Mathematics and the Physical World (Dover Books on Mathematics) by Morris Kline (PDF)

Description

Kline is a first-class teacher and an able writer. . . . This is an enlarging and a brilliant book. ― Scientific American”Dr. Morris Kline has succeeded brilliantly in explaining the nature of much that is basic in math, and how it is used in science.” ― San Francisco ChronicleSince the major branches of mathematics grew and expanded in conjunction with science, the most effective way to appreciate and understand mathematics is in terms of the study of nature. Unfortunately, the relationship of mathematics to the study of nature is neglected in dry, technique-oriented textbooks, and it has remained for Professor Morris Kline to describe the simultaneous growth of mathematics and the physical sciences in this remarkable book. In a manner that reflects both erudition and enthusiasm, the author provides a stimulating account of the development of basic mathematics from arithmetic, algebra, geometry, and trigonometry, to calculus, differential equations, and the non-Euclidean geometries. At the same time, Dr. Kline shows how mathematics is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, and other phenomena. Historical and biographical materials are also included, while mathematical notation has been kept to a minimum. This is an excellent presentation of mathematical ideas from the time of the Greeks to the modern era. It will be of great interest to the mathematically inclined high school and college student, as well as to any reader who wants to understand ― perhaps for the first time ― the true greatness of mathematical achievements.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Sure, the examples can be dated (like an $1,800 annual salary being good, and a planet with a 2 Billion population), but NO other old or current text explains math as clearly. The teaching methods are timeless and unique.Simple example. We’ve all seen dozens of ways to explain the first derivative (the rate of change) of say x^2 as 2x. These range from slope finding to falling objects to matrices. But nearly all I’ve seen assume a curve, tangents, etc. Kline blows the mind with a rarely seen example– a circle!He simply “animates” the circle and asks you to mentally extend the radius as it turns in the area-clock like the minute hand, only the size of the circumference. He then points out that the first derivative, the rate of change, is like extending the radius a bit, which “sweeps” out a larger circumference. Then he points out that y’ in that case changes (pi)r^2 to 2(pi)r, instantly connecting radius, area and circumference in motion!This may seem trivial until we remember that Feynman used the same clock face example to explain quantum mechanics verbally, which blew the math community away at the time. In fact, connecting Kline’s example with Feynman’s gives some really interesting “aha” moments of new understanding.The whole book is like this, with many fun stories of how math reflects the natural world. You’ll be amazed at the level of math he gets into with such simple assumptions as “very little math knowledge” before beginning. I mean, ALL applied math texts assume a LOT of math to begin. This is truly a rare gem, and a find for any High School STEM teacher wanting a real bridge to advanced concepts. Highly recommended, even in 2013 plus…

⭐I studied Chemical Engineering as an undergraduate and got to see more than my fair share of mathematics during that time. I got through the program, but there were a lot of fragmented mathematical concepts in my mind. Ten years after graduation I’m finding an interest in revisiting old math textbooks and this book has been a godsend. For me, it shows how the various fields of math fit together. There are just enough anecdotes to make the overall concepts memorable. Morris is a great writer and it feels like he is on your team as he explains the concepts. I started tutoring my 10 year old nephew and I’m taking lessons from this book to make sure he has a sound foundation for more advanced concepts later on. I absolutely loved this book and would recommend it highly.

⭐You can pay a lot of money for a book that doesn’t cover the subject as well as Kline’s. The heart of the book is its presentation of the historical scientific contexts of mathematical developments. The math is at the high school level and clearly presented. Kline’s writing is not flashy; it is simple and lucid, great qualities for a book like this.

⭐For the one who loves history of math and science, it’s a must. I always enjoyed reading Morris Kline and his vision of math as tool to decipher the world. I always also approved his way and his vision regarding math teaching.What is very interesting is that mathematician developed concepts before others could find a field of application. It’s like inventing a tool for a machine which doesn’t exist yet. It’s a part of the mystery of the human mind. I do not remember who wrote: “God is subtle!”.

⭐I highly recommend both Mathematics and the Physical World” as well as “Calculus: An Intuitive and Physical Approach” both of which were authored long ago by Morris Kline. If you are looking for a refresher or an aid for a current class, Kline’s books will prove highly valuable. The only way I was able to read both of these books is through the efforts of Dover, who has been reissuing out of print science and math books for many years. I was very happy to see that Dover is making at least some of these available in Kindle format.

⭐Aside from whatever merits there are in the author’s presentation of mathematical concepts, this is a tedious and badly-written book. The material could be covered in far fewer pages, but the author’s frequent digressions on philosophical, historical, and aesthetic topics are both mind-numbing and inept. For example, the author remarks: “If man’s environment were like that of birds, who constantly encounter changing cloud shapes, or of fish, who see before them just formless water, he would probably never have conceived the study of geometry. Not only are fixed shapes absent in those media but even the notion of a definite locale, a reference point, does not suggest itself.” (Pg. 73.)The idea that “fixed shapes” are not part of the experience of birds is simply false, as is the notion that “reference points” and “definite locales” do not exist underwater. Migratory birds navigate thousands of miles, and some fish species and marine mammals likewise conduct amazing navigational feats. Birds perch on wires, nest in trees, and fly along rivers; fish live near reefs or form geometrically shaped schools. Kline’s sentence is nonsense and could only be written by someone willing to write pompously on subjects he knows nothing about. The book is laced with passages like this, and by page 73, I had had enough.

⭐Excellent work. Very enjoyable read. Exellent for those studying history of math and science. Poor execution of port from print to digital: frequent errors that appear to be generated by an OCR scan that wasn’t thoroughly proofed, which probably won’t trip up math veterans. I’m about 30% through with it and will update this review if warranted.

⭐This book explains math in a very clear way, and connects it to reality. A feature which most math books lack.

⭐I would recommend this book to anyone with a curious mind as to how he/she could ever possibly be here to read it. In short, it’s a step by step presentation of one’s understanding why the way things are as a consequence of physical systems that exist from mathematics. It embraces all the heroes and shows them in the light of ordinary but exceptional persons who are the leading light of our journey through a dark passage with only a stick to guide us.

⭐Wonderful writing and clarity. A great way for the everyman to renew an interest in the maths behind the real world. Of course, a bit dated (log tables – remember those!) and wouldn’t it be wonderful if their were a successor to Professor Kline capable of writing a modern update of this wonderful book

⭐To unravel Nature and her designs you need to know the language she communicates with. This book is a testimony to that effort. Lucid and brilliantly written with the history on how we learnt the language step by step. A must read for anyone who wishes to be mathematically literate.

⭐I went into this book with an open mind, not really sure what lay in store. It is an interesting book but I didn’t find it as enjoyable as some of the recreational math books I’ve read. perhaps a rereading might be required.

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