Mathematical Ideas
15th Edition
by Charles D. Miller
Complete Chapter Solutions Manual
are included (Ch 1 to 15)
** Immediate Download
** Swift Response
** All Chapters included
, Table of Contents
Chapter 1 The Art of Problem Solving
1.1: Solving Problems by Inductive Reasoning ............................................................................................... 1
1.2: An Application of Inductive Reasoning: Number Patterns ...................................................................... 4
1.3: Strategies for Problem Solving ............................................................................................................... 12
1.4: Numeracy in Today’s World .................................................................................................................. 23
Chapter 1 Test ............................................................................................................................................... 25
Chapter 2 The Basic Concepts of Set Theory
2.1: Symbols and Terminology ...................................................................................................................... 28
2.2: Subsets and Diagrams ............................................................................................................................. 32
2.3: Set Operations ........................................................................................................................................ 36
2.4: Surveys and Cardinal Numbers .............................................................................................................. 41
Chapter 2 Test ............................................................................................................................................... 49
Chapter 3 Introduction to Logic
3.1: Statements and Quantifiers ..................................................................................................................... 52
3.2: Truth Tables and Equivalent Statements ................................................................................................ 55
3.3: The Conditional and Circuits .................................................................................................................. 64
3.4: The Conditional and Related Statements ................................................................................................ 73
3.5: Analyzing Arguments with Euler Diagrams ........................................................................................... 76
3.6: Analyzing Arguments with Truth Tables ................................................................................................ 81
Chapter 3 Test ............................................................................................................................................... 92
Chapter 4 Numeration Systems
4.1: Historical Numeration Systems .............................................................................................................. 96
4.2: More Historical Numeration Systems ................................................................................................... 100
4.3: Arithmetic in the Hindu-Arabic System ............................................................................................... 101
4.4: Conversion between Number Bases ..................................................................................................... 109
4.5: Arithmetic in Other Bases .................................................................................................................... 117
Chapter 4 Test ............................................................................................................................................. 132
Chapter 5 Number Theory
5.1: Prime and Composite Numbers ............................................................................................................ 135
5.2: Large Prime Numbers ........................................................................................................................... 139
5.3: Selected Topics from Number Theory ................................................................................................. 140
5.4: Greatest Common Factor and Least Common Multiple ....................................................................... 145
5.5: The Fibonacci Sequence and the Golden Ratio .................................................................................... 151
Chapter 5 Test ............................................................................................................................................. 155
Chapter 6 The Real Numbers and Their Representations
6.1: Real Numbers, Order, and Absolute Value .......................................................................................... 157
6.2: Operations, Properties, and Applications of Real Numbers ................................................................. 159
6.3: Rational Numbers and Decimal Representation ................................................................................... 162
6.4: Irrational Numbers and Decimal Representation .................................................................................. 169
6.5: Applications of Decimals and Percents ................................................................................................ 173
Chapter 6 Test ............................................................................................................................................. 178
Chapter 7 The Basic Concepts of Algebra
7.1: Linear Equations ................................................................................................................................... 180
7.2: Applications of Linear Equations ......................................................................................................... 188
7.3: Ratio, Proportion, and Variation .......................................................................................................... 202
7.4: Linear Inequalities ................................................................................................................................ 208
7.5: Properties of Exponents and Scientific Notation .................................................................................. 216
7.6: Polynomials and Factoring ................................................................................................................... 221
7.7: Quadratic Equations and Applications ................................................................................................. 225
, Chapter 7 Test ............................................................................................................................................. 235
Chapter 8 Graphs, Functions, and Systems of Equations and Inequalities
8.1: The Rectangular Coordinate System and Circles ................................................................................. 240
8.2: Lines, Slope, and Average Rate of Change .......................................................................................... 245
8.3: Equations of Lines ................................................................................................................................ 255
8.4: Linear Functions, Graphs, and Models ................................................................................................. 264
8.5: Quadratic Functions, Graphs, and Models............................................................................................ 268
8.6: Exponential and Logarithmic Functions, Graphs, and Models ............................................................. 275
8.7: Systems of Linear Equations ................................................................................................................ 282
8.8: Applications of Linear Systems ............................................................................................................ 290
8.9: Linear Inequalities, Systems, and Linear Programming ....................................................................... 299
Chapter 8 Test ............................................................................................................................................. 307
Chapter 9 Geometry
9.1: Points, Lines, Planes, and Angles ......................................................................................................... 311
9.2: Curves, Polygons, Circles, and Geometric Constructions .................................................................... 314
9.3: The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem .......................... 318
9.4: Perimeter, Area, and Circumference ..................................................................................................... 329
9.5: Volume and Surface Area..................................................................................................................... 339
