Introduction

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Welcome...

...To Math 223, Calculus III

I’m Doug Baldwin.

Why More Calculus?

Because the cosmic purpose of calculus is obviously computer animated snakes...

Or maybe computer generated but hyper-realistic landscapes...

While maybe not exactly the cosmic purpose of calculus, these things really do require generalizing the notion of “curve” to surfaces or curves in 3-dimensional space, of “derivative” to deal with tangents to surfaces in 3 dimensions rather than curves in 2, and of “integral” to allow integrating over volumes or arbitrary lines in space instead of just along part of the x axis. And any other calculus application to the real world probably ought to acknowledge that it’s 3 dimensional, that dependencies between things in it often require more than 1 variable to describe, etc. The ways functions can behave in those extra dimensions also introduce some math that’s interesting in its own right too. This is the course that extends calculus to those new dimensions.

Learning

Levels of Learning

Put the following statements in order, from indicating the least knowledge of math to indicating the most (I don’t expect these to all be true of you):

1. I can use facts from different areas of math (e.g., algebra, arithmetic, calculus, etc.) in combination to solve new problems.
2. I know the names of certain mathematical concepts (e.g., “addition,” “the quadratic formula,” “derivative,” etc.)
3. I see how math is a system of rules, definitions, and techniques, with certain relationships between those things, and can fit new things I learn about math into that system.
4. I have discovered new pieces of math.
5. I can carry out certain mathematical procedures (e.g., finding a derivative by using the chain rule, etc.)
6. Given a mathematical claim (e.g., “every even number can be written as a sum of 2 odd numbers”), I can determine whether it is true or false.

Our suggested order:

1. * I know the names of certain mathematical concepts (e.g., “addition,” “the quadratic formula,” “derivative,” etc.) Bloom’s 1: remembering
2. * I can carry out certain mathematical procedures (e.g., finding a derivative by using the chain rule, etc.) Bloom’s 2: understanding
3. * I see how math is a system of rules, definitions, and techniques, with certain relationships between those things, and can fit new things I learn about math into that system. Bloom’s 4 - analysis
4. ** I can use facts from different areas of math (e.g., algebra, arithmetic, calculus, etc.) in combination to solve new problems. Bloom’s 3 - application
5. * Given a mathematical claim (e.g., “every even number can be written as a sum of 2 odd numbers”), I can determine whether it is true or false. Bloom’s 5 - evaluation
6. I have discovered new pieces of math that no-one else knew before. Bloom’s 6 - creation

I invented these statements to illustrate “Bloom’s taxonomy” of learning. As indicated above, you put them in an order very close to the one Bloom proposed. Stars indicate emphasis in this course. It will focus on the application level (e.g., that’s generally where you need to be to pass the exams), but necessarily assumes remembering and understanding to get there, and will have some forays into analysis and evaluation in class discussions and problem sets.

Next

Ways of learning to get to the desired learning levels, and how I’ll run this course to facilitate them.

See the syllabus handout

Read over the syllabus, come to class prepared to point out, or ask questions about, parts you find particularly significant, puzzling, etc.

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