Review
The book was intended to help reform mathematics teaching in the UK, and more specifically in the University of Cambridge and in schools preparing to study higher mathematics. It was aimed directly at "scholarship level" students — the top 10% to 20% by ability. Hardy himself did not originally find a passion for mathematics only seeing it as a way to beat the other students, which he did decisively, and gain scholarships. However, his book excels in effectively explaining analytical number theory and calculus following the rigor of mathematics.
Whilst his book changed the way the subject was taught at university, the content reflects the era in which the book was written. The whole book explores number theory and the author constructs real numbers theoretically. It adequately deals with single-variable calculus, sequences, number series, properties of cos, sin, log, etc. but does not refer to mathematical groups, multi-variable functions or vector calculus. Each section includes some demanding problems. Hardy combines the enthusiasm of the missionary with the rigor of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit. Hardy's presentation of mathematical analysis is as valid today as when first written: students will find that his economical and energetic style of presentation is one that modern authors rarely come close to. Despite its limitations, it is considered a classic in its field. It is probably of most use to 1st year university students of pure mathematics.
Read more about this topic: A Course Of Pure Mathematics
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