173 study session and exam topics

We will have a study session on Wednesday, May 6, from 1:30 p.m. to 4:30 p.m. in room AA 362-B, which is a conference room located halfway between the Science and Business division offices, next to the photocopiers.

Following are the official objectives for this course, from the official outline, which you can always find on my website. I crossed out a few topics that we either didn't do or didn't do enough to put on the final. Everything else is something you should be ready to tackle.

A. solve problems involving volume, arc length, work and centroids of plane areas,
B. differentiates and integrates expressions involving transcendental functions,
C. define conics, vectors, sequence, limit of a sequence, infinite series, convergence and divergence of a series,
D. solve problems involving conics, rotation and translation of coordinate axes and polar coordinates,
E. find areas bounded by curves in polar form,
F. solve problems involving parametric equations, vectors,
G. solve problems involving improper integrals and infinite limits of integration,
H. find series representations of functions and use Taylor's Theorem with Remainder,
I. differentiate and integrate power series, solve problems in indeterminate form, and obtain competency in the use of a graphing utility

271 study session

I have reserved room AA-362 for our use on Tuesday, May 5 between 11 a.m. and 2 p.m. Hope we'll see you there!

174 computer-based assignment

These problems will account for 30% of Monday's test. 90 minutes' work should be plenty — great formality is not required.

From the author's website, this page, please choose Browse visuals on the left, then section 10.3 for Polar curves, then Exercises at top right, then problems 5, 6, 7, and 8. These can be done with a graphing calculator as well as with the online instrument gives a lot more information.

For those who are unable to see the problems online, here they are:

5. Investigate the family of curves given by r = 1 + b cos (theta). Describe how the shape of the curve changes as b varies.

6. Graph r = b cos(theta) + p sin(theta) for several values of b and p. What geometrical figure do you conjecture all polar graphs of the form r = b cos(theta) + p sin(theta) look like? [You should support this conjecture, of course.]

7. Consider the function r = 2 cos (theta) + sin (2 theta).

(a) By looking at the Cartesian graph [of y = r(t), as on page 643], where is r <= 0?

(b) Can you explain why Quadrants II and III of the polar graph are empty?

(c) How many values of theta for 0 <= theta <= 2 pi satisfy r = 1?

(d) The polar graph intersects the unit circle 4 times. Explain the discrepancy between this and part (c).

8. Graph the function r = 0.5 + 2 sin(3 theta) for 0 <= theta <= 2 pi. Looking at the Cartesian graph, can you explain the different-sized loops in the polar graph?

Here are links to some online graphers:

http://www.webmath.com/polar.html

http://fooplot.com/ (use dropdown box where you put in function to change Function to Polar

http://www.teachers.ash.org.au/mikemath/calculators.html

Not that you don't already own a grapher, of course, and not to mention the always-valuable Winplot — but the last of these links is actually to a French grapher Tracés animés that's a real prize.

174 cover sheet for Project Two

My thanks to alert student A.B. who asked where this was — click.

You're invited to outer space

Ah, the final frontier, at last!

The American Astronautical Society is having its annual Goddard Memorial Symposium, which takes place in Greenbelt, Maryland on Tuesday – Thursday, March 10 – 12, and you're invited. Just $30 for students — it's a steal! This year's theme is sustainable space exploration. See the student rate at the very end of the registration form.

I mean 174 more on the snow day

Looks like a great day for exploring some of the Wolfram sites I've found so enchanting lately: demonstrations, articles galore, the online integrator, and Calc101. Although one has to buy a membership ($25/year) for all of the details of an integration, Calc101 gives away abundant details on many other things, such as calculations of partial fractions.

In case you should try out Aurora, the Microsoft Word add-in for mathematics that I've been enthusiastic about lately, be aware that there's what I would call an error in the process. You should download and install the latest MiKTeX before installing Aurora. Considering the complexity of the inner works, I find that it all goes amazingly smoothly. Here's a sample of the results that I'm enthusiastic about: see the last page. I don't know of an easier way to get such good-looking results.

snow day 3/2/2009

Having signed up for NOVA Alert on my cell phone, I'm as up to speed as I'm ever going to be. I've received two messages so far today: closed till noon and then, moments ago, closed "all day."

