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6.4. WRITING EQUATIONS AND SPECIAL SYMBOLS BY LATEX 97Table 6.1: Useful mathematical symbols: arrows.→ An arrow to the right← An arrow to the left↔ An arrow to both directions⇒ A double line arrow to the right⇐ A double arrow to the left⇔ An double arrow to both directions3. A proper table should have a title and be referred from the text. Table6.1 gives an example. Check from http://www.cs.joensuu.fi/pages/whamalai/sciwri/articletemplate.tex how it is done!Write Table 6.2 yourself!Table 6.2: Welknown NP -complete problems.NameSatifiability (SAT)Independent set (IS)CliqueHamiltonian cycle (HC)ProblemGiven a Boolean formula of variables, parantheses,and connectives ∧ (and), ∨ (or), and ¬ (not),can the formula be true with any truth valueassignment?Does the given undirected graph contain kvertices which are not connected to each other?Does the given undirected graph contain k verticeswhich are all connected to each other?Does an undirceted graph contain a path which goesthrough all vertices exactly once and returns to the startingpoint?6.4 Writing equations and special symbols byLatex1. Write the following expressions by latex.a) (a + b) 2 = a 2 + 2ab + b 2b) (a − b)(a + b) = a 2 − b 2c) n! = 1 × 2 × ... × n
98 CHAPTER 6. L A TEXINSTRUCTIONS AND EXERCISESd) a = v/te) 1 + 2 + ... + n = (n+1)×n22. $, %, #, and are special characters in latex, and you cannot use themin the text as such. Can you find out how to do it? Hint: an escapecharacter \.3. Write the following mathematical expressions. You can find instructionshere:http://www.ift.uib.no/Fysisk/Teori/KURS/WRK/TeX/symALL.html(a) A = {a 1 , a 2 , ..., a n }(b) a i ∈ A for all i = 1, ..., n(c) B ⊆ A(d) |B| ≤ |A|(e) (a i ∈ B) ⇒ (a i ∈ A)(f) C = A ∪ {b}(g) |C| ̸= |A|4. Here is a list of useful mathematical symbols. Write mathematical expressions,where you use them! Remember to use the math mode! Youcan find more symbols in the latex manual.R \mathbb{R}P \mathcal{P}∅ \emptyset∞ \inftyx \overline{x}nn \atopkk. . . \ldots. \vdotsFor example, ( nk)is achieved by$\left( n \atop k \right)$5. Write the following definition using the definiton environment!
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Scientific Writing for ComputerScie
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Contents1 Introduction 11.1 Goal 1:
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CONTENTS 54.5.5 Phrases . . . . . .
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CONTENTS 76.9.1 Idea . . . . . . .
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2 CHAPTER 1. INTRODUCTION1.1.1 Prob
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4 CHAPTER 1. INTRODUCTIONAlg. 1 Wri
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6 CHAPTER 1. INTRODUCTION5. Final w
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8 CHAPTER 1. INTRODUCTION• Weed o
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10 CHAPTER 1. INTRODUCTIONHints:•
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12CHAPTER 2. SEARCHING, READING, AN
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2.5. REFERENCES 15• Sometimes the
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2.5. REFERENCES 17Examples:A journa
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2.5. REFERENCES 19• If an article
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2.7. YOUR OWN OPINIONS? 21• If yo
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Chapter 3Use of tables, figures,exa
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3.2. LISTS 25• The tables are enc
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3.5. EXAMPLES AND DEFINITIONS 27•
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3.6. EQUATIONS 293.6.3 Text inside
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Chapter 4Grammar with style notesVe
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4.1. VERBS 334.1.3 Active or passiv
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4.1. VERBS 35• ”be verb+ing”
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4.2. NOUNS 37ExerciseRead the given
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4.2. NOUNS 39”Statistics is the p
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4.4. ARTICLES 41• Some common phr
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4.4. ARTICLES 43When you refer to t
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4.4. ARTICLES 451. Without any arti
Page 54 and 55: 4.4. ARTICLES 47ExercisesTask 1: Ad
Page 56 and 57: 4.4. ARTICLES 49• weakness• use
Page 58 and 59: 4.5. PRONOUNS 514.5.4 Many vs. seve
Page 60 and 61: 4.6. ADJECTIVES 53Adjective type Co
Page 62 and 63: 4.7. ADVERBS 552. in the end, when
Page 64 and 65: 4.8. PARALLEL STRUCTURES 57• far,
Page 66 and 67: 4.8. PARALLEL STRUCTURES 59• Chan
Page 68 and 69: 4.8. PARALLEL STRUCTURES 61either -
Page 70 and 71: 4.9. PREPOSITIONS 634.9.1 Expressin
Page 72 and 73: 4.9. PREPOSITIONS 65opportunity of/
Page 74 and 75: 4.10. SENTENCES 672. Relative claus
Page 76 and 77: 4.10. SENTENCES 69• Adverbs which
Page 78 and 79: 4.10. SENTENCES 712. a conditional
Page 80 and 81: 4.10. SENTENCES 73• However, when
Page 82 and 83: 4.11. PARAGRAPHS 75• Other: For e
Page 84 and 85: 4.11. PARAGRAPHS 77If it is hard to
Page 86 and 87: 4.12. PUNCTUATION 79”Despite the
Page 88 and 89: 4.12. PUNCTUATION 814.12.6 Quotatio
Page 90 and 91: 4.14. ABBREVIATIONS 834.13.3 Posses
Page 92 and 93: Chapter 5Writing master’s thesis5
Page 94 and 95: 5.1. PARTS OF THE MASTER’S THESIS
Page 96 and 97: 5.2. MASTER’S THESIS PROCESS 895.
Page 98 and 99: 5.2. MASTER’S THESIS PROCESS 91
Page 100 and 101: Chapter 6LATEXinstructions and exer
Page 102 and 103: 6.3. BASIC LATEX 95• \begin{docum
Page 106 and 107: 6.5. WRITING REFERENCES 99Definitio
Page 108 and 109: 6.7. DRAWING FIGURES 101Figure 6.1:
Page 110 and 111: 6.8. SPELL CHECKING 103d+, −dq0 q
Page 112 and 113: 6.9. WRITING REFERENCES BY BIBTEX 1
Page 114 and 115: 6.10. WRITING ALGORITHMS IN LATEX 1
Page 116 and 117: 6.10. WRITING ALGORITHMS IN LATEX 1
Page 118 and 119: 6.11. SPECIAL LATEX NOTES 111\item[
Page 120 and 121: 6.11. SPECIAL LATEX NOTES 113\hline
Page 122 and 123: Chapter 7AppendicesAppendix A: A si
Page 124 and 125: 117\subsection{The title of the sec
Page 126 and 127: 119\title{The main title}\author{Yo
Page 128 and 129: 121\begin{figure}[!h]\begin{center}
Page 130: Bibliography[1] Barrass, R.: Scient
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