Introduction to the Theory of Numbers PDF Download

Author: Harold N. Shapiro
Publisher: Courier Corporation
ISBN: 0486466698
Category : Mathematics
Languages : en
Pages : 482

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Book Description
Starting with the fundamentals of number theory, this text advances to an intermediate level. Author Harold N. Shapiro, Professor Emeritus of Mathematics at New York University's Courant Institute, addresses this treatment toward advanced undergraduates and graduate students. Selected chapters, sections, and exercises are appropriate for undergraduate courses. The first five chapters focus on the basic material of number theory, employing special problems, some of which are of historical interest. Succeeding chapters explore evolutions from the notion of congruence, examine a variety of applications related to counting problems, and develop the roots of number theory. Two "do-it-yourself" chapters offer readers the chance to carry out small-scale mathematical investigations that involve material covered in previous chapters.

Author:
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 252

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Author: Alberto Cogliati
Publisher: Academic Press
ISBN: 012814274X
Category : Mathematics
Languages : en
Pages : 306

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Book Description
Writing Small Omegas: Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926 provides a general account of Lie's theory of finite continuous groups, critically examining Cartan's doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters. It evaluates pioneering attempts to generalize Lie's classical ideas to the infinite-dimensional case in the works of Lie, Engel, Medolaghi and Vessiot. Within this context, Cartan's groundbreaking contributions in continuous group theory, particularly in his characteristic and unique recourse to exterior differential calculus, are introduced and discussed at length. The work concludes by discussing Cartan's contributions to the structural theory of infinite continuous groups, his method of moving frames, and the genesis of his geometrical theory of Lie groups. - Discusses the origins of the theory of moving frames and the geometrical theory of Lie groups - Reviews Cartan's revolutionary contributions to Lie group theory and differential geometry - Evaluates many unpublished sources that shed light on important aspects of the historical development of Lie algebras

Author: Uwe Kähler
Publisher: Springer Nature
ISBN: 3031363752
Category : Mathematics
Languages : en
Pages : 696

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Book Description
This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

Author: Waldyr A. Rodrigues, Jr
Publisher: Springer
ISBN: 3319276379
Category : Science
Languages : en
Pages : 592

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Book Description
This book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research. This thoroughly revised second edition also adds three new chapters: on the Clifford bundle approach to the Riemannian or semi-Riemannian differential geometry of branes; on Komar currents in the context of the General Relativity theory; and an analysis of the similarities and main differences between Dirac, Majorana and ELKO spinor fields. The exercises with solutions, the comprehensive list of mathematical symbols, and the list of acronyms and abbreviations are provided for self-study for students as well as for classes. From the reviews of the first edition: “The text is written in a very readable manner and is complemented with plenty of worked-out exercises which are in the style of extended examples. ... their book could also serve as a textbook for graduate students in physics or mathematics." (Alberto Molgado, Mathematical Reviews, 2008 k)

Author: James Alexander Shohat
Publisher: American Mathematical Society(RI)
ISBN:
Category : Mathematics
Languages : en
Pages : 168

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Book Description
Presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. This book discusses the initial developments by Stieltjes, Markov, and Chebyshev, and later contributions by Hamburger, Nevanlinna, Hausdorff, and Stone.

Author: Jiri Neustupa
Publisher: Birkhäuser
ISBN: 3034882432
Category : Mathematics
Languages : en
Pages : 271

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Book Description
Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.

Author: Fabrizio Catanese
Publisher: Springer
ISBN: 3540782796
Category : Mathematics
Languages : en
Pages : 363

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Book Description
Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.

Author: Luigi Brugnano
Publisher: MDPI
ISBN: 3038976660
Category : Juvenile Nonfiction
Languages : en
Pages : 306

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Book Description
The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.

Author: Mohammad Ashrafuzzaman
Publisher: CRC Press
ISBN: 1003821642
Category : Science
Languages : en
Pages : 603

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Book Description
This textbook provides an introduction to the fundamental and applied aspects of biophysics for advanced undergraduate and graduate students of physics, chemistry, and biology. The application of physics principles and techniques in exploring biological systems has long been a tradition in scientific research. Biological systems hold naturally inbuilt physical principles and processes which are popularly explored. Systematic discoveries help us understand the structures and functions of individual biomolecules, biomolecular systems, cells, organelles, tissues, and even the physiological systems of animals and plants. Utilizing a physics- based scientific understanding of biological systems to explore disease is at the forefront of applied scientific research. This textbook covers key breakthroughs in biophysics whilst looking ahead to future horizons and directions of research. It contains models based on both classical and quantum mechanical treatments of biological systems. It explores diseases related to physical alterations in biomolecular structures and organizations alongside drug discovery strategies. It also discusses the cutting- edge applications of nanotechnologies in manipulating nanoprocesses in biological systems. Key Features: • Presents an accessible introduction to how physics principles and techniques can be used to understand biological and biochemical systems. • Addresses natural processes, mutations, and their purposeful manipulation. • Lays the groundwork for vitally important natural scientific, technological, and medical advances. Mohammad Ashrafuzzaman, a biophysicist and condensed matter scientist, is passionate about investigating biological and biochemical processes utilizing physics principles and techniques. He is a professor of biophysics at King Saud University’s Biochemistry Department in the College of Science, Riyadh, Saudi Arabia; the co- founder of MDT Canada Inc., and the founder of Child Life Development Institute, Edmonton, Canada. He has authored Biophysics and Nanotechnology of Ion Channels, Nanoscale Biophysics of the Cell, and Membrane Biophysics. He has also published about 50 peer- reviewed articles and several patents, edited two books, and has been serving on the editorial boards of Elsevier and Bentham Science journals. Dr. Ashrafuzzaman has held research and academic ranks at Bangladesh University of Engineering & Technology, University of Neuchatel (Switzerland), Helsinki University of Technology (Finland), Weill Medical College of Cornell University (USA), and University of Alberta (Canada). During 2013– 2018 he also served as a Visiting Professor at the Departments of Oncology, and Medical Microbiology and Immunology, of the University of Alberta. Dr. Ashrafuzzaman earned his highest academic degree, Doctor of Science (D.Sc.) in condensed matter physics from the University of Neuchatel, Switzerland in 2004.