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Math Notation, Graphing, and Resources Questions:

Math Notation, Graphing, and Resources Q&A

How do I post mathematics notation and symbols online?

The answer depends on a variety of things including what kinds of expressions you want to type, what software you have available, and your technological experience.

How do I type superscripts (powers) and subscripts in a discussion board?

To type a power (superscript) in a DB you can just use the caret symbol (looks like ^ and is above the 6 on a standard keyboard). For example x3 would be written as x^3.

If you prefer prettier formatting, use the superscript/subscript buttons in the DB message toolbar. For example type the base, click the x2 button, type the exponent, and click the x2 button again to leave the exponent area. The subscript button x2 is handy for typing logarithms such as LOG2x. Useful keys!

How do I type ASCII codes to quickly make math symbols?

ASCII codes are easy to produce using your numeric keypad. They are useful when typing math notation in an email or discussion board post. Some of the more useful ones are listed below. (I've included some HTML tags too for the programmers among you.)

WINDOWS: To make the symbol display on a Windows system, hold the ALT key down while typing the three or four digit ASCII code on your numeric keypad, then release the ALT key and the symbol should appear. (Note: don't type the +, just the digits.) On a laptop you may need to turn on your numeric keypad first (NumLk), then hold both the FN and ALT keys down as you type the three or four digit code on the numeric keypad, release both, and the symbol appears.

MAC: To make the symbol display on a MAC, hold the OPTION key down, press the key, release both, and the symbol appears.

Symbol ASCII Code - WIN ASCII Code - MAC HTML Tag
fractions ¼ ALT+0188   ¼
one-half ½ ALT+0189   ½
three-quarters ¾ ALT+0190   ¾
infinity sign ∞ ALT+236 OPT+5 ∞
pi symbol π ALT+227 OPT+p π
multiplication dot x·y ALT+0183   ·
division sign ÷ ALT+0247 OPT+/ ÷
approximately equal to ≈ ALT+8776 OPT+x ≈
not equal to ≠ ALT+8800 OPT+= ≠
less than or equal to ≤ ALT+243 OPT+< &le;
greater than or equal to ≥ ALT+242 OPT+> &ge;
Questioning equality ALT+8799   &questeq;
intersection ∩ ALT+239   &cap;
union ∪ just use U   &cup;
null set ∅     &empty;
plus or minus ± ALT+0177 OPT+Shift+= &plusmn;
square x² ALT+0178   &sup2;
cube x³ ALT+0179   &sup3;
radical sign √ ALT+251 OPT+v &radic;
absolute value bars | | Just use SHIFT \ on keyboard.
composition f º g ALT+0186    
angle mark     &ang;
degree mark ° ALT+248 or ALT+0176 OPT+0 (zero) or
perpendicular ⊥     &perp;
sum sign ∑ ALT+228 OPT+w &sum;
integral ∫   OPT+b &int;
dot product V•W ALT+0149 OPT+8 &bull;
cross product V×W ALT+0215   &times;
therefore ∴     &there4
implies ⇒     &rArr;
if and only iff ⇔     &hArr;
for all ∀     &forall;
there exists ∃     &exist;
such that ∋     &ni;
is an element of ∈     &isin;
is not an element of ∉     &notin;
delta/difference Δ   OPT+j &Delta;
differential operator ∇     &nabla;
integral sign ∫     &int;
Greek letters

Lower case: α β γ δ θ
π φ

Upper case: Α Β Γ Δ
ALT+224 for α
ALT+225 for β
  Lower case:
&alpha; &beta; &gamma; &delta; &theta; &pi; &phi; etc.
Upper case:
&Alpha; &Beta; &Gamma; &Delta; etc.

How do I type HTML tags to make math symbols in a discussion board?

If you are familiar with HTML programming you can use HTML tags to format your messages and produce some mathematical symbols. I have included some useful HTML tags in the chart above.

In WAMAP you can enter the HTML window in a DB message by clicking the "HTML" icon.

How do I type math expressions in plain text?

With the math editors available in WAMAP (or whatever CMS your class uses) it is no longer necessary to type mathematics in plain text (and have to deal with the very specific parentheses required for accurate notation and the inherent errors that can occur). So please see the next FAQ instead of using plain text!

However, for those working on a mobile device where an equation editor may not cooperate and/or when typing math in an email, the following document guides you through writing mathematical notation horizontally in plain text including writing rational expressions, radical expressions, and fractional exponents.

