Transcript mathwriting

MathWriting
1
In The Name Of God
MathWriting
2
Saeede Alinezhad
Fateme zhendijani
MathWriting
3
Different kinds of writing
•
•
•
•
•
Expository
Technical
Persuasive
Narrative
etc.
MathWriting
4
General Guidelines on
Mathematical Writing
• Know your audience.
• Be clear and concise.
• Idiosyncrasies of mathematical writing
MathWriting
5
Be clear and concise
• Never use synonyms for technical terms.
• Short and direct sentences often work best.
• Don't worry too much about the rhythm of
your technical writing
• Eliminate unnecessary words.
MathWriting
6
Idiosyncrasies of
mathematical writing
• The personal pronoun "I" is rarely used in technical
writing.
• If you don't like using passive voice, try using "we.“
• Use mathematical symbols to enhance the clarity
and precision of your writing, not to make your
writing look cool.
MathWriting
7
The main steps to guide your
writing of a math paper
1. First, tell the reader what the problem is.
Make sure the name of the problem or
proof is stated in the title of the paper and
then simply state what you are going to
solve.
Example
☞
Title: Addition of numbers to equal four.
Problem: In this paper we will solve for the summation of 2 + 2
MathWriting
8
The main steps to guide your
writing of a math paper(cont.)
2. Then, before any explanation, state in
WORDS the answer to your problem.
Example
☞
The summation of two plus two is equal to four, meaning that
when two is added to two, the answer is four with no remainder.
MathWriting
9
The main steps to guide your
writing of a math paper(cont.)
3. Discuss any assumptions you made and
any formulas you will use.
Example
☞
Using the basic notion of addition……(then I would state the
definition of addition and perhaps give an abstract example
of this such as x + y = z.)
MathWriting
10
The main steps to guide your
writing of a math paper(cont.)
4.Next, tell how the problem will be approached.
Explain how you will do each step of the problem and tell
why.
Example
☞
By simply adding two whole numbers two and two and using the
basic rule of addition I will determine the answer to be four. This
is a crucial step for higher level math. My example does not need
much explanation, but complex problems and proofs need to be
explained clearly and concisely. I’ll stop my example here since it
is pretty clear.
MathWriting
11
The main steps to guide your
writing of a math paper(cont.)
5. Label all diagrams, tables, pictures, etc.
The reader needs to know exactly what he
or she is looking at. Make a title that is
clear, concise, and understandable!
6. Define terms and variables, explain
formulas and their derivation (where did
they come from?), make sure your math is
correct!
MathWriting
12
Some notes on grammar
1.Sentence
2.Avoid errors of grammar and meaning
3.Avoid sources of confusion and
ambiguity
4.Points of principle
5. Make your mathematics flow with your
text
MathWriting
13
Sentences
1. Simple Statements
2. Commands
3. Compound sentences
4. Present participles :a warning
MathWriting
14
Simple Statements
• Each simple statement is about a single
subject
• The sentence has a verb which belongs to the
subject.
• The verb forms part of the predicate, which
describes what the subject is doing/has done /is
going to do or what state the subject is in.
MathWriting
15
Commands
• A command need not have a subject.
(some people say the subject is implied)
Examples : ☞
• “Let G be a group” . Compare with, “Let us take G to
be a group.”
• “Consider a set X”. Compare with, “We shall consider a
set X.”
MathWriting
16
Compound sentences
• Each compound sentence is a string of
clauses, each of which has its own
subject/predicate pair .These are joined by
conjunctions (e.g., and ,or) or appropriate
punctuation.
• A compound sentence should be able to be
broken down into simple statements or
commands without losing its sense.
MathWriting
17
Present participles
• The present participle is the -ing form of a
verb, e.g., having ,being ,doing ,calculating
,etc . It is easy to misuse these at the
start of a sentence.
Examples of misuse: ☞
• Substituting(3)into(4), the integral becomes
π²/4.
MathWriting
18
Avoid errors of grammar
and meaning
• Use “less” and “fewer” correctly:
“less” is for continuous variables,
“fewer” is for whole numbers.
☞“The polynomial f(x) has fewer roots than g(x).”
☞“The value of this root is less than the other roots.”
MathWriting
19
Avoid errors of grammar
and meaning
• Use “which” and “that” correctly.
That restricts while which amplifies and informs
☞ “Consider the values of f(x), which are positive,”
informs us that all the values of f(x) are positive.
☞ “Consider the values of f(x) that are positive,”
asks us to restrict our attention to the positive values only
MathWriting
20
Avoid sources of confusion
and ambiguity
• Avoid using“if”outside of the implication
“if…then…”.
It can be replaced by “whether” to achieve greater clarity.
Make sure you use the “if…then…” construction properly
☞
.
Misuse: “We will see if the zero of f(x) is positive, then we will take the
square root ,” says that we will take the square root regardless.
Correct: “We will see whether the zero of f(x) is positive. If it is [then]we will
take its square root.”
