Search Results for "mathematics-and-its-history-undergraduate-texts-in-mathematics"

Mathematics and Its History

Mathematics and Its History

  • Author: John Stillwell
  • Publisher: Springer Science & Business Media
  • ISBN: 144196052X
  • Category: Mathematics
  • Page: 662
  • View: 2308
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From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

Exploring Classical Greek Construction Problems with Interactive Geometry Software

Exploring Classical Greek Construction Problems with Interactive Geometry Software

  • Author: Ad Meskens,Paul Tytgat
  • Publisher: Birkhäuser
  • ISBN: 3319428632
  • Category: Mathematics
  • Page: 185
  • View: 3770
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In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software (IGS). The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of IGS the reader is confronted with the same problems that ancient mathematicians once faced. The reader can step into the footsteps of Euclid, Viète and Cusanus amongst others and then by experimenting and discovering geometric relationships far exceed their accomplishments. Exploring these problems with the neusis-method lets him discover a class of interesting curves. By experimenting he will gain a deeper understanding of how mathematics is created. More than 100 exercises guide him through methods which were developed to try and solve the problems. The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those students who are thinking of becoming a mathematics teacher and for mathematics teachers.

Geometry by Its History

Geometry by Its History

  • Author: Alexander Ostermann,Gerhard Wanner
  • Publisher: Springer Science & Business Media
  • ISBN: 3642291635
  • Category: Mathematics
  • Page: 440
  • View: 2268
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In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19thcentury. Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.

Analysis by Its History

Analysis by Its History

  • Author: Ernst Hairer,Gerhard Wanner
  • Publisher: Springer Science & Business Media
  • ISBN: 0387770364
  • Category: Mathematics
  • Page: 379
  • View: 9087
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This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

Number Theory and Its History

Number Theory and Its History

  • Author: Oystein Ore
  • Publisher: Courier Corporation
  • ISBN: 0486136434
  • Category: Mathematics
  • Page: 400
  • View: 4925
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Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.

Naive Lie Theory

Naive Lie Theory

  • Author: John Stillwell
  • Publisher: Springer Science & Business Media
  • ISBN: 9780387782157
  • Category: Mathematics
  • Page: 217
  • View: 9166
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In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

Mathematical Reviews

Mathematical Reviews

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 4777
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Innovative approaches to undergraduate mathematics courses beyond calculus

Innovative approaches to undergraduate mathematics courses beyond calculus

  • Author: Richard J. Maher
  • Publisher: Mathematical Assn of Amer
  • ISBN: 9780883851777
  • Category: Mathematics
  • Page: 173
  • View: 2482
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Newsletter

Newsletter

  • Author: New Zealand Mathematical Society
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 1871
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Bulletin

Bulletin

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 600
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