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.
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