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# The Nature of Mathematics (With InfoTrac)

We do not plan to review this book.

Prologue – Why Math? An Historical Overview.

1. THE NATURE OF PROBLEM SOLVING.

Problem Solving. Inductive and Deductive Reasoning. Scientific Notation and Estimation. Finite and Infinite.

2. 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.

3. THE NATURE OF NUMERATION SYSTEMS.

Early Numeration Systems. Hindu-Arabic Numeration Systems. Different Numeration Systems. Binary Numeration Systems. History of Calculating Devices.

4. THE NATURE OF NUMBERS.

Natural Numbers. Prime Numbers. Integers. Rational Numbers. Irrational Numbers. Groups, Fields, and Real Numbers. Discrete Mathematics. Cryptography.

5. THE NATURE OF ALGEBRA.

Polynomials. Factoring. Evaluation, Applications, and Spreadsheets. Equations. Inequalities. Algebra in Problem Solving. Ratios, Proportions, and Problem Solving. Percents. Modeling Uncategorized Problems.

6. THE NATURE OF GEOMETRY.

Geometry. Polygons and Angles. Triangles. Similar Triangles. Right Triangle Trigonometry. Golden Rectangles. Projective and Non-Euclidian Geometries.

7. THE NATURE OF MEASUREMENT.

Perimeter. Area. Surface Area, Volume and Capacity. Miscellaneous Measurements.

8. THE NATURE OF GROWTH.

Logarithms and Exponents. Exponential Equations. Logarithmic Equations. Applications of Growth and Decay.

9. THE NATURE OF SEQUENCES, SERIES AND FINANCIAL MANAGEMENT.

Interest. Installment Buying. Sequences. Series. Annuities. Amortization. Summary of Financial Formulas.

10. THE NATURE OF SET THEORY AND COUNTING.

Sets, Subsets, and Venn Diagrams. Combined Operations with Sets. Counting Formulas. Permutations. Combinations. Binomial Theorem. Counting without Counting. Rubik's Cube and Instant Insanity.

11. THE NATURE OF PROBABILITY.

Introduction to Probability. Mathematical Expectation. Probability Models. Calculated Probabilities. Binomial Probabilities. Guest Essay: Extrasensory Perception.

12. THE NATURE OF STATISTICS.

Frequency Distributions and Graphs. Measures of Central Tendency. Measures of Dispersion. The Normal Curve. Correlation and Regression. Polls and Margin of Error.

13. THE NATURE OF GRAPHS AND FUNCTIONS.

Cartesian Coordinates and Graphing Lines. Graphing Half-Planes. Graphing Curves. Conic Sections. Functions.

14. THE NATURE OF MATHEMATICAL SYSTEMS.

Systems of Linear Equations. Problem Solving with Systems. Matrix Solution of a System of Equations. Inverse Matrices. Systems of Inequalities. Modeling with Linear Programming.

15. THE NATURE OF NETWORKS AND GRAPH THEORY.

Euler Circuits and Hamiltonian Cycles. Trees and Minimum Spanning Trees. Topology and Fractals. Guest Essay: Chaos.

16. THE NATURE OF VOTING AND APPORTIONMENT.

Voting. Voting Dilemmas. Apportionment. Apportionment Flaws.

17. THE NATURE OF CALCULUS.

What is Calculus?. Limits. Derivatives. Integrals.

Epilogue – Why Not Math? Mathematics in the Natural Sciences, Social

Sciences, and in the Humanities.

Appendices:

A. Glossary.

B. Selected Answers.

C. Credits.

D. Index.

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