Nature of Mathematics
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Nature of Mathematics

Nature of Mathematics


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About the Book

This edition marks the 23rd anniversary of the publication of this book. Since the first edition, this text has helped liberal arts students experience mathematics rather than just do problems, and become involved with the concepts rather than just get the right answers. Now in its eighth edition, this text goes farther in helping students master mathematics. An emphasis on problem solving and estimation, new problems coupled with numerous in-text study aids, and a student-friendly writing style are designed to give readers the confidence and ability to function in the technological world.

Table of Contents:
The nature of problem solving: problem solving; problem solving with sets; inductive and deductive reasoning; scientific notation and estimation. 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. The nature of calculation: early numeration systems; Hindu-Arabic numeration systems; different numeration systems; history of calculating devices; computers and the binary numeration system. The nature of numbers: natural numbers; prime numbers; integers; rational numbers; irrational numbers; real numbers; a finite algebra; cryptography. The nature of algebra: polynomials; factoring; evaluation, applications, and spreadsheets; equations; inequalities; algebra in problem solving; ratios, proportions, and problem solving; modelling uncategorized problems; introduction to computer BASIC. The nature of sequences, series, and financial management: interest; installment buying; sequences; series; annuities; amortization; building financial power. The nature of geometry: geometry; polygons and angles; triangles; similar triangles; golden rectangles; Konigsberg bridge problem; topology and fractals; projective and non-Euclidean geometries; introduction to computer LOGO. The nature of measurement: precision, accuracy, and estimation; area; volume and capacity; miscellaneous measurements. The nature of probability: introduction to probability; mathematical expectation; probability models; counting formulas; calculated probabilities; Rubik's Cube and instant insanity. The nature of statistics: frequency distributions and graphs; descriptive statistics; the normal curve; correlation and regression; sampling. The nature of graphs and functions: graphing lines; graphing half-planes; graphing curves; functions; what is calculus?; limits. 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; modelling with linear programming. Appendixes: problem solving; table - trigonometric ratios; table - normal distribution; selected exercises.

Review :
"My overall feeling is the ideas presented in the preface, especially the focus on problem solving, pervade the entire book. The author succeeds in trying to reduce anxiety about the course by presenting topics and ideas that are fresh and relevant without begin out of reach of the student." "The author succeeds in providing a wide range of topics that give an instructor the flexibility to design an appropriate course based on individual needs. . . . The text is written in language that is appropriate for college students, yet is not too technical for students with limited backgrounds." "The Nature of Mathematics," by Karl J. Smith, is a terrific book. The author covers a multitude of mathematical topics ranging from arithmetic through computers. His style is most entertaining: inviting, thorough without being cumbersome, clear, and crisp. The text is illustrated in a multi-colored fashion; it is peppered with biographical information; it presents paradoxes and meets the student where 'he/she is at.' It is clear the author is a splendid mathematician and an educator of the first rank."


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Product Details
  • ISBN-13: 9780534349882
  • Publisher: Cengage Learning, Inc
  • Publisher Imprint: Brooks/Cole
  • Height: 248 mm
  • Returnable: N
  • Width: 216 mm
  • ISBN-10: 0534349889
  • Publisher Date: 07 Jan 1998
  • Binding: Hardback
  • Language: English
  • Weight: 1656 gr


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