Saturday, December 22, 2018
--- Math Resources ---
You don't have to have equipment to do mathematics as Arthur Benjamin explains in his book Secrets of Mental Math and the Teaching Company course Secrets of Mental Math (both of which I recommend highly.) but if you want to explore mathematics, you really should have a few pieces of equipment. If you already have a computer and/or a smart phone, many of these tools are free downloads.
I would recommend having a good spreadsheet and there is even a free download for that - LibreOffice (https://www.libreoffice.org) has a fine spreadsheet called Calc, but most office productivity suites have their own and, if you already have one, most of them work similarly enough that we can all talk about their spreadsheet and understand each other.
I also use Google Sheets on my smart phone. The nice thing about Sheets is that I can share the same documents between my phone and my computer and they don't take up space on either because they're saved in Google's cloud storage.
The nice thing about a spreadsheet is that it can do anything a scientific calculator can do, except it can do it a few million times at the same time (each cell on a spreadsheet is virtually a full function programmable scientific calculator with graphing capabilities and a whole lot more.
But a spreadsheet doesn't substitute for a graphing calculator. Although most spreadsheets have graphing capabilities, they are primarily designed for business and statistical charting. A good graphing calculator is designed to do mathematics. For instance, most spreadsheets won't give you a serviceable polar graph (I've programmed that ability into DANSYSX but there's still a lot that a graphing calculator will do that DANSYSX can't. I'm working on it....) Not to worry. There are two popular (free!) graphing calculators available for computers that will do everything - get them both because they both have they're strengths.
GraphCalc is a great little graphing calculator utility that will give you rectilinear or polar graphs in 2D or 3D, and it works just like a handheld graphing calculator (http://www.graphcalc.com).
GeoGebra is a mathematical visualization utility (https://www.geogebra.org/?lang=en) that has many extensions available, many of them specifically for teaching mathematical concepts. It has grown over time and now will change between a graphing calculator and a mathematical visualization utility.
There are a couple of "analog computers" that I will recommend simply because using them provides exceptional familiarity with numbers and arithmetic procedures.
It's hard to use an abacus without strengthening your mathematics skills and understanding deeply how numbers work. David Bagley has put out several versions of abaci and they're all on this site (http://www.sillycycle.com/abacus.html). Choose one that meets your needs.
To really get a grip on mathematical principles, learn how to use a slide rule. A slide rule will give you an intimate knowledge of arithmetic operations up to and including logarithms. The problem is that slide rules went out of style when scientific calculators came out and so they are very expensive now. On the other hand, there are online and downloadable slide rules available on the Internet. Here's one ( http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html). Derek's Virtual Slide Rule Gallery has several models for you to choose from (http://www.antiquark.com/sliderule/sim). And a portable version of the same is here (http://solo.dc3.com/VirtRule.html)
And I must plug my own works. They are free and I don't even ask for donations.
DANSYS is a spreadsheet built over LibreOffice Calc. It has many mathematical utilities built in and DANSYSX, the extension, has many more. I also offer ToolBook, a LibreOffice spreadsheet that has tools programmed into it such as randomizers, timers, and counters, and over time, I'm programming more into it. Both are available here (http://www.theriantimeline.com/excursions/labbooks). There's other stuff here, too, and I will be bringing that up as time goes on.
There are a lot of other mathematical utilities online for specialized use. For instance, if you want to explore differential equations, there are vector field maps and other visualization tools available.
I'll be showing you some of my toys as I explore mathematics in the field next year.
People ask me why anyone needs mathematics above what they teach in elementary school. My answer is usually that it enriches one's life. Mathematics is fun. If you like puzzles, then you would probably like mathematical problems. Further, there are things that you can probably figure out at home without resorting to college level mathematics, such as scaling recipes, but most advanced mathematical techniques were developed as shortcuts and labor saving devices and understanding them gives you the same advantages. Finally, mathematical knowledge gives you a one-upsmanship advantage in social interaction. Just think of how impressive you will be when someone asks you how fast you drove coming over and you return, "Do you mean average velocity or instantaneous velocity?"