Matrices based Calculus? Statistics?

[creekland]

Hi, I'm new here and have been looking around a bit, but haven't seen an answer to this question...

It has been suggested that my 'soon to be senior' take a Matrices based Calc course next year (looking to double major with business or economics and global development). I'm not at all familiar with who offers what for Calculus (other than knowing them by name).

For those of you with more direct experience, which one would you recommend? We've been using TT through their Pre Calc (added more to their matrix section). This son is math talented (700 on SAT), so should be able to use pretty much anything - just looking for what has the best 'matrices based' option.

On a similar line - who does Statistics with a homeschooling slant?

We could go community college, but it seems to be quite pricey when he doesn't really need the college credits from it at this point.

[nmoira]

who does Statistics with a homeschooling slant?Life of Fred (http://www.stanleyschmidt.com/FredGauss/index2.html)offers a robust Statistics text, and it's reasonably priced at $45 including the answer key.Descriptive Statistics (averages, measures of dispersion, types of distributions), Probability, Bayes’ Theorem, From a Given a Population Determine What Samples Will Look Like (7 tests), Techniques of Sampling, From a Given Sample Determine What the Population Was (14 tests), Determine Whether Two Given Samples Came From the Same Population (15 tests), Working With Three or More Samples (10 tests), Emergency Statistics Guide, Regression Equations, Field Guide, 16 Tables.
Here are some sample pages (http://www.stanleyschmidt.com/FredGauss/__LOF%20S%20%20sample23%20pages.pdf), including the TOC and index.

[creekland]

I'll check into that for Stats. Has anyone on here used it yet and taken the AP test to know how well it prepares the student?

Since there haven't been other replies to the Calc, I'm going to assume Calc is Calc as I suspected and pick from those (once I compare them).

It was a Business Prof. at Va Tech that suggested he take a matrices based Calc... I hadn't heard of such a thing (though I know part of Calc uses matrices later on). I'm a Physics major myself, hubby is Engineering. We weren't sure if Business used or preferred something else... hence the question.

[forty-two]

From a quick google search, matrix calculus is a different approach to calculus - definitely not "Calc is Calc" (Wikipedia entry (http://en.wikipedia.org/wiki/Matrix_calculus)). I found a few texts:

*Link to a free text (http://www.freebookcentre.net/maths-books-download/Matrix-Calculus.html) "Matrix Calculus", though I couldn't get the text to download when I tried.

*"Matrix Differential Calculus with Applications in Statistics and Econometrics (http://www.amazon.com/Differential-Calculus-Applications-Statistics-Econometrics/dp/047198633X/)"

I'm getting the feeling, though, that this probably isn't where a complete beginner starts, at least not without a very knowledgeable teacher. Most of what I've seen links matrix calculus with multivariate calculus. That's more like Calc 3, I think. I'm pretty sure beginners start with single-variable calculus.

[LoriM]

I think by "matrix based" Calc, he's probably meaning Vector Calculus. :) And yes, any good AP Calc text will work (I like Larson's series of Calculus textbooks--he's got a few!). It is probably that he just wants to see your student get beyond differentiation to three-dimensional spaces and integration. (Think AP Calc BC instead of AP Calc AB.)

My favorite Statistics texts for the AP exam are http://bcs.whfreeman.com/yates2e/default.asp?s=&n=&i=&v=&o=&ns=0&t=&uid=0&rau=0 or http://www.keycollege.com/catalog/titles/workshop_statistics3.html

I taught from "Workshop Statistics" to secondary education math ed majors last spring at the university here in town. It's a GREAT book, and really draws the student along in the best of statistical problem solving. It is a very reasonable text, but requires the use of Fathom or a graphing calculator (I highly recommend Fathom).

HTH,

LoriM

[forty-two]

I think by "matrix based" Calc, he's probably meaning Vector Calculus.

Well, Wikipedia (http://en.wikipedia.org/wiki/Matrix_calculus), at least (which is, of course, the most accurate source ever :tongue_smilie:), seems to differentiate ;) between vector and matrix calculus. As well, reading the descriptions and samples of various (http://www.amazon.com/Matrix-Calculus-Zero-One-Matrices-Applications/dp/0521807883) matrix (http://www.amazon.com/Differential-Calculus-Applications-Statistics-Econometrics/dp/047198633X) calculus (http://www.amazon.com/Problems-Solutions-Introductory-Advanced-Calculus/dp/9812702024/) texts (http://www.amazon.com/Calculus-Kronecker-Product-Applications-Programs/dp/9810232411/) on Amazon seems to indicate quite a bit of difference as well.

