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Mathematical Ideas, Expanded Edition (11TH 08  Old Edition)by Charles Miller
Synopses & ReviewsPlease note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.
Publisher Comments:One of the biggest issues college math instructors face is capturing and keeping student interest. Over the years, John Hornsby has refined a creative solutionbringing the best of Hollywood into his mathematics classroom. Mathematical Ideas applies this same strategy of engaging students through video clips from popular cinema and television to the textbook. Alongside fresh data and tools, this Eleventh Edition uses uptotheminute images as well as old favorites of math being done in Hollywood. In addition, examples are clarified with additional annotations, chapter summaries are made more intuitive to aid review, and chapter tests now include specific section references, making it easier for students to refer back to topics that need more attention. With great care and effort, the authors have crafted this new edition to serve the needs of today's students and instructors. Synopsis:This manual provides solutions to oddnumbered exercises in the exercise sets, the Extensions, and the Appendix exercises, as well as solutions for all the Chapter Test exercises. Chapter summaries review key points in the text, providing extra examples, and enumerate major topic objectives.
About the AuthorVern Heeren received his bachelor's degree from Occidental College and his master's degree from the University of California, Davis, both in mathematics. He is a retired professor of mathematics from American River College where he was active in all aspects of mathematics education and curriculum development for thirtyeight years. Teaming with Charles D. Miller in 1969 to write Mathematical Ideas, the pair later collaborated on Mathematics: An Everyday Experience; John Hornsby joined as coauthor of Mathematical Ideas on the later six editions. Vern enjoys the support of his wife, three sons, three daughters inlaw, and eight grandchildren.
John Hornsby When a young John Hornsby enrolled in Lousiana State University, he was uncertain whether he wanted to study mathematics education or journalism. Ultimately, he decided to become a teacher. After twenty five years in high school and university classrooms, each of his goals has been realized. His passion for teaching and mathematics manifests itself in his dedicated work with students and teachers, while his penchant for writing has, for twenty five years, been exercised in the writing of mathematics textbooks. Devotion to his family (wife Gwen and sons Chris, Jack, and Josh), numismatics (the study of coins) and record collecting keep him busy when he is not involved in teaching or writing. He is also an avid fan of baseball and music of the 1960's. Instructors, students, and the 'general public' are raving about his recent Math Goes to Hollywood presentations across the country. Table of Contents1 The Art of Problem Solving 1.1 Solving Problems by Inductive Reasoning 1.2 An Application of Inductive Reasoning: Number Patterns 1.3 Strategies for Problem Solving 1.4 Calculating, Estimating, and Reading Graphs Extension: Using Writing to Learn About Mathematics Collaborative Investigation: Discovering Patterns in Pascal’s Triangle Chapter 1 Test
2 The Basic Concepts of Set Theory 2.1 Symbols and Terminology 2.2 Venn Diagrams and Subsets 2.3 Set Operations and Cartesian Products 2.4 Surveys and Cardinal Numbers 2.5 Infinite Sets and Their Cardinalities Collaborative Investigation: Surveying the Members of your Class Chapter 2 Test
3 Introduction to Logic 3.1 Statements and Quantifiers 3.2 Truth Tables and Equivalent Statements 3.3 The Conditional and Circuits 3.4 More on the Conditional 3.5 Analyzing Arguments with Euler Diagrams Extension: Logic Problems and Sodoku 3.6 Analyzing Arguments with Truth Tables Collaborative Investigation: Logic Problems and Sodoku Revisited Chapter 3 Test
4 Numeration and Mathematical Systems 4.1 Historical Numeration Systems 4.2 Arithmetic in the HinduArabic System 4.3 Conversion between Number Bases 4.4 Clock Arithmetic and Modular Systems 4.5 Properties of Mathematical Systems 4.6 Groups Collaborative Investigation: A Perpetual Calendar Algorithm Chapter 4 Test
