PZ Math Calculus Prep Camp
There are four primary goals for the PZ Math Calculus Prep Camp:
- Give students a big picture view of the entire calculus curriculum,
- Review the algebra and trig skills that are crucial for calculus success,
- Introduce and study in depth the concept of derivative, the first fundamental idea of calculus, and
- Introduce mathematics as a way of thinking, including the best methods for learning and studying calculus throughout the entire academic year.
Big picture view of Calculus
Begin calculus with a big picture understanding of the two central ideas in the subject: 1) derivatives and rates of change, and 2) integrals and area. While one week is not enough time to teach the entire subject, we will teach you the central ideas, how they are related, and give an in depth look at the early topics.
Algebra and Trig Review
Success in calculus requires frequent computations involving both algebra and trig knowledge. It is not uncommon for students to understand the new ideas in calculus, yet get lost in computations because of poor algebra and trig skills. We will review the algebra and trig skills that are crucial for success in calculus.
The notion of a derivative is central to all of calculus. You will leave camp with: a thorough understanding of the limit definition of a derivative, including both algebraic and graphical representations; easier methods for computing derivatives; and an introduction to the many applications of a derivative, from physical laws of motion to optimization problems.
Math as a way of thinking
Learning mathematics is different than learning other subjects. While reading over notes and going through homework can be effective methods for studying some disciplines, they are simply not enough in math, especially calculus. In addition to teaching calculus content in this camp, we will give you the tools you need to continue learning throughout the school year and to study effectively for exams, including the AP exam. Mathematics is more than a set of tools, it’s a way of thinking -- thinking logically, analytically, and effectively. The utility of these skills transcends math. Learning mathematics can hone your problem solving and communication skills in any discipline.
To see how fun math can be, challenge yourself with one of these questions!
Challenge 1. Mr. Z, construction boss, has 3 boxes of building supplies, containing nails and screws. One is labeled ‘nails,” another is labeled ‘screws,” and the last is labeled ‘nails and screws.” We know that a tired employee labeled each box incorrectly. Taking only one item out of one box, how can we label the boxes correctly for Mr. Z?
Challenge 2. Andy encounters a strange island, where every creature has either green, purple, or blue hair on his head. He’s told by a reliable source that those with green hair always tell the truth, those with purple hair always lie, and those with blue hair make statements that are alternately true and false (though the order of which statements are true and which are false is unknown). One day, Andy meets three of the islanders, but each is wearing a very big hat which completely covers his hair. Andy asks each of the three the color of their hair, and the responses are as follows:
A: I have green hair.
B: I have purple hair.
C: 1. They are both lying. 2. I have blue hair.
Assuming that each of the three has a different color hair, determine the hair color of each of A, B, and C. Explain your answer fully. If we don’t assume that each has a different hair color, is it possible to determine the hair color of each islander? Explain fully.
The overall experience far exceeded my expectations…