Synopsis
A pioneering genius of pure and applied mathematics, Hermann Minkowski (1864?1909) founded the geometry of numbers and wrote extensively about his researches into the field. Until the distinguished American mathematician Harris Hancock interpreted Minkowski's writings, they were accessible only to a few specialists. Hancock elaborated on the master's writings, placing them in clear, readable form. This classic two-volume edition returns Hancock's brilliant exposition to the mathematics community after a long hiatus.
Development of the Minkowski Geometry of Numbers concerns itself primarily with geometric problems involving integers and with algebraic problems approachable through geometrical insights. In addition to demonstrating that geometric proofs and theorems in number theory are often simpler and more elegant than arithmetic proofs, the author illuminates many other algebraic and geometric topics. Starting with preliminary background and historical remarks, Volume 1 examines surfaces that are nowhere concave; the volume of bodies; linear forms; the arithmetical theory of a pair of lines; algebraic numbers; and the theory of continuous fractions. Some of Minkowski’s shorter papers are discussed as well. Topics featured in the subsequent volume include approximations of algebraic numbers and of real quantity through rational numbers, the arithmetic of the ellipsoid, and extreme standard bodies.
Development of the Minkowski Geometry of Numbers concerns itself primarily with geometric problems involving integers and with algebraic problems approachable through geometrical insights. In addition to demonstrating that geometric proofs and theorems in number theory are often simpler and more elegant than arithmetic proofs, the author illuminates many other algebraic and geometric topics. Starting with preliminary background and historical remarks, Volume 1 examines surfaces that are nowhere concave; the volume of bodies; linear forms; the arithmetical theory of a pair of lines; algebraic numbers; and the theory of continuous fractions. Some of Minkowski’s shorter papers are discussed as well. Topics featured in the subsequent volume include approximations of algebraic numbers and of real quantity through rational numbers, the arithmetic of the ellipsoid, and extreme standard bodies.
"synopsis" may belong to another edition of this title.
Other Popular Editions of the Same Title
Search results for Development of the Minkowski Geometry of Numbers: 1...
Stock Image
Development of the Minkowski Geometry of Numbers Volume 1 (Phoenix Edition)
Seller: J. HOOD, BOOKSELLERS, ABAA/ILAB, Baldwin City, KS, U.S.A.
Seller rating 5 out of 5 stars
Hardcover. Volumes I and II: total 837pp. BOTH VOLUMES: as new, clean, tight & bright condition. Seller Inventory # 177518
Stock Image
Development of the Minkowski Geometry of Numbers Volume 1 (Phoenix Edition)
Seller: HPB-Red, Dallas, TX, U.S.A.
Seller rating 5 out of 5 stars
hardcover. Condition: Good. Connecting readers with great books since 1972! Used textbooks may not include companion materials such as access codes, etc. May have some wear or writing/highlighting. We ship orders daily and Customer Service is our top priority! Seller Inventory # S_449628127
Stock Image
Development of the Minkowski Geometry of Numbers Volume 1 (Phoenix Edition)
Seller: GoldBooks, Denver, CO, U.S.A.
Seller rating 5 out of 5 stars
Condition: new. Seller Inventory # 65O40_37_0486446468