5 Number Theory 5.1 Prime and Composite Numbers 5.2 Selected Topics from Number Theory 5.3 Greatest Common Factor and Least Common Multiple Extension: Modern Cryptography 5.4 The Fibonacci Sequence and the Golden Ratio Extension: Magic Squares Collaborative Investigation: Investigating an Interesting Property of Number Squares Chapter 5 Test
6 The Real Numbers and Their Representations 6.1 Real Numbers, Order, and Absolute Value 6.2 Operations, Properties, and Applications of Real Numbers 6.3 Rational Numbers and Decimal Representation 6.4 Irrational Numbers and Decimal Representation 6.5 Applications of Decimals and Percents Extension: Complex Numbers Collaborative Investigation: Budgeting to Buy a Car Chapter 6 Test
7 The Basic Concepts of Algebra 7.1 Linear Equations 7.2 Applications of Linear Equations 7.3 Ratio, Proportion, and Variation 7.4 Linear Inequalities 7.5 Properties of Exponents and Scientific Notation 7.6 Polynomials and Factoring 7.7 Quadratic Equations and Applications Collaborative Investigation: How Does Your Walking Rate Compare to That of Olympic Racewalkers? Chapter 7 Test
8 Graphs, Functions, and Systems of Equations and Inequalities 8.1 The Rectangular Coordinate System and Circles 8.2 Lines and Their Slopes 8.3 Equations of Lines and Linear Models 8.4 An Introduction to Functions: Linear Functions, Applications, and Models 8.5 Quadratic Functions, Applications, and Models 8.6 Exponential and Logarithmic Functions, Applications, and Models 8.7 Systems of Equations and Applications Extension: Using Matrix Row Operations to Solve Systems 8.8 Linear Inequalities, Systems, and Linear Programming Collaborative Investigation: Living with AIDS Chapter 8 Test
9 Geometry 9.1 Points, Lines, Planes, and Angles 9.2 Curves, Polygons, and Circles Extension: Geometric Constructions 9.3 Perimeter, Area, and Circumference 9.4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem 9.5 Space Figures, Volume, and Surface Area 9.6 Transformational Geometry 9.7 NonEuclidean Geometry, Topology, and Networks 9.8 Chaos and Fractal Geometry Collaborative Investigation: Generalizing the Angle Sum Concept Chapter 9 Test
10 Trigonometry 10.1 Angles and Their Measures 10.2 Trigonometric Functions of Angles 10.3 Trigonometric Identities 10.4 Right Triangles and Function Values 10.5 Applications of Right Triangles 10.6 The Laws of Sines and Cosines: Area Formulas Collaborative Investigation: Making a Point about Trigonometric Function Values Chapter 10 Test
11 Counting Methods 11.1 Counting by Systematic Listing 11.2 Using the Fundamental Counting Principle 11.3 Using Permutations and Combinations 11.4 Using Pascal’s Triangle 11.5 Counting Problems Involving “Not” and “Or” Collaborative Investigation: Solving a Traveling Salesman Problem Chapter 11 Test
12 Probability 12.1 Basic Concepts 12.2 Events Involving “Not” and “Or” 12.3 Conditional Probability; Events Involving “And” 12.4 Binomial Probability 12.5 Expected Value Extension: Estimating Probabilities by Simulation Collaborative Investigation: Finding Empirical Values of π Chapter 12 Test
13 Statistics 13.1 Frequency Distributions and Graphs 13.2 Measures of Central Tendency 13.3 Measures of Dispersion 13.4 Measures of Position 13.5 The Normal Distribution Extension: How to Lie with Statistics 13.6 Regression and Correlation Collaborative Investigation: Combining Sets of Data Chapter 13 Test
14 Personal Financial Management 14.1 The Time Value of Money Extension: Annuities 14.2 Installment Buying 14.3 Truth in Lending 14.4 The Costs and Advantages of Home Ownership 14.5 Investing Collaborative Investigation: To Buy or to Rent? Chapter 14 Test
15 Graph Theory 15.1 Basic Concepts 15.2 Euler Circuits 15.3 Hamilton Circuits and Algorithms 15.4 Minimum Spanning Trees Collaborative Investigation: Finding the Number of Edges in a Complete Graph Chapter 15 Test
16 Voting and Apportionment 16.1 The Possibilities of Voting 16.2 The Impossibilities of Voting 16.3 The Possibilities of Apportionment 16.4 The Impossibilities of Apportionment Collaborative Investigation: Class Favorites, An Election Exploration Chapter 16 Test
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