Author | Gรฅrding, Lars. author |
---|---|
Title | Encounter with Mathematics [electronic resource] / by Lars Gรฅrding |
Imprint | New York, NY : Springer US, 1977 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-9641-7 |
Descript | X, 270 p. online resource |
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 The 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, Dedekindโs cuts, and Cantorโs 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 Document -- 8 Integration -- 8.1 Areas, volumes, and the Riemann integral -- 8.2 Some theorems of analysis -- 8.3 Integration in Rn 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