Author: Edouard Goursat
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 0

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Author: J-P. Serre
Publisher: Springer Science & Business Media
ISBN: 1468498843
Category : Mathematics
Languages : en
Pages : 126

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Book Description
This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.-J. Sansuc (Chapters I-IV) and J.-P. Ramis and G. Ruget (Chapters VI-VII). They were very useful to me; I extend here my gratitude to their authors.

Author: Isaac Newton
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Author: Morris Kline
Publisher: Oxford University Press
ISBN: 0199840423
Category : Mathematics
Languages : en
Pages : 468

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Book Description
This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the disciplines origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.

Author: Edouard Goursat
Publisher: Courier Corporation
ISBN: 0486446522
Category : Mathematics
Languages : en
Pages : 756

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Book Description
Classic three-volume study. Volume 1 covers applications to geometry, expansion in series, definite integrals, and derivatives and differentials. Volume 2 explores functions of a complex variable and differential equations. Volume 3 surveys variations of solutions and partial differential equations of the second order and integral equations and calculus of variations.

Author: Mary Pickering
Publisher: Cambridge University Press
ISBN: 1139479466
Category : Political Science
Languages : en
Pages : 689

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Book Description
This volume continues to explore the life and works of Auguste Comte during his so-called second career. It covers the period from the coup d'état of Louis Napoleon in late 1851 to Comte's death in 1857. During these early years of the Second Empire, Comte became increasingly conservative and anxious to control his disciples. This study offers the first study of the tensions within his movement. Focusing on his second masterpiece, the Système de politique positive, and other important books, such as the Synthèse subjective, Mary Pickering not only sheds light on Comte's intellectual development but also traces the dissemination of positivism and the Religion of Humanity throughout many parts of the world.

Author: D. B. Fuks
Publisher: American Mathematical Soc.
ISBN: 0821843168
Category : Mathematics
Languages : en
Pages : 482

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Book Description
The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 1475720637
Category : Mathematics
Languages : en
Pages : 530

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Book Description
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Author: Oliver Heaviside
Publisher:
ISBN:
Category : Earth (Planet)
Languages : en
Pages : 502

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Author: Richard P. Feynman
Publisher: Addison-Wesley Longman
ISBN:
Category : Computers
Languages : en
Pages : 328

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Book Description
Covering the theory of computation, information and communications, the physical aspects of computation, and the physical limits of computers, this text is based on the notes taken by one of its editors, Tony Hey, on a lecture course on computation given b