[creekland]

Multivariate calculus is what I am used to as a later class (so it actually does fit in with my thoughts of calc is calc). I agree that one needs to start with single-variable first... I mainly wasn't sure that business-minded folks were going the same way as science-minded folks. I didn't THINK there was a difference (or else I would have thought I'd have heard about it before now), but one never knows I suppose... It was worth asking - just to be certain.

With "Workshop Statistics," did you use just those or were those supplementing the other text? They look intriguing. We have a graphing calculator that does stats, plus I can get other stat programs for it from our public school stat teacher. How is Fathom different/better? (serious question, not sarcastic)

[creekland]

Ok, I take what I just wrote back. That book you linked to DOES look different and I'm not sure if it is a later course when it says part one does Matrix Algebra and part two introduces differentials...

I think I need to be heading to a college bookstore to look at some of these books in person to compare.

I know I work in our local high school math/science and I've never seen this type of course offered, but we're not exactly an 'advanced' school. We're rather average for our state. Could they really prefer business oriented students travel this path for advanced math instead of traditional calc? If so, that's the path we need to be on for my oldest...

[LoriM]

Multivariate calculus is what I am used to as a later class (so it actually does fit in with my thoughts of calc is calc). I agree that one needs to start with single-variable first... I mainly wasn't sure that business-minded folks were going the same way as science-minded folks. I didn't THINK there was a difference (or else I would have thought I'd have heard about it before now), but one never knows I suppose... It was worth asking - just to be certain.

With "Workshop Statistics," did you use just those or were those supplementing the other text? They look intriguing. We have a graphing calculator that does stats, plus I can get other stat programs for it from our public school stat teacher. How is Fathom different/better? (serious question, not sarcastic)

I taught from the red book (the different texts are just based on what software you use with the book--so the exercises are tailored to that program). Fathom is an awesome little statistics program. You have to understand, I "grew up" in statistics in the day when I wrote my programs in SPSS/SAS before a windows-interface. LOL. So, when I say Fathom is awesome, I mainly mean it's a click/drag intuitive program that will easily and quickly give you a scatterplot, draw a line of best fit, and calculates any and all statistics one might want instantly. You can cut and paste the figures into your Word documents...and it's cheap. Another great program is Tinkerplots (which is just about as easy to use as Tinker Toys! GRIN!). Tinkerplots is designed for grades 4-8 (but is powerful enough for some high school work), where Fathom is grades 8-college.

Workshop Statistics is the only text you'd need--it's not a supplement for another text. The title is a bit misleading, I think. Beth Chance (and I think it's outstanding to have a last name like Chance and be a statistician! LOL) is one of the authors--she's done a lot of writing and research with one of my grad school professors from NC State. She's considered a leader in the field of Statistics Education. But don't confuse Statistics Education with what "Math Education" did to the field of mathematics. :)

Lori

[creekland]

I "grew up" in statistics in the day when I wrote my programs in SPSS/SAS before a windows-interface. LOL.
Lori

You had computer programs when you had stats??? I guess I might be a few years older... we had pens, graph paper, and tables... I'm envious of those with graphing calculators (ditto that for calc).

Fathom does sound like a nice program...

Looking at that Matrix Calc book (online), I'm still thinking it's a later course - after one understands single variable calc.

[LoriM]

Well, the year I started college, we had our first "keyboard entry" on the mainframe. :) My DH has an AS in Data Processing, but never took any college course without punch cards! GRIN.

But SAS launched in 1976...here's a look at the history of statistical analysis (grin): http://www.sas.com/news/sascom/2008q4/column_bestblogs.html

Lori

[Kareni]

My favorite Statistics texts for the AP exam are http://bcs.whfreeman.com/yates2e/default.asp?s=&n=&i=&v=&o=&ns=0&t=&uid=0&rau=0 or http://www.keycollege.com/catalog/titles/workshop_statistics3.html



My daughter used the first of these two books (the one by Yates, Moore and Starnes) in the Pennsylvania Homeschoolers AP Statistics class that she just finished. She has no basis for comparison, as regards Statistics books, however, she did say that she found the book to be well written.

Also, if you are interested in an on-line course, I do recommend the class mentioned above.

Regards,
Kareni

[creekland]

To Lori... Ok, so I have to admit I'm old enough I COULD have used computers for stats - we just didn't in those days. I only needed stats for my Psych minor, so that may have been part it - I didn't major in it, nor math ed. I'm a Physics major, Math and Psych minor.

To Kareni... thanks for the thought on the book. I do plan to try to look at them if I can to compare. I'm not leaning toward an online course since they are pretty pricey and I can help him if he gets stuck (which he rarely does with math, but one never knows).