CiNii Books - Finite math

Use mathematical analysis in the real world Finite math takes everything you've learned in your previous math courses and brings them together into one course with a focus on organizing and analyzing information, creating mathematical models for approaching business decisions, using statistics principles to understand future states, and applying logic to data organization. Finite Math For Dummies tracks to a typical college-level course designed for business, computer science, accounting, and other non-math majors, and is the perfect supplement to help you score high! Organize and analyze information Apply calculation principles to real-world problems Use models for business calculations Supplement your coursework with step-by-step example problems If you're not a math person or just want to brush up on your skills to get a better grade, Finite Math For Dummies is your ticket to scoring higher!

Table of Contents

Introduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 2 Beyond the Book 3 Where to Go from Here 3 Part 1: Getting Started with Finite Math 5 Chapter 1: Feeling Fine with Finite Math 7 Getting in Line with Linear Statements 8 Making the Most with Matrices 8 Staying with the Program 9 Getting Set with Sets 10 Posing the Probability 11 Figuring in Financial Factors 13 Finding Statistical Satisfaction 14 Considering the Logical Side of Mathematics 15 Unlocking the Chains 16 Getting into Gaming 18 Chapter 2: Lining Up Linear Functions 19 Recognizing Equations of Lines 20 Identifying slope and its scope 20 Creating different forms of the equation 21 Writing the equation of a line 21 Graphing Lines on the Coordinate Plane 22 Graphing a line using two points 23 Using the slope and y-intercept to graph a line 24 Graphing special lines 25 Determining Relationships between Lines 27 Parallel and perpendicular lines 27 Intersecting versus coincidental lines 29 Solving for a Variable 30 Chapter 3: Solving Systems of Linear Equations 33 Solving Systems Using Elimination 34 Solving a system of two linear equations using elimination 34 Using elimination to solve a system of three linear equations 36 Solving Systems Using Substitution 38 Solving a system of two linear equations using substitution 38 Taking on a system of three linear equations using substitution 39 Dealing with Too Many or No Solutions 41 Too many solutions 41 No solution at all 42 Making Linear Equations Work for You 43 Determining the profit 44 Mixing it up with a solution 44 Counting on change 46 Chapter 4: Taking on Systems of Inequalities 49 Ruling with Inequalities 49 Graphing Linear Inequalities 51 Creating graphs of systems 53 Making graphs work for you 56 Part 2: Making Use of Available Methods 63 Chapter 5: Making Way for Matrices 65 Squaring Off with Matrix Basics 65 Identifying matrices and their components 66 Equalizing and transposing matrices 67 Performing matrix operations and processes 68 Investigating Row Operations 75 Performing the row operations 75 Creating inverses 77 Applying Matrices and Their Operations 80 Matrices and motorcycles 81 Taking matrices to the zoo 84 Chapter 6: Making Matrices Work for You 87 Solving Systems of Equations Using Matrices 88 Solving a linear system in two variables 89 Forging ahead with four variables 90 Stopping up short 92 Multiplying by the inverse 94 Discovering Multiple Solutions 97 Applying Matrices to Tasks 99 Considering input and output 99 Distributing temperatures 103 Taking Advantage of Special Formulas 105 Inverses of 2 x 2 matrices 105 Inverses of 3 x 3 matrices 107 Chapter 7: Getting Lined Up with Linear Programming 109 Setting Up Linear Programming Problems 110 Making the problem structure work 110 Solving a maximization problem 112 Going for a minimum 115 Going Three-Dimensional 118 Maximizing in three dimensions 119 Going for the minimum 122 Chapter 8: Simply the Simplex Method 125 Delineating Simplex Method Steps for Maximization 126 Setting up for the simplex method 126 Solving a maximization application 131 Making the Most of Minimization 135 Spelling out the format 135 Stepping through minimization 136 Giving minimization meaning 140 Part 3: Using Finite Math to Tackle World Situations 145 Chapter 9: Setting Up Sets 147 Introducing Set Notation 147 Describing large and small sets 148 Special types of sets 149 Performing Basic Operations 151 Using Venn Diagrams for Better Views 152 Elements shown 152 The number of elements shown 156 Chapter 10: Processing the Probability 161 Introducing Counting Methods 161 Multiplication method of counting 162 Using permutations for counting 163 Counting with combinations 165 Determining the Probability of an Event 167 Binomial distributions 169 Using probability trees 171 Applying Probability Techniques 174 Games of chance 174 Probability of being chosen 177 Chapter 11: Counting on the Mathematics of Finance 181 Considering Simple Interest 181 Compounding Things with Compound Interest 182 Continuous compounding 184 Effective interest rate 185 Presenting present value 185 Analyzing Annuities 188 Future value of an annuity 188 Present value of an annuity 189 Sinking funds 190 Amortization 191 Creating an amortization schedule 191 Accelerating to payoff 193 Chapter 12: Telling the Truth with Statistics 195 Presenting Data Graphically 195 Barring none with a bar graph 196 Histograms 197 Baking up a pie chart 198 Stem-and-leaf graphs 199 Measures of Central Tendency 200 Meaning it with the mean 200 Riding down the middle with the median 202 Making the most of the mode 202 Recognizing the geometric mean 203 Comparing measures of central tendency 203 Box-and-whisker plots 207 Variance and Standard Deviation 208 Variance 208 Standard deviation 209 Investigating the Normal Distribution 210 Chapter 13: Logic 213 Logically Presenting the Vocabulary 213 Finding the Truth with Truth Tables 215 Considering the conjunction 215 Displaying the disjunction 216 Looking into negativity 217 Conditionally making statements 217 Analyzing compound statements 218 Equivalent Statements 219 Studying the Conditional 221 Analyzing Arguments 222 Applying Logic to Circuits 225 Part 4: Employing the Tools of Finite Math to Expand and Investigate 229 Chapter 14: Markov Chains 231 Recognizing a Markov Chain 231 Coming to Terms with Markov Chains 232 Working with Transition Matrices 233 Using charts and trees 233 Dealing with diagrams 236 Probability Vectors 239 Absorbing Chains 242 Making Long-Term Predictions 244 Avoiding ruin 244 Alternating even and odd 246 Chapter 15: Playing Games with Game Theory 249 Playing Fairly 249 Playing by the Rules 252 Matrix representation 252 Vocabulary 252 Vocabulary illustrated 253 Getting Strategic 255 Yielding to Domination 258 Determining the Moves 259 Finding no saddle point 259 Getting down to business 263 Chapter 16: Applications of Matrices and Game Theory 267 Traffic Flow 267 Battle of the Bismarck Sea 270 The Game of Chicken 271 The Prisoner's Dilemma 272 The Traveler's Dilemma 273 Blotto's Rules 274 Jack Be Nimble 275 Nim with two heaps 275 Upping the Nim stacks to three 277 Part 5: the Part of Tens 279 Chapter 17: Ten Financial Formulas 281 The Rule of 72 281 Leverage Ratio 282 Gains and Losses 282 Determining Depreciation 283 Total Return on Investments 283 Expected Return 284 Inflation-Adjusted Return 284 Remaining Balance 285 Future Value of Annuity Due 286 Bond Pricing Formula 286 Chapter 18: Ten Important Graphing Calculator Functions 289 Graphing Lines for Intersections 289 Adjusting the Window 290 Entering Matrices 291 Adding, Subtracting, and Multiplying Matrices 292 Powering Up Matrices 293 Finding Matrix Inverses 294 Solving Systems of Equations Using Matrices 295 Decimals to Fractions 296 Counting with Permutations and Combinations 296 Making Statistical Statements 298 Glossary 301 Index 305

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Finite math

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