What do you think?
Rate this book
Mathematics for the Nonmathematician
Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen.
Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.
In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.
Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.
In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.
641 pages, Paperback
First published May 1, 1967
494 people are currently reading
3162 people want to read
About the author
Morris Kline
77 books104 followersMorris Kline was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 30 of 51 reviews
January 30, 2020
I enjoyed getting the survey of math. I've been kind of trying to get a better understanding of how different branches of math fit together and I think walking through the history of the development of math was helpful. I know other people have noted that the book is a little western-centric in their reviews but I mean it's written by some old white man in the 60's. I would just take everything he says, especially about the history of math, with a grain of salt. I wonder if there's some updated book I could read on math that surveys math and the different branches. I feel like a lot of what was covered in the book was stuff I learned already in school, especially high school. I do think it's worth a read for people who don't know much math and I think the exercises are pretty basic/accessible. Math really doesn't change much especially something like Euclidean Geometry. A 3.5 stars from me.
April 5, 2015
For a long time, I’ve been searching for a book exactly like this one. Somewhat embarrassed by my ignorance of math, I wanted to relearn what I had forgotten in college, and perhaps go further. But I didn’t want to simply learn math; I wanted to learn its history, how it shaped and was shaped by the cultures in which it grew. This is a tall order, requiring both historical and mathematical understanding; but Kline is equal (or, perhaps, almost equal) to the task.
Before I get into the positive qualities of this book, I should note its flaws. As another reviewer pointed out, Kline’s beginning chapter on history is inept, even offensive. He heaps praise upon praise when describing the accomplishments of the Greeks, and dismisses the contributions of the Arabs, Babylonians, Egyptians, and Indians with a wave of the hand. He even relays the story of the Muslims destroying the Library of Alexandria, which historians have seen fit to doubt as far back as Edward Gibbon. For Kline, mathematics made a brilliant beginning with the Greeks, and then stayed more or less the same until the Enlightenment. The extent to which that is true, I know not; but it at least seems unlikely to me.
Thankfully, the book gets markedly better after that. (One shouldn’t judge a book by the cover, or even the first chapter, apparently.) For, whatever Kline lacks as a historian, he makes up as a pedagogue. Kline doesn’t simply move from arithmetic to geometry to algebra to trigonometry, but instead situates every subject within a specific historical period and practical problem. For example, he teaches trigonometry by using the kind of problems that the Alexandrian Greeks, such as Ptolemy and Eratosthenes, were tackling: the distance from the earth to the moon, the radius of the earth, the establishment of longitude and latitude. Every chapter comes with biographical sketches of the major thinkers involved, as well as some practical problem that the mathematical theory would solve.
Following this procedure, Kline manages to take the most abstract of all abstract subjects, and to make it exquisitely human. In school, we are taught trigonometry by showing us how to plug numbers into a calculator. Kline shows us that trigonometry allows us to chart the earth, and to map the skies. We encounter Newton measuring the refraction of light, and Galileo plotting the course of cannonballs. We learn how sinusoidal motion allows us to quantify time, and how the Renaissance painters invented projective geometry in their attempt to create realistic perspective.
In sum, Kline shows mathematics for what it is: a tremendously exciting intellectual endeavor—one that has expanded our knowledge of the universe immeasurably. Math is not born of the dreams of philosophers (at least, not exclusively), but has been, and continues to be, integral to the solution of everyday problems. It’s curious that something only accessible to the mind allows us to make sense of our senses. In short, Kline has given me the greatest gift a teacher can give—not knowledge, but curiosity.
Before I get into the positive qualities of this book, I should note its flaws. As another reviewer pointed out, Kline’s beginning chapter on history is inept, even offensive. He heaps praise upon praise when describing the accomplishments of the Greeks, and dismisses the contributions of the Arabs, Babylonians, Egyptians, and Indians with a wave of the hand. He even relays the story of the Muslims destroying the Library of Alexandria, which historians have seen fit to doubt as far back as Edward Gibbon. For Kline, mathematics made a brilliant beginning with the Greeks, and then stayed more or less the same until the Enlightenment. The extent to which that is true, I know not; but it at least seems unlikely to me.
