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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;
intersection ∩ ALT+239   &cap;
union ∪ just use U   &cup;
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      
is an element of ∈     &isin;
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.

EXAMPLES: Typing x^3 with the carat symbol (^) will produce an exponent.
Typing (x-1)/(x+2) will produce a fraction in a pretty vertical form.
Typing sqrt(x+3) will produce a nice looking square root and root(3)(x) a nice looking cube root.
Typing log_2(x) will produce a log-base-2-of-x in textbook format.
[More Examples] [Even More Examples]

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, eg. 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.

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:

What settings are available for controlling what I see when hovering over an expression created in WAMAP's math editor?

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

You can also control your settings to zoom in on the 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:

Right click -> Math Settings -> Zoom Trigger -> Hover
Right click -> Math Settings -> Zoom Factor -> pick a percentage

How do I choose which image display option offered at Wamap login?

Depending on your browser set-up generally choose the default. But if the math editor is not working properly for you see WAMAP help - display options at login.

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 iCEE or How to use iCEE for Calculus and for a keyboard shortcut sheet see Tips for iCEE. 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 MathXL 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 MML'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 message in your CMS.

Online LaTeX Equation Editor is an open-source free online equation editor by CodeCogs.com. 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.

For a more robust, but also costly, math editing software consider Math Type Software. If you purchase be sure to take advantage of the academic pricing (student/teacher discount) and try the "trial" version first to be sure it works well.

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

Most discussion boards allow for posting of images. 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) or Jing screenshot,
-- Hand-drawn graph or diagram scanned into your computer,
-- Graph or diagram hand-drawn on a tablet,
-- Digital photo of a hand-drawn graph or sketch,
-- Image created using online grapher or paint software,
-- Image (*) from the web (cite source!),
-- Graph transferred from your calculator via cable or bluetooth.

Note: Embedding graphics on DB is fine, but NOT actual work/steps. See next FAQ.

Once you have the image you want to post saved to your computer you just need to "embed" it into your post. See How do I embed an image in a discussion board message?.

* If the image is displayed on a webpage 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 scanned image or screenshot?

NO, all work/steps to solving a problem must be typed into the body of the DB message. Posting a scan/screenshot or a graph, sketch, or diagram as an embedded image is fine (encouraged!), but do NOT post a the actual work/steps as a scan, screenshot, etc. (There are many reasons for this ... harder to refer back to a specific line, server space, etc. Thanks.)

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 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.

www.take-a-screenshot.org provides directions for Windows, Mac, iOS, Android, and more.

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

How do I use Jing to take a screenshot or mini-movie?

Jing is a free screenshot software. See Add Zing with Jing from Clark Cannell Library or Jing Instructions from Jolene Morris, Univ. of Phoenix Online. With Jing you may be able to cut-and-paste your screenshot graphic from a webpage directly into an discussion board message with no "embed" needed.

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 grapher?

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

Online graphers and graphing software generally allow you to save the graph as a file that can then be embedded in a DB post. Below are directions for using one such online grapher to plot a quick graph which can then be posted to most CMS discussion boards.

Go to iMathAS's Graphing Calculator (or whichever grapher you prefer) and plot your graph. Follow the directions below to save it to your desktop as a .GIF or .PNG file. 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?

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 usb 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 .jpg 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". I'm sure MAC has something similar (and MACs have a terrific built in graphing calculator! See below.).

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

Want to save money by not buying a graphing calculator?

* 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.

SageMath 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. Matlab and MathCad 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?

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 the TI-89 or higher in 100-level courses. Engineering majors may benefit from a Hewlett-Packard (HP) calculator instead.

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) and the Clark Mathematics Department (BHL-110) has some "loaner" calculators for students who can't afford other options.

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:

Where online can I find some free printable graph paper?

Try www.incompetech.com/graphpaper or www.printfreegraphpaper.com.

Where can I find math tutorial videos on the internet?

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.

Note: Khan Academy.org
I recommend that you AVOID this site for math help! The math videos are not well thought-out and some contain blatant errors (-12 is NOT 1, Mr. Khan). They are an example of "quantity over quality" in my opinion (and many math professors 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), as he suggests, be "teacher to the world".

Where can I find math websites, resources, lessons, and help on the internet?


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

MAA > MathDL > Math in the News
New York Times > Science > Mathematics
Plus Magazine > News from the World of Math
Science Daily > Mathematics News

I have math anxiety. Do you have any suggestions to help?

Math anxiety can be a debilitating problem, but one that you can work to overcome! It often comes from bad experiences with math in the past, not having a positive attitude (e.g. saying to yourself that you "can't do it" or that your "brain isn't wired for math" are real killers!), and being ill-prepared / not practicing enough / not truly putting in quality study time. There are several well researched things you can do to relieve math anxiety. Some suggestions:

I have test anxiety. Do you have any suggestions to help?

The Clark College Career and Employment Services Center runs "Test Anxiety" and "Test-Taking Tips and Strategies" workshops every quarter under their "Student Success Workshops" program. These are free seminars and well worth taking advantage! See www.clark.edu/campus-life/careers/success_workshops.php for schedule.

In addition or instead you can schedule a private meeting (again a free service) with a Clark College counselor. The person who runs the test anxiety workshop is Tani McBeth. You can call the Clark College Counseling Center to set up a 30 minute appointment with her to assist you with test anxiety avoidance strategies. Any of the counseling staff are available for appointments -- see www.clark.edu/campus-life/student-support/counseling for contact info.

On a personal note, I suffer test anxiety. I can be well prepared for a test but as soon as it starts I feel like I am going to black out. I wish I could say it got better during my college years but for me it got worse. The more important the class/text the worse I suffered. Argh! But there were some things that helped so here are my tips for what they are worth. Don't cram - study and prepare early but don't study within 24 hours of a test if you can avoid it. Organizing notes though is a comforting helpful thing to do on that last day. In preparing notes I take my "complete" wordy notes, reduce them to a single page, then the main points to a notecard, on which I highlight important phrases. (Then when taking the test the phrase reminds me of the statement on the card that takes me back to the paragraph on the page that takes me back to the section in my original notes.) Right before the test I take a brisk walk to clear my fears then have a quick healthy snack. During the test sucking a lollipop is helpful. I know it sounds silly (and unhealthy), but there is something calming about it. Lastly, keep a positive attitude! You can do this and anyway, it's only a test, really! (Did I just say that?!)

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:

means "is an element of" means "angle"
means "implies" means "if and only if" (IFF)
means "therefore" means "such that"
means "for all" means "there exists"

In trig diagrams, what is the symbolism of the 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° means the measure of angle at vertex A is 80°.  Actually they should write, A=80°, where means the measure of the angle.  I will use either convention.

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

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

In a standard right triangle,
= 90°, and c is the hypotenuse.

Copyright 2000 Sally Keely