Syllabus Discussion

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Questions?

Syllabus

Grades

Imagine you end this course with an overall average grade of 70%. What letter grade would you expect that to be? It’s probably a solid B.

Also see the sample grade translation and distribution.

Take-Away: Grades will seem harsher than what you expect, but won’t really be, and will probably be a little fairer.

Book

Where do you buy the book? You don’t (unless you really want a paper copy); it’s a free download or web document via the links in the syllabus.

My version gives you fewer trivial typos for the first 2 weeks or so of the semester, and 1 fewer major typo in the middle.

Take-Away: The book is a free download in lots of formats.

Office Hours

Which of the following are available for office hours visits?

• 10:00 AM Wednesdays. Yes.
• 1:30 AM Saturdays. Don’t be silly.
• 5:00 PM Thursdays. No (I’m pretty protective of time after 5:00 in order to give myself time to do the things I can’t do other times during the day because of all the office hours appointments).

I’ll demonstrate making appointments through Google Calendar as the due date for the first problem set approaches.

Take-Away: Office hours are very flexible but with some limits.

Extra Credit

Can you come up with some examples of “real-world math bounty” problems?

• Modeling the physical world around you (e.g., fans and air flow)
• Volumes of real-world objects, especially ones more complicated than what you could do as volumes of revolution in Calc 1.
• 3D engineering problems.

Other extra credit opportunities, e.g., math colloquia, will be announced from time to time in class.

Take-Away: There will be extra credit opportunities, and not just the real-world math bounty ones.

Next

Positions and distances in 3D space

Basic Idea

Describe positions in 3 dimensions as distances from an origin along 3 mutually perpendicular axes, usually called x, y, and z.

For example, the tip of my nose might be at position (2,1,1). Or, when I sit down, (2,1,-1) -- “directions” are either positive or negative, just as in 2D coordinate systems; z is usually taken to be the vertical dimension.

Four Dimensions?

You can’t really draw or visualize what a 4-dimensional coordinate system would look like, but you can describe it.

The key parts of a coordinate system are its axes and an origin point.

The relations between these are that the axes are all perpendicular to each other (mutually perpendicular), and all start at the origin. There are as many axes as there are dimensions to describe.

So a 4-dimensional coordinate system must have 4 mutually perpendicular axes (most of us don’t have the imagination or experience to tell what that would look like), which all start at an origin point.

Going Further

Read the “Three Dimensional Coordinate Systems” and “Writing Equations in R³” subsections of section 2.2

Also.... where do we meet Thursday? Fraser 213 (not our usual room).

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