9.6: Transformational Geometry.................................................................................................................. 345
9.7: Non-Euclidean Geometry and Topology .............................................................................................. 349
9.8: Chaos and Fractal Geometry ................................................................................................................ 350
Chapter 9 Test ............................................................................................................................................. 353
Chapter 10 Counting Methods
10.1: Counting by Systematic Listing .......................................................................................................... 356
10.2: Using the Fundamental Counting Principle ........................................................................................ 369
10.3: Using Permutations and Combinations ............................................................................................... 375
10.4: Using Pascal’s Triangle ...................................................................................................................... 383
10.5: Counting Problems Involving “Not” and “Or” ................................................................................... 386
Chapter 10 Test ........................................................................................................................................... 392
Chapter 11 Probability
11.1: Basic Concepts ................................................................................................................................... 395
11.2: Events Involving “Not” and “Or” ....................................................................................................... 403
11.3: Conditional Probability and Events Involving “And” ........................................................................ 409
11.4: Binomial Probability .......................................................................................................................... 421
11.5: Expected Value and Simulation.......................................................................................................... 426
Chapter 11 Test ........................................................................................................................................... 433
Chapter 12 Statistics
12.1: Visual Displays of Data ...................................................................................................................... 438
12.2: Measures of Central Tendency ........................................................................................................... 443
12.3: Measures of Dispersion ...................................................................................................................... 449
12.4: Measures of Position .......................................................................................................................... 461
12.5: The Normal Distribution .................................................................................................................... 466
Chapter 12 Test ........................................................................................................................................... 472
Chapter 13 Personal Financial Management
13.1: The Time Value of Money ................................................................................................................. 476
13.2: Consumer Credit ................................................................................................................................. 483
13.3: Truth in Lending ................................................................................................................................. 488
13.4: The Costs and Advantages of Home Ownership ................................................................................ 495
13.5: Financial Investments ......................................................................................................................... 503
13.6: Income Tax Liability .......................................................................................................................... 510
Chapter 13 Test ........................................................................................................................................... 513
15th Edition
by Charles D. Miller
Complete Chapter Solutions Manual
are included (Ch 1 to 15)
** Immediate Download
** Swift Response
** All Chapters included
, Table of Contents
Chapter 1 The Art of Problem Solving
1.1: Solving Problems by Inductive Reasoning ............................................................................................... 1
1.2: An Application of Inductive Reasoning: Number Patterns ...................................................................... 4
1.3: Strategies for Problem Solving ............................................................................................................... 12
1.4: Numeracy in Today’s World .................................................................................................................. 23
Chapter 1 Test ............................................................................................................................................... 25
Chapter 2 The Basic Concepts of Set Theory
2.1: Symbols and Terminology ...................................................................................................................... 28
2.2: Subsets and Diagrams ............................................................................................................................. 32
2.3: Set Operations ........................................................................................................................................ 36
2.4: Surveys and Cardinal Numbers .............................................................................................................. 41
Chapter 2 Test ............................................................................................................................................... 49
Chapter 3 Introduction to Logic
3.1: Statements and Quantifiers ..................................................................................................................... 52
3.2: Truth Tables and Equivalent Statements ................................................................................................ 55
3.3: The Conditional and Circuits .................................................................................................................. 64
3.4: The Conditional and Related Statements ................................................................................................ 73
3.5: Analyzing Arguments with Euler Diagrams ........................................................................................... 76
3.6: Analyzing Arguments with Truth Tables ................................................................................................ 81
Chapter 3 Test ............................................................................................................................................... 92
Chapter 4 Numeration Systems
4.1: Historical Numeration Systems .............................................................................................................. 96
4.2: More Historical Numeration Systems ................................................................................................... 100
4.3: Arithmetic in the Hindu-Arabic System ............................................................................................... 101
4.4: Conversion between Number Bases ..................................................................................................... 109
4.5: Arithmetic in Other Bases .................................................................................................................... 117
Chapter 4 Test ............................................................................................................................................. 132
Chapter 5 Number Theory
5.1: Prime and Composite Numbers ............................................................................................................ 135
5.2: Large Prime Numbers ........................................................................................................................... 139
5.3: Selected Topics from Number Theory ................................................................................................. 140
5.4: Greatest Common Factor and Least Common Multiple ....................................................................... 145
5.5: The Fibonacci Sequence and the Golden Ratio .................................................................................... 151
