Methods of Mathematics Applied to Calculus, Probability, and Statistics

Richard W. Hamming: The Computer IconRichard W. Hamming (1915–1998) was first a programmer of one of the earliest digital computers while assigned to the Manhattan Project in 1945, then for many years he worked at Bell Labs, and later at the Naval Postgraduate School in Monterey, California. He was a witty and iconoclastic mathematician and computer scientist whose work and influence still reverberates through the areas he was interested in and passionate about. Three of his long-lived books have been reprinted by Dover: Numerical Methods for Scientists and Engineers, 1987; Digital Filters, 1997; and Methods of Mathematics Applied to Calculus, Probability and Statistics, 2004. In the Author's Own Words:"The purpose of computing is insight, not numbers.""There are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think." "Whereas Newton could say, 'If I have seen a little farther than others, it is because I have stood on the shoulders of giants, I am forced to say, 'Today we stand on each other's feet.' Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way." "If you don't work on important problems, it's not likely that you'll do important work." — Richard W. Hamming

• PrefaceI. Algebra and Analytic Geometry1. Prologue2. The Integers3. Fractions—Rational Numbers4. Real Numbers, Functions, and Philosophy5. Analytic Geometry. 6. Curves of Second Degree—ConicsII. The Calculus of Algebraic Functions7. Derivatives in Geometry8. Geometric Applications9. Nongeometric Applications10. Functions of Several Variables11. Integration12. Discrete Probability13. Continuous ProbabilityIII. The Transcendental Functions and Applications14. The Logarithm Function15. The Exponential Function16. The Trigonometric Functions17. Formal Integration 18. Applications Using One Independent Variable19. Applications Using Several Independent VariablesIV. Miscellaneous Topics20. Infinite Series21. Applications of Infinite Series22. Fourier Series23. Differential Equations24. Linear Differential Equations25. Numerical Methods26. EpilogueAppendixesAnswers to Some of the ExercisesIndex