Tom M. Apostol – författare

This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. Among the strong points of the book are its clarity of exposition and a collection of exercises at the end of each chapter. The first ten chapters, with the exception of one section, are accessible to anyone with knowledge of elementary calculus; the last four chapters require some knowledge of complex function theory including complex integration and residue calculus.

This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. The second volume presupposes a background in number theory com­ parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj(r), and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series. Both volumes of this work emphasize classical aspects of a subject which in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T.M.A. January, 1976 * The first volume is in the Springer-Verlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory.

An introduction to the Calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.

An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation -- this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.

Developed from the author's successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization. To accommodate a variety of backgrounds, the text begins with a review of prerequisites divided into precalculus and calculus prerequisites. It continues to cover vector algebra, analytic geometry, linear spaces, determinants, linear differential equations and more.

This innovative physics textbook intended for science and engineering majors develops classical mechanics from a historical perspective. The presentation of the standard course material includes a discussion of the thought processes of the discoverers and a description of the methods by which they arrived at their theories. However the presentation proceeds logically rather than strictly chronologically, so new concepts are introduced at the natural moment. The book assumes a familiarity with calculus, includes a discussion of rigid body motion, and contains numerous thought-provoking problems. It is largely based in content on The Mechanical Universe: Introduction to Mechanics and Heat, a book designed in conjunction with a tele-course to be offered by PBS in the Fall of 1985. The advanced edition, however, does not coincide exactly with the video lessons, contains additional material, and develops the fundamental ideas introduced in the lower-level edition to a greater degree.

This 1987 second volume of the Mechanical Universe studies electricity and magnetism, their relation to each other and light, and shows how the problem of light led to the special theory of relativity. Then, it moves on to modern physics, where particles may behave like waves and where some of the great verities of Newtonian physics appear less certain. Along with the first volume, this book is based on, though independent of, a public television series broadcast in the United States. Physics is presented as a human endeavor, with historical development forming a thread throughout the text. The prerequisites are minimal, only basic algebra and trigonometry since the necessary calculus is developed in the text, with physics providing the motivation. New concepts are introduced at the natural, logical point with many historical references to place physics in a social perspective. Many topics from twentieth-century physics are included. The book is attractively illustrated and will be a stimulating alternative to other, less-thorough treatments.

This important textbook is based on, though independent of, an educational TV series The Mechanical Universe broadcast on public television in the United States. Its aim is to guide students and general readers to an understanding of how the physical world works; physics is presented as a human endeavour, with historical development forming a thread throughout the text. The prerequisites are minimal, only basic algebra and trigonometry since the necessary calculus is developed in the text, with physics providing the motivation. New concepts are introduced at the natural, logical point with many historical references to place physics in a social perspective. Many topics from twentieth-century physics are included, for example energy, low temperature physics, relativity and black holes. The book is attractively and profusely illustrated and will be welcomed by students and also by general readers for whom this will be a stimulating alternative to other, less-thorough treatments.

Developed from the author''s successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization. To accommodate a variety of backgrounds, the text begins with a review of prerequisites divided into precalculus and calculus prerequisites. It continues to cover vector algebra, analytic geometry, linear spaces, determinants, linear differential equations and more.

Developed from the author''s successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization. To accommodate a variety of backgrounds, the text begins with a review of prerequisites divided into precalculus and calculus prerequisites. It continues to cover vector algebra, analytic geometry, linear spaces, determinants, linear differential equations and more.

This innovative physics textbook intended for science and engineering majors develops classical mechanics from a historical perspective. The presentation of the standard course material includes a discussion of the thought processes of the discoverers and a description of the methods by which they arrived at their theories. However the presentation proceeds logically rather than strictly chronologically, so new concepts are introduced at the natural moment. The book assumes a familiarity with calculus, includes a discussion of rigid body motion, and contains numerous thought-provoking problems. It is largely based in content on The Mechanical Universe: Introduction to Mechanics and Heat, a book designed in conjunction with a tele-course to be offered by PBS in the Fall of 1985. The advanced edition, however, does not coincide exactly with the video lessons, contains additional material, and develops the fundamental ideas introduced in the lower-level edition to a greater degree.

This innovative physics textbook intended for science and engineering majors develops classical mechanics from a historical perspective. The presentation of the standard course material includes a discussion of the thought processes of the discoverers and a description of the methods by which they arrived at their theories. However the presentation proceeds logically rather than strictly chronologically, so new concepts are introduced at the natural moment. The book assumes a familiarity with calculus, includes a discussion of rigid body motion, and contains numerous thought-provoking problems. It is largely based in content on The Mechanical Universe: Introduction to Mechanics and Heat, a book designed in conjunction with a tele-course to be offered by PBS in the Fall of 1985. The advanced edition, however, does not coincide exactly with the video lessons, contains additional material, and develops the fundamental ideas introduced in the lower-level edition to a greater degree.

This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. Among the strong points of the book are its clarity of exposition and a collection of exercises at the end of each chapter. The first ten chapters, with the exception of one section, are accessible to anyone with knowledge of elementary calculus; the last four chapters require some knowledge of complex function theory including complex integration and residue calculus.

This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. The second volume presupposes a background in number theory com­ parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher''s convergent series for the partition function, Lehner''s congruences for the Fourier coefficients of the modular functionj(r), and Hecke''s theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr''s theory of equivalence of general Dirichlet series. Both volumes of this work emphasize classical aspects of a subject which in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T.M.A. January, 1976 * The first volume is in the Springer-Verlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory.