Thankfully, the book gets markedly better after that. (One shouldn’t judge a book by the cover, or even the first chapter, apparently.) For, whatever Kline lacks as a historian, he makes up as a pedagogue. Kline doesn’t simply move from arithmetic to geometry to algebra to trigonometry, but instead situates every subject within a specific historical period and practical problem. For example, he teaches trigonometry by using the kind of problems that the Alexandrian Greeks, such as Ptolemy and Eratosthenes, were tackling: the distance from the earth to the moon, the radius of the earth, the establishment of longitude and latitude. Every chapter comes with biographical sketches of the major thinkers involved, as well as some practical problem that the mathematical theory would solve.
Following this procedure, Kline manages to take the most abstract of all abstract subjects, and to make it exquisitely human. In school, we are taught trigonometry by showing us how to plug numbers into a calculator. Kline shows us that trigonometry allows us to chart the earth, and to map the skies. We encounter Newton measuring the refraction of light, and Galileo plotting the course of cannonballs. We learn how sinusoidal motion allows us to quantify time, and how the Renaissance painters invented projective geometry in their attempt to create realistic perspective.
In sum, Kline shows mathematics for what it is: a tremendously exciting intellectual endeavor—one that has expanded our knowledge of the universe immeasurably. Math is not born of the dreams of philosophers (at least, not exclusively), but has been, and continues to be, integral to the solution of everyday problems. It’s curious that something only accessible to the mind allows us to make sense of our senses. In short, Kline has given me the greatest gift a teacher can give—not knowledge, but curiosity.
October 27, 2016
My first review in English and I'm sure it's full of errors!
There are two main flaws in this book. History of mathematics and philosophy of mathematics. Other reviewers have correctly mentioned Kline's unfair views on history. Throughout the book it was clear that Kline considers mathematics merely a mental construction. Although I don't find it plausible, but it's acceptable that a mathematician have such approach towards ontological issue since (at least as far as I understand) the topic is very well open. So far I was OK, but in last chapter while discussing the structure of mathematics he limits realism in ontology to ancient Greeks and only adds: "This view of mathematics was undoubtedly the dominant one until well into the eighteenth century and is held by some even today". Then he starts defending his view that mathematics is "entirely a human creation" and he concludes: "Only the relatively universal acceptance of mathematics [...] may lure us into getting that subject an objective existence". I find it totally unacceptable how he covers this topic of high importance and complexity especially in a book that has been written to non mathematicians. His inaccuracy and unfairness on history is evident even if reader knows nothing of mathematics' history but the flaw on philosophic issue is very well hidden!
Beyond these flaws, it's really a good book for someone who has been away from mathematics after high school or college. Concepts are beautifully explained with historic approach and it gives a clear picture of how mathematics has developed.
There are two main flaws in this book. History of mathematics and philosophy of mathematics. Other reviewers have correctly mentioned Kline's unfair views on history. Throughout the book it was clear that Kline considers mathematics merely a mental construction. Although I don't find it plausible, but it's acceptable that a mathematician have such approach towards ontological issue since (at least as far as I understand) the topic is very well open. So far I was OK, but in last chapter while discussing the structure of mathematics he limits realism in ontology to ancient Greeks and only adds: "This view of mathematics was undoubtedly the dominant one until well into the eighteenth century and is held by some even today". Then he starts defending his view that mathematics is "entirely a human creation" and he concludes: "Only the relatively universal acceptance of mathematics [...] may lure us into getting that subject an objective existence". I find it totally unacceptable how he covers this topic of high importance and complexity especially in a book that has been written to non mathematicians. His inaccuracy and unfairness on history is evident even if reader knows nothing of mathematics' history but the flaw on philosophic issue is very well hidden!
Beyond these flaws, it's really a good book for someone who has been away from mathematics after high school or college. Concepts are beautifully explained with historic approach and it gives a clear picture of how mathematics has developed.
August 31, 2010
Mr. Kline and his book are a remnant of a happily bygone era. I can only assume that the good people at Dover books who consent to repackage and sell this chauvinistic relic from 1967 must be equally unenlightened, and greedy into the mix.
I gave up on this thing after the 'historical overview' bit (chapters 1-4). I'm just not content with a history of numbers that spends 20 pages on the drama of the Pythagoreans and irrational numbers, and then gives us this on the invention of negative numbers:
"Perhaps because the Hindus were in debt more often than not, it occurred to them that it would also be useful to have numbers which represent the amount of money one owes."
