For instructors of liberal arts mathematics classes who focus on problem-solving, Harold Jacobs's remarkable textbook has long been the answer, helping teachers connect with of math-anxious students. Drawing on over thirty years of classroom experience, Jacobs shows students how. This is a go-to reference for math project ideas (I'm a teacher), more often as a source of inspiration than ready-made things. It also activates the "wonder" factor . Elementary Algebra by Harold R. Jacobs Hardcover $ Mathematics: A Human Endeavor (3rd Edition) Student Workbook for Jacobs Mathematics: A Human Endeavor.
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Mathematics : A Human Endeavor 3rd
These were then translated into the graffiti you see here. Art lovers may cringe, yet it is likely that Seurat would have been intrigued by this augmentation of his work. The movement Seurat kick-started with this painting — Neo-Impressionism — drew inspiration from the scientific study of how our vision works. Particularly influential was the pioneering research of Hermann von Helmholtz, a German physician, physicist and philosopher and author of a seminal book, Handbook of Physiological Optics, on the way we perceive depth, color and motion.
Consider that the lines above were drawn in just three minutes. If we saw all those movements as we made them, our view of the world would be a blur of constant motion. A short movie of an eye making saccades, shown in slow motion. Credit: Weekend Way via Giphy The Secrets of Seeing Beginning with the basics: The only things we can ever hope to see are those that send or reflect light toward our eyes, where it might end up hitting the retina, a layer of nervous tissue that covers the back two-thirds of the inner eyeball.
There, the complex image of whatever we are looking at is first translated into activity of individual light-sensitive photoreceptor cells. This pattern is then transmitted to a variety of neurons in the retina that specifically respond to certain colors, shapes, orientations, movements or contrasts. The signals they produce are sent up to the brain through the optic nerve, where they are interpreted and put back together in a progression of specialized areas in the visual cortex.
Since that would be rather unwieldy, only one tiny area of the retina — called the fovea — provides this kind of resolution. So in order to grant all the interesting features of our environment their moment in the foveal spotlight, we move our eyes around — a lot — in darts that scientists call saccades. Saccades are guided by what we are paying attention to, even though we are often blissfully unaware of them.
This illustration laying out the basic structure of the eye shows where the fovea — where images are rendered in high resolution — is situated. Eye jerks known as saccades allow different parts of a scene to come into the line of sight of the fovea. Scientists refer to this phenomenon as visual masking, and it is thought to be very common in real-life situations where a lot is going on at the same time.
If scientists set up experiments in a way that avoids this visual masking, it reveals that our brains can perceive the less noticeable things. This can be done, Morrone explains, by showing people nothing but very faint and short-lived visual stimuli on an otherwise empty background. Under these conditions, surprising things may happen. Since we do not notice our constant saccades, this suggests that the brain specifically suppresses the signals that reach our retina while a saccadic eye movement is in process.
And indeed, experiments have shown that if something appears during a saccade, we may miss it entirely. This book stretches the confines of your mind and imagination. John L. Five Golden Rules is replete with intriguing information - not only for curious lay people but also for seasoned mathematicians and scientists. Casti has produced a truly stunning survey of mathematics' manifold consequences. Casti Mathematical Mountaintops: The Five Most Famous Problems of All Time "The recent boom in mathematics bestsellers has contributed a great deal towards raising the public profile of the subject.
But such books ignore a significant section of potential readers, namely those who have more of a mathematical background that the general reader but who are not professional mathematicians. Such mathematical enthusiasts have no doubt enjoyed some of the popular books, but would really prefer a more technical treatment. This is exactly what John Casti provides in Mathematical Mountaintops. It is nether a textbook nor a pop math book, rather it is a serious in-depth look at the great problems of mathematics.
Calvin C. Clawson Mathematical Mysteries: The Beauty and Magic of Numbers "Many of the dazzling beauties of higher mathematics are just as accessible to an ordinary untrained spectator as are similar wonders of great literature, visual art, and music. This well-kept secret is finally blown wide open in Calvin Clawson's latest book.
Perseus, pp, Clawson Mathematical Sorcery: Revealing the Secrets of Numbers "Few mathematicians today have the ability to write about math more entertainingly, with greater enthusiasm and clarity, than Calvin Clawson. A splendid introduction to the great ideas of mathematics, their powerful magic, and their intricate, mysterious beauty.
ISBN X. Also available, the Worksheets some say all you need John Horton Conway and Richard K. Guy "A fascinating review of numbers: from Egyptian fractions to surreal numbers; prime numbers, Fibonacci numbers, Catalan numbers, Fermat numbers; from numbers so large they cannot be imagined and barely be named to ruler-and-compass.
Philip J. Davis and Reuben Hersh The Mathematical Experience "A brilliant and engrossing view of the development of mathematics Keith Devlin Life by the Numbers "Most of us think mathematics is about numbers and counting.
