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Scientific American Library Series #52
Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe
To most people, mathematics means working with numbers. But as Keith Devlin shows in Mathematics: The Science of Patterns, this definition has been out of date for nearly 2,500 years. Mathematicians now see their work as the study of patterns real or imagined, visual or mental, arising from the natural world or from within the human mind.
Using this basic definition as his central theme, Devlin explores the patterns of counting, measuring, reasoning, motion, shape, position, and prediction, revealing the powerful influence mathematics has over our perception of reality. Interweaving historical highlights and current developments, and using a minimum of formulas, Devlin celebrates the precision, purity, and elegance of mathematics.
Using this basic definition as his central theme, Devlin explores the patterns of counting, measuring, reasoning, motion, shape, position, and prediction, revealing the powerful influence mathematics has over our perception of reality. Interweaving historical highlights and current developments, and using a minimum of formulas, Devlin celebrates the precision, purity, and elegance of mathematics.
216 pages, Paperback
First published January 1, 1994
About the author
Keith Devlin
81 books152 followersDr. Keith Devlin is a co-founder and Executive Director of the university's H-STAR institute, a Consulting Professor in the Department of Mathematics, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 26 books and over 80 published research articles. Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. He is "the Math Guy" on National Public Radio.
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Displaying 1 - 10 of 10 reviews
February 8, 2016
The first chapter is about number theory, the second about proofs and logic, the third about motion. Six chapters in all, suitable for a layperson with only high school math. Each chapter is organized chronologically, with new theories often presented as attempts to resolve known contradictions. I wish that I had read math books of this kind when I was younger.
January 15, 2014
Mathematics the science of patterns written by keith devlin published by scientific america library
was a refreshing read. At 216 pages it took me about 3 weeks to read on and off although if I calculate total time it took to read this probably happened in a four or five day span. With those days being days of high concentration for this work. This book reminded me of the history of mathematics which was so nessicary in helping me to understand some fundamental concepts that I simply missed in other readings.
The topics in the contents where as such
Preface
Prologue
Counting
Reasoning and Communicating
Motion and Change
Shape
Symmetry and regularity
Position
Postscript
Further Readings
Sources of Illustration
Index.
I think that the artist that did the layout did a good job. Although I would not say that the book was as complete artistically as many roleplaying texts it still was lovely.
Which is something I think one should aspire for in their work is a cohesive tour de force of content and layout with both balancing one another.
The purpose of this text is to give one a sense of the purpose of the study of the science of pattern going into a slurry of topics that shows the connection and the beauty of the study of pattern.
Further the work hopes to describe and works with the idea of abstraction and how evermore the day we abstract some still from the hopes of the infinite region.
Chapter 1 Couting.
Here it recalls the rise of counting and its purpose and how people counted and why.
In the beginning of counting their was set to be a matching system where one would match an object with another object and then compare. Then their was idyllic markings placed in soft clay or on envelopes of tokens to keep track of things. So even then it might be seen that man was cybernetic storing important information outside of themselves.
Then as a subtopic we move to Greek Mathematics.
The description then starts to enter and entertain the possibility that our abstraction grew sometime before this yet it was unknown and although this had occurred we would further abstract previous works.
Area of a truntacated square pyramid
V = 1/3h(a^2 +ab +b^2)
The seven liberal arts where
Quadrivium
Arithmetica(number theory)
Harmonia(music)
Geometria(geometry)
Astrologia(astronomy)
Trivium
Logic
Grammar
Rhetoric
These where necessary of an educated man at the time.
I think that part of the undercurrent and the design of this work is in this vein as well whereas the fellow covers in some degree all of these topics. I wonder if he was speaking out through the ages to times now past to remember and respect these aspects of the mind.