Does that mean all through the evening, too? I don't know, so I await another message.

Meanwhile, Math 174 gets more time for the problems in 7.5 (call me at home for a hint if you're stuck), and we'll finish Chapter 7 on Wednesday, and we'll have our test on 6.2 – 6.5, 7.1 – 7.6 and 7.8 on Monday, March 16. What a day that will be, with projects due then, too.

Meanwhile, some students in my other class reminded me of the site InteractMath.com. There you can find an abundance of fully-worked examples from a number of textbooks other than our own — they're all substantially the same, but the Adams book (first in the long list) seems to have the greatest number of online problems.

271 notes for Chapter 3

Click here.

174 valuable links

Here's a handsome grapher that works for implicit functions etc. and might have a better interface than Winplot, my old faithful. To copy to the clipboard, you'll need to download two Java files to your computer. I found it with keywords online graph implicit function.

The other day I found this site for integrals online. It led me to another site, Calc101, that has lots of capability for $25 a year. It gives step-by-step solutions: don't let it short-circuit your thinking.

Here is the table of integrals from page 484 in Chapter 7.5 of our text.

I have also found a wonderful solution for getting math into MS Word documents: Aurora plugs in TeX bits so that one's math looks just right. There's enough help on the site that you can figure out all the TeX you'll want to know.

174 project format and sample

Keep in mind that your objective is to write what other students can fully understand. Find values with a calculator when you can, and be sure to show why you are finding them! Read your work out loud to someone. (I will listen if you ask me before class on Monday or on Tuesday.)

Here are format guidelines and a sample. You do not have to use a word processor. I went kind of over the top with mine...

Since I was later than I wanted to be in getting these documents to you, I will change the due date from Monday to Wednesday.

174 homework problems

Here's what we've already done and enough to carry us through the next few weeks: click

271 homework problems, Chapters 1 and 2

Here's the homework. Problems in (parentheses) are the ones that I plan to do in class. You don't need to do them.

Homework is finished when you can do new problems of the same complexity without referring to your notes or the book. Students who get an A or B will probably spend six or more hours a week doing homework and other studying. Put it into your plans!

• 1.1 Slopes and equations of lines 
  3, 13, 23, 29, 31, 59, 65, 69, 71, 72
  
• 1.2 Linear functions and applications 
  27, 29, 31, 35
  
• 1.3 Least squares don't do these yet 
  3, 9, 15, 19 (4)
  
• Chapter 1 review 
  p. 49, 1-12; p 50, 1, 32, 33, 37, 41, 45, 47 (38, 42)
  
• 2.1 Properties of functions 
  21-35 odd, 36, 37-57 eoo, 61, 65, 67, 69, 75, 77, 79
  (22, 24, 30, 32, 34, 44, 50, 62, 76, 80)
  
• 2.2 Quadratic functions; translation and reflection 
  1-8, 9, 11, 19, 21-30, 31, 43, 44, 45, 49, 53, 55, 59
  (3-8, 21-26, 27-30, 50, 56)
  
• 2.3 Polynomial and rational functions 
  3, 7-19 eoo, 20, 23, 25, 29, 39, 45, 47, 51, 57
  (4, 30, 40, 44, 56)
  
• 2.4 Exponential functions 
  1, 2, 3-9 odd, 13, 17, 19, 21, 33, 37
  (14, 18, 26, 34, 38)
  
• 2.5 Logarithmic functions 
  1-39 odd, 41-61 eoo, 63, 67, 69, 71
  (2, 4, 8, 10, 16, 22, 24, 46, 55)
  
• 2.6 Applications 
  15, 17, 19 (18, 20)
  

Welcome Spring 2009

Here's what I'm doing this spring:

• Math 174, Calculus II, MW 2 p.m. to 4:20 p.m.
  outline  •  syllabus
  
• Math 271, Applied Calculus I, TR 9:30 a.m. to 10:45 a.m. outline  •  syllabus
  
• CSC 201, Computer Science I, MW 5:30 to 7:20 p.m.,
  and its required lab
  CSC 185, Programming Tools, M 4:30 to 5:20 p.m.
  outlines 201 and 185  •  syllabus for both  •  CSC weblog
  

I look forward to meeting you!

