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Author: W.S. Anglin
Publisher: Springer Science & Business Media
ISBN: 9401102856
Category : Mathematics
Languages : en
Pages : 393
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Book Description
Like other introductions to number theory, this one includes the usual curtsy to divisibility theory, the bow to congruence, and the little chat with quadratic reciprocity. It also includes proofs of results such as Lagrange's Four Square Theorem, the theorem behind Lucas's test for perfect numbers, the theorem that a regular n-gon is constructible just in case phi(n) is a power of 2, the fact that the circle cannot be squared, Dirichlet's theorem on primes in arithmetic progressions, the Prime Number Theorem, and Rademacher's partition theorem. We have made the proofs of these theorems as elementary as possible. Unique to The Queen of Mathematics are its presentations of the topic of palindromic simple continued fractions, an elementary solution of Lucas's square pyramid problem, Baker's solution for simultaneous Fermat equations, an elementary proof of Fermat's polygonal number conjecture, and the Lambek-Moser-Wild theorem.
Author: W.S. Anglin
Publisher: Springer Science & Business Media
ISBN: 9401102856
Category : Mathematics
Languages : en
Pages : 393
Get Book
Book Description
Like other introductions to number theory, this one includes the usual curtsy to divisibility theory, the bow to congruence, and the little chat with quadratic reciprocity. It also includes proofs of results such as Lagrange's Four Square Theorem, the theorem behind Lucas's test for perfect numbers, the theorem that a regular n-gon is constructible just in case phi(n) is a power of 2, the fact that the circle cannot be squared, Dirichlet's theorem on primes in arithmetic progressions, the Prime Number Theorem, and Rademacher's partition theorem. We have made the proofs of these theorems as elementary as possible. Unique to The Queen of Mathematics are its presentations of the topic of palindromic simple continued fractions, an elementary solution of Lucas's square pyramid problem, Baker's solution for simultaneous Fermat equations, an elementary proof of Fermat's polygonal number conjecture, and the Lambek-Moser-Wild theorem.
Author: Jay Goldman
Publisher: CRC Press
ISBN: 1439864624
Category : Mathematics
Languages : en
Pages : 550
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Book Description
This book takes the unique approach of examining number theory as it emerged in the 17th through 19th centuries. It leads to an understanding of today's research problems on the basis of their historical development. This book is a contribution to cultural history and brings a difficult subject within the reach of the serious reader.
Author: Laurie Wallmark
Publisher:
ISBN: 9781939547637
Category : Juvenile Nonfiction
Languages : en
Pages : 0
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Book Description
"This picture book traces the impressive career of Sophie Kowalevski, the first woman to receive a doctorate in mathematics requiring original research. As a girl, Sophie is fascinated by the equations her father uses to wallpaper her room. She proves herself a prodigy, and tutors are impressed enough to give her private lessons. Despite universities that refuse to allow women on campus or to pay them to teach, Sophie is able to distinguish herself with her research into partial differential equations. Sophie receives a doctorate and becomes the first female professional mathematician in Northern Europe. The book mentions several of Kowalevski's mathematical contributions and closes with an encouraging message about women in mathematics"--
Author: Albert H. Beiler
Publisher: Courier Corporation
ISBN: 0486210960
Category : Games & Activities
Languages : en
Pages : 383
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Book Description
Number theory proves to be a virtually inexhaustible source of intriguing puzzle problems. Includes divisors, perfect numbers, the congruences of Gauss, scales of notation, the Pell equation, more. Solutions to all problems.
Author: Eric Temple Bell
Publisher:
ISBN: 9780758187109
Category :
Languages : en
Pages : 437
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Book Description
Author: Jean-Pierre Marquis
Publisher: Springer Science & Business Media
ISBN: 1402093845
Category : Science
Languages : en
Pages : 316
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Book Description
From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane’s work in the early 1940’s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics. From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.
Author: John Hudson Tiner
Publisher: New Leaf Publishing Group
ISBN: 161458155X
Category : Religion
Languages : en
Pages : 159
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Book Description
Numbers surround us. Just try to make it through a day without using any. It's impossible: telephone numbers, calendars, volume settings, shoe sizes, speed limits, weights, street numbers, microwave timers, TV channels, and the list goes on and on. The many advancements and branches of mathematics were developed through the centuries as people encountered problems and relied upon math to solve them. For instance: What timely invention was tampered with by the Caesars and almost perfected by a pope? Why did ten days vanish in September of 1752? How did Queen Victoria shorten the Sunday sermons at chapel? What important invention caused the world to be divided into time zones? What simple math problem caused the Mars Climate Orbiter to burn up in the Martian atmosphere? What common unit of measurement was originally based on the distance from the equator to the North Pole? Does water always boil at 212? Fahrenheit? What do Da Vinci's Last Supper and the Parthenon have in common? Why is a computer glitch called a "bug"? It's amazing how ten simple digits can be used in an endless number of ways to benefit man. The development of these ten digits and their many uses is the fascinating story you hold in your hands: Exploring the World of Mathematics.
Author: John Polkinghorne
Publisher: OUP Oxford
ISBN: 0191621897
Category : Mathematics
Languages : en
Pages : 176
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Book Description
Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics. The chapters are written by some of the world's finest mathematicians, mathematical physicists and philosophers of mathematics, each giving their perspective on this fascinating debate. Every chapter is followed by a short response from another member of the author team, reinforcing the main theme and raising further questions. Accessible to anyone interested in what mathematics really means, and useful for mathematicians and philosophers of science at all levels, Meaning in Mathematics offers deep new insights into a subject many people take for granted.
Author: John A. Adam
Publisher: Princeton University Press
ISBN: 1400841011
Category : Mathematics
Languages : en
Pages : 408
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Book Description
From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.
Author: Robin Wilson
Publisher: Oxford University Press
ISBN: 0192514067
Category : Mathematics
Languages : en
Pages : 200
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Book Description
In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, eiπ + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.
