Someone trying to learn calculus for the first time could do far worse than using this work as their primer. As I expected, it brought back memories of learning calculus at school although I don't recall the subject being so clearly explained as in this book. The author does indeed present the subject in a way that is easy to understand, and in a style that is entertaining. I was attracted to this book by its title, which struck me as unusual for 1914, when my edition was published, and its contents didn't disappoint. I studied calculus at school, and used it occasionally at university, but I've not needed it since so this was a trip down memory lane. This was a book that I skimmed through, rather than thoroughly digested, not least because much of each chapter consists of worked examples and exercises which I didn't attempt. Thompson's little book is the best that I've seen, yet. The idea of calculus is so simple, and Mr. There are so many things I wish had been done to illuminate the subject more thoroughly, but perhaps one day I'll have to write it myself. But no, this little gem had seen by then three dozen reprintings starting in 1910. When I first found this book in the mid-80's, I thought at first that it was one of those "made easy" trend books I had been seeing so much of. The simplicity that they had mangled has all been straightened out under the compassionate and clear pen of Sylvanus P. Then I would realize what both of them were trying to say. I would read in one until I couldn't go any farther, then I would read in the other up to the same subject point. They may have known their subject, but this math whiz (straight "A's" in high school through Advanced Algebra & Trig) found those other authors' abilities to communicate far less than optimum. Prior to this book, I had attempted to wade through a couple of college entry-level calculus textbooks, but found the style of both authors to be obtuse and obfuscating. Thompson was both irreverent and witty in his development of the subject. Of all the math books I've read, this one is by far the most exciting. So highly recommended to a bright high-schooler or baffled undergrad, ideally to be followed by A Primer of Infinitesimal Analysis, if you can convince people that you don't need the standard analysis curriculum. Heck, Thompson wrote while mainstream analysis was still being worked out. To be fair to Thompson, though, the simplicity comes in part from using infinitesimals rather than limits, and the logical basis for infinitesimals wouldn't achieve rigor until non-standard analysis circa 1965, or smooth infinitesimal analysis circa 1974. The invective against obscurantism in mathematics is also spot on.īut let's be honest: the coverage is extremely rudimentary, and since there's no analytical treatment, the path to generalization to more complex problems is far from clear, so one star off. The style is conversational, even breezy. I really got a feel for how important it was for Thompson to remove the intimidation from calculus. Mad props for being the first calculus text I didn't hate, and actually being fun. You could give this to a motivated 9 year old. The only impediment is the Edwardian prose, which tends to make sentences twice as long as they have to be. Masterstroke! He takes you into confidence against "ordinary mathematicians", he states it all in things you already know, and he directly addresses your misgivings. When you see an expression that begins with this terrifying symbol, you will henceforth know that it is put there merely to give you instructions that you are now to perform the operation (if you can) of totalling up all the little bits that are indicated by the symbols that follow. The word “integral” simply means “the whole.”. Now any fool can see that if x is considered as made up of a lot of little bits, each of which is called dx, if you add them all up together you get the sum of all the dx's. Thus ∫dx means the sum of all the little bits of x. (2) ∫ which is merely a long S, and may be called (if you like) “the sum of.” But you will find that these little bits (or elements) may be considered to be indefinitely small. Ordinary mathematicians think it more polite to say “an element of,” instead of “a little bit of.” Just as you please. Thus dx means a little bit of x or du means a little bit of u. (1) d which merely means “a little bit of.” The preliminary terror, which chokes off most fifth-form boys from even attempting to learn how to calculate, can be abolished once for all by simply stating what is the meaning – in common-sense terms – of the two principal symbols. Shame there's not one of these for every subfield of maths. He takes your intuitions about little bits and bigness and leads you to the door of the great machine. Ridiculously clear and friendly and quick.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |