Leseprobe
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Elements of Mathematics
John Stillwell
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Naturwissenschaften, Medizin, Informatik, Technik / Geometrie
Beschreibung
An exciting look at the world of elementary mathematics
Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits.
From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics.
Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.
Kundenbewertungen
Elementary function, Elementary mathematics, Computable number, Number theory, Mathematician, Successor function, Variable (mathematics), Pythagorean theorem, Robinson arithmetic, Predicate logic, Factorization, Integer factorization, Prime factor, Scientific notation, Abstract algebra, Gaussian integer, Summation, Constructible number, Non-Euclidean geometry, Time complexity, Halting problem, Set theory, Turing machine, Zermelo–Fraenkel set theory, Divisibility rule, Complex number, Bolzano–Weierstrass theorem, Logic, Real number, Fundamental theorem of algebra, Continuous function, Extended Euclidean algorithm, Axiom, Method of exhaustion, Fundamental theorem, Computation, Exponentiation, Projective line, Mathematics, Polynomial, Theorem, Prime number, Arithmetic, Rational number, Subset, Equation, Addition, Rectangle, Vector space, Algebra, Probability, Natural number, Combinatorics, Coefficient, Dedekind cut, Euclidean geometry, Significant figures, Integer, Mathematical induction, Binomial coefficient, Pigeonhole principle, Special case, Gödel's incompleteness theorems, Commutative property, Continuum hypothesis, Dirichlet's approximation theorem, Calculation, Algebraic number, Geometry, Reverse mathematics