--- 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?"

--- Using computers ---

2016

Long ago, in the late 60s, my brother was a computer technician in the Air Force. That gave me my first deep exposure to computers because I got to look through his training materials and he got permission to show us around what was then the Southeastern Defense installation. Back then, the Southeastern Defense computer was stored in a three and a half story, air-conditioned block house. The block house was air conditioned because the computer was made of vacuum tubes that would explode in the Southeastern summer if they were not kept cool. The computer could be programmed using assembly language but a lot of work was still done in machine code - all 1s and 0s.

Later, in the seventies, I took computer courses at Auburn University and even programmed as a work study student using strange languages like APL, PL-1, FORTRAN, and (Yuck!) COBOL. The computer I used was scattered across the campus. I programmed using punch cards (look it up!) but there was a new medium - paper tape that could be punched and kept in a roll until the code was compiled. A favorite program for up and coming programmers was a few lines that would make the tape punching machine spit out a prodigious pile of paper tape before an administrator could shut it off.

Back then, I would punch lines of code on paper card and carry the deck over to the computer department where I would wait a couple of days until they compiled the code. Hopefully the printout would say what I wanted it to say instead of ERROR.

In the 80s, I worked for Radio Shack and sold TRS-80 personal computers and Color Computers. My first personal computer was a 256K (that's a whopping 256 kilobytes of random access memory) Color Computer with a printer and, for external storage, a tape recorder. There were modules available that could be plugged into the side of the computer. I had an early spreadsheet and (my favorite) a synthesizer that I could program to play four-part harmonies. Some of my original pieces (now available for listening or download on the Therian Timeline) were composed on that computer. 256K - laugh if you want but that computer was more powerful than the Southeastern defense computer my brother worked on. I could program in BASIC!. A new thing at that time was a sorta cool thing called the Internet.

To that point, a computer user was also a computer programmer. Then, user friendly computer programs began coming out and, today, many, if not most computer users have no experience in programming.

When I finally began my professional life in Selma, Alabama, I was equipped with a computer with a few megabytes of RAM, a CRT monitor, and Windows 3.0. I had a job search program which always included Brain Surgeon in the list of possible jobs. I was trying to complete a Masters research project and the work computer couldn't handle my data set. By the time I retired in 2013, I had graduated to a Windows XP machine. I couldn't upgrade further because the program I had built over the 20 years in Selma to process my client information would not work on later versions of Microsoft Office. They had dropped the Visual Basic macro language I was using to program.

I have graduated now to a 581 Gigabyte computer with a Terabyte external hard drive and four CPUs, and a telephone (a telephone, mind you!) with 3.74 gigabytes of RAM  and 29.71 gigabytes of internal memory.

And I still get impatient waiting the few minutes it takes for my computer to finish doing what it's doing.

The Yale-New Haven Teacher's Instiute (http://www.yale.edu/ynhti/) has a quaint module called "Computing" from 1981 (That's about the time I was buying my first computer). You might want to read it - it has historical interest.

But, although they used BASIC then, I still use a version of BASIC to program. The Basic that's used as a macro language for OpenOffice and LIbreOffice is both more and less powerful than the BASIC I learned as a first programming language. It's more powerful because it is able to access and manipulate just about all the objects that make up the LibreOffice productivity suite. It's less powerful because the programming part of the language is only a subset of BASIC. For instance, it doesn't have the Data....Read structure that allows BASIC to load tables of data from strings of data contained in the code. I missed that so badly that I ended up programming a couple of functions to do approximately the same thing. "Real" programmers today use languages like Python, C, Java, and Drupal.

Not long ago, a striking shift occurred in the world. Suddenly, paper was not the preferred medium for storage. Before, even with computers, you printed a text and put it on a shelf or in a filing cabinet. Now, people save everything on digital media and, if they want to send something to someone else, they send an electronic file. And there is something called a cloud in which you can save all your stuff on the Internet, in cyberspace.

I often say that my father saw more change in his lifetime than was seen in the entire history of mankind before him. I have seen more change in my lifetime than has been seen in the entire history of mankind before me. My nephew has seen more change in his lifetime than has been seen in the entire history of mankind before him. It's daunting.

When I started to college, students were required to know how to use the greatest portable ever - the (nope, not the graphing calculator) slide rule. Now students have to be effective with a calculator that does logarithms, calculus, and graphs functions. When I started to college, a four function calculator (add, subtract, multiply, and divide) was just coming down to below a hundred dollars. I still like slide rules. They don't require batteries or the sun - but now they're antiques so they cost over a hundred dollars.

Another change.....do you know what an analog computer is? Twenty years ago, analog computers were a thing.