Chapter 5 Test ............................................................................................................................................. 155
Chapter 6 The Real Numbers and Their Representations
6.1: Real Numbers, Order, and Absolute Value .......................................................................................... 157
6.2: Operations, Properties, and Applications of Real Numbers ................................................................. 159
6.3: Rational Numbers and Decimal Representation ................................................................................... 162
6.4: Irrational Numbers and Decimal Representation .................................................................................. 169
6.5: Applications of Decimals and Percents ................................................................................................ 173
Chapter 6 Test ............................................................................................................................................. 178
Chapter 7 The Basic Concepts of Algebra
7.1: Linear Equations ................................................................................................................................... 180
7.2: Applications of Linear Equations ......................................................................................................... 188
7.3: Ratio, Proportion, and Variation .......................................................................................................... 202
7.4: Linear Inequalities ................................................................................................................................ 208
7.5: Properties of Exponents and Scientific Notation .................................................................................. 216
7.6: Polynomials and Factoring ................................................................................................................... 221
7.7: Quadratic Equations and Applications ................................................................................................. 225
, Chapter 7 Test ............................................................................................................................................. 235
Chapter 8 Graphs, Functions, and Systems of Equations and Inequalities
8.1: The Rectangular Coordinate System and Circles ................................................................................. 240
8.2: Lines, Slope, and Average Rate of Change .......................................................................................... 245
8.3: Equations of Lines ................................................................................................................................ 255
8.4: Linear Functions, Graphs, and Models ................................................................................................. 264
8.5: Quadratic Functions, Graphs, and Models............................................................................................ 268
8.6: Exponential and Logarithmic Functions, Graphs, and Models ............................................................. 275
8.7: Systems of Linear Equations ................................................................................................................ 282
8.8: Applications of Linear Systems ............................................................................................................ 290
8.9: Linear Inequalities, Systems, and Linear Programming ....................................................................... 299
Chapter 8 Test ............................................................................................................................................. 307
Chapter 9 Geometry
9.1: Points, Lines, Planes, and Angles ......................................................................................................... 311
9.2: Curves, Polygons, Circles, and Geometric Constructions .................................................................... 314
9.3: The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem .......................... 318
9.4: Perimeter, Area, and Circumference ..................................................................................................... 329
9.5: Volume and Surface Area..................................................................................................................... 339
9.6: Transformational Geometry.................................................................................................................. 345
9.7: Non-Euclidean Geometry and Topology .............................................................................................. 349
9.8: Chaos and Fractal Geometry ................................................................................................................ 350
Chapter 9 Test ............................................................................................................................................. 353
Chapter 10 Counting Methods
10.1: Counting by Systematic Listing .......................................................................................................... 356
10.2: Using the Fundamental Counting Principle ........................................................................................ 369
10.3: Using Permutations and Combinations ............................................................................................... 375
10.4: Using Pascal’s Triangle ...................................................................................................................... 383
10.5: Counting Problems Involving “Not” and “Or” ................................................................................... 386
Chapter 10 Test ........................................................................................................................................... 392
Chapter 11 Probability
11.1: Basic Concepts ................................................................................................................................... 395
11.2: Events Involving “Not” and “Or” ....................................................................................................... 403
11.3: Conditional Probability and Events Involving “And” ........................................................................ 409
11.4: Binomial Probability .......................................................................................................................... 421
11.5: Expected Value and Simulation.......................................................................................................... 426
Chapter 11 Test ........................................................................................................................................... 433
Chapter 12 Statistics
12.1: Visual Displays of Data ...................................................................................................................... 438
12.2: Measures of Central Tendency ........................................................................................................... 443
12.3: Measures of Dispersion ...................................................................................................................... 449
12.4: Measures of Position .......................................................................................................................... 461
12.5: The Normal Distribution .................................................................................................................... 466
Chapter 12 Test ........................................................................................................................................... 472
Chapter 13 Personal Financial Management
13.1: The Time Value of Money ................................................................................................................. 476
13.2: Consumer Credit ................................................................................................................................. 483
13.3: Truth in Lending ................................................................................................................................. 488
13.4: The Costs and Advantages of Home Ownership ................................................................................ 495
13.5: Financial Investments ......................................................................................................................... 503
13.6: Income Tax Liability .......................................................................................................................... 510
Chapter 13 Test ........................................................................................................................................... 513