163 optional take-home problems

If you submit these on Wednesday, they will be graded as an extra test: click

241 test for 7 and 8

Here's a copy of the problems for the strangely missing test, which has indeed turned up. It would make me blush to tell you where and how.

FYI final exam schedule

I was making another copy of the final exam schedule for myself and thought that you might like one, too. click

173 graph I wanted

With a graph showing on the screen of a TI-83 or -84, do Calc menu (above Trace button), then 7:[integral]f(x)dx. This gets you a Lower limit? and Upper limit? and then shades the area involved, as well as calculating the result.

In class, we had this sequence:

  

Next, calling on the integral:

  

And here's the result:

 

Unfortunately, you have to do this over again for different limits of the integral. To get around that, you have two options: [1] imagination; [2] write a program!

173 Riemann sums in the TI-83, 84, and 89 calculators

So sorry: I am unable to keep my promise to put enhanced instructions here this evening. While we are waiting, I refer you, if you please, to the TI-83 manual, which has a chapter on programming, and note that in the TI-89 one can do almost the same thing we did in class by going to the Apps key. Will have it all here ASAP.

241 Statistics Hacks, a book

Publisher O'Reilly has a lot of "hacks" books, most of them IT-related, but there are also mind hacks, how interesting, and a book of statistics hacks, from which I took this presentation on outcomes of hypothesis tests. You can pay real $$ for the marvelous books that this company publishes or read all of them for free on Safari, provided by the library. If off-campus, go through the library website instead and log in with your SIS ID.

241 Minitab assignment

This is a Minitab assignment on confidence intervals. Find CIs as directed in the problem statement for problems 7-2-10 and 7-3-17. Use the directions on pages 359-360 (special attention to steps 1 and 2!) and 367-368. Make a probability plot for each problem. (See page 368.)

Cut and paste the Minitab results into a word-processing file. Write a brief introduction for each problem and interpret the results. In particular, comment on the normality or not-normality of the population, as reflected in the sample, and its impact on your results.

Due date: 12:30 p.m. sharp, Tuesday, November 18, 2008

241 connecting confidence intervals and hypothesis tests

From a paper by Greg Kochanski:

How are confidence intervals related to Hypothesis Tests?

They are very much equivalent. If the confidence interval doesn’t include H0, then a hypothesis test will reject H0, and vice versa. In fact, if you made up a vast number of different null hypotheses, one after the other, then tested them, the accepted null hypotheses would mark out the confidence interval.

Confidence intervals put the focus on the measured number; hypothesis testing puts the focus on the theory that you are testing.

Reader "clemTNT" writes in a comment below:

I came accross this yesterday: Ten Reasons Why You Should Ignore Exit Polls

1. Exit polls have a much larger intrinsic margin for error than regular polls. This is because of what are known as cluster sampling techniques. Exit polls are not conducted at all precincts, but only at some fraction thereof. Although these precincts are selected at random and are supposed to be reflective of their states as a whole, this introduces another opportunity for error to occur (say, for instance, that a particular precinct has been canvassed especially heavily by one of the campaigns). This makes the margins for error somewhere between 50-90% higher than they would be for comparable telephone surveys.

Does this relate to what we did in class yesterday?

http://www.fivethirtyeight.com/2008/11/ten-reasons-why-you-should-ignore-exit.html

Yes, I would say that this article certainly does relate to confidence intervals, especially CIs for proportions, which we discussed on Thursday of this week.

The best reason for discounting exit polls (I would not say ignoring) is that participants are self-selecting. Someone wants to ask you as you leave the poll, Whom did you vote for? Many people will avoid the pollster on sight.

However, contrary to the article, precincts are not chosen at random: they compose a stratified sample. Our textbook says, "Researchers obtain stratified samples by dividing the population into groups (called strata [which means layers]) according to some characteristic that is important to the study, the sampling from each group." So precincts are chosen to try to replicate the overall vote with regard to, for example, socioeconomic status, ethnicity, etc.

