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(A Course of Pure Mathematics is a classic textbook in int...)

A Course of Pure Mathematics is a classic textbook in introductory mathematical analysis, written by G. H. Hardy. It is recommended for people studying calculus. First published in 1908, it went through ten editions (up to 1952) and several reprints. It is now out of copyright in UK and is downloadable from various internet web sites. It remains one of the most popular books on pure mathematics.

Godfrey Hardy was a British mathematician and educator, known for his achievements in number theory and mathematical analysis.

Background

Godfrey Harold Hardy was born on February 7, 1877, in Cranleigh, Surrey, United Kingdom. His father, Isaac Hardy, was bursar and an art master at Cranleigh school. His mother Sophia had been a teacher at Lincoln Teacher's Training School. Both his parents came from poor families and were unable to afford university education for themselves, but they were people with a taste for intellectual and cultural pursuits and had made a place for themselves as schoolteachers. They took great pains to educate their children well, and both Hardy and his sister Gertrude inherited their parent’s love for education and the intellect.

Education

Hardy attended Cranleigh school up to the age of 12 with great success, but he did not appear to have the passion for mathematics that many mathematicians experience when young. He won a scholarship to Winchester College in 1889, entering the College the following year. While at Winchester, Hardy won an open scholarship to Trinity College Cambridge, which he entered in 1896.

Hardy initially chose to attend Cambridge rather than Oxford because of its standing in mathematics, and Trinity College was the premier institution for the subject in England. During his first years at Cambridge, however, he very nearly gave up mathematics altogether, in disgust over the examination system then in existence. Mathematics students had to take the Tripos examination, which consisted of eight days of solving problems. Hardy disliked the system because, rather than gauging the ability and insight of the student, he believed it tested endurance and the ability to memorize formulae and equations. Special private coaches trained students for Tripos, while lecturers at the universities pursued their own mathematical research. Hardy considered Tripos an utter waste of time, and he tried to change his course of study to history. What kept him in the field was his professor, A. E. H. Love, who recognized Hardy’s affinity for pure mathematics.

Upon his graduation in 1899, he was named a fellow of Trinity College at Cambridge.

Hardy started his career, lecturing in mathematics at Trinity College from 1906 to 1919. In 1912 Hardy published, with John E. Littlewood, the first of a series of papers that contributed fundamentally to many realms in mathematics, including the theory of Diophantine analysis, divergent series summation, Fourier series, the Riemann zeta function, and the distribution of primes. The collaboration between Hardy and Littlewood is one of the most celebrated in 20th-century mathematics.

Besides Littlewood, Hardy’s other important collaboration was with Srinivasa Ramanujan, a poor self-taught Indian clerk whom Hardy immediately recognized as a mathematical genius. Hardy arranged for Ramanujan to be brought to Cambridge in 1914, filled in the gaps in his mathematical education by private tutoring, and coauthored several papers with him before Ramanujan returned to India in 1919.

In 1919 Hardy left Cambridge to take the Savilian Chair of Geometry at Oxford in the aftermath of the Bertrand Russell affair during World War I. In 1928–29 he was a visiting professor at Princeton, exchanging places with Oswald Veblen. He returned to Cambridge in 1931 as Sadleirian Professor of Pure Mathematics and remained there until his death.

Quotations:
"A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas."

"It is never worth a first-class man's time to express a majority opinion. By definition, there are plenty of others to do that."

"We have concluded that the trivial mathematics is, on the whole, useful, and that the real mathematics, on the whole, is not."

Membership

Hardy was a member of the Royal Society of London and London Mathematical Society.

Personality

Hardy was extremely shy as a child and was socially awkward, cold and eccentric throughout his life. He was uncomfortable being introduced to new people, and could not bear to look at his own reflection in a mirror. It is said that, when staying in hotels, he would cover all the mirrors with towels.