Lars Garding (1919–2014)

Indeholder "Preface", "1. Models and reality", "1.1 Models", "1.2 Models and reality", "1.3 Mathematical models", "2. Number theory", "2.1 The primes", "2.2 The theorems of Fermat and Wilson", "2.3 Gaussian integers", "2.4 Some problems and results", "2.5 Documents", "3. Algebra", "3.1 The theory of equations", "3.2 Rings, fields, modules, and ideals", "3.3 Groups", "3.4 Documents", "4. Geometry and linear algebra", "4.1 Euclidean geometry", "4.2 Analytical geometry", "4.3 Systems of linear equations and matrices", "4.4 Linear spaces", "4.5 Linear spaces with a norm", "4.6 Boundedness, continuity and compactness", "4.7 Hilbert spaces", "4.8 Adjoints and the spectral theorem", "4.9 Documents", "5. Limits, continuity, and topology", "5.1 Irrational numbers, Dedekind's cuts, and Cantor's fundamental sequences", "5.2 Limits of functions, continuity, open and closed sets", "5.3 Topology", "5.4 Documents", "6. The heroic century", "7. Differentiation", "7.1 Derivatives and planetary motion", "7.2 Strict analysis", "7.3 Differential equations", "7.4 Differential calculus of functions of several variables", "7.5 Partial differential equations", "7.6 Differential forms", "7.7 Differential calculus on a manifold", "7.8 Documents", "8. Integration", "8.1 Areas, volumes, and the Riemann integral", "8.2 Some theorems of analysis", "8.3 Integration in R^n and measures", "8.4 Integration on manifolds", "8.5 Documents", "9. Series", "9.1 Convergence and divergence", "9.2 Power series and analytic functions", "9.3 Approximation", "9.4 Documents", "10. Probability", "10.1 Probability spaces", "10.2 Stochastic variables", "10.3 Expectation and variance", "10.4 Sums of stochastic variables, the law of large numbers, and the central limit theorem", "10.5 Probability and statistics, sampling", "10.6 Probability in physics", "10.7 Document", "11. Applications", "11.1 Numerical computation", "11.2 Construction of models", "12. The sociology, psychology, and teaching of mathematics", "12.1 Three biographies", "12.2 The psychology of mathematics", "12.3 The teaching of mathematics", "Appendix", "Index".

Et forsøg på at give lidt historie og baggrund til førsteårs matematikstuderende på universitetsniveau.… (más)