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8 people found this helpful

ByNumber 16on 4 July 2010

This is the book on mathematics I have been hoping to find for many years.

For a non-mathematician who wants to get a good functioning overview and practical understanding of the whole subject this book is perfect. The book takes a historical and philosophical approach taking us from the Egyptians, Babylonians, Greeks, Hindus and Arabs up to the modern era and Einstein. However, despite all of the fascinating background historical information, this is not a history of mathematics, it is a real mathematics book and is full of clear examples of problems and additional exercises (with answers).

The book progresses from logic, to arithmetic, algebra, geometry, trigonometry, calculus, statistics, probability, and non-Euclidian geometries.

The book is also rich on its discussions of mathematical applications and goes into some depth regarding astronomy, painting and perspective, physical laws of motion and gravity, and music.

Morris Kline was Emeritus Professor of Math and New York University. The book was first published in 1967 and is a real classic.

For a non-mathematician who wants to get a good functioning overview and practical understanding of the whole subject this book is perfect. The book takes a historical and philosophical approach taking us from the Egyptians, Babylonians, Greeks, Hindus and Arabs up to the modern era and Einstein. However, despite all of the fascinating background historical information, this is not a history of mathematics, it is a real mathematics book and is full of clear examples of problems and additional exercises (with answers).

The book progresses from logic, to arithmetic, algebra, geometry, trigonometry, calculus, statistics, probability, and non-Euclidian geometries.

The book is also rich on its discussions of mathematical applications and goes into some depth regarding astronomy, painting and perspective, physical laws of motion and gravity, and music.

Morris Kline was Emeritus Professor of Math and New York University. The book was first published in 1967 and is a real classic.

6 people found this helpful

Byanti-thesison 14 February 2014

Just a quick note to warn readers of a few of the inaccuracies and untruths present in this book.

Consider these:

"The final destruction of Alexandria in 640 AD was the deed of the Arabs". Wrong! This view has been widely discredited. What is particularly irritating is that even at the time writing (1960s) Mr. Kline would or should have known that this opinion - and it is merely that - was contentious, but this doesn't prevent him from presenting it as an uncomplicated 'fact'.

"...the Arabs contributed little that was original in Mathematics..." Again wrong. The Arabs made many significant original contributions; Algebra and algorithm should have been clues as to but a few of their contributions, but Mr Kline sees fit to pass by these.

And what can one make of this gem:

"the Arabs manfully [?] resisted the lures of exact reasoning in their contributions" - Pure nonsense!

Or what about this piece of work:

"The Arabs, who suddenly appeared on the scene of history in the role of destroyers" - Can you hear the crackle of hate coming off the page? The caliber of the man is clearly shown in this statement.

Mr Kline is equally dismissive of the Indian and Chinese contributions - though he reserves most of his scorn for the 'Arabs' - and describes the Franks and Germanic peoples of early Europe as "primitive indeed". I could go on giving examples of this crude, hostile, and patronizing attitude towards anything that's not ancient Greek and modern European; the book is replete with unsubstantiated, high-handed, pompous assertions.

I would encourage readers to be very wary of the book's historical and cultural aspects - which are integral to its treatment of mathematics - because some of it is simply wrong, vacuous, opinionated, and in places is either verging on the bigoted or has tipped into outright bigotry. Apart from the actual mathematics, the book is now very outdated. It's a shame that for a 'man of reason' Mr Kline indulges in such shallow and frankly speaking, ignorant assertions - dressed up as 'fact' - that are more worthy of a hack journalist.

Consider these:

"The final destruction of Alexandria in 640 AD was the deed of the Arabs". Wrong! This view has been widely discredited. What is particularly irritating is that even at the time writing (1960s) Mr. Kline would or should have known that this opinion - and it is merely that - was contentious, but this doesn't prevent him from presenting it as an uncomplicated 'fact'.

"...the Arabs contributed little that was original in Mathematics..." Again wrong. The Arabs made many significant original contributions; Algebra and algorithm should have been clues as to but a few of their contributions, but Mr Kline sees fit to pass by these.

And what can one make of this gem:

"the Arabs manfully [?] resisted the lures of exact reasoning in their contributions" - Pure nonsense!

Or what about this piece of work:

"The Arabs, who suddenly appeared on the scene of history in the role of destroyers" - Can you hear the crackle of hate coming off the page? The caliber of the man is clearly shown in this statement.

