Assignment: "The Special Instrument"

"As it campfires glow against the dark, every culture tells stories to itself about how the gods lit up the morning sky and set the wheel of being into motion. The great scientific culture of the West, our culture, is no exception. The calculus is the story this world told itself as it became the modern world.
"It is the calculus that for the first time allowed mathematicians access to the Book, and in Newton's hands it is the calculus that became his special instrument... and ours.
"However much Newton may have passionately pursued pure mathematics, he was not in his heart purely a mathematician; during the year of miracles, it was something else that seized his imagination, some supected barely felt connection between the mathematical garden in which he had wandered with such careless authority and the massive collocation of astronomical and terrestial facts that were his to touch and tame as well. Like Einstein, his spiritual heir and only equal, Newton viewed mathematics as an instrument. In thinking about the calculus, Newton was already thinking beyond the calculus, planets in motion and falling objects moving across the enormous corridors of his mind. Let them move and tumble, those pale planets and falling objects. Something is forming itself.
"Time and space make up the the world's great vault. It is within that vault that change occurs. The night sky is lit by moonlight, the great trees sway, birds shriek, and then the opalescent light vanishes and the sun appears. Something has changed because some things have changed. This is the familiar, the continuous world. and it is this world that Newton represented by a series of daring correlations."

-- David Berlinski from Newton's Gift and A Tour of the Calculus.

Assignment: After reading "The Special Instrument" handout, list some things that are important in your life that are continuous. What would your world be like if we could not explain these things?

Functions

"Mathematics is conceived in the fires of the real world, and the functions that bring twitching life to the calculus represent processess beyond the closed coffin of a coordinate system -- things that take place in time and that take place in space. The maturation of an egg and the education of an undergraduate both represent processess; so does the circumnavigation of the moon, the beating of the human heart, and the dense shifting of the seas under the influence of the lunar tides. But not every functional relationship, it is important to recall, is a relationship between numbers. There is a world of relationships beyond the world of mathematics in which men and women pair off, children are raised, scores are settled, and fathers age and then die, and none of this correlated with the real numbers. And not every relationship between numbers expresses an interesting mathematical function. Surrounded somewhere in Las Vegas by blue-haired women and hard-eyed men, a roulette wheel spins in the soulless night. It generates a string of random numbers. The association between those numbers and the time at which they are generated describes a matching of numbers to numbers and so a function. It is an association without structure and so without interest. The functions of the calculus represent, they embody, the mathematician's canonical instruments for the depiction of change. They have up to now appeared as a collection. Mathematics is, in part, a rhapsodic subject, full of dark mystery; but it is also a discipline like comparative anatomy in which things are put in their mathematical places and places found for mathematical things." David Berlinski, A Tour of the Calculus

Assignment: Favorite Functions

What is your favorite function?


Mine is good ol' f(x) = x squared. He is my favorite for many reasons. First he is always in a good mood and is never negative. Secondly, he is even-tempered -- f(-x) always equals f(x). I also like him because no matter what x-value I choose, f(x)'s rate of change is always constant and ends up being twice the x value. Finally, I think he is cool because whether his x-values go toward positive or negative infinity, his graph climbs toward the sky.

Name your favorite function and explain why you chose him/her.

Free Advice from 2004-2005

The day after the AP Exam this year while we were sitting around enjoying our donuts, I asked the class to write down any and all advice they wanted to give the incoming class on how to succeed in AP Calc. Listed below are their comments.......Food for thought as you embark upon your Calculus careers......

1. Expect to work hard.
2. Don't procrastinate on the Calculus Portfolio or life will s___ really bad.
3. Do your homework!
4. Don't be afraid to ask questions and go in for extra help outside of class.
5. Don't be shy....or you die! -- MM.

