Mathematics Experiments

By: Falai Chen, Jiansong Deng, Shangzhi Li, Yaohua Wu, Yunhua Zhang

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Hardcover | 19 February 2003

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228 Pages

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22.86 x 15.88 x 1.91

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Owing to the advent of computers, experiments are becoming an increasingly important part of mathematics. This text provides guidance to students doing experiments in mathematics. The aim is to stimulate interest in mathematics through examples and experiments. Each experiment in the book starts with a problem. The students are expected to work with these problems on computers, try to find the solutions themselves, and experience the scientific exploration in the process. The problems which the authors have chosen cover a wide spectrum in mathematics, ranging from calculus, number theory, coding and probability to geometry and chaos. The volume should be useful not only to mathematics students, but also to students in all areas of sciences who are interested in learning some of the mathematical tools. It provides a hands-on approach to the most fundamental issues in mathematics - an approach which may help to revolutionize the teaching of mathematics.

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Fundamental of Calculus	p. 1
Functions and Their Graphs	p. 1
The Number e	p. 5
Integral and Natural Logarithm	p. 9
Harmonic Series	p. 12
How to Calculate [pi]	p. 15
Method of Numerical Integral	p. 15
Method of Using Taylor Series	p. 17
Monte Carlo Method	p. 19
Best Approximations by Fractions	p. 23
Best Approximation of an Irrational Number by Fractions	p. 24
Frequency Ratio of the Musical Notes	p. 25
Expanding Real Numbers into Continued Fractions	p. 26
Calculating the Value of Logarithm	p. 30
Integer Solutions of Binary Linear Equations	p. 33
Sequences and Series	p. 39
The Fibonacci Sequence	p. 40
Harmonic Series	p. 43
Questions	p. 44
Prime Numbers	p. 49
Discrimination and Calculation of Prime Numbers	p. 49
Formula of Producing Prime Numbers	p. 53
Distribution of Prime Numbers	p. 55
Further Problems	p. 57
The Probability	p. 61
The Classical Definition of Probability	p. 61
The Statistical Definition of Probability	p. 64
Binomial Distribution and Poisson Distribution	p. 67
Normal Distribution	p. 70
The First Arc Sine Law	p. 71
Geometric Transformations	p. 73
Linear Transformations and Affine Transformations	p. 74
Eigenvectors of Linear Transformations	p. 77
Projective Transformations	p. 81
Non-Euclidean Geometry	p. 83
A Proof of the Fundamental Theorem in Algebra	p. 88
Celestial Movement	p. 95
Acceleration of the Planetary Motion	p. 96
Celestial Movement under the Universal Gravitation	p. 99
Mathematical Simulation of Other Physical Phenomena	p. 104
Iteration(I)--Finding Solutions to Equations	p. 113
Finding Roots of Equations	p. 113
Iterative Solutions to Linear Equations Sets	p. 116
Iterative Solutions to Nonlinear Equations Sets	p. 119
Optimization	p. 125
The Law of Light's Refraction	p. 125
Dashing for the Optimal Point	p. 133
Least Squares Method	p. 138
Brachistochrone	p. 143
Calculation of Time	p. 143
Looking for the Brachistochrone	p. 146
The Figure of the Brachistochrone	p. 147
Tautochrone	p. 151
Iteration(II)--Fractal	p. 159
Creation Element	p. 160
Iteration of Complex Function	p. 164
IFS Iteration	p. 167
Iteration(III)--Chaos	p. 179
The Periodic Point and Periodic Orbit	p. 179
Iteration of Quadratic Functions	p. 180
The Feigenbaum Diagram	p. 181
Properties of Chaos	p. 182
Sensitivity to the Initial Values	p. 183
Chaos Is Not Random	p. 183
Iteration of Other Functions	p. 184
Listening to Chaos	p. 185
Cryptography	p. 189
Monoalphabetic Cipher	p. 189
Polyalphabetic Cipher	p. 191
Modern Stream Cipher	p. 194
Public Keys	p. 198
Mechanical Proving of Elementary Geometrical Theorems	p. 203
Converting Geometrical Problems to Algebraic Ones	p. 204
Derivation and Proving of Algebraic Relational Expressions	p. 208
Bibliography	p. 217
Table of Contents provided by Ingram. All Rights Reserved.

Mathematics Experiments

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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