Obwohl statistische Analysen aufgrund der technischen Moglichkeiten immer einfacher werden, ist das grundlegende Verstandnis und die Kenntnis von den Moglichkeiten und Grenzen statistischer Verfahren umso wichtiger. Mit vielen ausfuhrlichen Beispielen aus dem wirtschaftswissenschaftlichen Bereich zeigt dieses Buch die Vielfalt der Anwendungsmoglichkeiten auf. Durch die Behandlung sowohl der beschreibenden als auch der induktiven Statistik lasst sich das Lehrbuch in Modulen zur Statistik und zur empirischen beziehungsweise quantitativen Forschungsmethodik einsetzen."
Durch die Behandlung sowohl der beschreibenden als auch der induktiven Statistik lasst sich das Lehrbuch in Modulen zur Statistik und zur empirischen beziehungsweise quantitativen Forschungsmethodik einsetzen."
Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently, this is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition; it shows how to discover the outline of a proof in the form of the theorem and how logical structures determine the forms that proofs may take. Throughout, the text asks the reader to pause and work on an example or a problem before continuing, and encourages the student to engage the topic at hand and to learn from failed attempts at solving problems. The book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics. The whole concludes with a set of "Laboratories" in which students can practice the skills learned in the earlier chapters on set theory and function theory.
In particular, he observes that Pólya's heuristic strategies actually are whole
categories of related strategies, and that attempts by students to implement them
from Pólya's general descriptions founder at least in part on this lack of detail (
see ...
From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems." Bulletin of the American Mathematical Society
This picture shows G. Pólya (r.) and G. Szegó (1.) delivering their original
manuscript to Springer in Berlin in 1925 (courtesy of G. Alexanderson). George Pólya Born in Budapest, December 13, 1887, George Pólya initially studied law,
then ...
Mathematician and bestselling author Robin Wilson--himself a sudoku aficionado--offers 52 tried and tested tips and tactics for solving these brainteasers.
Mathematician and bestselling author Robin Wilson--himself a sudoku aficionado--offers 52 tried and tested tips and tactics for solving these brainteasers.
And 34 Other Really Interesting Uses of Mathematics
Can you outrun a bullet? How do you build an electronic brain? Is it possible to create an unbreakable code? Could you slow down time? How do you unleash chaos? If you thought mathematics was all about measuring angles in a triangle or factorizing equations, think again ... How to Build a Brain and 34 Other Really Interesting Uses of Mathematics demystifies the astonishing world of maths in a series of intriguing, entertaining and often extraordinary scenarios - that explain key concepts in plain and simple language. You'll find out how to unknot your DNA, how to count like a supercomputer and how to become famous for solving mathematics most challenging problem. You'll learn essential survival skills such as how to survive in a whirlpool, how to slay a mathematical monster and how to be alive and dead at the same time. And along the way you'll discover some plain old cool stuff like how to unleash chaos, how to create an unbreakable code and how to use the mathematics to win at roulette or avoid going to prison. So if you want to get to grips with the great questions of number theory and geometry, the mysteries of the prime numbers or Plato's classification of regular polyhedra, or if you are really more interested in learning how to have beautiful children or how to make a million on the stock market, this is the perfect introduction to the fascinating world of modern mathematics.
... Meiko Kwan, in 1962. Kwan found a way to solve the problem: he provided a
simple set of instructions (or an algorithm, see How to bring down the internet)
that will always produce an optimal solution to the Chinese postman problem.
Delve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.
Euler was unable to give a solution, and even to this day there is no complete solution for this problem. One of the most famous of unsolved problems, which
can be stated in terms of elementary concepts, is known as Fermat's Last
Theorem.