This is typical for many kinds of polls and tests, such as new-product roll-outs and audience surveys. "Will it play in Peoria?" is not just an old vaudeville joke: products really are tested there.

241 on polling

From the Wall Street Journa, October 13, 2008:

Good Polling Means Not Influencing the Outcome

I appreciate Thomas Riehle's review of my book, "The Opinion Makers: An Insider Exposes the Truth Behind the Polls" ("The Art of Yes, No and Maybe," Sept. 26), because I think it reflects more generally the industry's response to my concerns about the way most media polls distort public opinion. My concern is on the substantive opinions reported by media polls and why we can't trust them.

Measuring public opinion should include measuring how many people don't have strongly held views, as well as those who do. The failure of most polls to differentiate between the lightly and strongly held views of the public is one reason we can't trust the polls to reflect the will of the people.

My view is that providing information to respondents in a sample results in a distortion of what the public at large is really thinking. Different pollsters give different information, and then present the results, which often conflict with each other, as though they represent the American people.

Just three days before his review was published, three major media polls, all conducted in the same time period, illustrated the problems I discuss in the book. They came up with three wildly different pictures of public opinion on the bailout of the financial industry: The Los Angeles Times/Bloomberg Poll found a 24-point majority of Americans against the bailout, while the Pew Research Center found a 27-point majority in favor. In the middle was the ABC/Washington Post, which found the public evenly divided. Those are hardly useful "insights." Instead, they make a mockery of polling and of the claim that polls can measure the will of the public.

Until pollsters address the consequences of their manipulation of respondents into giving meaningless answers to poll questions, public-opinion polls will continue to confuse more than enlighten.

David W. Moore
Durham, N.H.

173 Mr. Wilkin's notes for calculus

Jon Wilkin, head of math and computer science at the Alexandria campus and general guru for the faculty, has offered his lecture notes for Calculus I. You are free to print them out and bring them to use in class if you like.

241 online help

There's a website that I've recommended for other classes that I recommend for this one, too. It's called interactmath.com, and it has guided solutions for problems from many textbooks. For statistics, I would recommend choosing from Sullivan, Triola, Weiss, or McClave. Each time you refresh the browser, you can have another problem of the same type with different numbers.

241 test results

Upon reflection, I find that I don't want after all to post results of our first test here, even anonymously, but they are all marked and I will be happy to tell you how you did if you call or to return your paper to you in person on Monday.

173 test Monday

Our test on Monday is on all of Chapter 2. You can get extra exercises at a site called interactmath.com. Although ours isn't one of the textbooks there, other books cover the same material, and the site will take you through problems step-by-step if necessary and create new ones for you. "Hass: University Calculus," Chapters 2 and 3.1, would be a good choice from the textbooks menu. You will need to have a Flash player installed in your browser.

163 test Monday

Our test on Monday will be on Chapters 1.1–1.4, 11.1, and 11.4. I urge you to visit interactmath.com for extra help. If you're having trouble with a particular problem, the site will help you through it step-by-step and then create other problems of the same type for you. Choose "Sullivan: Precalculus w/ Graphing Utilities 5e" to get our book.

lotso blogs

a list of top ten blogs in many areas of interest

173 quiz 2.1 – 2.6

Here are a revised solution to problem 2.7 / 14 and the quiz.

The covers more sections and is worth twice what a typical quiz is, and the problems are a little more challenging, too. Step-by-step details to show your reasoning are essential.

Please leave the blank lines along the right edge empty: they're not for your answers, but rather for the scores. If you need more space than provided, please attach more sheets of plain paper.

2 p.m. sharp on Monday! E-mail or fax your paper (703/845-6006) before then if you can't attend.

241 about test on Tuesday, September 16

Our first test will cover Chapters 1, 2, and 3 of our text.

A student asked which graphs you need to be able to work with. The answer is, all of the ones in the computer graphics assignment. You will be asked both to create graphs and to interpret data shown in graphs.