I mean, come on. Up yours, Morris.
I gave up on this thing after the 'historical overview' bit (chapters 1-4). I'm just not content with a history of numbers that spends 20 pages on the drama of the Pythagoreans and irrational numbers, and then gives us this on the invention of negative numbers:
"Perhaps because the Hindus were in debt more often than not, it occurred to them that it would also be useful to have numbers which represent the amount of money one owes."
I mean, come on. Up yours, Morris.
April 27, 2016
Someone asked me to compile a list of the 10 most influential books I had ever read. This ranked near the top. I read it for the first time in my early twenties and it (among other things) began the process of turning my life around after half a decade of stupid choices.
Stated quickly: There is more to mathematics than the memorization of arithmetic and the mechanical transformations of algebra. They are to real math what pronunciation and grammar are to rhetoric, composition, and poetry (That is: critical prerequisites, but beside the point.)
Stated quickly: There is more to mathematics than the memorization of arithmetic and the mechanical transformations of algebra. They are to real math what pronunciation and grammar are to rhetoric, composition, and poetry (That is: critical prerequisites, but beside the point.)
June 30, 2019
We are in 1967, Kline is trying to thrill us, nonmathematicians, with mathematics. Bravo! He dares to go through the centuries explaining how the foundations of mathematics have been evolving. Of course, his accounts on history and philosophy throughout this book are naturally biased because he is madly in love with mathematics. However, he makes mathematics very interesting. By showing it as a growing body of knowledge defining, in precise terms, the chain of ideas that have been pushing civilization forward. Incredible. Here goes my favorite example. Non-Euclidean geometry set mathematicians FREER because it showed that mathematics is NOT a body of truths. It is a body of consistent reasoning being slowly developed within the rise and fall of civilizations. And the main source of mathematical ideas is nature herself.
June 10, 2015
This book isn't just about mathematics. It's about history, science, philosophy, the arts, and astronomy. One of my best reads ever. Reread many times.
January 31, 2021
Fairly nice popular tour of some of the more famous concepts of mathematics I read this as a physics student in the late 1990s. Good stuff from what I recall.
August 3, 2015
Many years ago, I hated math. Let be clear: this was a thorough loathing of the subject. Also many years ago, at one particular crossroads in my academic and professional paths, I realized I needed to get back into mathematics--and move well into calculus (at least). I walked into my local bookstore and saw this book. I bought it, and within minutes of having purchased it, I found I couldn't stop reading it.
I walked the entire way home from the bookstore (never mind I had driven to get there), reading this book the whole way home. Since that time, I have read this book no fewer than a dozen times, and my first copy remains my most treasured book of all. I have bought subsequent copies to lend and gift to others who don't care for math, but find themselves needing more strength in it.
The hook for me is the (surprisingly) engaging history of mathematics and of the (unsurprising) wonderfully odd people who contributed so much to both the art and science of mathematics. There is no question that the book is densely packed with a good deal of math (my paperback copy has around 550 pages of it), but the writing style is clear and non-technical, and the graphs and figures are very helpful and informative.
As I write this review, I'm thinking it may just be time for another read through.
I walked the entire way home from the bookstore (never mind I had driven to get there), reading this book the whole way home. Since that time, I have read this book no fewer than a dozen times, and my first copy remains my most treasured book of all. I have bought subsequent copies to lend and gift to others who don't care for math, but find themselves needing more strength in it.
The hook for me is the (surprisingly) engaging history of mathematics and of the (unsurprising) wonderfully odd people who contributed so much to both the art and science of mathematics. There is no question that the book is densely packed with a good deal of math (my paperback copy has around 550 pages of it), but the writing style is clear and non-technical, and the graphs and figures are very helpful and informative.
As I write this review, I'm thinking it may just be time for another read through.
March 8, 2007
So you really want to feel stupid? Read this and have all the memories of 8th grade geometry come back to you. Why is it that I can remember every detail of Josh Engels' hair, but I can't remember how to do a proof? The mind reels.
March 17, 2022
Part textbook, part history, part survey of the field, if the layperson is willing to put the work in, this book can give you a very solid, broad foundation in mathematical thinking and concepts. But even if you skip over the review exercises, you can enjoy a fascinating story of how math has progressed over the millennia and been applied to the world.