Mr Kline is equally dismissive of the Indian and Chinese contributions - though he reserves most of his scorn for the 'Arabs' - and describes the Franks and Germanic peoples of early Europe as "primitive indeed". I could go on giving examples of this crude, hostile, and patronizing attitude towards anything that's not ancient Greek and modern European; the book is replete with unsubstantiated, high-handed, pompous assertions.

I would encourage readers to be very wary of the book's historical and cultural aspects - which are integral to its treatment of mathematics - because some of it is simply wrong, vacuous, opinionated, and in places is either verging on the bigoted or has tipped into outright bigotry. Apart from the actual mathematics, the book is now very outdated. It's a shame that for a 'man of reason' Mr Kline indulges in such shallow and frankly speaking, ignorant assertions - dressed up as 'fact' - that are more worthy of a hack journalist.

ByNumber 16on 4 July 2010

This is the book on mathematics I have been hoping to find for many years.

For a non-mathematician who wants to get a good functioning overview and practical understanding of the whole subject this book is perfect. The book takes a historical and philosophical approach taking us from the Egyptians, Babylonians, Greeks, Hindus and Arabs up to the modern era and Einstein. However, despite all of the fascinating background historical information, this is not a history of mathematics, it is a real mathematics book and is full of clear examples of problems and additional exercises (with answers).

The book progresses from logic, to arithmetic, algebra, geometry, trigonometry, calculus, statistics, probability, and non-Euclidian geometries.

The book is also rich on its discussions of mathematical applications and goes into some depth regarding astronomy, painting and perspective, physical laws of motion and gravity, and music.

Morris Kline was Emeritus Professor of Math and New York University. The book was first published in 1967 and is a real classic.

For a non-mathematician who wants to get a good functioning overview and practical understanding of the whole subject this book is perfect. The book takes a historical and philosophical approach taking us from the Egyptians, Babylonians, Greeks, Hindus and Arabs up to the modern era and Einstein. However, despite all of the fascinating background historical information, this is not a history of mathematics, it is a real mathematics book and is full of clear examples of problems and additional exercises (with answers).

The book progresses from logic, to arithmetic, algebra, geometry, trigonometry, calculus, statistics, probability, and non-Euclidian geometries.

The book is also rich on its discussions of mathematical applications and goes into some depth regarding astronomy, painting and perspective, physical laws of motion and gravity, and music.

Morris Kline was Emeritus Professor of Math and New York University. The book was first published in 1967 and is a real classic.

ByA customeron 24 September 1996

A Fantastic piece of literature. It is a guide to an amazing

new world for those of us, who will never become the next

Fermat or Gauss. Kline writes in such a way that you are

drawn into the whole mathematic principle, from history to

thought processes all of the time keeping the reader aware

of the implication of this new concept on our reality.

Brillant!!!!

new world for those of us, who will never become the next

Fermat or Gauss. Kline writes in such a way that you are

drawn into the whole mathematic principle, from history to

thought processes all of the time keeping the reader aware

of the implication of this new concept on our reality.

Brillant!!!!

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ByFrancis Doornaerton 28 February 2014

The author reawoke my love for mathematics. Reading his book is akin to having an excellent teacher by your side, doing mathematics together. I used this book to review high school mathematics, but I got a lot more out of it.

There are many good exercises, which are easy enough for someone who knows elementary algebra. But that is not the only reason you should buy the book. The math is embedded in its historical context; it's this mix of elegant prose and exercises which makes this book invaluable.

There are many good exercises, which are easy enough for someone who knows elementary algebra. But that is not the only reason you should buy the book. The math is embedded in its historical context; it's this mix of elegant prose and exercises which makes this book invaluable.

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ByMunaon 18 July 2015

The book is a journey through the all major human conceptual and analytical thinking that have more than anything else shaped our modern day world and at the same time it can serve as a manual for self-study. This rather unusual approach to his subject is doubtlessly a work of art in itself and can only increase our appreciation for Mathematics, that some modern-day physicists are proclaiming to be only substantial reality behind the Universe and phenomenon of existence...

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ByOrangutanon 29 October 2014

A really well written book - very well explained with lots of interesting examples.

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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 "Mathematic s: 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 been 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 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!

Like his earlier book "Mathematic s: 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 been 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 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!

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

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 "Mathematic s: 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 been 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 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!

Like his earlier book "Mathematic s: 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 been 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 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!

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

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 "Mathematic s: 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 been 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 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!

Like his earlier book "Mathematic s: 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 been 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 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!

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

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 "Mathematic s: 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 been 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 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

Like his earlier book "Mathematic s: 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 been 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 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

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

Like his earlier book "Mathematic s: 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 been 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 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!

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

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