You will also be asked, once for all time, to show in detail how to calculate the standard deviation of a small data set. You should create columns x, x - mu, (x - mu)^2 and totals as shown in class. Naturally, you can check your work with a calculator.

You should expect to give examples of terms that were defined in class, to perform calculations beyond those mentioned here, and to reason about everything that we have talked about in class in the past three weeks.

163 solving linear systems with matrices

The best website I have found for solving linear systems with matrices in a TI-83-type calculator is here. And here is the handout from class with the changed homework assignment for Chapter 11.1.

Next week we will have a second day of working with matrices and, on Wednesday, September 17, a test on sections 1.1 – 1.4 and our matrix work.

241 beyond box plots

Here's a concise illustration of a several types of graph besides the box plot that give information about a statistical distribution. These become relevant now because we're talking about percentiles, and will mean more as we learn about the normal distribution.

173 challenge problems

For some thumb-suckers related to Chapter 2.6, click here.

163 online tutorial

For an online practice site, go to www.interactmath.com. No account number or anything is needed. You tell it which book you're using (Sullivan Precalculus, 5e) and download a plug-in, if necessary. (I had to download an updated Adobe Flash plug-in.)

The problems are like the problems in the book, and you can get as many examples of a particular type as you like.

For the application or story problems, following the examples offered on the site might be especially helpful.

241 computer lab is ON in AA 447

We will meet in a computer lab on Tuesday, September 2, in room AA 447, on the routh floor not far from our regular classroom.
Links for the day:

our assignment and a sample with a few notes

the Minitab website and a free-to-try 30-day download if you don't have a CD

click here for a big old zip file containing the data from the appendices of the textbook ("Bluman data"); the "corrected" databank (databank_fix.mtp), as I will explain in class; and Minitab-portable versions of all the datasets in the book

Carnegie-Mellon's DASL dataset, a useful resource

National Center for Health Statistics' FastStats page

If you find statistical sites that are especially friendly for our kind of work, please let me know and I will ad them to our list.

All done!

All grades for the Spring 2008 semester have been posted. Usually they turn up on NovaConnect pretty quickly — worst case is tomorrow morning, I believe, and best case is now.

random number generation

As you know, this is one of my favorite things. This short article <click> gives a concise overview of one of many methods for cooking up random numbers.

The basic idea for all RNG algorithms that I have seen is to pick a starting value, call it X0, then to let X1 be a function of X0, X2 a function of X1, ... Xn a function of X(n-1), ... And these X values provide a sequence of pseudo-random numbers, a sequence actually completely determined by its starting point.

In this case, one chooses a several X values and combines them for the new X. The constants in this algo look pretty silly, but still you get the flavor of the thing. You can choose much smaller numbers for the constants and program the algorithm in a TI calculator using sequence operations, which are described in the TI manuals, for which links are given on many a math teacher's home page.

242 last test revised

Click here. Thanks to the alert students who have pointed out my error: the protocol to follow for the third problem is on page 690, not page 693.

242 pictures from class

Students are listening to other students practicing their presentations. These pictures are very exciting for me!

241 take-home part of test for Chapters 6 & 7

Click here.

242 what is the Fulano de Tal statistic?

To begin with, Fulano de Tal is not a real person.

However, if there were a Fulano de Tal statistic and I needed a brief explanation of it, I would use these Google keywords:

site:.edu "Fulano de Tal" statistics

The first bit site: is a Google operator that restricts searches to a particular site or kind of website, in this case, to colleges and universities. (Be sure not to inject any spaces between the operator and operand.) This combination will help you find find other instructors' web pages, usually better for our purposes than unfiltered Google results. Somewhere an instructor posted just what you need to understand about Box-Cox, Kaplan-Meier, whatever.

Fulano de Tal is in quotes so that it won't be broken apart by the search engine. And statistics may be superfluous, but who knows? Maybe Fulano de Tal did work in a variety of fields.

242 citations for project

Although our project write-up is comparatively informal, we nonetheless must cite our resources so that the interested reader can find them. There are many acceptable forms: honesty, clarity, and consistency are our priorities.