This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. The second volume presupposes a background in number theory com­ parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj(r), and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series. Both volumes of this work emphasize classical aspects of a subject which in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T.M.A. January, 1976 * The first volume is in the Springer-Verlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory.

This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology du ring the last 25 years. The second volume presupposes a background in number theory com­ parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher''s convergent series for the partition function, Lehner''s congruences for the Fourier coefficients of the modular functionj( r), and Hecke''s theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr''s theory of equivalence of general Dirichlet series. Both volumes of this work emphasize classical aspects of a subject wh ich in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T. M. A. January, 1976 * The first volume is in the Springer-Verlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory.

New Horizons in Geometry represents the fruits of 15 years of work in geometry by a remarkable team of prize-winning authors Tom Apostol and Mamikon Mnatsakanian. It serves as a capstone to an amazing collaboration. Apostol and Mamikon provide fresh and powerful insights into geometry that requires only a modest background in mathematics. Using new and intuitively rich methods, they give beautifully illustrated proofs of results, the majority of which are new, and frequently develop extensions of familiar theorems that are often surprising and sometimes astounding. It is mathematical exposition of the highest order. The hundreds of full color illustrations by Mamikon are visually enticing and provide great motivation to read further and savor the wonderful results. Lengths, areas, and volumes of curves, surfaces, and solids are explored from a visually captivating perspective. It is an understatement to say that Apostol and Mamikon have breathed new life into geometry.

This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. Among the strong points of the book are its clarity of exposition and a collection of exercises at the end of each chapter. The first ten chapters, with the exception of one section, are accessible to anyone with knowledge of elementary calculus; the last four chapters require some knowledge of complex function theory including complex integration and residue calculus.

The MathFilm DVD presents a juried collection of innovative short math videos. The films are winners of the international competition of the MathFilm Festival 2008. Following the May premiere in Berlin, the festival films are shown in public viewings throughout Germany. The festival is part of the "Year of Mathematics" initiative of the Federal Ministry of Education and Research. The films target a broad audience of students, teachers, and everyone with an interest in mathematics. The topics range from geometry to graphics, from computing to visualization, from historic to modern achievements, from abstract mathematical worlds to real-world applications. The DVD provides entertaining and informative insights into modern mathematics and is an exciting resource for lively school and university courses.

Die MathFilm DVD präsentiert eine Sammlung preisgekrönter mathematischer Kurzfilme. Bei den Filmen handelt es sich um die Gewinner des internationalen Wettbewerbs zum MathFilm Festival 2008. Seit der Premiere des Festivals im Mai 2008 in Berlin werden die Filme öffentlich in vielen Städten in Deutschland vorgeführt. Das MathFilm Festival 2008 ist Teil des „Jahres der Mathematik", einer Initiative des Bundesministeriums für Bildung und Forschung. Die Filme richten sich an einen breiten Zuschauerkreis: Schüler, Studenten, Lehrer und alle jene mit einem Interesse an den bunten Seiten der Mathematik. Die Themen reichen von Geometrie bis Computergraphik, vom wissenschaftlichen Rechnen bis Visualisierung, von historischen zu modernen Errungenschaften, von abstrakten mathematischen Ideen bis zu Anwendungen in der realen Welt. Die DVD vermittelt unterhaltsame und informative Einblicke in die moderne Mathematik und bietet anschauliche und fesselnde Filme für lebendige Schul- und Universitätskurse.

El profesor T. M. Apostol, cuyos buenos textos de Análisis y Calculus tuvieron siempre gran aceptación, publica ahora una introducción a la teoría de números, en la que, con un orden y una claridad expositiva ejemplares, muestra al lector, desde un punto de vista moderno, las sorprendentes proposiciones de esta antigua rama de la Matemática, y la introduce en la problemática de una de las teorías más sugestivas de esta Ciencia.

Esta edição apresenta modificações mais significativas que as anteriores - o texto foi revisto e reescrito; alguns capítulos foram desdobrados em vários outros, seja por razões didáticas, seja para enfatizar certos tópicos de maior importância; e as Notas históricas ao final de cada capítulo foram bastante ampliadas, numa resposta aos nossos leitores, que têm apreciado bastante esse material. Elas de fato estimulam o leitor em seu interesse pela disciplina, ao mesmo tempo que oferecem uma visão m ais completa do papel do Cálculo no contexto científico, histórico e cultural dos últimos quatro séculos.

En esta nueva edición, de espíritu más moderno que la excelente primera, se puede repetir el elogio que se hizo anteriormente: su estilo preciso y riguroso, en un programa equilibrado pero suficientemente amplio, le da carácter de texto básico.

Los dos tomos de este Calculus sirven muy adecuadamente como textos de dos primeros cursos en estudios que requieran una sólida base matemática, pues a las notables cualidades didácticas de un libro destinado a introducir al estudiante en el espíritu y práctica de la Matemática básica, se añade la ponderación y rigor lógico en la exposición de las teorías, lo que da carácter modélico a esta obra.

Los dos tomos de este Calculus sirven muy adecuadamente como textos de dos primeros cursos en estudios que requieran una sólida base matemática, pues a las notables cualidades didácticas de un libro destinado a introducir al estudiante en el espíritu y práctica de la Matemática básica, se añade la ponderación y rigor lógico en la exposición de las teorías, lo que da carácter modélico a esta obra.