Showing papers in "The Mathematical Gazette in 1975"
TL;DR: Intended for introductory courses in numerical analysis, this book features a comprehensive treatment of major topics in this subject area using an algorithmic approach and provides numerous worked examples with computer output, and flowcharts and programs.
1,154 citations
TL;DR: In this article, the authors give a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients, and their study has developed into a fertile and extensive theory enriching many branches of pure mathematics.
Abstract: First published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.
644 citations
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TL;DR: Graph Theory with Applications to Engineering and Computer as mentioned in this paper is an excellent introductory treatment of graph theory and its applications that has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject.
Abstract: Graph Theory with Applications to Engineering and Computer ... This outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject. The first nine chapters constitute an excellent overall introduction, requiring only some knowledge of set theory and matrix algebra.
16 citations
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TL;DR: The number π (as all or nearly all the world doth know) signifies the ratio of the circumference of a circle to its diameter and is also equal to the proportion of the area to the square of the radius as mentioned in this paper.
Abstract: The number π (as all—or very nearly all—the world doth know) signifies the ratio of the circumference of a circle to its diameter and is also equal to the ratio of the area to the square of the radius. This suggests two generalisations of π which apply to plane figures of any shape:
TL;DR: A detailed study of the discovery of the area law of planetary motion was made in this article, which led to a detailed reconstruction of Kepler's path to the elliptical orbit and the area-law.
Abstract: In his Newtonian studies Alexandre Koyre remarked that, from the area law of planetary motion, Kepler erroneously deduced that the planets move in their orbits with speeds inversely proportional to the distances from the sun. It was this assertion, which I suspected to be false, that led me to make a detailed study of the discovery of the area law. Quite independently and unknown to me, Curtis Wilson had been making a similar study of the discovery of the elliptical orbit. Since the arguments leading to the two Keplerian laws are inter-dependent, our researches may be described as variations on the same theme. What I wish to do this evening is to explain in simple terms our reconstruction of Kepler’s path to the elliptical orbit and the area law.