Math Notation, Graphing, and Resources Questions:
 Typing Math Notation and Symbols Online in a Discussion Board:
 Posting Images and Graphs on a Discussion Board:
 Calculators, Graphing, and Mathematics Software:
 Resources for Mathematics on the Internet:
 Math and Test Anxiety:
 Math Symbols in Advanced Courses:
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 x^{3}
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 x^{2} button, type the exponent, and click the x^{2}
button again to leave the exponent area. The subscript button x_{2} is
handy for typing logarithms such as LOG_{2}x. 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 
onehalf ½ 
ALT+0189 

½ 
threequarters 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+< 
≤ 
greater than or equal to ≥ 
ALT+242 
OPT+> 
≥ 
intersection ∩ 
ALT+239 

∩ 
union ∪ 
just use U 

∪ 
plus or minus ± 
ALT+0177 
OPT+Shift+= 
± 
square x² 
ALT+0178 

² 
cube x³ 
ALT+0179 

³ 
radical sign √ 
ALT+251 
OPT+v 
√ 
absolute value bars   
Just use SHIFT \ on keyboard.


composition f º g 
ALT+0186 


angle mark ∠ 


∠ 
degree mark ° 
ALT+248 or ALT+0176 
OPT+0 (zero) or
OPT+Shift+8 
° 
perpendicular ⊥ 


⊥ 
sum sign ∑ 
ALT+228 
OPT+w 
∑ 
integral ∫ 

OPT+b 
∫ 
dot product V•W 
ALT+0149 
OPT+8 
• 
cross product V×W 
ALT+0215 

× 
therefore ∴ 


&there4 
implies ⇒ 


⇒ 
if and only iff ⇔ 


⇔ 
for all ∀ 


∀ 
there exists ∃ 


∃ 
such that 



is an element of ∈ 


∈ 
delta/difference Δ 

OPT+j 
Δ 
differential operator ∇ 


∇ 
integral sign ∫ 


∫ 
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:
α
β γ δ θ π φ
etc.
Upper case:
Α Β Γ Δ 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:
POWERS: Typing x^3 with the caret symbol (^) will produce an exponent, x^{3}.
FRACTIONS: Typing (x1)/(x+2) will produce a fraction in a pretty vertical form.
RADICALS: Typing sqrt(x+3) will produce a nice looking square root,
√x+3, and typing root3(x) a nice looking cube root.
LOGARITHMS: Typing log_2(x) will produce a logbase2ofx, log_{2}(x), in textbook format.
DEGREE MARK: Typing cos(30^o) with a small letter "O" will produce cos(30°).
[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, 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 templatestyle math editor?
WAMAP's "Math Symbols" feature provides a palette of math symbols (integral, xth root, etc.) that you can use to type complete problems / solutions and post them to the discussion board in a wellformatted 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 (eg. 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. Rightclick 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 builtin 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? Checkout there three tutorials:
 How to Enter Answers Using the MathXL Player Tour is the best one to start
with.
 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..
 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 copiedandpasted into a DB message in your CMS.
Online LaTeX Equation Editor is an opensource 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 copyandpaste 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?
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,
 Handdrawn graph or diagram scanned into your computer or drawn on a tablet,
 Digital photo of a handdrawn 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 web page you may be able to cutandpaste it right into your post depending on your CMS (course management system).
Am I allowed to post handwritten work as a photo, 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 of a graph, sketch, or diagram as an embedded image is OK, but do NOT post a the actual work/steps as a scan, screenshot, etc. Learning to use math tech tools like the math notation editor is an objective of this class. There are other reasons for this too ... unfair to visually impaired classmates, access on mobile devices, data use, server space, harder to refer back to a specific line, 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 .fig 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.
takeawayascreenshot.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 message. How do
I insert an image in a discussion board message?
How do I use Jing to take a screenshot or minimovie?
Jing is a free screenshot software. See Add Zing with Jing from Clark Cannelloni Library or Jing Instructions from Jolene Morris, Univ. of Phoenix Online. With Jing you may be able to cutandpaste your screenshot graphic from a web page 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 builtin 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 builtin 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 geographers 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 Mattias's Graphing Calculator (or DESMOS 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 or take a screenshot. Now go to the DB message you are writing, "embed" the image file in the body of your message, 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 TIConnect 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 TIConnect 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". I'm sure MAC
has something similar (and Macs have a terrific built in graphing calculator!
See below.).
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 RREF Calculator. Here are directions for use if you need them. If you want one that also shows the row reducing steps to go from the augmented matrix to the row reduced echelon form of the matrix try Matrix Row Reducer instead. My actual favourite is Online Row Reducer but as of this writing (1/21/2019) it is broken (bummer!).
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 smartphone:
Check your app store for free or lowcost 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!):
Demos Calculator  very user friendly, also graphs conics and nonfunctions Recommended for 2D! Free phone app too.
Holt Learning's Graphing Calculator  table feature included
Mathias Graphing Calculator  functions, parametric, polar
Mathias 3D Grapher for multivariate functions
Meta Calculator  matrix and statistics calculator
Wolfram  Alpha  advanced grapher/solver (see * note below)
 Online 3D Graphers (free!):
CalcPlot3D Recommended for 3D!
Fairly comprehensive interactive colour 3D graphing software (Javabased). Detailed directions at CalcPlot3D Help Manual.
3D Vector Plotter from Acedemo is userfriendly 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 easytouse.
Mathias 3D Grapher for multivariate functions
Wolfram  Alpha  advanced grapher/solver
 Graphing Software (freeware and shareware):
Goegebra 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 builtin!
"Macintosh HD > applications > utilities > grapher" 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 200level 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 userfriendly, 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 userfriendliness. The TI84 is a good choice for sub100 level math courses and the TI89 or higher (TIInspire) in 100level courses. Engineering majors may benefit from a HewlettPackard (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).
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 oncampus STEM Help Center for a graphing minilesson.
(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 etextbook as they often include graphing calculator guides.
Where online can I find some free printable graph
paper?
Try incompetent/graphpaper or www.printfreegraphpaper.com.
Where can I find math tutorial videos on the internet?
 Algebra Test Helper
Full lessons in prealgebra and algebra only with topics listed alphabetically
 Krista King
Playlists for calculus I, II, III.
 Math is Power 4U recommended!
Arithmetic through calculus and differential equations. Plenty of single example short 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
Playlists for precalculus, trigonometry, calculus, along with the sciences.
 PatrickJMT Just Math Tutorials recommended!
Arithmetic, algebra, statistics, trigonometry, calculus, DE, and higher. Full lessons.
 Professor Leonard
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 iTunesU.
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, (1^{2} is NOT 1, Mr. Khan). The examples are poorly chosen, just not well thoughtout, 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
PRECALCULUS ALGEBRA: TheMathPage.com  PreCalc
PRECALCULUS TRIGONOMETRY: TheMathPage.com  Trig and Dave's Short Course in Trig
CALCULUS:
Paul Dawkin's Online Math Notes and Dale Hoffman's Contemporary Calculus
Where can I find mathinthenews 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
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 illprepared / 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 "TestTaking 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/enroll/careers/events/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/campuslife/studentsupport/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" 
For a more extensive list see List of Mathematical Symbols, Prof. Ciardo, Univ. of Iowa.
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 ("alfah"),
= beta ("baytah"),
= gamma ("gammah"),
= theta ("thaytah"), and
= phi ("fee", not "fie"!).