• Don't wait until the night before your Calculus portfolio is due to do it.
• It always takes much longer to type it than you expect...every time.
• If you finish MM's sentences on funny comments/philosophies he sometimes gives extra points.
• Do the homework every night!
• Ask MM for help outside of class time.
• Get a study buddy or people you know you can call to ask questions about homework. Math really is easier as a "Team Sport."
• Know your unit circle.
• Even when you get really really frustrated, just try to remember that eventually you will get it.
• Know your Saturday Night Live, Monty Python, and Caddyshack ("Be the ball.").
• MM loves jelly bellies.
• Cover your book.

1. Do your HW every night. It helps.
2. The Calculus portfolio takes longer to type than you think.
3. If you are going for multiple AP classes, prepare to have minimal social life.
4. Laziness is extremely dangerous.
5. Finish his sayings out loud.
6. Ask for help outside of class.
7. Make sure there is at least one other Math god or goddess in each of your classes so you have someone to share inside jokes with.
8. Watch a lot of SNL, Monty Python, Best of Will Ferrell and Caddyshack so you understand.

Don't ever wait until the night before your portfolio is due. It takes longer to type than you think.
Don't wait until the night before to study for a test. Study a few nights out, so you can hit your weak points the night before.
Speak up in class. He likes to see that you are at least trying, even if you are wrong.
Don't be afraid to speak up if you think others are wrong and you have justification as to why. Everyone makes mistakes.
Always do your homework. The practice helps a lot and you can identify mistake you made.
When MM says, "You'll need to remember this," you will! Write it down.
If you are confused, don't be embarassed, ask because at least 1 more person is as confused as you are (usually).

• Don't play basketball at the Calculus Lock-In, you might break your foot!!!
• Don't focus on grades. When all is said and done it is more fulfilling to know that you truly understand the Calculus than it is to have an A. Also when it comes time for the (AP) Exam your grade in the class won't help you.
• Don't avoid learning things that you have trouble with. They will never go away and they will only add stress to your life.
• Pay attention during class. If you miss a single step because of daydreaming you won't understand anything that follows.
• Don't ever say you hate math, at least not in front of MM. Never challenge his ability to win the Iron Man competition.

1. Do not be afraid to ask for help.
2. Be ready to study for hours for tests.
3. Calculus portfolio - don't wait until the last night unless you simply hate sleeping.
4. Watch out for yams, ferrets, and sheds.
5. Be the ball; you need more cow bell; scoff at the shed.

• Do your hw.
• Expect to work hard.
• Learn the concepts.
• Remember the formula for area of a triangle.
• Enjoy the journey!
• Stay focused!

- Start studying before the night before a test.
- Don't blow off the midterms; especially the last one of 1st semester. It can make or break your semester grade.
- Don't let senioritis set in until after the AP Exam.

As a pain as it may be, do your portfolio gradually, not the night before it is due. When MM keeps emphasizing something in class, chance are it will be on the test. Look at the questions at the end of the chapters. If it inolves a yam, it will be on the test. Finish his quirky sayings and you get extra points. Do your homework -- just do it. Or you will fail horribly. Don't pull all nighters more than twice a week -- you will crash and burn. Make sure your first period is a BS class so you can study. Design the Calculus t-shirt before the last minute. Watch SpaceBalls, Paper Chase, Will Ferrell Live, Field of Dreams, Caddyshack and the scene from Saturday Night Live with the cow bell so you won't be truly lost with his inside jokes. Mutter cuss words under your breath in order to confuse your fellow classmates. Don't leave bits of trash on the floor. If you're lost, grow some ____ and raise your hand and ask what on earth is going on. Stay in Calculus because you get donuts.


Do your homework
Eat your yams,
Don't let senioritis
Kick in till after exams.

Don't be ______
Pay attention take notes,
If you check the van
Be sure to bring coats.

Take the advice
Of Godfather M___
Bring a cowbell
And you'll all sing "Dao"

The beginning is tough,
So don't turn red.
And if you study the right thing
You'll scoff at this shed.

1. Do your homework
2. Don't be too cocky.
3. You're responsible for your own grade. There isn't any coddling.
4. Be motivated.
5. Learn to study.