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In The Name Of God
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• Saeede Alinezhad
• Fateme zhendijani

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Different kinds of writing

• Expository
• Technical
• Persuasive
• Narrative
• etc.

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General Guidelines on Mathematical Writing

• Know your audience.
• Be clear and concise.
• Idiosyncrasies of mathematical writing

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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.

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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.

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The main steps to guide your writing of a math
paper

• 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

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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.

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The main steps to guide your writing of a math
paper(cont.)

• 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.) 

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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. Ill stop my example here since it
  is pretty clear. 

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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! 

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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

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Sentences

• Simple Statements
• Commands
• Compound sentences
• Present participles a warning

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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.

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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.

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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.

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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
  p²/4.

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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.

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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

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Avoid sources of confusion and ambiguity

• Avoid usingifoutside of the implication
  ifthen.
• It can be replaced by whether to achieve
  greater clarity.
• Make sure you use the ifthen 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 thenwe will take its square
  root.

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Avoid sources of confusion and ambiguity

• Make explicit all quantifiers in equations
  
• ? misuse Consider x²y²1 ,xlt y,
• Exactly what is meant here?
• ? correct Consider x²y²1 for x lt y.

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Points of principle

• Avoid contractions (its ,dont, cant, 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

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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

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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 gt0
  ?
• Good For all real numbers greater
  than zero , ?
• or For all x ? R with xgt0
  ..

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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.

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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.

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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?

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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?

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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
  )

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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 )

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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.

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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.

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Mathematical Ideas into Writing

• Organizing your paper.
• Writing for your audience.
• Defining variables and formulas.
• Using pictures in mathematics.

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THE END

• Bad thinking never produces good writing
  (Lamport).
• Good writing promotes good thinking

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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)

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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

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Any Question?