A History of MathematicsDescription |
For a junior or senior level course in the history of mathematics for math and math education majors. Blending relevant mathematics and history, this text immerses the student in the full, rich detail of mathematics. Students not only get a description of mathematics but they also learn how mathematics was actually practiced throughout the millennia by past civilizations and great mathematicians alike. As a result, students gain a better understanding of why mathematics developed the way it did.  |
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Features |
- Detailed treatment of mathematics of the past-Not just a description of the mathematics, this is a math book.
- Reliance on original source material.
- Exercises, stated and solved, using period methods.
- Emphasizes the impact of secular history on mathematics.
- The importance of history in teaching is emphasized.
- Conjectures and propositions and demonstrations and proofs are distinguished.
- Hundreds of diagrams and worked examples.
- Learning by doing approach.
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Table of Contents |
1. Egyptian Mathematics.
Numeration. Arithmetic Operations. Problem Solving. Geometry.
2. Babylonian Mathematics.
Numeration and Computation. Problem Solving. Geometry.
3. Greek Arithmetic.
Numeration and Computation. The Pythagoreans. The Irrational.
4. Pre-Euclidean Geometry.
Thales and Pythagoras. The Athenian Empire. The Age of Plato.
5. The Elements.
Deductive Geometry. Rectilinear Figures. Parallel Lines. Geometric Algebra. Circles. Ratio and Proportion. The Quadratic Equation. Number Theory. The Method of Exhaustion. Book XIII.
6. Archimedes and Apollonius.
Circles. Spheres, Cones, and Cylinders. Quadratures. Large Numbers. Vergings and Loci. Apollonius's Conics. Loci and Extrema.
7. Roman Era.
Numeration and Computation. Geometry and Trigonometry. Heron of Alexandria. Diophantus. The Decline of Classical Learning.
8. China and India.
Chinese Numeration and Computation. Practical Mathematics in China. Indian Problem Solving. Indian Geometry.
9. The Islamic World.
Numeration and Computation. Al Khwarizami. Other Algebras. Geometry and Trigonometry.
10. Medieval Europe.
The Early Medieval Period. Leonardo of Pisa. The High Middle Ages. Nicholas Oresme.
11. Renaissance.
Trigonometry. The Rise of Algebra. The Cossists. Simon Stevin. Francois Viete. The Development of Logarithms.
12. The Era of Descartes and Fermat.
Algebra and Geometry. Number Theory. The Infinite and Infinitesimals. The Tangent and Quadrature Problems. Probability. The Sums of Powers. Projective Geometry.
13. The Era of Newton and Leibniz.
John Wallis. Issac Barrow. The Low Countries. Isaac Newton. Fluxions. Leibniz. Johann Bernoulli.
14. Probability and Statistics.
Jakob Bernoulli. Abraham De Moivre. Daniel Bernoulli. Paradoxes and Fallacies. Simpson. Bayes's Theorem.
15. Analysis.
Leonhard Euler. Calculus Textbooks. Mathematical Physics. Trigonometric Series.
16. Algebra.
Newton and Algebra. Maclaurin. Euler and Algebra.
17. Number Theory.
Euler and Fermat's Conjectures. The Berlin Years. Return to St. Petersburg.
18. The Revolutionary Era.
Analysis. Algebra and Number Theory. Probability and Statistics. Mathematics of Society.
19. The Age of Gauss.
The Roots of Equations. Solvability of Equations. The Method of Least Squares. Number Theory. Geometry.
20. Analysis to Midcentury.
Foundation of Analysis. Abel. Fourier Series. Transcendental Numbers. Chebyshev.
21. Geometry.
Analytic and Projective Geometry. Differential Geometry. The Fifth Postulate. Consistency of Geometry.
22. Analysis After Midcentury.
Analysis in Germany. The Real Numbers. The Natural Numbers. The Infinite. Dynamical Systems.
23. Algebras.
The Algebra of Logic. Vector Algebra. Matrix Algebra. Groups. Algebra in Paris.
24. The Twentieth Century.
The Hilbert Problems. The Consistency of Arithmetic. Real Analysis. Topology. The Theory of Games. Computer Science. Solved Problems. Unsolved Problems.
Appendix A: Answers to Selected Exercises.
Appendix B: Select Bibliography.
Index.
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