Duke University's library provides a very concise and easy-to-use collection of citation forms. Ours will be based on the Council of Science Editors stylebook, which you can find, along with other manuals of style, near the reference desk in our campus library.

I am using an article that was in the New York Times online, but not, as far as I can tell, in the printed version, and I got a PDF for the scholarly source online, too. I will cite my sources in this fashion:

0. Identification

[1] Parker-Pope, Tara. Boy or Girl? The Answer May Depend on Mom’s Eating Habits. The New York Times [Internet]. 2008 April 23 [cited 2008 April 24]. Available from http://well.blogs.nytimes.com.

[2] Mathews, F., Johnson, P. J., & Neil, A. You are what your mother eats: evidence for maternal preconception diet influencing foetal sex in humans. Proceedings of The Royal Society B [Internet]. 2008 May 1 [cited 2008 April 24]. Available from http://journals.royalsociety.org/content/w260687441pp64w5/fulltext.html.

The elements of these citations are:

• author(s)
  
• article title
  
• journal title
  
• date of publication
  
• date of access, if this applies
  
• URL, if this applies

If I had actually used a printed version of my resource, I would replace date of access and URL with volume and page numbers. The URL of the Times article was actually one of those insanely long ones, and I abbreviated it. Do so only in case of insanity.

Then, when I quote or paraphrase from one of these references in my own paper, I will say, for example,

They say that one would expect that we humans would have evolved "facultative sex ratio variation" [2], but little evidence that we have done so has yet been discovered.

(Not necessarily a real sentence from my paper!)

The project is mostly based on one described in Teaching Statistics: a bag of tricks by Andrew Gelman and Deborah Nolan, Oxford University Press, 2002, ISBN 0-19-857224-7, and I thank OUP for contributing the book. The collaborative group work that we do is based on the teaching of Mary Pierce Brosmer, founder of Women Writing for (a) Change, who has helped me personally with ideas and strategies.

Alive Day

I encourage all students to attend the Alive Day showing in AA 158 (across from the computer lab) at 5:30 p.m. on Tuesday, April 29. Marine Michael Jernigan, one of the wounded Iraq veterans featured in the HBO program, is a student on this campus, and he will be speaking at this event.

RFID embedded in concrete

Here's a great article from NVCC construction management professor and guru Denise Cantwell about how RFID chips are being used to build a new stadium in New Jersey. RFID means "radio frequency ID." These tiny radio transmitters are used for identifying all kinds of things — some people are wrapping their wallets in foil so as not to be identified, which is not as crazy as it sounds.

242 project overview

May 12: attend presentations

May 5: submit your paper and attend presentations

The class meetings leading up to the presentations all included group work inspired by the teaching of Mary Pierce Brosmer, founder of Women Writing for (a) Change, who has consulted with me on this project. Some of the guidelines I have given you come directly from her.

April 28: practice your presentation in your group

April 21: your outline should be coming together now; plan to share it with colleagues

from April 14, name your statistics and an outline of what you are to present and submit (these are the same document, two pages)

from April 7, one plain sentence to summarize the whole thing

from March 24, name your sources

from March 5 (?), the original project overview

242 in the lab Monday, April 14

Today we will have a few exercises with chi-squared tests and ANOVA using Minitab in the computer lab. Problems 11-3-8 and 11-3-30 are easy to put in by hand. Here are files for problems 12-3-16 and 12-3-9, which we will do in that order. Here's the plan for this part of class. We will also work on the final project. Note: On Thursday afternoon I will consolidate all the project docs we have so far in a new posting on the weblog.

And here is a copy of the take-home part of next week's test on Chapters 11 and 12. Note: I found the hard copies of this — will put them on table next to my desk if you want to pick one up.

You will get all the necessary hard copies in class, natch, so no need to print them out if you're there.

Random numbers in your car

This is the article How your Key Fob Works by Marshall Brain. I sure didn't know this!

163 solution for SuperQuiz 3.4

Click here for 3-page PDF.

242 example problem Chapter 12

Here is the ANOVA problem that we did in class this week, showing both Scheffe and Tukey tests for pairwise differences of the factor populations.