November 23, 2017
As noted in a lot of comments, the first few chapters vary between heavily biased or outright blatantly Eurocentric. Watching Marcus Du Sautoy's The Story of Math series will be far more effective in getting a sense of the history of Mathematics.
That said. This is a wonderful work, Kline's explanation of very abstract concepts in a very clear way makes it well worth reading. His anticipation of questions that might arise when encountering a new subject in Mathematics is always on target. Much of what is infuriatingly missing in classic college textbooks is addressed here. Who came up with this concept, why is it important, how does it relate to other fields, how does it relate to the real world?
Kline walk as perfect line between just enough complexity and details about a subject to keep the reader engaged, while adding in a concrete example just at the right time. He balances the theoretical and practical almost effortlessly.
He focuses on the understanding of mathematics, not just the functional aspect of carrying out.
That said. This is a wonderful work, Kline's explanation of very abstract concepts in a very clear way makes it well worth reading. His anticipation of questions that might arise when encountering a new subject in Mathematics is always on target. Much of what is infuriatingly missing in classic college textbooks is addressed here. Who came up with this concept, why is it important, how does it relate to other fields, how does it relate to the real world?
Kline walk as perfect line between just enough complexity and details about a subject to keep the reader engaged, while adding in a concrete example just at the right time. He balances the theoretical and practical almost effortlessly.
He focuses on the understanding of mathematics, not just the functional aspect of carrying out.
December 24, 2017
While mathematics has recently risen to prominence as the "M" in STEM, mathematical literacy has often been neglected in education and society at large. Too often, people are introduced to mathematics via dry technical books with a positivist focus on numerical operations. They gain little context for quantitative reasoning and the transformative, civilizing force that mathematics has been throughout the centuries. Consequently, a majority of people--myself included--finish their formal education with little appreciation of the subject, its significance, its power, and its allure. If our education system did a better job telling the (hi)story of math, we'd have a society more equipped and enthusiastic for reason, problem solving, and critical thinking.
Kline provides the missing context to math that I wish I'd had growing up. Like Bertrand Russell's eminently readable History of Western Philosophy, Kline shows the human side of his subject, recounting the mathematical problems societies have struggled with over the centuries and the ingenious ways these problems have been solved. We see mathematics as part of the revolutionary rational search for truth in ancient Greece; math's instrumentality to profound questions in cosmology in Hellenistic Greece, the Renaissance, and beyond; how mathematical laws of nature helped to usher in the scientific revolution; and how math opened the door to the study of social sciences with statistics and probability. Maybe the most interesting section is the discussion of non-Euclidean geometry, its discovery, and its implications for society and truth.
Along the way, Kline introduces the many fascinating personalities behind the ingenious mathematics ideas: Galileo, Descartes, Newton, Cardan, Pascal, Fermat, Gauss, and many more.
The book never gets bogged down in technicalities, though for the non-mathematician, the math at times gets complicated very fast. This wasn't at all an impediment to my overall enjoyment of the book.
Kline is an expert teacher with a comprehensive grasp of and contagious enthusiasm for his subject. I've added a few more of his books to my list.
Kline provides the missing context to math that I wish I'd had growing up. Like Bertrand Russell's eminently readable History of Western Philosophy, Kline shows the human side of his subject, recounting the mathematical problems societies have struggled with over the centuries and the ingenious ways these problems have been solved. We see mathematics as part of the revolutionary rational search for truth in ancient Greece; math's instrumentality to profound questions in cosmology in Hellenistic Greece, the Renaissance, and beyond; how mathematical laws of nature helped to usher in the scientific revolution; and how math opened the door to the study of social sciences with statistics and probability. Maybe the most interesting section is the discussion of non-Euclidean geometry, its discovery, and its implications for society and truth.
Along the way, Kline introduces the many fascinating personalities behind the ingenious mathematics ideas: Galileo, Descartes, Newton, Cardan, Pascal, Fermat, Gauss, and many more.
The book never gets bogged down in technicalities, though for the non-mathematician, the math at times gets complicated very fast. This wasn't at all an impediment to my overall enjoyment of the book.
Kline is an expert teacher with a comprehensive grasp of and contagious enthusiasm for his subject. I've added a few more of his books to my list.
