Search Results for "what-is-mathematics-an-elementary-approach-to-ideas-and-methods"

What is Mathematics?

What is Mathematics?

An Elementary Approach to Ideas and Methods

  • Author: Richard Courant,Herbert Robbins,Ian Stewart
  • Publisher: Oxford University Press, USA
  • ISBN: 9780195105193
  • Category: Mathematics
  • Page: 566
  • View: 9853
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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

What Is Mathematics?

What Is Mathematics?

An Elementary Approach to Ideas and Methods

  • Author: the late Richard Courant,Herbert Robbins
  • Publisher: Oxford University Press
  • ISBN: 9780199754878
  • Category: Mathematics
  • Page: 592
  • View: 3765
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For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.

What is Mathematics?

What is Mathematics?

An Elementary Approach to Ideas and Methods

  • Author: Richard Courant,Herbert Robbins
  • Publisher: Oxford University Press, USA
  • ISBN: 0195105192
  • Category: Mathematics
  • Page: 566
  • View: 8775
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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

Concepts of Modern Mathematics

Concepts of Modern Mathematics

  • Author: Ian Stewart
  • Publisher: Courier Corporation
  • ISBN: 0486134954
  • Category: Mathematics
  • Page: 368
  • View: 6874
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In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

What is Mathematics, Really?

What is Mathematics, Really?

  • Author: Reuben Hersh
  • Publisher: Oxford University Press, USA
  • ISBN: 9780195130874
  • Category: Mathematics
  • Page: 343
  • View: 7759
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Reflecting an insider's view of mathematical life, the author argues that mathematics must be historically evolved, and intelligible only in a social context.

Introduction to Calculus and Analysis

Introduction to Calculus and Analysis

  • Author: Richard Courant,Fritz John
  • Publisher: Springer Science & Business Media
  • ISBN: 9783540665694
  • Category: Mathematics
  • Page: 556
  • View: 9163
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Biography of Richard Courant Richard Courant was born in 1888 in a small town of what is now Poland, and died in New Rochelle, N.Y. in 1972. He received his doctorate from the legendary David Hilbert in Göttingen, where later he founded and directed its famed mathematics Institute, a Mecca for mathematicians in the twenties. In 1933 the Nazi government dismissed Courant for being Jewish, and he emigrated to the United States. He found, in New York, what he called "a reservoir of talent" to be tapped. He built, at New York University, a new mathematical Sciences Institute that shares the philosophy of its illustrious predecessor and rivals it in worldwide influence. For Courant mathematics was an adventure, with applications forming a vital part. This spirit is reflected in his books, in particular in his influential calculus text, revised in collaboration with his brilliant younger colleague, Fritz John. (P.D. Lax) Biography of Fritz John Fritz John was born on June 14, 1910, in Berlin. After his school years in Danzig (now Gdansk, Poland), he studied in Göttingen and received his doctorate in 1933, just when the Nazi regime came to power. As he was half-Jewish and his bride Aryan, he had to flee Germany in 1934. After a year in Cambridge, UK, he accepted a position at the University of Kentucky, and in 1946 joined Courant, Friedrichs and Stoker in building up New York University the institute that later became the Courant Institute of Mathematical Sciences. He remained there until his death in New Rochelle on February 10, 1994. John's research and the books he wrote had a strong impact on the development of many fields of mathematics, foremost in partial differential equations. He also worked on Radon transforms, illposed problems, convex geometry, numerical analysis, elasticity theory. In connection with his work in latter field, he and Nirenberg introduced the space of the BMO-functions (bounded mean oscillations). Fritz John's work exemplifies the unity of mathematics as well as its elegance and its beauty. (J. Moser)

Mathematics and the Physical World

Mathematics and the Physical World

  • Author: Morris Kline
  • Publisher: Courier Corporation
  • ISBN: 0486136310
  • Category: Mathematics
  • Page: 512
  • View: 6895
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Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

What is Mathematics?

