Another in our WWWTF (What in the World Will I ever use This For?) series:
Math Concept: Integration
Having spent multiple hours over the past week helping official oldest daughter of Env-Econ (OODEE) work through calculus problem after calculus problem in preparation for the pending AP exam, I thought it might be helpful to see how she might eventually move past solving math problems to applying the concepts. Right now I'm going to focus on integration, and hopefully later I will come back and talk about differentiation (seems backwards, but integration is fresh in my mind right now). In what follows, I assume a working knowledge of basic integral calculus--otherwise why would you care what you use this for?
As a reminder, a definite integral is defined as:
where f'(x) is the derivative of the function f(x) with respect to the variable x.
Graphically, the integral represents the area under the function y=f'(x) over the closed domain [a,b].
An example might help. Consider the simple linear function f'(x)=6-2X. What is the definite integral of f'(x) over the closed domain [1,3]?
What does this look like graphically?
Notice that for this case of a linear function (a line), the area under the function makes a triangle. A simple way to check your integration is to just find the area of the triangle on the graph.
The area of the triangle is .5(Base x Height) = .5(2 x 4) = 4. This is the same result we got for the intergral. For more complicated functions (non-linear), the area under the function isn't a nice neat geometric shape.
I know what you're thinking: Nice pictures and it's great fun to think about math, but WWWTF? (What in the World Will I ever use This For?). Keep reading for an application to environmental economics.
I had my second exam scheduled today and next week is Spring Break. From the inbox:
All classes are canceled Friday, March 7. Campus is closed until noon for employees.
This makes an entire week that the university has canceled my MWF 10-10:50 Stats II class. Each time the cancellation was a good decision. With most students living off campus and public transportation not running, it is just too risky to have thousands of people on slick roads.
That said, a week of class is a long time. A significant chunk of material that I (optimistically) hoped to cover will not be covered this semester (nonparametric statistics, time-series analysis). Several years ago the TR morning classes missed two weeks of class. A few falls ago the university basically canceled finals week due to snow.
There are significant educational costs that have been ignored as part of our adverse weather policy and there is too much snowy weather in Boone to ignore these costs. The only things I can think of is to have (a) some extra class days built in to the academic calendar or (b) have all classes with web content to mitigate the cancellations. When will this happen? Maybe never. In terms of (a) the academic calendar is already too jam packed with two sessions of summer school and a two week break for 12 month contract upper administrator vacations. Our "reading day" before final exams has routinely been moved to a Saturday. In terms of (b) the majority of faculty still don't have the technical skills to get a lecture or quiz online. And given the low morale in the UNC system, faculty are in no mood to have the legislature, UNC general administration or Appstate upper administration pile on any sort of extra work.
The university makes sure to tell faculty that if we are out of town for a conference then we need to have some sort of educational opportunity as a substitute (guest lecture, online quiz). There is no such thing when the administration decides to cancel class. How seriously should I, as a part-time administrator (i.e., department chair), take the upper administration's mandate that I monitor all classes and make sure that faculty don't simply cancel class when they are out of town on university approved travel?
Which brings me back to the awkward logistics of my class. When do I have the exam? Most of the students had already studied by the time class was canceled. The Monday after spring break doesn't sound appealing (half the class will still be on their way back from their Colorado/Utah ski vacation). The Wednesday after makes it two weeks since the last lecture on the material on the exam. Complicating that is the CEO lecture that my students will attend on Friday during class time (I'll be at a conference and business students are strongly encouraged to attend the CEO lecture).
Update: The roads were fine by 11 am. The decision to cancel Friday afternoon classes was nothing more than a "hey, it is spring break and classes won't be doing anything anyway" decision. Sad that the administration has the same attitude as the college students.
I've been department chair for almost five years now and I haven't much enjoyed a 40% decrease to our department budget and trying to allocate a one-time 1.3% (or something like that) raise. News like this is disheartening (but I'll add a caveat at the bottom):
In a memo on Feb. 28, [Art Pope, the state budget director] took university leaders to task, saying they’re asking for far too much money at a time when the state has competing priorities such as Medicaid and raises for K-12 teachers and state employees. He said the university system had basically ignored his office’s instructions in December to come forward with budget expansion requests of no more than 2 percent. ...
This year, the UNC system received $2.5 billion in state money for operations and another $64 million for building repairs and construction.
Pope said the board has requested an increase of $288 million, or 11.3 percent over the current year’s state budget for UNC. Those figures do not include any raises for employees.
While the state’s economy is improving, an 11 percent increase is a fantasy, he said. Such a spending increase for UNC, Pope said, would require the governor and legislature “to make major reductions in other state agencies and programs, such as our courts, the ‘K-12’ public schools, and health care.” ...
From 2007-08 to 2012-13, appropriations per student have declined 7 percent while tuition receipts per student have jumped 47 percent, according to the university system’s budget proposal. Controlling for inflation, education spending per degree at UNC has declined by 18 percent, UNC said. ...
Pope, too, seems to be casting his eye toward the university’s ability to pay its own bills.
He pointed out that the system had a cash balance of nearly $269 million by the end of the 2012 fiscal year and collected $228 million in overhead payments accompanying grants and contracts, mostly from the federal government.
“How much of the overhead receipts are being used for the repairs and renovations for the facilities used to generate the overhead receipts, as opposed to requesting $163 million in General Fund appropriations for repairs and renovations?” Pope asked in his memo.
Appstate is looking for something like $90 million, I think, for a new nursing building. That is a lot of money in the current budget environment.