December 23, 2022
Ha-ha fooled you
If you were expecting math theory without the math or an opportunity to replace algebra with arithmetic tricks then you will be sorely disappointed.
Like his earlier book "Mathematics: a cultural approach) this is a sneaky way to introduce liberal arts students to the world of mathematics by showing them a practical approach. Don't by any means mistake this for what it is not; it is not a way to cut corners as by the time you finish this book you will be introduced to just about every phase of mathematics and geometry.
Although it can be a fun approach, you will need to be prepared to learn some stuff about things such as the theory of gravity.
It starts off with the historical orientation to math and why math is important.
To give you an idea of the simplicity of this book here is a sample of the contents:
A historical orientation
Logic and mathematics
Number: the fundamental concept
Algebra, the higher arithmetic
The nature and use of Euclidean geometry
Charting the earth and the heavens
The mathematical order of nature
The awakening of Europe
Mathematics and painting in the Renaissance
Projective geometry
Coordinate geometry
The simplest formulas in action
Parametric equations and curvilinear motion
The application of formulas to gravitation
The differential calculus
The integral calculus
Trigonometric functions and oscillatory motion
The trigonometric analysis of musical sounds
Non-Euclidean geometries and their significance
Arithmetic’s and their algebras
The statistical approach to the social and biological sciences
The theory of probability
Nature and the values of mathematics
As you can see you're in for a lot of fun especially if you liked mathematics for non-mathematicians. Ha!
If you were expecting math theory without the math or an opportunity to replace algebra with arithmetic tricks then you will be sorely disappointed.
Like his earlier book "Mathematics: a cultural approach) this is a sneaky way to introduce liberal arts students to the world of mathematics by showing them a practical approach. Don't by any means mistake this for what it is not; it is not a way to cut corners as by the time you finish this book you will be introduced to just about every phase of mathematics and geometry.
Although it can be a fun approach, you will need to be prepared to learn some stuff about things such as the theory of gravity.
It starts off with the historical orientation to math and why math is important.
To give you an idea of the simplicity of this book here is a sample of the contents:
A historical orientation
Logic and mathematics
Number: the fundamental concept
Algebra, the higher arithmetic
The nature and use of Euclidean geometry
Charting the earth and the heavens
The mathematical order of nature
The awakening of Europe
Mathematics and painting in the Renaissance
Projective geometry
Coordinate geometry
The simplest formulas in action
Parametric equations and curvilinear motion
The application of formulas to gravitation
The differential calculus
The integral calculus
Trigonometric functions and oscillatory motion
The trigonometric analysis of musical sounds
Non-Euclidean geometries and their significance
Arithmetic’s and their algebras
The statistical approach to the social and biological sciences
The theory of probability
Nature and the values of mathematics
As you can see you're in for a lot of fun especially if you liked mathematics for non-mathematicians. Ha!
April 18, 2008
My math skills are underdeveloped. I'll freely admit that. I am seeking to remedy that as quickly as I can.
To that end, this book was a fantastic help for me. It really should be a standard text in at least college, if not in high school. The fun part of this wasn't just having math explained clearly, but also the history of the math. Kline has
brief biographies of the major players behind the ideas, where the ideas came from, where they led, and different aspects of the whys and wherefores.
It's a math book that is also a history of math.
It is a very accessible book, Kline presents the math clearly and neatly, with plenty of practice problems to reinforce the principles (answers are in the back of the book, thankfully!).
If you are looking to brush up on rusty math skills, or have a strange yearning to get a quick overview of math history, this book is a great choice.
I loved it, but I know that there is something wrong with me ;)
To that end, this book was a fantastic help for me. It really should be a standard text in at least college, if not in high school. The fun part of this wasn't just having math explained clearly, but also the history of the math. Kline has
brief biographies of the major players behind the ideas, where the ideas came from, where they led, and different aspects of the whys and wherefores.
It's a math book that is also a history of math.
It is a very accessible book, Kline presents the math clearly and neatly, with plenty of practice problems to reinforce the principles (answers are in the back of the book, thankfully!).
If you are looking to brush up on rusty math skills, or have a strange yearning to get a quick overview of math history, this book is a great choice.
