Mathscribe 2.5.1 Usage Notes

from www.mathscribe.com

This document contains Mathscribe usage details, for your reference. We suggest you start with the Mathscribe Tips command in the Help (or "?") menu, and then refer to these usage notes only when necessary.

I. Overview

Mathscribe is a dynamic graphing and mathematical modeling tool designed for algebra, trigonometry and precalculus classes. It calculates and graphs elementary functions, i.e. ones formed from polynomial, rational, algebraic, trigonometric, exponential and logarithmic functions. Mathscribe also plots observed scientific data, and compares it to theoretical (computed) values. The student can vary a parameter's value simply by clicking or dragging, and the graphs will immediately be updated, thus promoting a "hands-on" learning style. Applications include many high school math and science subject areas.

We've found that the most educational use of computers is to support and connect both symbolic and visual thinking through guided discovery. Based on this, the Mathscribe web site includes standards-based computer lab assignments covering a full range of Algebra course topics.

Mathscribe runs on any computer running Mac OS 7.0 or later, or Windows 95 or later. See www.mathscribe.com for upgrades and more information.

The free version of Mathscribe is named Mathscribe Lite. The full version includes support for inequalities, and n-ary relations instead of just functions. For instance, it can graph x^2+y^2=r^2, even though y is not a single-valued function of x.

Mathscribe allows for full-keyboard input of mathematical formulas and data, using standard mathematical notation and formatting. Here is a simple screen snapshot (explained below):

Mathscribe files store mathematical models, conventially signified by a ".mm" filename extension. Models have six components:

Independent and Dependent Variables, with their graph limits and colors
Constraints - relations that the variables must satisfy, according to the model
Parameters - other variables, such as coefficients, together with each one's limits and a slider controlling its current value
Table - a table of observed values or expressions which may involve the parameters, and values computed from the model
Graphs - one graph for each independent variable, showing all the dependent variables as functions of that independent variable (with all the other independent variables held constant)
Solutions - Mathscribe's reformulation of the Constraints

II. Editing Tips

A model's main window shows its Variables, Constraints, Parameters and Solutions, and has links to its Table and Graphs "subwindows". Choose a link (for instance by clicking on it) to open a subwindow. While the subwindow is open, the link will appear in italics.

To add a row to a table, press the Return (Mac) or Enter (PC) key. To move between fields, press Tab, or Shift+Tab to move backwards.

Editing mathematical expressions is more complicated than simply editing text, because the program needs enough information to format and interpret expressions correctly. The next few tips should make this relatively painless.

You must type * for multiplication and ^ for exponentiation. (They'll be invisible in the Solutions.)
A right parenthesis ) is automatically added after you type a left parenthesis (. You then type whatever you want inside the parentheses. To move the blinking insertion point past the ), you can just type ).
Mathscribe obeys the usual rules for precedence of operators. For example, to group a sum of two terms inside a product, fraction, or exponent, you'll need to use parentheses. If the sum is already typed in, it's easiest to Cut (or Copy) it and then Paste it where you want it. It will be parenthesized automatically.
You can only Cut and Paste in meaningful ways - basically you can only replace complete subexpressions. If you can't select (highlight) or Paste exactly what you want, first isolate your desired selection by temporarily inserting a Return (Enter) character before and/or after it.
The blinking cursor shows where a letter or digit will be placed if you type one. If you type an operator like + or * inside an unparenthesized exponent, numerator, or denominator, then the operator's placement will depend on its precedence.
To start a subscript, press Option+Return (Mac) or Alt+Enter (PC), i.e. hold down the Option/Alt key while you press the Return/Enter key.
To type a greek letter (or other character in the Symbol font), press Option+g (Macintosh) or Alt+g (Windows), followed by typing the letter, or < for <=, or > for >=. Standard Macintosh characters also include Option+p for pi, and Option+v for square root.
Mathscribe knows about +, -, *, /, ^, sqrt, e, the greek letter pi, sin, cos, tan, cot, sec, csc, asin, acos, atan, ln, log base b, log2 (log base 2), log10 (log base 10), and abs. Press Return (Mac) or Enter (PC) between equations. Any number with a decimal point is considered approximate - use fractions for exact values. Numbers appearing with the letter "e" or "E" in them are also considered approximate, and are in "scientific notation" - the digits after the "e" or "E" denote what power of 10 to multiply by. For example, 1.75e3 is the same as 1750.0.

Inside a graph in the Graphs window, you can set the value of that graph's independent variable by clicking or dragging. Shift-clicking will then select a range of values. The midpoint of the range will be used for computations, but the endpoints will also be used to plot 3-curve families. Alternatively, left- and right-arrow keys will move a selected value by 1 pixel, or 5 pixels if the Option/Alt key is held down. Shift+arrow and Option/Alt+Shift+arrow combinations also work. Parameter sliders work similarly, and update the Table window also if it is open.

Also inside each graph, observed data values are plotted. Such a dot appears brighter if all "side variables" (independent variables other than the one on that graph's horizontal axis) are close to the values for that observation. The full Mathscribe shades inequality solution sets in pink, blue and yellow, and blends these colors on overlaps. Finally, singularities and near-vertical ranges where Mathscribe cannot evaluate a function accurately are indicated by vertical strips in a lighter color.

III. Notes on Menu Commands

Close - This closes a window and its subwindows. If a file is read-only (locked), and its simple name ends in a digit or a digit followed by a single letter, then closing the file discards any changes automatically. Also, note that when a file with such a name is opened, Next File and Previous File buttons will be created if a file with the next or previous file name also exists.

Page Setup (Macintosh) - New windows are sized according to the current screen and printer. Thus by changing your printer's orientation or magnification, you can affect your default window width.

Print - This prints the active (frontmost) window, and also any other open windows on the same file.

Undo and Redo - Currently the Undo and Redo commands remember your 10 most recent changes to each window.

Copy Picture - This copies the selection to the clipboard as a graphic, rather than as data encoded using text. For example, this is useful for pasting an equation or graph into a word processing or other desktop publishing document.

Select More - This command can be very handy during editing, especially when you are tabbing and typing instead of mousing.

Solve - This solves the equations under "Constraints" for the dependent variables, expressing them in terms of the parameters and independent variables.

Table - This opens or selects the Table window, creating its table if necessary. Dependent variables appear with two headings: one for observed values, and another prefixed by ~ for values computed according to the mathematical model (i.e., the Constraints). If there are no dependent variables, then the table won't contain any ~ or Notes columns.

Graph - This creates new graphs. This is useful after changing variables, graph limits, colors, or Constraints. Each dependent variable's value and root-mean-square error is also displayed. (This error is defined as the square root of the average of the square of the computed variable's difference from each observation.) Below each graph, the Constraints are displayed, with parameters and side variables (the other independent variables) replaced by their values, unless the resulting expressions are too wide to fit below the graph. Finally, when Mathscribe creates a Graphs window that is too tall to fit below its model's main window, then the main window is automatically shrunk to show only its Constraints and Parameter sliders.

Calculate - This recomputes the current window. This is useful after typing in a new value, for instance. Note that this command is actually done for you automatically when needed, or after a short pause in typing.

Colors - This gives you a palette of colors to Copy and Paste into the Variables tables as needed.

Disclaimer: Any approximate result could be in error. Also, we cannot guarantee the complete absence of bugs. Please check all important results.

Tools for Scientific Minds