That's just the basics, though, and Keith Devlin's companion book to the PBS series "Life by the Numbers" gives examples of the versatility of math as a tool for understanding just about everything. Devlin loves math--he calls it 'one of the greatest creations of mankind' in a chapter entitled 'It's an M World'--and he wants everyone to love it. For a long time I suspected that there was some connection between our ability to do math and our possession of language.
Now, that connection is made dazzlingly clear in a language that even a mathematical ignoramus like myself can understand. A must-read for anyone who has ever wondered what makes us human. Charting the most significant developments that have taken place in mathematics since , Devlin expertly describes these advances for the interested lay person and adroitly summarizes their significance as he leads the reader into the heart of the most interesting mathematical perplexities - from the biggest known prime number to the Shimura-Taniyama conjecture for Fermat's Last Theorem.
Douglas Downing "An algebra text in the form of a fantasy novel, with the story's characters solving problems by using algebra. Douglas Downing Trigonometry the Easy Way "Here's a complete, easy-to-grasp course in trigonometry that takes the form of a fantasy novel. The King of Carmorra and his subjects have many practical problems to solve, and their answers can be found by applying principles of trigonometry.
Readers follow along and learn to solve many different problems that can be reduced to triangular diagrams. They learn the laws of sine and cosine, trigonometric functions and inverse functions, waves, conic sections, polynomial approximation, and much more.
The book is filled with instructive exercises and their solutions, plus illustrative drawings, graphs, and diagrams. This new edition contains updated coverage on using graphing calculators and computer spreadsheets for solving trigonometric problems. It is fascinating thus far 80 pages in. Received it as a late holiday gift from close friends. I think it appeared in Greek in '92 and in English just last year. I'd love to hear what others thought of it and to recommend it to those who like literature and mathematics with some history thrown in.
A mathematical conjecture unsolved for two centuries; a mathematical genius uncle driven mad trying to solve it; an ambiguous relation with a mathematically-minded nephew; and acute human observation all come together in Uncle Petros to make a very funny, tender, charming and, to my mind, irresistible novel. In the tradition of Fermat's Last Theorem and Einstein's Dreams, a novel about mathematical obsession.
Underwood Dudley Mathematical Cranks "On the one hand, mathematics is the great leveler of the sciences. Anyone can do mathematical research, with no equipment but pencil and paper.
On the other hand, mathematics is the only science where something can be proven, irrefutably and for all time, to be impossible. These two ingredients make mathematics one of the most fertile grounds for inspiring crankery. This book is not only entertaining, the broadness of its examples provides a fascinating insight into the mind of cranks.
I couldn't put it down. He devotes each chapter to a principal result of mathematics, such as the solution of the cubic series and the divergence of the harmonic series. Not only does this book tell the stories of the people behind the math, but it also includes discussions and rigorous proofs of the relevant mathematical results". Penguin, William W.
All proofs and equations are introduced through easy-to-follow, step-by-step explanations. Discusses some of the most intriguing mysteries such as Russell's Paradox. Features brief biographies of many great mathematicians including Isaac Newton, Bertrand Russell and Hypatia of Alexandria. Hans Magnus Enzensberger "In 12 dreams, a year-old boy who hates math discovers the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without end.
I approach mathematics as a subject necessary, but always painful, to learn. Dare I say I love this book? Some of the short stories are humorous, some are endearing, some have common characters. All deal with mathematics in one way or another. Fadiman's book succeeded where so many others failed--it interested me. I think, though, that it's very important to present mathematics as the language for interpreting the world that it is Yikes, did I say that?
It is another way to know why your baseball is going to break the window, how to build a spaceship in your back yard, and how to teleport to Argentina in 0 seconds flat. A real tangible benefit to reading this book was learning the derivation of Pythagoras' Theorem. In two pages, this book explained it so clearly to me that I laughed out loud. Sarah Flannery In Code: A Mathematical Journey "British best-seller by and about the year-old who stunned the world by inventing a way of making public-key encryption much more efficient; an engaging, almost playful, book in which the reader is encouraged to spend lots of time working out mathematical puzzles.
George Gamow One Two Three Infinity: Facts and Speculations of Science "This book changed lives around the world. Many of us began our journey into science and mathematics with this book. The reviews at the other book site show how many of us were changed in our young lives by this book.
download it for every child you know. Dover, pp, reprint Martin Gardner Knotted Doughnuts and Other Mathematical Entertainments One of his many collections of his columns from the Scientific Americans, and contains an entirely new set of problems, paradoxes, teasers and tricks.
Investigates mathematical games such as Sim, Chomp, and Race Track; also investigates coincidences that seem to violate the laws of probability. Freeman, pp, any book he wrote on math and science is good! James Gleick Chaos: Making a New Science This new science offers a way of seeing order and pattern where formerly only the random, the erratic, the unpredictable--in short, the chaotic--had been observed.
Chaos is a history of discovery. It chronicles, in the words of the scientists themselves, their conflicts and frustrations, their emotions and moments of revelation. After reading Chaos, you will never look at the world in quite the same way again. Viking Penguin, pp. Larry Gonick "You'll find lucid explanations of probability, distributions, error functions, hypothesis testing, and other basic tools of statistics.