Writing Mathematical Expressions in Plain Text - Examples and Cautions.

How do I type math expressions using WAMAP's math editor?

WAMAP's "Add New Math" feature allows you to type math in plain text and it will convert it to well formatted math notation. To start an inline expression click the icon shown below. In the red box you can type an expression in plain text. Click outside the red box when you are done and it will convert the expression to a "pretty" format.

POWERS: Typing x^3 with the caret symbol (^) will produce an exponent, `x^3`.
FRACTIONS: Typing (3x)/(x+2) will produce a fraction in a proper vertical form, `(3x)/(x+2)`.
RADICALS: Typing sqrt(x+1) will produce a nice looking square root, `sqrt(x+1)`, and typing root3(x) a nice looking cube root, `root3(x)`.
LOGARITHMS: Typing log_2(x) will produce a log-base-2-of-x, `log_2(x)`, with the base dropped as needed.
DEGREE MARK: Typing cos(30^o) with a small letter "O" will indicate the angle in degrees, `cos(30^o)`.
[More Examples] [Even More Examples] [Even More Examples!] [Full Tech Documentation]

For a visual example see the 1:00 minute mark of this tutorial video:
How to use the discussion board and math editor in WAMAP

Prof. Keely's Shortcut: Personally I like to type the expression in plain text, e.g. x^2/sqrt(x+1), first and then select the expression, click the ∑+ icon, then click outside the red box (that appears around the expression) to see the properly formatted expression, `x^2/sqrt(x+1)`.

How do I use WAMAP's template-style math editor?

WAMAP's "Math Symbols" feature provides a palette of math symbols (integral, x-th root, etc.) that you can use to type complete problems / solutions and post them to the discussion board in a well-formatted manner. This is a more advanced feature than the method in the previous Q&A. Students comfortable with the technology are welcome to check out the more advanced "template style" math editor accessed through the icon marked in red below:

How can I view the code used to make a math expression in someone's post?

When reading a post in WAMAP that contains an expression created in the math editor, you can hover your cursor over the expression to see the code used to create it. This helps you to learn how to create certain expressions yourself.

When viewing an expression created in WAMAP's math editor, what settings are available (e.g. zoom)?

When reading a post in WAMAP that contains an expression created in the math editor, you can zoom in on the displayed expression so it is easier to read -- useful as a disability accommodation or just old/tired eyes. Right-click on an expression to get some global options for how expressions are displayed. For instance I like to click on the expression to make it display twice as large. This can be set by:

Right click -> Math Settings -> Zoom Trigger -> Click
Right click -> Math Settings -> Zoom Factor -> 200%

Other accessibility options are available to personalize your experience with the math editor. Check them out by right clicking on an expression. Also see link in next FAQ.

What accessibility options and display preferences are available in WAMAP?

Personalize your experience with WAMAP and the math editor. See WAMAP Accessibility and Display Preferences.

How do I use the math editors in Canvas?

Canvas has two built-in math editors (ICEE and WIRIS) that you can use to type nicely formatted math expressions in a discussion post via a typical WYSIWYG palette of options. For a tutorial video see How to use ice or How to use ice for Calculus and for a keyboard shortcut sheet see Tips for ice. Also, Tutorial for How to Use WIRIS Math Editor and How to use WIRIS in Canvas.

How do I use the math palette and graphing tools in MyMathLab?

Need help entering math notation or using the graphing tool in MML exercises or tests? Check-out there three tutorials:

  1. How to Enter Answers Using the Math-XL Player Tour is the best one to start with.
  2. When working exercises or tests in MML there is a math palette (on the left of the screen) that allows you to enter mathematical symbols. Pearson's Math Palette Help teaches you how to use it..
  3. Some questions require you to produce a graph using Mme's graphing tool. Learn how to use it via Pearson's Graphing Tool Help.

How do I use external LaTeX equation editing software?

Using the equation editor that is built into your CMS is best, but if you want a more robust online equation editor then external LaTeX editors can be used to create mathematical expressions which can be copied-and-pasted into a DB post, email, etc.

Online LaTeX Equation Editor is an open-source free online equation editor by Decompress. It takes some practice to use, but is quite complete (including symbols for calculus, chemistry, physics) and produces cleanly formatted expressions.

Follow the steps below to create the expression and its LaTeX code. To copy-and-paste the expression into your CMS: select (highlight) the expression, copy CTRL+C, then paste CTRL+V into the body of your DB message.