After almost 25 years in the UNC system, I've gotten way tired of the mission creep. ECU wanted to move up the Carnegie ladder and when we did they immediately announced a goal of moving up the next rung. Universities want new PhD programs, engineering schools, dental schools and et cetera. I've always wondered: why don't we just try to do better the stuff we are currently doing?
From a former PhD student of our department (who graduated last May):
...60 undergrads at Penn State have now read your recent article (assuming they listen to my instructions) on CV analysis and critiquing Hausman. I had several classes on non-market values and used it to motivate CV analysis and its use in valuation.
From time to time, we find online college syllabi among those sites referring us traffic, and some professors have told us that they use Retraction Watch in their classes. We’re pleased and humbled by that.
In a new paper published in the Journal of College Science Teaching, three professors at Clayton State University in Morrow, Georgia, discuss why retractions are good case studies for teaching ethics and examining the scientific process in class. Stephen Burnett, Richard H. Singiser, and Caroline Clower write:
In this article, we discuss our experience using articles that have been “abandoned” (where their results are no longer accepted due to new evidence) and/or retracted as methods for teaching students about scientific literature in general and specifically about scientific ethics. Being presented with a more accurate picture of primary literature can help students develop an improved understanding of how science is actually practiced and how scientific ideas change over time. By examining retracted articles in which ethical lapses have been uncovered, students are able to develop a more clear understanding of the types of ethical problems that can occur and improve their ability to recognize them.
From retracted articles it is easy to stimulate discussion on a variety of issues, even if the specific methods might be too advanced. We have found that the best way to help define ethics is to show examples of ethical failures. Students can clearly see what is wrong in most of the retracted papers, and when they cannot see why a paper has been retracted, it becomes an important teaching tool to help them understand ethical conduct.
I'll be considering this to help prep for the next time I teach senior seminar (while the journal says this article is free, I haven't overcome the challenge of obtaining the PDFit took awhile but I was able to obtain the free PDF).
A slight majority of Americans favor the controversial Keystone XL oil pipeline that President Obama is expected to approve or reject this year, finds a poll conducted for USA TODAY.
About 56% say they favor the northern leg of the billion-dollar, Canada-to-U.S. project and 41% oppose it, according to the poll of 801 U.S. adults completed last month by Stanford University and Resources for the Future (RFF), a non-partisan research group.
More men (60%) than women (53%) support the 1,179-mile pipeline extension, which would carry heavy tar sands from Alberta through Montana and South Dakota to Steele City, Neb. Support was consistent regardless of education level but much stronger among self-described conservatives than liberals, a slight majority of whom oppose it. ...
The pipeline, proposed by Calgary-based TransCanada, has become one of the most contentious issues of Obama's presidency. Environmentalists have waged a grass-roots war against it, saying tar sands' development would worsen global warming and its delivery could risk oil spills. The oil industry and other backers say it would increase jobs and reduce U.S. dependence on unreliable foreign sources of oil. ...
The poll of n = 801 has a margin of error of +/- 4%. As I now well know (since I'm teaching stats and I know everything that is in the book!), the margin of error is determined by the formula +/- z x SQRT[(.5 x (1 - .5))/n]. With a 95% confidence level, z = 1.96 and the margin of error is 3.5%. So, where does the 4% come from? Are they just rounding up from 3.5%?
What does EZ stand for in EZtestonline? It can't be "easy" because EZtestonline is not easy! Please help me find the Doane and Seward testbank. Also, why do I need to log in with my password every time I try to navigate to another page?
I'm going to resort to cutting and pasting from the Word document. Jeez.
Here is a great illustration of what professors can do with nonmarket valuation in the classroom:
An economics class at St. Mary’s College of Maryland took a look this fall at the costs of deer/vehicle collisions as well as a theoretical way to cut down on such accidents.
“Valuation in Environmental and Natural Resource Economics” is an experimental survey and statistics class new to the campus this semester.
Amy Henderson, assistant professor of economics, teaches the upper-level course, which is designed to engage students in applied economic analysis outside the classroom. ...
Henderson taught students how to assign value to intangible amenities using advanced statistics coursework, a process called contingent valuation. ...
One question asked residents their opinion of a one-time tax on county households to fund a deer-fencing project.
Henderson said that based on the 200 responses, households said they would be willing to pay $28.31 to fund the theoretical project. Multiplied by the number of homes in the county, the class statistically analyzed the survey data and concluded that residents placed an estimated $1 million value on the proposal.
McInerney and his classmates presented the project earlier this month to Rebecca Bridgett, St. Mary’s County administrator, George Erichsen, director of public works and transportation, and the county commissioners. ...
“My goal is to get students to see the potential of what they’ve been learning all along,” Henderson said.
She said she hopes her lessons will motivate students to tackle meaningful projects in their futures.
“It was certainly a very interesting experience to work with the community and get opinions on not only the survey, but the topic as well,” senior Kara Kotler said. “I feel it is important for the college to engage with [members of the] community because they are a great resource for the college.”
The course is expected to be offered every fall. Students will study a different topic each year.
"This blog aims to look at more of the microeconomic ideas that can be used toward environmental ends. Bringing to bear a large quantity of external sources and articles, this blog presents a clear vision of what economic environmentalism can be."
... the Environmental Economics blog ... is now the default homepage on my browser (but then again, I guess I am a wonk -- a word I learned on the E.E. blog). That is a very nice service to the profession. -- Anonymous
"... I try and read the blog everyday and have pointed it out to other faculty who have their students read it for class. It is truly one of the best things in the blogosphere." -- Anonymous