MathWriting
21
Avoid sources of confusion
and ambiguity
• Make explicit all quantifiers in equations
☞ misuse: “Consider x²+y²=1 ,x< y”,
Exactly what is meant here?
☞ correct :“Consider x²+y²=1 for x < y”.
MathWriting
22
Points of principle
•
Avoid contractions (it’s ,don’t, can’t, etc) in formal
written work.
•
Avoid abbreviations like “i.e.” (use “that is”), ”e.g.”
(use “for example”) and “etc.” (use “and so on”).
Use them correctly if you use them at all and punctuate them properly.
•
Small whole numbers (less than ten )are usually
written in text
☞ example:
“The first four theorems are of no use to us”
MathWriting
23
Points of principle (cont.)
• Prefer the active voice to the passive voice It helps
keep the reader awake
Passive: “The equation was solved using the standard method.”
Active: “ We solved the equation using the standard method.”
Passive: “ An example is now given to demonstrate the point.”
Active: “ Let us now give an example to demonstrate the point.”
• Capitalize proper nouns :
Hermitian matrix ,Lagranges theorem ,the Heidelberg method
MathWriting
24
Points of principle (cont.)
•
Avoid using logical symbols in text.
Bad :”We consider x²-1 ∀ x ∈ Z”
☒
Good :”We consider x²-1 for all integers x,” or “…for all x∈ Z.”
•
☑
Do not mix up symbols with text.
Bad:” For all real numbers >0 …“
☒
Good:” For all real numbers greater than zero …,”
or “For all x ∈ R with x>0 ..”
MathWriting
☑
25
Points of principle (cont.)
• Do not start a sentence with a symbol.
Bad: ”G is a group with prime order.”
Good:” The group G has prime order”
•
☒
☑
Use sparingly the following words :
“actually” ,”in fact”, “very thing” ,”interesting” ,”Most”, “nice”
,”quite”.
MathWriting
26
Make your mathematics flow
with your text
• Any sentence, whether or not it contains mathematical
symbols, should obey the rules of grammar. The
symbols all represent words or phrases, and it should
be possible to translate the entire sentence into
grammatical, well- punctuated English. Be particularly
careful about this when dealing with sentences
containing displayed equations. The display should not
affect the grammar or punctuation.
MathWriting
27
A mathematical writing
checklist
• Is your paper neatly typed?
• Has the paper been proofread?
In college, sloppy work is not appreciated.
Do check over everything.
•
•
•
•
Is there an introduction?
Did you state all of your assumptions?
Are the grammar, spelling, and punctuation correct?
Is the writing clear and easy to understand?
MathWriting
28
A mathematical writing
checklist (cont.)
• Are the mathematical symbols used correctly?
• Are the words used correctly and precisely?
• Are the diagrams, tables, graphs, and any other
pictures you include clearly labeled?
• Is the mathematics correct?
• Did you solve the problem?
MathWriting
29
Good Phrases to Use in
Math Papers
• Therefore (also: so, hence, accordingly, thus, it
follows that, we see that, from this we get, then )
• I am assuming that (also: assuming, where, M
stands for; in more formal mathematics: let, given, M
represents )
• show (also: demonstrate, prove, explain why, find )
MathWriting
30
Good Phrases to Use in
Math Papers (cont.)
• (see the formula above ). (also: (see *), this tells us
that . . . )
• if (also: whenever, provided that, when )
• notice that (also: note that, notice, recall )
• since (also: because )
MathWriting
31
Miscellaneous comments
• Use mathematical notation correctly.
As you learn to write more complicated formulas, it is all too easy to leave out
symbols from formulas. Learn how to use symbols properly!
• Try to write as simply and directly
as possible. No one likes to read
ponderous pretentious prose.
• Don't turn in pages of unreadable
scribbles to your professor.
MathWriting
32
Miscellaneous comments (cont.)
• Use language precisely and correctly.
Make sure that the words you use
really mean what you think they mean.
• While it is a good idea to type your
paper, you may have to leave out
the formulas and insert them by hand later.
MathWriting
33
Mathematical Ideas into
Writing
• Organizing your paper.
• Writing for your audience.
• Defining variables and formulas.
• Using pictures in mathematics.
MathWriting
34
THE END …
• “Bad thinking never produces good writing”
(Lamport).
• Good writing promotes good thinking …
MathWriting
35
books on mathematical
and technical writing
• Nicolas Higham, Handbook of Writing in the
Mathematical Sciences, 2nd ed, SIAM
• Lyn Dupre, BUGS in Writing: A Guide to Debugging
Your Prose, 2nd ed, Addison-Wesley
• Steven Krantz, A Primer of Mathematical Writing,
AMS
• Donald Knuth, Tracy Larrabee, Paul Roberts,
Mathematical Writing, MAA Notes Number 14 (great,
but hard to find)
MathWriting
36
References:
• A Guide to Writing Mathematics by Dr. Kevin P. Lee.
• Writing Math Research Papers: Enrichment for Math
Enthusiasts, Dr. Robert Gerver
• http://www.calumet.purduue.edu
MathWriting
37
Any Question?
MathWriting
38