# Epiphanie Tutorial

Welcome to Epiphanie tutoring! This site is here to help you with math and other technical subjects. Do you already have a tutor? That’s great! This system is designed to work with you and your tutor and teacher to help you learn when they can’t be there with you. You can even share reports with them about the material that you need to work on (under development - watch for updates soon).

How do I Use Epiphanie?

You’ve already taken the first step - signing up. Next, start working on some problems! Epiphanie is designed to work with whatever math problems you currently have - create an assignment, enter your problem, and do your work step-by-step in the Epiphanie system. We’ll give you pointers along the way to help you when you run into challenges. When you’re done you can print out an assignment to turn it in.

Our initial release only has some basic advice for Algebra I-type problems and issues, but the system can already be useful and point out mistakes in more complex subjects like Precalculus and Calculus, even before we’ve developed our AI tutoring algorithms for those subjects.

On every page there are also links to ask for help or make suggestions about how we can make Epiphanie better for you. Let us know what you think, and thank you for trying Epiphanie AI Tutoring!

Best regards,
Kevin Moore
Founder, Epiphanie Tutoring

Usage Details

For now, the Epiphanie site only allows the entry of equations. Each equation can only have one equal sign in it - systems of equations and inequalities are not supported yet. There are workarounds to handle other types of problems such as simplifying or expanding algebraic expressions; see below for details.

Certain functions are supported by the system - you can find them and enter them with the drop-down “functions” menu or type them in manually.

If a problem has multiple solutions, you need to enter this using one of the following two formats:

• x = -3 or 3
• x = {-3, 3}

Note that many functions will only work correctly if you enter them with parentheses. For example, x=ln 6 or y=sin pi/2 might not work correctly without the parentheses.

If you want to refer to Euler’s constant e=2.71828…, you need to use the capital letter E for now. Lower case e is not recognized either as this constant or as a variable. The imaginary number i=√-1 can be represented by capital I, however i and complex numbers in general are not supported yet. Domains or intervals for solutions (such as 0 ≤x< 2π) are not supported yet. We’re working on this!

Here are some useful keyboard shortcuts:

• ^ (shift-6) Exponent (x2)
• _ (underscore) Subscript (H2O)
• → (right arrow) Escape an exponent, subscript, fraction, or other function
• Mouse to select text
• Shift-→, Shift-← Select text manually to use in a fraction or to copy
• Arrows traverse and edit equation
• Function →, ← Beginning / end of line
• Home, End Beginning / end of line
• +- = ±
• >=
• <=
• “\” Allows LaTeX keyboard function shortcuts
• \sqrt square root
• \pi π, the mathematical constant
• \theta θ (not supported as a variable yet)
• \int Integral sign (not working properly yet)
• \sum Summation sign (in testing but not on the main site yet)
• \pm PlusMinus symbol (not supported yet)
• Copy, Cut, Paste The usual shortcuts work (Ctrl-C or ⌘-C, Ctrl-X, Ctrl-V)

Examples:

• Let’s say you wanted to enter the equation x^2-4x+3=0. You can do this with the following key combinations:
• x ^ 2 → - 4 x + 3 = 0 ↵
• The ^ key creates an exponent; the arrow key will cause the cursor to leave the exponent of x2
• You could also use the exponent function in the GUI to help enter this
• Note that you don’t actually need to use the right-arrow key after the 2 in x^2. We’ve tried to make entering equations as easy as possible, and some keys will automatically pop you out of the exponent or subscript. +, -, and = are three of those keys - if you type one of these characters in an exponent, it will go on the main line (not in the exponent)
• If you actually wanted a + sign or one of these other characters in the exponent, you can still put one there but it’s a little tricky. The character can’t be the last character in the exponent while you’re typing. So if you wanted to enter this:
x^{2+3}=32
• You would have to type the following keys:
• x ^ 2 3 ← + → = 32
• You have to enter the character after the + sign first, then backspace to enter the plus sign. We’re trying to make the typical use cases as fast as possible for you, and we’ll adjust this if we need to.
• To enter x = log_2(32), you could type:
• x = log _ 2 → ( 3 2 ) ↵
• The underscore key creates the subscript, the arrow key leaves the subscript
• The parenthesis are needed for the log function
• You could also use the GUI functions to enter this

Unsupported Math / Future Improvements
For now, the site is only designed to give feedback on basic algebra - the equivalent of Algebra I level material. But it can already be used for other classes too! Here are some current known limitations for Algebra I and more advanced math:

Known Limitations (see Workarounds below):

• The tutoring capabilities are only designed for Algebra at this point. Advice and functionality for advanced functions such as trigonometric functions, logarithms, integrals, e, and complex numbers may be limited or untested. The Epiphanie system will not provide specific advice on these advanced topics yet.

However you may find the system is still useful without specific advice on your subject.

• All equations must have a variable and one equal sign in them.
• That variable cannot “vanish” from the equation. E.g., x+3 = (2x+6)/2 won’t work properly - see “workarounds” below.
• Inequalities are not supported yet.
• Our system is designed for exact answers only for now. If you enter “1.414” for \sqrt(2), the system will mark it as incorrect. So questions where you’re asked to use your calculator and “round to 2 decimal places” won’t work here yet.
• Only one plusminus (±) symbol is allowed in an equation. (When multiple ± symbols are allowed, they will be correlated; e.g. 1±2±3 = 1+2+3 or 1-2-3, but not 1+2-3 or 1-2+3.)
• Complex numbers and any other domains other than “All Reals” are not supported yet. For example, there’s no way to limit the solution range to [0,2π)
• For trigonometric functions, all angles must be in radians for now. Support for degrees is planned for a future release. But solving trigonometric equations is not recommended due to the limits on domain (and there’s no way to enter solutions like π+2πn yet).
• Lists of solutions cannot be combined with other math. e.g. x = 2 + {-3 or 3} is not supported. However you can enter x-2 = {-3 or 3}
• In some situations when a digit is entered on a mobile device, that digit will be duplicated. We’re investigating this - we believe it happens when transitioning from using the GUI to enter functions to the Android keyboard on some phones.
• Epiphanie is not designed to handle Geometry or graphing problems yet
• Word problem interpretation is not supported yet (but you can enter the initial equation into the system and solve it there)

Workarounds:

• All equations need a variable in them (and the variables can't all vanish from the equation). You can do this by:
• Adding x to an equation that would otherwise be an identity or “prove that” problem.
• Add “x =” to a problem where you need to simplify or expand an expression.
Examples:
• Problem: Expand (x+3)(x-5)
• Enter y=(x+3)(x-5) and expand the right side
• Problem: Factor x^2-5x+4
• Enter y=x^2-5x+4 and factor the right side
• Problem: 3y=y+10
• Change the problem to “3x=x+10”
• Problem: Prove the identity “sin(y)/csc(y)+cos(y)/sec(y)=1
• Change the problem to “sin(y)/csc(y)+cos(y)/sec(y)=1+x (so all variables don’t disappear from the equation)
• Problem: Change “log28=3” to exponential form
• Change the problem to “log28=3x”, so there’s an x in the equation

We know these workarounds aren’t perfect, but they may help you use the Epiphanie system now as we work on solutions and advice for more advanced math problems.