1. 1 COMMUNICATING USING $ Y M B 0L$ AND WORDS Also I think therefore I am The literature is full of … I regret to inform you In the limit as Introduction

2. 2 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

3. 3 Writing helps you learn 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

4. 4 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)

5. 5 Math writing blends two languages (natural and math) – Natural language is rich and allows for ambiguity – Math language is concise and must be unambiguous What is different about Math writing?

6. 6 What is good notation 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

7. 7 Use suggestive notation (easy to remember)

8. 8 Utilize useful second meanings

9. 9 Avoid harmful second meanings

10. 10 Order and connection of signs should suggest the order and connections of things

11. 11 Simplify notation by giving meaning to extreme cases

12. 12 The possibilities are endless!

13. 13 OFDM Transmission

14. 14 Be Consistent! Scalars: Vectors: Matrices: Freq domain variables: Time dependence:

15. 15 Utilize useful second meanings 00000000000000000 0000000000000000000000 Order and connection of signs should suggest the order and connections of things

16. 16

17. 17 Only variables of the same type interact with each other; formulas can be written by inspection; need not developed from first principles

18. 18 Notation is important in elementary school!

19. 19 Who contributed more to calculus?

20. 20 Examples continue in the college years

21. 21 “Notation is everything” Van Loan “FFT and Sparse Factorization idea”

22. 22

23. 23 We prefer a wordy paper “ I Like words more than numbers” Unknown

24. 24 Words vs Symbols Prefer wordy paper Use symbols if idea is too cubmres Use words if they don’t take much more space

25. 25 Use words if they don’t take much more space

26. 26 Expressions are part of the sentence

27. 27 Expressions must respect punctuation and grammar

28. 28 There are some exceptions

29. 29 Parallelism Parallelism aids in readability and understanding

30. 30 Parallelism should be maintained at all levels Theorem 1: (Steady state for data nonlinearities) Theorem 2: (Error nonlinearities at steady state) Parallelism at ALL levels

31. 31 We can number objects

32. 32 It is better to name objects

33. 33

34. 34 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)

35. 35 While reading Math is not like reading fiction, it can still be entertaining!