I loved it, but I know that there is something wrong with me ;)
August 17, 2016
This book was pretty good. It covers the history of mathematics and how it is made manifest in the liberal arts. It starts with the Babylonians and the Egyptians, goes to the Arabs and then the Western Europeans and so on. It has some problems in it that you can do, hence my calling it a Textbook. The problems aren't really serious or tough, and since it was written in the 1960s or something, it still has trigonometric tables, but not logarithms. I don't know why. Maybe because they figured you could get the answer yourself.
In any case, the math wasn't hard, and the history was interesting, but I had already read a book on the History of Mathematics so it wasn't really new to me. However, it was well done so it gets a 4 out of 5.
In any case, the math wasn't hard, and the history was interesting, but I had already read a book on the History of Mathematics so it wasn't really new to me. However, it was well done so it gets a 4 out of 5.
May 23, 2008
This book simplifies complex mathematical topics. This is precisely what a good math teacher will do for their students. This book gives an overview regarding where some of the math which has been studied comes from. It also explores subjects ranging from basic math to Calculus and gives problems and solutions in a simple, easy to understand, practical way.
December 14, 2007
Wish I had read this in grade school. It was *that* easy to understand...
February 22, 2008
Interesting insight into the history of math.
September 25, 2008
A good, if dated (and very euro-centric) history of mathematics. Can be read relatively easily without knowing too much mathematics in advance -- by a late high-school or college level reader.
Want to read
June 24, 2009I've been reading this book on and off for years. This books contains things that I have never been exposed to, and it contains things which I, sadly, did not retain from any of my schooling.
Want to read
March 29, 2009Starting my business school pre-work. I'm enjoying so far that this provides a history of mathemtics and is written for a liberal arts major.
August 20, 2012
One of the most important books of my life (so far)
July 4, 2024
This book is intended as a survey course in mathematics for liberal arts students. There is accordingly a special emphasis on the history of the development of mathematical thought and applications to art, music, and especially science. The goal is to make learning math feel relevant to students pursuing studies in non-math fields, but the text is equally well suited as a review course for people who maybe took a lot of math classes earlier back in school but maintain a general interest in the subject. Chapters 1 and 2 serve as an introduction and review of the historical contributions of different civilizations to mathematics. Chapter 3 is about the logic and definitions pertaining to mathematical axioms, theorems, and proofs. Chapter 4 covers arithmetic, Chapter 5 algebra, Chapter 6 Euclidean geometry, and Chapter 7 basic trigonometry. There is special (perhaps a little too much) emphasis on applications of trigonometry to calculations involving the Earth, moon, and sun - but these can be skipped over if not interested. Chapters 8 and 9 are again historical, covering the development of mathematics in Ancient Greece and the Renaissance. Chapter 10 is one of the more interesting historical asides focusing on the development of linear perspective in art. Chapter 11 on projective geometry was one of the more difficult for me. Much of this math was not part of the geometry curriculum I had in school. Chapter 12 on coordinate geometry is mostly about graphing curves and introduces new concepts like slope and equations for conic sections. Chapter 13 introduces functions and specifically the mathematics of projectile motion. One annoyance in this and many of the other chapters is that imperial/US units are used rather than the more common metric/SI forms of the equations typically taught in school. Chapter 14 covers parametric equations, again with applications to projectile motion. Chapter 15 is a deep dive into Newtonian classical mechanics. The two calculus chapters are fairly basic. The concept of limits is introduced along with the fundamental idea behind derivatives and indefinite and definite integrals. The basic method of performing these operations is described, but obviously a dedicated calculus course is necessary to really understand the subject. Chapter 18 explains how to use trigonometric functions to understand periodic/oscillatory motion, with Chapter 19 looking specifically at applying these mathematical ideas to sound waves and music. Chapters 20 and 21 on non-Euclidean geometry and number theory are more advanced and like the chapter on projective geometry were not concepts I had covered in my high school and limited college math curriculum. Chapters 22 and 23 on statistics and probability are like the calculus chapters fairly basic. Measures of center, standard deviation, sampling concepts, and basic probability with applications to normal distributions are covered. For anyone with college-level stats or science coursework this will be completely review. The final chapter is about the philosophy of mathematics with a rather controversial (I think) conclusion that math is a human creation rather than a collection of discovered truths about the universe.
