Precalculus

Precalculus DVDIf you are wondering whether to skip from Algebra 2 directly to Calculus or whether to take Precalculus first, the answer (almost always) is to take Precalculus first.  Gaining depth is more important than racing ahead, and the depth offered through this course is tremendous.  Recording this course has been a remarkable experience for me, personally.  I have grown in my appreciation for Foerster’s work in the process.  In my career I have taught out of several other Precalculus textbooks, but none of them is in the same league with Foerster when it comes to teaching problem solving and real-world applications.

I am using the 3rd edition of Foerster’s Precalculus with Trigonometry (ISBN 978-1-60440-044-1), available from Kendall Hunt, which recently took over its publication from Key Curriculum Press.  (Follow the Kendall Hunt link and use the order form on the right side of their web page.)  The videos are usable (less conveniently) with the 2nd edition as well (ISBN 978-1-55953-788-9), which is available from various used book dealers, using this cross-reference table for finding which videos correspond with which chapters.  There are major rearrangements, but except for a few modified sections and the addition of Chapter 16 in the 3rd edition, most of the content is the same.

Here is the list of problems whose solutions are worked out in the videos (listed in 3rd edition order).  These would constitute reasonable assignments.  For additional practice most of the odd numbered problems have (bare) answers in the back of the student edition of the book.

The DVD course makes heavy use of computational tools, primarily a scientific calculator, spreadsheet programming, Geogebra, and Sage.

I have been working a lot with the new software tool, Geogebra and am using it heavily in lieu of “graphing calculators.” Download it and start playing with it. (The Geogebra files referenced in the Precalculus course can be downloaded here.)  Graphing calculators are severely limited by their clumsy user interfaces and small screen sizes.  All students using these DVDs are using computers, so software on a larger platform makes sense.

One step I am taking in this course is to introduce RPN calculators, the system developed for scientific calculators by Hewlett-Packard.  A pocket calculator should be optimized to be able to evaluate expressions fluently and reliably.  RPN logic takes some learning at first, but it is wonderful for its fluency and reliability.  I describe my HP calculator as an “extension of my brain.”  (I highly recommend students at this level invest in an HP-35s calculator, in the $50 range.)  The on-screen calculator Calc98, which Math Without Borders students have seen since Algebra 1, has the ability to switch into RPN mode.  Download it and use it to familiarize yourself with RPN notation!  Students are free to use any calculator they have in any mode they like, but in this course I will be doing the on-screen calculations in RPN.

The Joys of RPN

(Make Your Calculator an Extension of your Brain)

 

Another even more powerful computational tool, introduced in the last quarter of the Precalculus course, is Sage, available to use online or download from http://www.sagemath.org. Sage is useful all the way from high school math through university and professional level mathematics.  Many of the tutorials available online are aimed at university level mathematics and might overwhelm Precalculus mathematics students. I have therefore recorded a short introduction to Sage that covers most of the needs of this course and posted it to YouTube. You can watch it here.

In Introduction to Sage for Matrix Operations

For practice you can access the Sage file shown in the video and interact with it directly here:  Zip file of the Sage file shown in the video.  Download this file, then unzip it to your desktop.  Start Sage, then upload the sws file into Sage.

Also check out the YouTube “channel” http://www.youtube.com/user/sagemath. Linda Fahlberg-Stojanovska has created a number of Sage video tutorials at a simple level that are relevant to a number of the topics in this course.

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Errata (Corrections of errors and omissions)