An Introduction to Mathematics A N Whitehead 9781484007976 Books
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THE ABSTRACT NATURE OF MATHEMATICS The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigor of its methods, all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it 'Tis here 'tis there, 'tis gone" and what we do see does not suggest the same excuse for illusiveness as sufficed for the ghost, that it is too noble for our gross methods. A show of violence," if ever excusable, may surely be offered" to the trivial results which occupy the pages of some elementary mathematical treatises. The reason for this failure of the science to live up to its reputation is that its fundamental ideas are not explained to the student disentangled from the technical procedure which has been invented to facilitate their exact presentation in particular instances. Accordingly, the unfortunate learner finds himself struggling to acquire the knowledge of a mass of details which are not illuminated by any general conception. Without a doubt, technical facility is a first requisite for valuable mental activity we shall fail to appreciate the rhythm of Milton, or the passion of Shelley, so long as we find it necessary to spell the words and are not quite certain of the forms of the individual letters. In this sense there is no royal road to learning. But it is equally an error to confine attention to technical processes, excluding consideration of general ideas. The object of the following Chapters is not to teach mathematics, but to enable students from the very beginning of their course to know what the science is about, and why it is necessarily the foundation of exact thought as applied to natural phenomena. All allusion in what follows to detailed deductions in any part of the science will be inserted merely for the purpose of example, and care will be taken to make the general argument comprehensible, even if here and there some technical process or symbol which the reader does not understand is cited for the purpose of illustration. The first acquaintance which most people have with mathematics is through arithmetic. That two and two make four is usually taken as the type of a simple mathematical proposition which everyone will have heard of. Arithmetic, therefore, will be a good subject to consider in order to discover, if possible, the most obvious characteristic of the science. Now, the first noticeable fact about arithmetic is that it applies to everything, to tastes and to sounds, to the ideas of the mind and to the bones of the body. The nature of the things is perfectly indifferent, of all things it is true that two and two make four. Thus we write down as the leading characteristic of mathematics that it deals with properties and ideas which are applicable to things just because they are things, and apart from any particular feelings, or emotions, or sensations, in any way connected with them. This is what is meant by calling mathematics an abstract science. This point has usually been misunderstood, from being thought of in too narrow a way. Pythagoras had a glimpse of it when he proclaimed that number was the source of all things. In modern times the belief that the ultimate explanation of all things was to be found in Newtonian mechanics was an adumbration of the truth that all science as it grows towards perfection becomes mathematical in its ideas. The chapters contain THE ABSTRACT NATURE OF MATHEMATICS VARIABLE METHODS OF APPLICATION DYNAMICS THE SYMBOLISM OF MATHEMATICS GENERALIZATIONS OF NUMBER IMAGINARY NUMBERS IMAGINARY NUMBERS (CONTINUED) COORDINATEGEOMETRY CONICSECTIONS FUNCTIONS PERIODICITY IN NATURE TRIGONOMETRY SERIES THE DIFFERENTIAL CALCULUS GEOMETRY QUANTITY
An Introduction to Mathematics A N Whitehead 9781484007976 Books
Striking review of fundamental concepts from a distinguished teacher. This is enlightening + engaging because you get the concepts plus its importance within the body of knowledge. Not to mention the historical context. For instance, Whitehead remember us that Archimedes was killed by a Roman soldier while contemplating a mathematical diagram and no Roman ever died in such conditions. This book is full of insights; go for it if you want to refresh your view of Mathematics having lots of fun.Product details
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An Introduction to Mathematics A N Whitehead 9781484007976 Books Reviews
Anyone who has studied mathematics through differential and integral calculus will enjoy the historical and philosophical allusions in this book. I particularly enjoyed the exposition on trigonometry and triangulation.
One of the best books on the subject I've ever read. If you hated math in school read this book to rehabilitate yourself and just blame your teacher for being a lunatic just like I did. This book can open the doors to a beautiful adventure.
