LabBooks

My dream job is "tutor". I enjoy seeing "the light go on" when someone grasps a difficult concept, such as differentiation. 

I've heard people say that calculus is hard because, unlike arithmetic, it's not intuitive. I've even heard people grudgingly say that algebra and trigonometry are intuitive. But not calculus.

Things are intuitive when we are exposed to them so much that they become second nature. We aren't exposed to fractions - we are exposed to parts of objects and fractions are the way we are taught to think about parts. Why are fractions intuitive and derivatives aren't? Derivatives are the way we learn to mathematically handle change and we are surrounded by change.

Why is, say, multiplication, intuitive? You probably know how to multiply two big numbers using long, or partial product, multiplication. You multiply one long number by each digit of the other long number and then you add the products together, but you have to position each of them just right before you add them. Why do you do that and why should you be confident that such a complicated procedure will work every time?

Is that intuitive?

Did you know that all the arithmetic you use is based on a handful of assumptions that nobody tries to prove. One is: a=a. Everything is equal to itself. That might be true in a single case, but how do we know that it's always true? I'm not at all equal to the me of five years ago, but then, I wasn't the same person five years ago that I am today. This instant, I am equal to myself.

Can you divide and always come up with whole number answers. There's a perfectly legitimate and useful way to do that and you might not remember it, but I can just about guarantee that you did it in elementary school! 

How do you know that 2+2=4, and why would you think that it is always the case? Can you prove it? We take an awful lot for granted.

Isaac Asimov was a great popularizer. Through most of his publication history, word processors didn't exist. Have you ever used a typewriter? Typewriters were what we used to create documents when I was in college. Word processors came out while I was in college. The typewriter word processors let you look at sentences you typed before you committed them to paper, but the computer programs were really cool. You could type an entire book, then go back and make corrections, change formats, and even add pictures (!!) before you printed it out. And then there were desktop publisher applications that made it all much easier and added a lot of options.

But the end result was still what I call "flat copy". The page just sat there while you read it. I still use word processors, for instance, I am typing this blog on a word processors app, Google Docs, on my cellphone. While you are reading it, it just sits there. I have embedded videos into some of the blogs, but they're still not anything you could call "interactive".

What I really enjoy using for educational materials is a spreadsheet application.

There's a link up there to the right that will take you to the download page of my other website. The page is called "Excursions". Most of the free downloads there are programs (like the statistics spreadsheet DANSYS) and their user guides, and LabBooks.

LabBooks are textbooks that are spreadsheet documents. Since they are spreadsheets, they're not flat copy. While you're reading them you can be doing other things, too.

LabBooks are lifelong projects for me. I might not live long enough to finish one, but I place them on my Excursions page when I update them. I just reposted the Mathematics LabBook. I waited until I had completed the first part of the first section. It's about the natural numbers (AKA the whole numbers) and the basis of arithmetic. All those questions I asked above? Read the Mathematics LabBook and you will understand the answers.

It has exercises you can do on the page and some buttons you can push to generate problems and get the answers. And you can do your own calculations in it.

I like to open up a concept and show how the insides work.

There are a few loose ends I need to tie up in the rest of the first section. For instance, I've been saying that I will show you how to memorize long numbers in mental calculations, and I will do that on the next sheet.

Talking about interactive documents, I would think the next wave of educational software might be virtual reality. A housemate is into VR. It makes me dizzy but I can imagine "Mister Wizard in a can." 

--- 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?"

--- Structuring programs ---

2016

My big project is a software package programmed into Calc, the LibreOffice spreadsheet component. The strength of this approach is that the statistics package already has all the utilities of a powerful spreadsheet. I call it DANSYS - the Data ANalysis System.

I'll be using DANSYS to talk about how to program in LibreOffice Basic. The manual, available at the LibreOffice website, is useful but there's a lot it doesn't explain how to do, and I've picked up a lot of tricks and workarounds over time. I'm working on an expanded version of DANSYS and I'll take you along on the journey.

I had to decide whether I wanted to just keep expanding DANSYS or make two versions: a basic version that does the most common statistical procedures and the expanded version that's much bigger and clunkier but will do many, many more cool things. I decided to go with the two version plan and both will be available on my other website (http://www.theriantimeline.com/excursions/labbooks) as I develop them. Currently, DANSYS and a statistics decision tree and glossary are available. I'm working on a user's manual for DANSYS and you'll see my progress on DANSYSX here.

Programming is a lot easier if you take a structured approach. Some languages (like Python) requires you to structure your programs. Others, like modern BASIC make it easy to structure programs but do not require it. Structured programming uses indentation to indicate levels of code (that will become much clearer as we go along). It also helps if you add notes to your code as you go along. This documentation serves two big functions: it reminds you what sections of code do if you need to go back and modify the code (which you often will), and it allows other people who use your code to understand what you've done.

I will admit that I sometimes slack off when it comes to documentation, but I will try to be responsible with the code in DANSYSX.

I try to maintain a five section structure for my LibreOffice Basic programs. The first section is the header. The first line of LibreOffice Baisc code names the program, tells whether the program is a subroutine or a function, and passes all the necessary information into the program.

The second section defines all the variables I'll be using in the program using DIM (DIMension) statements. I usually precede this section with a long comment explaining the program.

The third section initializes whatever variables need to start with some specific value.

The fourth section is where all the good stuff happens. It contains the works of the program.

The fifth and last section formats and outputs the data from the program.

Flow charts are useful to some people to help plan out complicated programs. I tend more to plot the way the program is supposed to work in pseudocode. Pseudocode describes the working of a program in descriptive English, line by line. For instance, if I want to add 1 to the variable bx over and over until it reaches 15, I might describe it with the following pseudocode:

bx=0
When bx reaches 15, jump out of the following loop
Add 1 to bx
Continue looping

More often, I type a scaffold of comments before I even start programming and then fill in the code. A comment in LibreOffice Basic looks like this:

'This is a comment. Notice that it begins with an apostrophe.
'LibreOffice Basic will ignore any statement beginning with an apostrophe.

[Note: If you've tried to use any of the in-text links to the Timeline, you will have found that they don't work anymore. That will be because I've moved it to a more secure site. I keep the links in the link section at the upper right of my webpages updated, and those do work.]

--- Computer Bookshelf ---

2016

First, if you get new software, download the documentation for it, especially the user guide and tutorials. If the home site for the software doesn't have tutorials, search on the web for the software's name plus "tutorial". In my experience, the best way to learn how to use a program is to play with it, but it helps to have some guided examples to run through.

Here are some other books I like:

Musciano, Chuck (1988) HTML: The Definitive Guide, 3rd edition. O'Reilly and Associates. Actually, the definitive guide, and you know you're going to want to spruce up a webpage one day.

Verschuuren, Gerard (2008) Excel 2007 for Scientists and Engineers. Holy Macro! Books, Uniontown, OH. It's for Excel users, but most of it is also applicable for general spreadsheet use, and you know how much I like spreadsheets.

Wikibooks.org (2013) Basic Computing Using Windows. Ditto the other Wikibook, and this one can be downloaded at: https://en.wikibooks.org/wiki/Basic_Computing_Using_Windows

Wikibooks.org (2013) Computers for Beginners. This wikibook, from Wikipedia, is  a good guide for people who have never used a computer before and it can be downloaded for free at: https://en.wikibooks.org/wiki/Computers_for_Beginners