What kinds of images can be posted to a discussion board?

Do NOT post an image of actual math steps. You work needs to be typed-out in your post. (See How do I type mathematics notation and symbols online?)

However, to support your work or explanation, posting graphs, diagrams, photos, etc. is fine. Recommended formats include .GIF, .JPG, or .PNG, but others may not display properly or may exceed the size limitations of your online classroom.

From where might the original image have come?
-- Screenshot of something on your computer screen (e.g. a graph),
-- Hand-drawn graph or diagram scanned into your computer or drawn on a tablet,
-- Digital photo of a hand-drawn graph or sketch,
-- Graph or sketch created using an online grapher or paint software,
-- Image (*) from the web (cite source!),
-- Graph transferred from your calculator via cable or bluetooth.

Once you have the image you want to post saved to your computer you just need to "insert" or "embed" it into your post. (See How do I insert an image/graphic in a discussion board post?) Remember, NO separate attached files allowed.

* If the image is displayed on a web page you may be able to cut-and-paste it right into your post depending on your CMS (course management system).

Am I allowed to post handwritten work as a photo, screenshot, or scanned image?

NO, all work/steps to solving a problem must be typed into the body of your DB post. Posting a photo/screenshot/scan of a graph, sketch, or diagram as an embedded image is OK, as long as ALT text is included, but do NOT post the actual work/steps as an image. Learning to use math tech tools like the math notation editor built-in to the DBs is an objective of this class. There are other reasons for this too, but most importantly handwritten work in an image is not conducive to sharing with classmates who have a visual impairment.

How do I take a screenshot in Windows or on MAC?

Windows has a screenshot software included called the Snipping Tool. Drag your cursor to place a rectangle around the screen item you want to capture, click "save as", and save as a .gif, .jpg, or .png file to your desktop.

Mac press command + shift + 3 to capture the whole screen, press command + shift + 4 to crop and capture the part you want to save, and save as a file to your desktop.Pressing command + shift + 5 provides a variety of options!

Take-a-ScreenShot.org provides directions for Windows, Mac, OS, Android, and more.

Once you have the file created and saved, you can use it in an online post. How do I insert an image in a discussion board post?

How do I use WAMAP's grapher to post a graph to a DB?

WAMAP has a built-in grapher to enable you to easily insert graphs in a discussion board message. Check it out!

How do I use an external online grapher and post the graph to a DB?

If your class meets in WAMAP the discussion forums have a built-in grapher! If you choose to take advantage of it ignore this FAQ and instead see How do I use WAMAP's built-in grapher?

If you choose not to use WAMAP's built in grapher, or your class meets in a different CMS, then ....

Graph the curve in the online grapher of your choice. Save the file as a .GIF or .PNG file or take a screenshot. Note where you saved your file so you can find it later. Now go to the DB mesage you are writing, use the "insert image" tool to embed the image file in the body of your message, and post.
See How do I insert an image/graphic in a discussion board message?

Below are screenshots for David Lippman's iMathas Graphing Calculator, but instead you can use DESMOS or whichever grapher you prefer.

How do I transfer a graph from my TI calculator to my computer and post it to a DB?

First download and install the TI-Connect software from the Texas Instruments website. Then use the sub cable that came with your calculator to connect to your computer. Produce the graph on your calculator and make sure the graph is displayed on your calculator screen. Launch the TI-Connect program, select the TI screen capture option, and save the capture as a .jog file on your computer. Now go to the DB message you are writing, "embed" the file, and post! See How do I embed an image in a discussion board message?.

Where can I find a scientific calculator for my computer?

On a Windows computer, click "start -> all programs -> accessories -> calculator". In "view" click "scientific" rather than "standard". On MAC, "Macintosh HD -> applications -> Calculator.app ". There are also lots of scientific calculators online. One of the most complete is desmos.com/calculator, click the keyboard icon at the bottom left of the screen, then click "functions" and explore the tabs.

Where can I find an online linear system (RREF) solver?

My top recommendation for an online solver of linear systems (ie, row reduced echelon form, RREF) is the free web-based RREF Calculator. Here is an example of how to use it. Super easy!

Example showing a 3 by 3 linear system, how to set-up the dimensions, fill-in the numbers, press calculate to solve, and retrieve the answers.

Where can I find a free online grapher, graphing software, or graphing app?

Want to save money by not buying a graphing calculator?

