COMMUNICATING USING
$YMB0L$ AND WORDS
I regret to inform you
The literature is full of …
Introduction
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Listen to the words of an authority
“Word-smithing is a much greater percentage of what I am
supposed to be doing in life than I would ever have thought”
Prof Donald Knuth
Computer Science Dept
Stanford University
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Writing helps you learn
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In writing, you clarify your thoughts
Grasp your thoughts for the first time
Writing is a way of thinking
Writing generates your ability to think
Discover thoughts you hardly knew you had
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Writing helps you learn
• Writing brings out gaps in your understanding
by forcing you to focus on steps that you might
otherwise skip
• Good writing reflects clear thinking (and vise
versa)
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What is different about Math writing?
Math writing blends two languages (natural and math)
– Natural language is rich and allows for ambiguity
– Math language is concise and must be unambiguous
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What is good notation
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Unambiguous
Easy to remember
Avoid harmful second meanings
Take advantage of useful second meanings
Order and connection of signs should suggest
the order and connections of things
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Use suggestive notation (easy to remember)
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Utilize useful second meanings
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Avoid harmful second meanings
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Order and connection of signs should
suggest the order and connections of things
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Simplify notation by giving meaning to
extreme cases
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The possibilities are endless!
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OFDM Transmission
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Be Consistent!
• Scalars:
• Vectors:
• Matrices:
• Freq domain variables:
• Time dependence:
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Utilize useful second meanings
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Order and connection of signs should suggest the
order and connections of things
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Only variables of the same type interact with each other;
formulas can be written by inspection;
need not developed from first principles
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Notation is important in elementary school!
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Who contributed more to calculus?
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Examples continue in the college years
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“Notation is everything”
Van Loan “FFT and Sparse Factorization idea”
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We prefer a wordy paper
“ I Like words more than numbers”
Unknown
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Words vs Symbols
• Prefer wordy paper
• Use symbols if idea is too cubmres
• Use words if they don’t take much more
space
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Use words if they don’t take much more space
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Expressions are part of the sentence
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Expressions must respect punctuation and
grammar
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There are some exceptions
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Parallelism
• Parallelism aids in readability and
understanding
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Parallelism at ALL levels
• Parallelism should be maintained at all
levels
Theorem 1: (Steady state for data
nonlinearities)
Theorem 2: (Error nonlinearities at steady
state)
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We can number objects
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It is better to name objects
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Technical Writing Guides
• Halmo’s essay “How to write Mathematics”
• “Mathematical writing” – a course by Knuth,
Stanford 1987
• IEEE Journal on Professional Communicatios
• Handbook for Academic Authors (writers of
academic books)
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While reading Math is not like
reading fiction, it can still be
entertaining!
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