HarperCollins, pp, Denis Guedj Numbers: the Universal Language "Numbers, like letter forms, have a rich and complex history. Who first invented the? How old are they, and how were they developed? How did they come to represent a world of abstract ideas and universal concepts? How do they differ throughout the world today?
Mathematics : A Human Endeavor 3rd
Abrams, pp, , Jan Gullberg Mathematics: From the Birth of Numbers "If a family is to have only one mathematics book on the reference shelf, then this is the one Very well written.
Norton, pp, Nina Hall, editor Exploring Chaos: A guide to the New Science of Disorder In the past few years, a new line of scientific inquiry called "chaos theory" has caught the popular imagination. Young people, in particular, have taken to the complex computer-generated patterns that seem to teeter precariously between order and randomness. A dazzling mathematical object, the Mandelbrot set, now decorates posters, record sleeves, and pop videos as well as the back cover of this book jacket.
Chaos theory, it turns out, has a deeper meaning for our understanding of nature. All sorts of phenomena - from dripping faucets to swinging pendulums, from the unpredictability of the weather to the majestic parade of the planets, from heart rhythms to gold futures - are best perceived through the mathematical prism of chaos theory.
In this collection of incisive, front-line reports, ably edited by Nina Hall for New Scientist magazine, internationally recognized experts such as Ian Stewart, Robert May, and Benoit Mandelbrot draw on the latest research to explain the roots of chaos in modern science and mathematics. Hardy A Mathematician's Apology 'This is a profoundly sad book, the memoir of a man who has reached the end of his ambition, who can no longer effectively practice the art that has consumed him since he was a boy.
But at the same time, it is a joyful celebration of the subject--and a stern lecture to those who would sully it by dilettantism or attempts to make it merely useful.
Hardy declares, "like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way.
Beauty is the first test: there is no permanent place in the world for ugly mathematics. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Goedel. It also looks at the prospects for computers and artificial intelligence AI for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.
Douglas R. After a few years of pleasure he was replaced by someone else who among other things wrote on the joys of Rubik's cube and I found myself wasting weeks of time and filling notebooks with my quest to explore and solve the cube. That columnist was Douglas Hofstadter, who brought the same skill at sharing his enthusiasm for his topic that created the amazing, mind shattering 'Goedel, Escher, Bach'.
His column, that occupied the same place as "Mathematical Games", was called "Metamagical Themas" looking closely at those two names will tell you a lot about Douglas Hofstadter and lasted for 13 issues. This book is a compilation of those columns, each with a new endnote by Hofstadter and some letters received by the magazine and his reply.
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There is also lots of history in it. The same author has a history- of -math book, with wonderful illustrations, that I often give to children and arts friends.
It really inspired me as a kid. It may be a tale of a dot and a line, but it means so much more. It says the age is from but I think people of all ages will enjoy the story of the dot and the line.
Five stars, try six stars. It's great! Starting with the great invention of zero as a place holder, Kaplan takes you through the use of zero in algebra, and in calculus, through the importance of the null set. His book closes with that unthinkable question, 'Why is there something rather than nothing? My students enjoyed the moral lessons that it taught. The stories had a set of mathematical problems at the end for the students to work. Many of the problems could be changed to different grade levels.
Margaret Kenda and Phyllis S.
Mathematics : A Human Endeavor 3rd
Williams Over math puzzles, games and designs for kids, also available as a kit with a protractor, various triangles, a ruler, compass, and other essential tools Ages 8 to 12 Barron's, pp, An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field.
Every real number is surrounded by a host of new numbers that lie closer to it than any other "real" value does. The system is truly 'surreal. However, this isn't a textbook - it's a collection of 3 dialogues Lang gave in Paris in the 80s.
Certainly the discussions are very interesting.
The interactions between Lang and the audience, comprising mostly 'ordinary' people but also high-school and college students, set this book apart from a textbook. Of course, with this come problems - Lang only skims over the material and much of what he says is not supported by proof. Springer-Verlag, pp, Lawrence S. The problems in the book range from easy to challenging some just tedious that will help and prepare students for tests and other standardized exams.
What I really like about this book is that it lays down all of the concepts in a very clear way without using too many words. The book should be used more as a supplement, a reminder, and a guide to help you solve problems.
It's not the most colorful and fun book to read, but it is worth all your money if you are looking for a good outlined approach to the subject. They were the basis of the slide rule that was the totemic wand of the trade, listed in huge books consulted in every library. Then hand-held calculators arrived, and within a few years slide rules were museum pieces.If we saw all those movements as we made them, our view of the world would be a blur of constant motion.
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But such books ignore a significant section of potential readers, namely those who have more of a mathematical background that the general reader but who are not professional mathematicians.
Ecco "This is an extremely entertaining book written in a lively style. Features brief biographies of many great mathematicians including Isaac Newton, Bertrand Russell and Hypatia of Alexandria. Jack , There is no real reason why, with patience, an ordinary person should not understand what mathematicians do, why they do it, and what mathematics is.