  • Apps for a tablet or smart-phone:

    Check your app store for free or low-cost graphing calculator apps. For iphone/ipad there are three FREE apps that I believe are worth considering: Pockets Lite, Free Graphing Calculator, and Quick Graph. Each has an upgraded version costing between $1 and $10.

  • Online 2D Graphers (free!):

    ClassCalc Graphing Calculator
    Demos Grapher - very user friendly, also graphs conics and non-functions Recommended for 2D! Free phone app too.
    Mathias Graphing Calculator - functions, parametric, polar
    Meta Calculator - includes matrix and statistics calculators (see previous FAQ for RREF solver)
    Wolfram | Alpha - advanced grapher/solver (see * note below)

  • Online 3D Graphers (free!):

    3D Vector Plotter from Acedemo is user-friendly software to display 3D vectors, make adjustments to see the effect, and spin to view from different perspectives. Also from Acedemo, 3D Surface Plotter is limited but easy to use.
    CalcPlot3D Recommended for 3D!
    Fairly comprehensive interactive colour 3D graphing software (Java-based). Detailed directions at CalcPlot3D Help Manual.
    Mathias 3D Grapher for multivariate functions
    Parametric Space Curves animated vector-valued functions
    Wolfram | Alpha - advanced grapher/solver

  • Graphing Software (free-ware and shareware):

    Geogebra Recommended for robust graphing [How to 3D]
    Graph 4.3 (open source)
    Microsoft Mathematics (be careful which file you download)

  • Got a MAC? You already have a great graphing calculator built-in!
    "Macintosh HD -> applications -> utilities -> Grapher.app" capable of graphing in 2D and 3D
* In Wolfram Alpha note that the natural logarithm ln(x) is written log(x) and the common logarithm log(x) is written log(10,x). Careful!

I want to obtain mathematics computing software. What are my options?

If you are a mathematics major or plan to take several 100 and 200-level math classes then you may benefit by having mathematics computer algebra system (CAS) software. Warning: all CAS's require learning specific commands and notation and take time with which to become proficient. Instead of purchasing a CAS, Wolfram | Alpha may provide you sufficient capabilities, is user-friendly, and available free online.

Sage-math is a free open source alternative to the commercial programs Maple, Mathematica, etc.

If you do choose to purchase a CAS, look for education/student pricing. Maple is the most popular choice at Clark College. Some of Clark's upper math classes require Maple software and Maple is installed in some Clark College computer labs. Personally I prefer Mathematica, but it is more expensive and geared more to professional mathematicians and educators than to students. Mat-lab and Math-Cad are also possibilities but generally less supported that Maple and Mathematica.

I want to purchase a handheld graphing calculator. Which one should I buy/rent and where?

While I recommend free graphers not purchasing a handheld graphing calculator, if you choose to purchase a handheld graphing calculator, I generally suggest Texas Instruments (TI) over other brands due to their user-friendliness. The TI-84 is a good choice for sub-100 level math courses and pre-calculus courses. The TI-89 or higher (TI-Inspire) is useful in calculus-level courses and higher. Engineering majors may benefit from a Hewlett-Packard (HP) calculator instead. Note: some instructors/colleges will not allow a CAS calculator (one that can solve algebraic equations like TI-89) on tests.

You can buy a new graphing calculator at the Clark College bookstore, office supply stores, electronic stores, or new/used online. The Clark College bookstore has used graphing calculators for rent (subject to availability).

I need a tutorial on how to use my graphing calculator. Where can I turn for help?

Calculator help from Clark College mathematics faculty:

Calculator help from textbook publishers, calculator makers, and other sources:

Additional suggestions:

  • Ask a tutor in the on-campus STEM Help Center for a graphing mini-lesson.
    (To maximize your 1:1 time pick an off peak hour or make an appointment.)
  • Ask your instructor for help during an open office hour.
  • Post questions to your class discussion board.
  • Check the supplemental tools that come with your e-textbook as they often include graphing calculator guides.

Where online can I find some free printable graph paper?

Try incompetent/graph-paper or www.printfreegraphpaper.com.

What lecture-like resources does Prof. Keely provide?

These resources are linked from your online classroom organized by unit/week/topic so that is the best place from which to access these resources. But FWIW,

Where can I find math tutorial videos on the internet?