Subtopics of couting
Prime Numbers
Finite Arithmetic
Prime Number Patterns
Message Encryption
Fermat's Last Theorem
Chapter 2 Reasoning and Communication
Greek logic
Venn Diagrams
Booles Logic
Vector Algebra
Propositional Logic
Predicate Logic and Patterns of Language
Abstraction and the Axiomatic Method
Set Theory
Numbers from Nothing
Hilberts Program Godel's Theorem
Proof theory
Model theory
Set theory
Computability theory
Patterns of Language
Motion and Change
Paradox of Motion
Number Patterns in Motion
Infinite Series
Functions
Computing gradients
Gradient of straight line from p to q
((x+h)^2 - x^2) / h
Fathers of calculus
Fourier Analysis
Differential Calculus
Differentional Equations
Integration
Real Numbers
Complex Numbers
Fundamental Theorem of algebra
eulers formula
e^ix = cosx + i sinx
Analytic Number Theory
Shape
Eucilds Axioms
Euclids Elements
The golden ratio
(x+1) / x = x/1
Platos Atomic Theory
Keplers Planetary Theory
Cartesian Geometry
Three Classic Problems
Non Euclidean Geometries
Projective Geometry
Cross Ratio
Dimension
Symmetry and Regularity
Symmetry Groups
Symmetry in greek is ice
Sphere Packing
Wallpaper Patterns
Tiling
Position
Networks
Topology
Classification of Surfaces
Knots
Genetic Knots
Fermat's Last Theorem Again
Postscript
This describes the many things that where not discussed throughout the book which is to say a great many.
Further Reading
Sources of Illustration
was a refreshing read. At 216 pages it took me about 3 weeks to read on and off although if I calculate total time it took to read this probably happened in a four or five day span. With those days being days of high concentration for this work. This book reminded me of the history of mathematics which was so nessicary in helping me to understand some fundamental concepts that I simply missed in other readings.
The topics in the contents where as such
Preface
Prologue
Counting
Reasoning and Communicating
Motion and Change
Shape
Symmetry and regularity
Position
Postscript
Further Readings
Sources of Illustration
Index.
I think that the artist that did the layout did a good job. Although I would not say that the book was as complete artistically as many roleplaying texts it still was lovely.
Which is something I think one should aspire for in their work is a cohesive tour de force of content and layout with both balancing one another.
The purpose of this text is to give one a sense of the purpose of the study of the science of pattern going into a slurry of topics that shows the connection and the beauty of the study of pattern.
Further the work hopes to describe and works with the idea of abstraction and how evermore the day we abstract some still from the hopes of the infinite region.
Chapter 1 Couting.
Here it recalls the rise of counting and its purpose and how people counted and why.
In the beginning of counting their was set to be a matching system where one would match an object with another object and then compare. Then their was idyllic markings placed in soft clay or on envelopes of tokens to keep track of things. So even then it might be seen that man was cybernetic storing important information outside of themselves.
Then as a subtopic we move to Greek Mathematics.
The description then starts to enter and entertain the possibility that our abstraction grew sometime before this yet it was unknown and although this had occurred we would further abstract previous works.
Area of a truntacated square pyramid
V = 1/3h(a^2 +ab +b^2)
The seven liberal arts where
Quadrivium
Arithmetica(number theory)
Harmonia(music)
Geometria(geometry)
Astrologia(astronomy)
Trivium
Logic
Grammar
Rhetoric
These where necessary of an educated man at the time.
I think that part of the undercurrent and the design of this work is in this vein as well whereas the fellow covers in some degree all of these topics. I wonder if he was speaking out through the ages to times now past to remember and respect these aspects of the mind.
Subtopics of couting
Prime Numbers
Finite Arithmetic
Prime Number Patterns
Message Encryption
Fermat's Last Theorem
Chapter 2 Reasoning and Communication
Greek logic
Venn Diagrams
Booles Logic
Vector Algebra
Propositional Logic
Predicate Logic and Patterns of Language
Abstraction and the Axiomatic Method
Set Theory
Numbers from Nothing
Hilberts Program Godel's Theorem
Proof theory
Model theory
Set theory
Computability theory
Patterns of Language
Motion and Change
Paradox of Motion
Number Patterns in Motion
Infinite Series
Functions
Computing gradients
Gradient of straight line from p to q
((x+h)^2 - x^2) / h
Fathers of calculus
Fourier Analysis
Differential Calculus
Differentional Equations
Integration
Real Numbers
Complex Numbers
Fundamental Theorem of algebra
eulers formula
e^ix = cosx + i sinx
Analytic Number Theory
Shape
Eucilds Axioms
Euclids Elements
The golden ratio
(x+1) / x = x/1
Platos Atomic Theory
Keplers Planetary Theory
Cartesian Geometry
Three Classic Problems
Non Euclidean Geometries
Projective Geometry
Cross Ratio
Dimension
Symmetry and Regularity
Symmetry Groups
Symmetry in greek is ice
Sphere Packing
Wallpaper Patterns
Tiling
Position
Networks
Topology
Classification of Surfaces
Knots
Genetic Knots
Fermat's Last Theorem Again
Postscript
This describes the many things that where not discussed throughout the book which is to say a great many.