What is Mathematics?

An Elementary Approach to Ideas and Methods

  • Author: Richard Courant,Herbert Robbins
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: 521
  • View: 1035
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The Foundations of Mathematics

The Foundations of Mathematics

  • Author: Ian Stewart,Professor of Math and Gresham Professor of Geometry Ian Stewart,David Tall,David Orme Tall
  • Publisher: Oxford University Press on Demand
  • ISBN: 9780198531654
  • Category: Fiction
  • Page: 263
  • View: 9924
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"There are many textbooks available for a so-called transition course from calculus to abstract mathematics. I have taught this course several times and always find it problematic. The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books

Mathematics

Mathematics

Its Content, Methods and Meaning

  • Author: A. D. Aleksandrov,A. N. Kolmogorov,M. A. Lavrent’ev
  • Publisher: Courier Corporation
  • ISBN: 0486157873
  • Category: Mathematics
  • Page: 1120
  • View: 9396
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Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

The Great Mathematical Problems

The Great Mathematical Problems

  • Author: Ian Stewart
  • Publisher: Profile Books
  • ISBN: 1847653510
  • Category: Mathematics
  • Page: 340
  • View: 6589
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There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincar Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.

Mathematics for the Nonmathematician

Mathematics for the Nonmathematician

  • Author: Morris Kline
  • Publisher: Courier Corporation
  • ISBN: 0486316130
  • Category: Mathematics
  • Page: 672
  • View: 3019
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Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.

Book of Curves

Book of Curves

  • Author: E. H. Lockwood
  • Publisher: Cambridge University Press
  • ISBN: 0521044448
  • Category: Mathematics
  • Page: 212
  • View: 3308
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This book examines the shape of curves and their mathematical relationships.

Makers of Mathematics

Makers of Mathematics

  • Author: Stuart Hollingdale
  • Publisher: Courier Corporation
  • ISBN: 0486174506
  • Category: Mathematics
  • Page: 464
  • View: 802
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Each chapter of this accessible portrait of the evolution of mathematics examines the work of an individual — Archimedes, Descartes, Newton, Einstein, others — to explore the mathematics of his era. 1989 edition.

Mathematics

Mathematics

  • Author: Timothy Gowers
  • Publisher: Sterling Publishing Company, Inc.
  • ISBN: 9781402768972
  • Category: Mathematics
  • Page: 180
  • View: 1561
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Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as “infinity,” “curved space,” and “imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.

Journey through genius

Journey through genius

the great theorems of mathematics

  • Author: William Dunham
  • Publisher: Egully.com
  • ISBN: N.A
  • Category: Mathematics
  • Page: 300
  • View: 3005
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A rare combination of the historical, biographical, and mathematicalgenius, this book is a fascinating introduction to a neglected field of human creativity. Dunham places mathematical theorem, along with masterpieces of art, music, and literature and gives them the attention they deserve.

Mathematical Mindsets

Mathematical Mindsets

Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching

  • Author: Jo Boaler
  • Publisher: John Wiley & Sons
  • ISBN: 1118418271
  • Category: Education
  • Page: 320
  • View: 8974
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Banish math anxiety and give students of all ages a clear roadmap to success Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler—Stanford researcher, professor of math education, and expert on math learning—has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students. There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. Mathematical Mindsets: Explains how the brain processes mathematics learning Reveals how to turn mistakes and struggles into valuable learning experiences Provides examples of rich mathematical activities to replace rote learning Explains ways to give students a positive math mindset Gives examples of how assessment and grading policies need to change to support real understanding Scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals—until now. Mathematical Mindsets provides a proven, practical roadmap to mathematics success for any student at any age.

Elementary Mathematics from an Advanced Standpoint

Elementary Mathematics from an Advanced Standpoint

Geometry

  • Author: Christian Felix Klein
  • Publisher: N.A
  • ISBN: N.A
  • Category: Geometry
  • Page: 214
  • View: 6876
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