Review Problems

January 30, 2009 in Math 148

Somebody sez Brutus is absent today for good reason & she’s been asked to take the notes. Which is a bunch of exercises. And Brutus reads the blog. So here goes, quick and dirty.1. The order of transformations matters. Demonstrate this by graphing the “original” graph y = | x| , then (i) Shift up [...]

Our Story So Far: Part I

January 28, 2009 in Math 148

OK. The snow day probably means postponing the exam again. Meanwhile, here are some remarks while I’m thinking about writing the doggone thing.All of our work thus far takes place in (various subsets of) (the Real Numbers) or (the xy-plane). We are particularly concerned with real-valued functions of a real variable; typically these are given [...]

Aleph-Null Mathematicians Walk Into A Bar…

January 27, 2009 in Links

Gowers on massively collaborative mathematics.

Quadratic Formula Lore

January 27, 2009 in Cool Tricks, Math 148, QF

I never learned the doggone thing until I was the teacher and had to, for one thing. I was trying to cop some math-geek attitude (“Never memorize what can be understood instead!”—it turns out this is sort of a damfool commitment). I knew I could derive it (by Completing The Square, of course) and that [...]

More Old Lecture Notes. Whee!

January 26, 2009 in Uncategorized

Here’s a little eight-pager I like to call “Counting Heads” (PDF): deriving the formula for expanding the n^th power of a binomial, from first principles, and applying it to “coin toss” problems. (Not to be confused with D. Marusek’s outstanding novel.)

It’s Not The Cheat, It’s The Futility

January 23, 2009 in Math 148, Rants, Textbooks

The transformations section of the text begins, to my predictable chagrin, with a graphing-calculator “Exploration”: adding (or subtracting) a constant value at the end of a function (in the Function Editor [i.e., the "Y=" screen] of the grapher) produces the by-now familiar (to any student in regular attendance) vertical shift. “We are led to the [...]

Go Love Without The Help Of Anything On Earth

January 23, 2009 in Links

Rolfe Schmitt is introducing binary numbers to his kids.

Big Day For Former Math Professor

January 22, 2009 in Textbooks

Turns out you can create PDF files with the Xerography device down the hall. Here at long last are 67 pages of Numbers, Sets, and Logic by yours truly. You couldn’t really print it all out and use it with your own classes—yet; it’s got scribblings by me from classroom use on some early pages [...]

While You’re Up Get Me A Grant

January 22, 2009 in Links

The coffee-shop lingering function explained by John D. Cook.Archimedes and revisited by Mark Dominus.Desperately seeking well-written topology papers.MathTV.com plugged.David Eppstein on drawing graphs in Illustrator.

Message: I Care

January 22, 2009 in Math 148, Notations

I’d been groping for the right notation for Transformations of Graphs since the first day; I settled it over the weekend. By I will mean a certain Transformation of the xy-plane (at this point I tend to write “” on the board; of course , but none of this “set-theoretical” language has made it into [...]