9780538737586

Nature of Mathematics

by
  • ISBN13:

    9780538737586

  • ISBN10:

    0538737581

  • Edition: 12th
  • Format: Hardcover
  • Copyright: 1/1/2011
  • Publisher: Brooks Cole
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Summary

Written for liberal arts students and based on the belief that learning to solve problems is the principal reason for studying mathematics, Karl Smith introduces students to Polya's problem-solving techniques and shows them how to use these techniques to solve unfamiliar problems that they encounter in their own lives. Through the emphasis on problem solving and estimation, along with numerous in-text study aids, students are assisted in understanding the concepts and mastering the techniques. In addition to the problem-solving emphasis, THE NATURE OF MATHEMATICS is renowned for its clear writing, coverage of historical topics, selection of topics, level, and excellent applications problems. Smith includes material on such practical real-world topics as finances (e.g. amortization, installment buying, annuities) and voting and apportionment. With the help of this text, thousands of students have "experienced" mathematics rather than just do problems--and benefited from a writing style that boosts their confidence and fosters their ability to use mathematics effectively in their everyday lives.

Table of Contents

Prologue: Why Math?
A Historical Overview
The Nature Of Problem Solving
The Nature of Problem Solving
Problem Solving
Inductive and Deductive Reasoning
Scientific Notation and Estimation
Summary
The Nature Of Sets
Sets, Subsets, and Venn Diagrams
Operations with Sets
Applications of Sets
Finite and Infinite Sets
Summary
The Nature Of Logic
Deductive Reasoning
Truth Tables and the Conditional
Operators and Laws of Logic
The Nature of Proof
Problem Solving Using Logic
Logic Circuits (Optional)
Summary
The Nature Of Numeration Systems
Early Numeration Systems
Hindu-Arabic Numeration System
Different Numeration Systems
Binary Numeration System
History of Calculating Devices (Optional)
Summary
The Nature Of Numbers
Natural Numbers
Prime Numbers
Integers
Rational Numbers
Irrational Numbers
Groups, Fields, and Real Numbers
Discrete Mathematics
Cryptography (Optional)
Summary
The Nature Of Algebra
Polynomials
Factoring
Evaluation, Applications, and Spreadsheets
Equations
Guest Essay: "Chaos"
Inequalities
Algebra in Problem Solving
Ratios, Proportions, and Problem Solving
Percents
Modeling Uncategorized Problems
Summary
The Nature Of Geometry
Geometry
Polygons and Angles
Triangles
Similar Triangles
Right Triangle Trigonometry (Optional)
Mathematics, Art, and Non-Euclidean Geometries (Optional Sections)
Summary
The Nature Of Networks And Graph Theory
Euler Circuits and Hamiltonian Cycles
Trees and Minimum Spanning Trees
Topology and Fractals
Guest Essay: "What Good Are Fractals?"
Summary
The Nature Of Measurement
Perimeter
Area
Surface Area, Volume and Capacity
Miscellaneous Measurements (Optional)
U.S.-Metric Conversions
Summary
The Nature Of Growth
Exponential Equations
Logarithmic Equations
Applications of Growth and Decay
Summary
The Nature Of Sequences, Series, And Financial Management
IntereSt. Installment Buying
Sequences
Series
Annuities
Amortization
Summary of Financial Formulas
Summary
The Nature Of Counting
Permutations
Combinations
Counting without Counting
Rubik's Cube and Instant Insanity (Optional)
Summary
The Nature Of Probability
Introduction to Probability
Mathematical Expectation
Probability Models
Calculated Probabilities
The Binomial Distribution (Optional)
Guest Essay: "Extrasensory Perception"
Summary
The Nature Of Statistics
Frequency Distributions and Graphs
Descriptive Statistics
The Normal Curve
Correlation and Regression
Sampling (Optional)
Summary
The Nature Of Graphs And Functions
Cartesian Coordinates and Graphing Lines
Graphing Half-Planes
Graphing Curves
Conic Sections
Functions
Summary
The Nature Of Mathematical Systems
Systems of Linear Equations
Problem Solving with Systems
Matrix Solution of a System of Equations
Inverse Matrices
Modeling with Linear Programming (Optional)
Summary
The Nature Of Voting And Apportionment
Voting
Voting Dilemmas
Apportionment
Apportionment Flaws
Summary
The Nature Of Calculus (Optional)
What Is Calculus?
Limits
Derivatives
Integrals
Summary
Epilogue: Why Not Math?
Mathematics in the Natural Sciences, Social Sciences, and in the Humanities
Appendices
Glossary
Selected Answers
Index
Table of Contents provided by Publisher. All Rights Reserved.

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