Mathematics and Plausible Reasoning, Volume 1 (eBook)

Induction and Analogy in Mathematics

G. Polya (Autor)

eBook Download: PDF

2020
296 Seiten
Princeton University Press (Verlag)
978-0-691-21830-4 (ISBN)

Infos

A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. I, on Induction and Analogy in Mathematics, covers a wide variety of mathematical problems, revealing the trains of thought that lead to solutions, pointing out false bypaths, discussing techniques of searching for proofs. Problems and examples challenge curiosity, judgment, and power of invention.

Produkt-Details

• Erscheint lt. Verlag: 1.9.2020
• Sprache: englisch
• Themenwelt: Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika
• Themenwelt: Geisteswissenschaften ► Philosophie ► Logik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Schlagworte: A Course of Pure Mathematics • algebraic equation • analogous • Analogy • analytic geometry • Applied mathematics • Approximation • Arc (geometry) • auxiliary problem • Axiom • Ball (mathematics) • Bayesian probability • Billiards • Calculus of Variations • Cartesian coordinate system • Cauchy's theorem (geometry) • commutative property • Computation • conjecture • Cross section (physics) • Curve • Degeneracy (mathematics) • demonstrative reasoning • Diagram (category theory) • Differential Calculus • differential equation • Divisibility rule • E6 (mathematics) • Elementary algebra • Elementary proof • Equation • equilateral triangle • Euclidean Geometry • Euler's formula • Euler's Theorem • Explicit formulae (L-function) • favorable sign • geometric mean • geometric progression • Geometric series • Geometry • Geophysical Exploration • Goldbach's conjecture • Harmonic series (mathematics) • Homogeneous differential equation • Hypotenuse • inductive reasoning • inference • Infinite product • Integer • Integral calculus • integral equation • Intersection (set theory) • Isoperimetric inequality • isoperimetric problem • isoperimetric theorem • Kepler's attitude • Latent reasons • Limit (mathematics) • Logic • Mathematical beauty • Mathematical fallacy • Mathematical Induction • Mathematical Notation • Mathematical Physics • Mathematical problem • Mathematical Proof • Mathematical Sciences • mathematician • Mathematics • Mathematische Zeitschrift • Maxima and minima • more credible • Natural number • not convex • Numbering (computability theory) • Number Theory • Numerical analysis • Opera omnia • ordinary differential equation • parallelogram • Parity (mathematics) • physical mathematics • Plane Geometry • plausible reasoning • polyhedron • Prime number • Prism (geometry) • Probability Theory • Problems • Projection (linear algebra) • Proportionality (mathematics) • Pure Mathematics • Pyramid (geometry) • Pythagorean Theorem • Quantity • Rational number • real number • rectangle • regular polygon • Reinterpretation • result • right double pyramid • Right triangle • scientific atmosphere • scientific notation • Series (mathematics) • Sign (mathematics) • Similarity (geometry) • Simultaneous Equations • solid geometry • Special case • Special right triangle • Spherical trigonometry • Summation • Tangent Space • Tentative • tetrahedron • Theorem • Traditional mathematics • Variable (mathematics) • various consequences
• ISBN-10: 0-691-21830-7 / 0691218307
• ISBN-13: 978-0-691-21830-4 / 9780691218304