图书简介

Measuring space: accuracy and geometry; 1.1 Representing numbers exactly and approximately; 1.2 Angles and triangles; 1.3 three-dimensional geometry; Representing and describing data: descriptive statistics; 2.1 Collecting and organizing data; 2.2 Statistical measures; 2.3 Ways in which we can present data; 2.4 Bivariate data; Dividing up space: coordinate geometry, lines, Voronoi diagrams, vectors; 3.1 Coordinate geometry in 2 and 3 dimensions; 3.2 The equation of a straight line in 2 dimensions; 3.3 Voronoi diagrams; 3.4 Displacement vectors; 3.5 The scalar and vector product; 3.6 Vector equations of lines; Modelling constant rates of change: linear functions and regressions; 4.1 Functions; 4.2 Linear models; 4.3 Inverse functions; 4.4 Arithmetic sequences and series; 4.5 Linear regression; Quantifying uncertainty: probability; 5.1 Theoretical and experimental probability; 5.2 Representing combined probabilities with diagrams; 5.3 Representing combined probabilities with diagrams and formulae; 5.4 Complete, concise and consistent representations; Modelling relationships with functions: power and polynomial functions; 6.1 Quadratic models; 6.2 Quadratic modelling; 6.3 Cubic functions and models; 6.4 Power functions, inverse variation and models; Modelling rates of change: exponential and logarithmic functions; 7.1 Geometric sequences and series; 7.2 Financial applications of geometric sequences and series; 7.3 Exponential functions and models; 7.4 Laws of exponents - laws of logarithms; 7.5 Logistic models; Modelling periodic phenomena: trigonometric functions and complex numbers; 8.1 Measuring angles; 8.2 Sinusoidal models: f(x) = asin(b(x-c)) d; 8.3 Completing our number system; 8.4 A geometrical interpretation of complex numbers; 8.5 Using complex numbers to understand periodic models; Modelling with matrices: storing and analyzing data; 9.1 Introduction to matrices and matrix operations; 9.2 Matrix multiplication and properties; 9.3 Solving systems of equations using matrices; 9.4 Transformations of the plane; 9.5 Representing systems; 9.6 Representing steady state systems; 9.7 Eigenvalues and eigenvectors; Analyzing rates of change: differential calculus; 10.1 Limits and derivatives; 10.2 Differentiation: further rules and techniques; 10.3 Applications and higher derivatives; Approximating irregular spaces: integration and differential equations; 11.1 Finding approximate areas for irregular regions; 11.2 Indefinite integrals and techniques of integration; 11.3 Applications of integration; 11.4 Differential equations; 11.5 Slope fiels and differential equations; Modelling motion and change in 2D and 3D: vectors and differential equations; 12.1 Vector quantities; 12.2 Motion with variable velocity; 12.3 Exact solutions of coupled differential equations; 12.4 Approximate solutions to coupled linear equations; Representing multiple outcomes: random variables and probability distributions; 13.1 Modelling random behaviour; 13.2 Modelling the number of successes in a fixed number of trials; 13.3 Modelling the number of successes in a fixed interval; 13.4 Modelling measurements that are distributed randomly; 13.5 Mean and variance of transformed or combined random variables; 13.6 Distributions of combined random variables; Testing for validity: Spearman’s hypothesis testing and x2 test for independence; 14.1 Spearman’s rank correlation coefficient; 14.2 Hypothesis testing for the binomial probability, the Poisson mean and the product moment correlation coefficient; 14.3 Testing for the mean of a normal distribution; 14.4 Chi-squared test for independence; 14.5 Chi-squared goodness-of-fit test; 14.6 Choice, vaildity and interpretation of tests; Optimizing complex networks: graph theory; 15.1 Constructing graphs; 15.2 Graph theory for unweighted graphs; 15.3 Graph theory for weighted graphs: the minimum spanning tree; 15.4 Graph theory for weighted graphs - the Chinese postman problem; 15.5 Graph theory for weighted graphs - the travelling salesman problem; Exploration

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