The Probability That I’ve Reached the Limit

Starting off this week, the first test in Calculus. All about limits, laws, proofs, and continuity.

Next on the agenda (Thursday), Probability and Statistics. Let’s just say that I love statistics and hate probability; of course the bulk of this semester will be an in-depth exploration of probability. Here’s a little taste via an example in class:

There are 3 rooms. You are placed in one of them. The chance of you being placed in a room has different probabilities. Now, in the room, there is a coin. Of course, there are different probabilities for each room that you will toss a head. Based on these “facts”, what is the probability that you are in Room #1?

I walk out of that class dizzy.

The good news is that I cannot, yet, calculate the probability that I have reached my own personal limit. In fact, all I can see is a line that stretches out to infinity some point that cannot be defined. Ach spfft!

We Love New Words

Cross posted at Agricola.

 

Our culture is evolving at a rate that seems to be directly proportional to the evolution of technology in our personal lives. Some scientists have even made the claim that our species has evolved more in the last 300 years than in the previous 30,000 years as the divide between the physical and the cultural disappears.

Languages evolve, too, and provide a useful barometer to understand where we are going as a culture.

Herewith a few examples of new entries in our lexicon:

“Teamsmanship,” “embed,” and “guybrarian” – just a sampling of the creative new words and expressions recently submitted by the public to Merriam-Webster’s Open Dictionary. Read on for their definitions…

embed (noun): an instance or period of a journalist traveling with a military unit; an instance or period of being embedded.

Example of use: If we’re on an embed and we’re dealing with these Iraqi forces, they’re going to be very careful in what they say, because their American paymasters essentially are standing around.

guybrarian (noun): A male librarian in a female dominated field.

Example of use: With so many women studying library science, Tim felt conspicuous as the only guybrarian in the class.

pitawich (noun): A sandwich made with pita bread instead of the usual loaf.

Example of use: I enjoy a tasty tuna pitawich while watching Star Trek.

teamsmanship (noun): the practice and skill of being able to work as a team.

Example of use: Football players constantly display excellent teamsmanship.

vanity sizing (noun): the practice of setting the sizes of manufactured clothing such that the garment is larger than the established norm for a given size in order to persuade the purchaser that a smaller size is appropriate.

Example of use: Without vanity sizing I would not be the owner of the only pair of size 6 jeans that I have ever managed to get into.

Great stuff, via

Brittanica Blog.

It’s Hard

We’re three weeks into the semester. The excitement of new classes has been replaced by a gathering sense of  anxiety; the difficulty of the new material is becoming more evident. New things have to be learned; to be learned they must be understood; to be understood requires practice, practice, reading, and memorization.

Calculus, probability & statistics, and programming are not skills acquired through reading and taking notes, as was the case with my old friends, English and History. My writing skills cannot gloss over any lack of knowledge in terms of calculating the precise limit of a function, or determining the probability that A intersects B intersects C and derives a certain value. or, God forbid, writing an accumulator program that performs some function based on user input.

No, the material must be mastered. It’s hard.

A New Member of the Blogroll

Please welcome The Chicken to the blogroll of honor here at Gates of Academe. A mysterious character, found often in the company of marine biologists, the chicken seems to pose more questions than answers with every sighting. The daily rituals of Man, travel to the far corners of the globe, social intercourse, and a deep understanding of modern culture; all seem to have been embraced by a creature previously considered to be a part of the food chain. Now a significant member of a social hierarchy, he has transmigrated from one milieu to another. Could he be the missing link?

Elucubration Today

To work late into the night. Originally this was by the light of an oil lamp or candle. More recently, the phrase is used figuratively, alluding back its use before electric lighting.

No matter the archaic form of the word. For me, burning the midnight oil has the same context as that of France Quarle, who penned these words:

“Wee spend our mid-day sweat, or mid-night oyle;
Wee tyre the night in thought; the day in toyle.”

This semester is no leisurely walk through the ivy-covered halls of the humanities. This is the time for mathematics, computer science, and statistics. No time for thought, barely enough time to write, read, study, and do homework. Too frequently included are quizzes with near daily regularity, and homework turned in for a grade. Every step in the process must be explained, learned, measured, and reported.

Time is flying because time has disappeared. I am caught in a timeless void of data seeking patterns, just beyond the reach of my consciousness. The oil flickers, the professor’s demands do not.

It’s grand, I tell you.

The Enemy of My Enemy

Several times during the spring semester I reported on my adventures with algebra. It was a struggle, and I did feel as if I was being attacked from all sides by an implacable foe. Although my victory could not be considered a resounding defeat of the dastardly algebrii, I nevertheless moved forward, on to the next fight. I knew the algebrii would be to my rear, and, as such, could still wreak havoc in my baggage-train unless I paid them close attention at all times.

Well, the battle is joined with Calculus. The fighting is hard, but there has been a surprising development. I have an unexpected, but welcome ally. The algebrii are helping me in this campaign. It seems that having forced them aside, while in the process becoming familiar with their operations, that I have been able to use some of their formations and tactics in this larger fight. Other combatants have reported this strange effect to me, but I would not believe until I experienced it firsthand.

Others in this fight, having managed to flank the algebrii and move forward without battle, are finding themselves attacked in their rear by the unvanquished functions, angles, and graphs of the algebra forces. I, on the other hand, have been strengthened by the fight.

I have a good ally. My chances for victory are much improved.

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Hidden Costs III

A while back, when I was new and fresh in the academic adventure, I expressed my dismay about the cost of textbooks. As professors are wont to kindly say, they are helping us “save” money by continuing to use older editions of texts. Such beneficence!

My calculus text is out of print. The beloved 4th edition of Calculus, Early Transcendentals 4th Edition (1999), has been replaced by the 5th Edition (2002). The 4th edition is required, at my school, for three sequences of calculus. Most science majors are required to take the first two sequences, and a small subset must take all three (and then some!).

Think about it. The school requires its students to use a finite resource, i.e., the textbook. There is a limited supply that, by definition, decreases each year. Some books wear out after too much abuse, some books are kept by students for future reference, and some are held by other students for at least 3 semesters. The number of students enrolling in calculus classes is a constant. It make sense to assume that a constant demand for a shrinking resource induces a stress on the supply, and price, of the product. In the college textbook world, I think that means that the price the market will bear for used textbooks is higher than if the supply was infinite. Our professors are saving us money by forcing us to buy used textbooks, but demand and pricing are driving prices higher. I think we are trapped in a paradox.

There are several students in my calculus class that still, after 2 weeks, cannot buy a textbook. I would have gone insane by now.

I do want to buy my favorite accessory, the student solutions manual, which I have used with great effect in earlier math classes. Guess what? The publisher no longer supports the 4th edition student solutions manual. Why should they?

Today, I found, after a long search, a student solutions manual. If you followed the link, you know that some enterprising person has managed to put the solutions manual (at least the questions and solutions) on the web. You will also see that the basic service is free (good enough for me), but the premium features require a subscription. Looks like the marketplace has provided yet another source of profit for someone other than the publisher and the school.

Maybe, when I take an economics course, I can study this market in more detail. Maybe our economics department should, too, and forward the results to our school officials. Or maybe the textbook market is like the health insurance market, just too complex for simple students to understand and too unwieldy for bureaucrats to manage.