The Geometry of Numbers PDF Download
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Author: C. D. Olds
Publisher: Cambridge University Press
ISBN: 9780883856437
Category : Mathematics
Languages : en
Pages : 198
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Book Description
A self-contained introduction to the geometry of numbers.
Author: C. D. Olds
Publisher: Cambridge University Press
ISBN: 9780883856437
Category : Mathematics
Languages : en
Pages : 198
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Book Description
A self-contained introduction to the geometry of numbers.
Author: C. R. Wylie
Publisher: Courier Corporation
ISBN: 0486141705
Category : Mathematics
Languages : en
Pages : 578
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Book Description
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.
Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 1461206871
Category : Mathematics
Languages : en
Pages : 348
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Book Description
A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of calculus, without being a calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He covers the main ideas of Euclid, but with 2000 years of extra insights attached. Presupposing only high school algebra, it can be read by any well prepared student entering university. Moreover, this book will be popular with graduate students and researchers in mathematics due to its attractive and unusual treatment of fundamental topics. A set of well-written exercises at the end of each section allows new ideas to be instantly tested and reinforced.
Author: Károly Bezdek
Publisher: Springer Science & Business Media
ISBN: 1441906002
Category : Mathematics
Languages : en
Pages : 171
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Book Description
Geometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast developing eld called discrete geometry. One can brie y describe this branch of geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, also includes the theory of polytopes and tilings in addition to the theory of packing and covering. D- crete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mat- matics, including convex and combinatorial geometry, coding theory, calculus of variations, di erential geometry, group theory, and topology, as well as geometric analysis and number theory.
Author: Denise Gaskins
Publisher: Tabletop Academy Press
ISBN: 1892083248
Category : Education
Languages : en
Pages : 288
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Book Description
Author: G. J. O. Jameson
Publisher: Cambridge University Press
ISBN: 9780521891103
Category : Mathematics
Languages : en
Pages : 266
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Book Description
At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
Author: Edmund Hlawka
Publisher: Springer Science & Business Media
ISBN: 364275306X
Category : Mathematics
Languages : en
Pages : 247
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Book Description
In the English edition, the chapter on the Geometry of Numbers has been enlarged to include the important findings of H. Lenstraj furthermore, tried and tested examples and exercises have been included. The translator, Prof. Charles Thomas, has solved the difficult problem of the German text into English in an admirable way. He deserves transferring our 'Unreserved praise and special thailks. Finally, we would like to express our gratitude to Springer-Verlag, for their commitment to the publication of this English edition, and for the special care taken in its production. Vienna, March 1991 E. Hlawka J. SchoiBengeier R. Taschner Preface to the German Edition We have set ourselves two aims with the present book on number theory. On the one hand for a reader who has studied elementary number theory, and who has knowledge of analytic geometry, differential and integral calculus, together with the elements of complex variable theory, we wish to introduce basic results from the areas of the geometry of numbers, diophantine ap proximation, prime number theory, and the asymptotic calculation of number theoretic functions. However on the other hand for the student who has al ready studied analytic number theory, we also present results and principles of proof, which until now have barely if at all appeared in text books.
Author: Álvaro Lozano-Robledo
Publisher: American Mathematical Soc.
ISBN: 147045016X
Category : Mathematics
Languages : en
Pages : 506
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Book Description
Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
Author: Michal Krizek
Publisher: Springer Science & Business Media
ISBN: 0387218505
Category : Mathematics
Languages : en
Pages : 280
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Book Description
The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.
Author: Richard Evan Schwartz
Publisher: American Mathematical Soc.
ISBN: 1470422093
Category : Juvenile Nonfiction
Languages : en
Pages : 246
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Book Description
This book is a unique teaching tool that takes math lovers on a journey designed to motivate kids (and kids at heart) to learn the fun of factoring and prime numbers. This volume visually explores the concepts of factoring and the role of prime and composite numbers. The playful and colorful monsters are designed to give children (and even older audiences) an intuitive understanding of the building blocks of numbers and the basics of multiplication. The introduction and appendices can also help adult readers answer questions about factoring from their young audience. The artwork is crisp and creative and the colors are bright and engaging, making this volume a welcome deviation from standard math texts. Any person, regardless of age, can profit from reading this book. Readers will find themselves returning to its pages for a very long time, continually learning from and getting to know the monsters as their knowledge expands. You Can Count on Monsters is a magnificent addition for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual interested in exploring the visually fascinating world of the numbers 1 through 100.
