**Learn to Communicate Mathematically.**

**Read, write, and orally communicate mathematical concepts.**

**A Few Basic Rules**

No significance should be attached to the order in which these basic rules are presented.

“The fact that some mathematics conventions have been universally adopted around the world suggests that they accomplish something important.” [Maurer]

For that reason it is unwise for a novice to vary from standard conventions, even though they are not absolute rules.

- Write with a pencil so that errors may be erased and replaced with correct work.
- Use complete sentences, correct grammar, and correct spelling.
- Symbols (like the + symbol) that have a specific mathematical meaning are reserved for mathematical use.
- Do not submit your first draft.
- Many mathematical adjectives and nouns have precise mathematical meanings,
- Emulate the writing style found in the textbook and/or lectures.
- Start each sentence with a word, not a mathematical symbol.
- An English synonym will not serve as a replacement. For example, “element” and “part” are not interchangeable when referring to an element of a set.
- Honor the equal sign.
- Avoid the use of imprecise terms.
- Two mathematical expressions or formulas in a sentence should be separated by more than just a space or by punctuation; use at least one word.
- Words have meanings: be aware of them. For example, an equation has an equal sign in it.
- Do not use abbreviations.
- Do not end a line with an equal sign or an inequality sign.
- Insure that every statement is mathematically correct.
- Strive for a good balance between words and symbols.
- Use different letters for different things.
- Remember mathematics is case sensitive.
- Define any terms or variables which you use.
- Once a variable has been assigned a meaning, do not re-use it with a different meaning in the same context.
- There is a distinction between the definite article (“the”) and the indefinite articles (“a” and “an”).
- Do not start a sentence with a formula.

** Examples of Incorrect Mathematics Writing**

- It is incorrect to speak or write of the quotient of a and b. When speaking or writing about division, statements must make it clear which is the divisor and which is the dividend.
- It is incorrect to speak or write of the difference of a and b. When speaking or writing about subtraction, statements must make it clear which is the subtrahend and which is the minuend.
- It is incorrect to connect several different equations with equal signs, where the intermediate equal signs are intended to convey “equivalent to”. For example, x = y – 3 = x + 3 = y is very confusing and altogether wrong.
- It is incorrect to speak of “moving a number or variable”; there is no mathematical operation called “move”.
- Equations can be equivalent but cannot be equal.
- Writing “solve” when the action is “compute” or “evaluate”.
- Writing f = x + 1 instead of f(x) = x + 1.
- Writing n = even = 2n instead of “If n is even, then n = 2k for some k”.
- Writing n
^{2}= 16 = n = ±4 instead of n^{2}= 16 implies n = ±4 - Writing k = k+ 1 instead of “replace k by k + 1”.
- Writing (2, 3, 8) instead of {2, 3, 8}.
- Writing instead of .
- Writing “length + area” instead of “length and area”.
- Writing a decimal approximation instead of an irrational number.
- Confusing the words equation, expression, and function.
- An expression is an algebraic combination of terms containing no verb.
- An equation is a mathematical statement which contains an equal sign.
- A function consists of a domain, range, and rule.

- Confusing the terms polynomial, polynomial equation, and polynomial function.

**Common Syntax Errors to Avoid**

- It is incorrect to write 3 + – 4. Correct syntax is 3 + (- 4)
- It is incorrect to write 3 ¸- 4. Correct syntax is 3 ¸ (- 4)
- It is incorrect to write 3 – – 4. Correct syntax is 3 – (- 4)

It is incorrect to write two operation symbols next to each other.

** Never Violate Long-Standing Word Usage**

“The fact that some mathematics conventions have been universally adopted around the world suggests that they accomplish something important.” [Maurer]

- It is correct to write: divide both sides of the equation by 10
- It is incorrect to write: divide 10 to both sides of the equation
- It is incorrect to write: divide 10 by both sides of the equation
- It is correct to write: subtract 5x from both sides of the equation
- It is incorrect to write: subtract 5x to both sides of the equation
- It is incorrect to write: subtract both sides by 5x
- It is incorrect to write: minus 5x from both sides of the equation
- It is incorrect to write: – 5x from both sides of the equation

**References:**

[Lee] “A Guide to Writing Mathematics”

http://www.cs.ucdavis.edu/~amenta/w10/writingman.pdf

[Lee] “Tips for Reading Mathematics”

http://ems.calumet.purdue.edu/mcss/kevinlee/mathwriting/readingtips.pdf

[Lee] “A Mathematical Writing Checklist”

http://ems.calumet.purdue.edu/mcss/kevinlee/mathwriting/writingcheck.pdf

[Maurer] “Advice for Undergraduates on Special Aspects of Writing Mathematics”

http://www.swarthmore.edu/documents/WRITE_PRIMUS.pdf

[Berry] “Writing Mathematics”

http://agora.cs.wcu.edu/~jlawson/teaching/writing/writing.pdf

[Grayson] “Course Description for Math 248 at The University of Illinois”

http://www.math.uiuc.edu/~dan/Courses/2003/Fall/248/

[McCain Library – Agnes Scott College] “Writing in Math is Integral”

http://writing_center.agnesscott.edu/handouts/34_math.html .

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