  • Krista King
    Playlists for calculus I, II, III.
  • Math is Power 4U highly recommended!
    Arithmetic through calculus and differential equations. Plenty of single example short videos.
  • Math the Beautiful
    Playlists for Calculus, Differental Equations, and Linear Algebra. Longer lecture-style videos.
  • Math TV.com
    Student videos created mostly by clever high school students.
  • Math Videos Online.com
    Algebra, geometry, and probability.
  • Nanci Pi
    Algebra, precalculus, trigonometry, and calculus ideas with some accompanying notes.
  • Online Math Learning.com
    Topics down left side menu: algebra, precalculus, trigonometry, and more.
  • Organic Chemistry Tutor recommended
    Playlists for precalculus, trigonometry, calculus, along with the sciences.
  • PatrickJMT Just Math Tutorials highly recommended!
    Arithmetic, algebra, statistics, trigonometry, calculus, DE, and higher. Full lessons.
  • Professor Leonard recommended for calculus
    Playlists for calculus I, II, III, and DE. Full lessons.
  • AVOID Khan Academy! See next FAQ, below.
You may also find videos on specific topics by conducting a search using descriptive terms on sites such as YouTube EDU or TeacherTube or iTunes-U.

Why should I avoid Khan Academy?

I strongly recommend that you AVOID Khan Academy for mathematics help. Their math videos include some major misconceptions and blatant errors they refuse to fix, (-12 is NOT 1, Mr. Khan). The examples are poorly chosen, just not well thought-out, and inadequately peer reviewed. They are an example of "quantity over quality" in my opinion (and most mathematicians and math educators agree). Good educators go to great lengths to think through which problem would best exemplify a concept and how best to present a new concept. Sal Khan brags that he does NOT do this but rather makes his math videos "off the top of his head" (and it shows). For other unfavourable opinions see [ 1 | 2 | 3 | 4 ]. Please don't let one person (especially a former hedge fund manager) be, as he suggests, "teacher to the world". Instead stick to the sites recommended above.

What math lesson websites are recommended?

ALL LEVELS: MathWords.com, an online mathematics dictionary, and Math Study Skills, study tips from PCC.
ALGEBRA: PurpleMath.com and MathsIsFun.com - Algebra
PRE-CALCULUS ALGEBRA: TheMathPage.com - PreCalc and Interactive Mathematics
PRE-CALCULUS TRIGONOMETRY: TheMathPage.com - Trig and Dave's Short Course in Trig
CALCULUS: Paul Dawkin's Online Math Notes and Dale Hoffman's Contemporary Calculus and Interactive Mathematics

Where can I find math-in-the-news stories?

New York Times > Science > Mathematics
Plus Magazine > News from the World of Math
Science Daily > Mathematics News
Various math blogs and social media accounts from MAA

What fun educational math video sites are recommended?

Blue3Brown1, Grant Sanderson
Mathologer, Burkard Polster
NumberPhile, Brady Haran
StandUp Mathematician, Matt Parker
ViHart, Vi Hart

What are the meaning of these math symbols?

If you are in Calculus or higher, here are some math symbols with which you should become familiar:

`in` means "is an element of" `/_` means "angle"
`rArr` means "implies" `hArr` means "if and only if" (IFF)
`:.` means "therefore" means "such that"
`AA` means "for all" `EE` means "there exists"

For a more extensive list see List of Mathematical Symbols, Prof. Ciardo, Univ. of Iowa.

In trig diagrams, what is the symbolism of the Greek lettering?

Generally, capital letters represent points or vertices, small letters represent sides or lengths, and Greek letters represent measures of angles. However, sometimes textbook authors use capital letters to represent vertices and the measure of the angle at that vertex, e.g., `A=80^o` means the measure of angle at vertex `A` is `80^o`.  Actually they should write, `/_A=80^o`, where `/_` means the measure of the angle.  I will use either convention.

The most common Greek letters used in trig are `alpha` = alpha ("al-fah"), `beta` = beta ("bay-tah"), `gamma` = gamma ("gam-mah"), `theta` = theta ("thay-tah"), and `phi` = phi ("fee", not "fie"!).

In a standard triangle,
`alpha` is the angle at vertex `A` across from side `a`, 
`beta` is the angle at vertex `B` across from side `b`, and 
`gamma` is the angle at vertex `C` across from side `c`.

In a standard right triangle,
`gamma = 90^o`, and `c` is the hypotenuse.

Obtuse triangle with legs length a, b, hypotenuse length c across from obtuse angle gamma at vertex C.