Further Reading
Sources of Illustration
October 25, 2010
Maybe it's hard to imagine a book on maths as something you would read in your spare time. I did, however, and it was one of the most fascinating and intellectually stimulating books I have ever read.
The weird thing about mathematics is that it is incredibly simple in its origins. You just start with one number and if you keep adding ones you get the essential series of 1, 2, 3, 4, 5 etc. (And of course you can further complicate it by making numbers negative, or fractions like 0,25 and 1/4, but those are just modifications that don't change a lot to the basic system)
But when you start looking at the relations between the numbers, unexpected patterns emerge. For instance, Euclid defined something like a 'perfect number'. It is a number that is equal to the sum of its divisors. 6 can be divided by 1, 2 and 3. Oddly enough, 6 is also the sum of 1+2+3, thus making it a perfect number. The next one is 28 (1+2+4+7+14) and then they quickly become rare, with 496 and 8128 as the next perfect numbers in line. Euclid also discovered a rather simple formula involving primes to find the next perfect numbers.
That proves a strange relation between primes and the arbitrary concept of a 'perfect number'. Primes themselves are even a lot weirder, but I can't go into that here. Other interesting parallels can be found between the Golden Ratio and the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21 and so on.
I guess there are many accessible introductions to mathematics around, some good, some bad. Of Devlin's book I can say that it is an excellent one, very readable and though it sometimes demands a little effort to understand a problem, you are always rewarded by a fascinating new insight.
The weird thing about mathematics is that it is incredibly simple in its origins. You just start with one number and if you keep adding ones you get the essential series of 1, 2, 3, 4, 5 etc. (And of course you can further complicate it by making numbers negative, or fractions like 0,25 and 1/4, but those are just modifications that don't change a lot to the basic system)
But when you start looking at the relations between the numbers, unexpected patterns emerge. For instance, Euclid defined something like a 'perfect number'. It is a number that is equal to the sum of its divisors. 6 can be divided by 1, 2 and 3. Oddly enough, 6 is also the sum of 1+2+3, thus making it a perfect number. The next one is 28 (1+2+4+7+14) and then they quickly become rare, with 496 and 8128 as the next perfect numbers in line. Euclid also discovered a rather simple formula involving primes to find the next perfect numbers.
That proves a strange relation between primes and the arbitrary concept of a 'perfect number'. Primes themselves are even a lot weirder, but I can't go into that here. Other interesting parallels can be found between the Golden Ratio and the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21 and so on.
I guess there are many accessible introductions to mathematics around, some good, some bad. Of Devlin's book I can say that it is an excellent one, very readable and though it sometimes demands a little effort to understand a problem, you are always rewarded by a fascinating new insight.
October 18, 2009
I enjoyed the look at various patterns in mathematics. The history and evolution of various areas of mathematical study is interesting, however I wished there was more examples and more for each area about the patterns themselves instead of the mathematical theories already learned.
May 17, 2011
Remarkably accessible coverage of many of the major Mathematical discoveries, incorporating some of the latest advances. Tries to share knowledge and understanding rather than blindly impressing with whizz-bangs. A noble attempt.
December 14, 2022
Highly recommend. Probably the best book on the big picture of mathematics I've read. Fairly accessible, positively breezy for a math book, and offering a good taste of the various branches of research math.
December 19, 2008
Fantastic book on the history and trivia around mathematics as well as a good premise that math is all about finding patterns. So many things I learned from this book.
June 20, 2010
Beautiful book.
September 25, 2012
best of my readings ever من أجمل ما قرأت
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March 3, 2018good
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Displaying 1 - 10 of 10 reviews