the hint was improved, a little a 12:26 PM on the 28th of April.

DANGER! You must take the final. Do not make plans to leave town before the date of the final.



Click here to review counting, with singer Feist.


Mark Zajac

Mark Zajac
University of Utah
Department of Mathematics,
155 S 1400 E RM 233
Salt Lake City, UT, 84112-0090
USA