DON'T BUY THIS VERSION!!!! This is a great book by a great mathematical philosopher, but the translation to the kindle version is truly awful. It advertises itself as having a plus- full mathematical notation. But that is a fraud. In reality, it is an extremely sloppy digital conversion which has numerous errors of run-together words, split words, mistaken character reading (e.g. Do you want to know about ARABLE numbers?) and long sections of text which have been erroneously translated as image information and have such small type that the text is not readable. After buying this version on the basis of its advertised "plus", I tried to soldier through the problems but gave up. I have purchased the plain version, which cheaper, and so far very readable.
Do you have a passing interest in the world of mathematics? If so, Whiteheads "Introduction to Mathematics" is an excellent place to pick up where those wretched school textbooks leave off. Clearly written, well laid out, and eminently graspable, "An Introduction to Mathematics" won't illuminate a mathematician, but gives a very good account of itself to the layman.
Unfortunately, this edition has serious shortcomings. While the quality of the printing is poor (lifted directly from an earlier edition, perhaps?) the printing gives out entirely for equations involving division. The result is a mess of a book, with the reader having to fill in the equations him or herself.
It was a good refresher for a guy who's favorite subject was math -- 50 years ago. But because this book was written so long ago, I found the grammar sometimes tedious.
I neglected my mathematical education. I thought this would be an interesting way to learn more. To be fair, I did learn some things, particularly at the beginning. As he noted in the post script, the actual math can get in the way of most people learning. I enjoyed the historical and theoretical points, which is really what I wanted, but after a while the equations got to me and I realize I just do not have the time, or inclination, to concentrate hard enough to learn it. I do not know how you do it without actually treating it as a course. So, I sped through, glomming the easy parts. I really do think there are ways to generally explain math simply to people with mild interest only in the history, objective and general outline of the discipline without going through complex equations and diagrams. This wasn't it.
I did see a mistake or so early on in the diagrams (e.g., an "x" that came out "y"), but that may be the printing and not his fault. Perhaps the book is better than I know and it is my shortcomings that keep me from appreciating it. And perhaps if I have more time and patience some day, I will try again.
This is a nice, little book short, clear, and very well written. I confess, though, that I'm not sure who its best audience really is. If you know some math, and have thought and read AT ALL about the philosophy of math, you will not find much new in this book; still, since it will be quick and easy to read, you will probably find it worthwhile, for the occasional new insight or alternative way of looking at things. I found the section on series particularly worth reading, because series were not well covered in my own math education. I also found the comments on the measurement of time to be subtle and thought-provoking.
If you know little or no math, you MIGHT find this a good introduction (as the title implies), but don't expect any detailed exposition on the actual PRACTICE of math. This book is really an introduction to the philosophy of math. It is concerned with WHY we do math, and why math takes the form that it does. Whitehead's goal is to introduce some key concepts, common to all math, such as variables and abstraction. Any actual proofs or expositions in the book are included only as examples of how these concepts play out in seemingly different areas of study.
Perhaps the reader best served by this book would be one who is comfortable with the practice of math at least through the basic high school level (geometry, algebra, trigonometry), and possibly more, but is just starting to think about the underlying philosophy the "why" of math as opposed to the "how" of it.
For those who don't know, Whitehead was, of course, one of the premier philosophers of math of the early 20th century, co-author with Bertrand Russell of the 3-volume magnum opus "Principia Mathematica". The present book was written around 1911, and is definitely dated in spots - for instance he talks about electro-magnetic vibrations in the "ether" - but that doesn't detract from either its usefulness or readability.
Striking review of fundamental concepts from a distinguished teacher. This is enlightening + engaging because you get the concepts plus its importance within the body of knowledge. Not to mention the historical context. For instance, Whitehead remember us that Archimedes was killed by a Roman soldier while contemplating a mathematical diagram and no Roman ever died in such conditions. This book is full of insights; go for it if you want to refresh your view of Mathematics having lots of fun.
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