March 27, 2023
Don't get me wrong, this is a pretty good book if you want to understand the basics on how mathematics works, its development and some of its core ideas and applications.
I think, as far as concepts, Kline is solid, they are laid out in a very intuitive way, yet not trivial.
Applications are well fitted in, like measuring the dimensions and the distances of the earth from other planets using just basic trigonometry to resemble the methods of ancient astronomers, or calculating trajectories of projectile of cannons, ecc.. Most of this application are context related in respect to the discovery of the mathematical principles, which is good.
The downside is the cultural and historical part: the bias toward greeks and western culture in general is annoying but is somewhat forgivable, given the time the book was published, but in general the historical recostructions, the cultural, sociological and biographical parts are a bit weak and unispiring, something i wasn't expecting from a book intended for the students of liberal arts.
Maybe i picked up the wrong book from the author, but i feel it is a 3,5/5 for me.
I think, as far as concepts, Kline is solid, they are laid out in a very intuitive way, yet not trivial.
Applications are well fitted in, like measuring the dimensions and the distances of the earth from other planets using just basic trigonometry to resemble the methods of ancient astronomers, or calculating trajectories of projectile of cannons, ecc.. Most of this application are context related in respect to the discovery of the mathematical principles, which is good.
The downside is the cultural and historical part: the bias toward greeks and western culture in general is annoying but is somewhat forgivable, given the time the book was published, but in general the historical recostructions, the cultural, sociological and biographical parts are a bit weak and unispiring, something i wasn't expecting from a book intended for the students of liberal arts.
Maybe i picked up the wrong book from the author, but i feel it is a 3,5/5 for me.
May 3, 2022
Prof Morris Kline released his book “Mathematics for the Non-mathematician” in 1967. It was rereleased by Dover Publications in 1985. At the time of publication Morris Kline was Professor Emeritus of Mathematics at New York University. His exceptional book presents the historical development of mathematical principles, formula construction techniques, and cultural impacts of mathematics from Greco-Roman periods to the Age of Enlightenment into our present day. He explains mathematical logic in the context of equations, curvilinear motion, trigonometries, calculus, advance forms of statistical methods, and probability constructs, to mention a few. His book also discusses the theory of relativity and non-Euclidean geometry. I enjoyed reading the book very much. (P)
August 17, 2020
I got this book after reading some good reviews. But it delivers what it promises: it's a practical approach to maths for those who have not studied this science much but have an interest in it. I have a degree in mathematics and I'm a math teacher ata a high school, and in this book I have not learned anything nor have I come across any interesting approach or explanation. My fault, I guess.
Nevertheless, the book it's OK, and it could be recommended for people with a lower background in mathematics, looking for a complete but not very deep guide to enter the most important branches of mathematics.
Nevertheless, the book it's OK, and it could be recommended for people with a lower background in mathematics, looking for a complete but not very deep guide to enter the most important branches of mathematics.
May 1, 2023
Most surprising page-turner! Perfect for my continued search for providing integration within my homeschool curriculum. Places mathematics within its historical contexts, showing its inception in ancient cultures as a practical tool and its elevation to its abstract form by the Greeks. Also I was surprised to finally find (in a math book!) the clearest, most succinct explanation of why western civilization was borne mainly from the Greeks. Very well written and accessible for this non-mathematician! I know my teenagers will like this too.
August 29, 2021
Mayyyyybe a better title could be, Mathematics for the Nonmathematician Who Is Reasonably Comfortable With Mathematics.
Doubles almost as a history of mathematics, up to the end of the 18th century, with extra material on statistics and probability. Kline's approach, which I approve of, is always to try to combine the actual math with its development and the problems that people were trying to solve at the time.
Doubles almost as a history of mathematics, up to the end of the 18th century, with extra material on statistics and probability. Kline's approach, which I approve of, is always to try to combine the actual math with its development and the problems that people were trying to solve at the time.
April 2, 2023
I'll say this, I gave it my best shot. Granted, one learns by doing, and unless one can solve math problems you better not think you understand math. I did all the problems up to page 168, at which point I realized I won't finish before I'm dead. However, to Kline's great credit, his book can be read without solving the problems because he writes about math generally, its history, utility, applications, etc. This I appreciated very much.
Displaying 1 - 30 of 51 reviews