History of the Theory of Numbers, Volume II: Diophantine Analysis (Dover Books on Mathematics Book 2) by Leonard Eugene Dickson (PDF)

Description

The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms.Featured topics include polygonal, pyramidal, and figurate numbers; linear diophantine equations and congruences; partitions; rational right triangles; triangles, quadrilaterals, and tetrahedra; the sums of two, three, four, and n squares; the number of solutions of quadratic congruences in n unknowns; Liouville’s series of eighteen articles; the Pell equation; squares in arithmetical or geometrical progression; equations of degrees three, four, and n; sets of integers with equal sums of like powers; Waring’s problem and related results; Fermat’s last theorem; and many other related subjects. Indexes of authors cited and subjects appear at the end of the book.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Great historical reference useful as is and not directly to learn number theory. This reference seems very complete but I haven’t read completely today !

⭐Another outstanding math book

⭐If you are looking for a quick concise history of any technical number theoretical topic (300BC–1900) this set of volumes is a masterpiece and stands alone–very few fields have such a fine authoritative concise summary of their history. The author clearly spent years combing libraries and trying to catalog all of what had been done in number theory. For this reason, these volumes are truly excellent reference books that all large libraries should own (but few individuals).They are reference books. Do not buy them to sit down and learn about the history of number theory. They are not narratives. No quaint stories. No pictures. Very few definitions. Just very long lists of very terse concise references arranged by topic and then listed chronologically. To fault these volumes for being boring is to entirely miss their purpose, they are not written to entertain you.I love my copies, and enjoy seeing who did what on archaic areas of number theory that are no longer explored, but I think others should look in a library and know what they are buying before they do. And especially do not buy just one volume before knowing if it covers parts of the field you care about.Like a very specialized tool, these are invaluable to certain craftsmen, and totally useless to the general public.

⭐EXCELLENT

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