Linear Algebra Through Geometry
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Linear Algebra Through Geometry
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Author : Thomas Banchoff
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Algebra Through Geometry written by Thomas Banchoff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space. Topics include systems of linear equations in n variable, inner products, symmetric matrices, and quadratic forms. The final chapter treats application of linear algebra to differential systems, least square approximations and curvature of surfaces in three spaces. The only prerequisite for reading this book (with the exception of one section on systems of differential equations) are high school geometry, algebra, and introductory trigonometry.
Linear Algebra Through Geometry
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Author : T. Banchoff
language : en
Publisher: Springer
Release Date : 1983-05-02
Linear Algebra Through Geometry written by T. Banchoff and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-05-02 with Mathematics categories.
In this book we lead the student to an understanding of elementary linear algebra by emphasizing the geometric significance of the subject. Our experience in teaching beginning undergraduates over the years has convinced us that students learn the new ideas of linear algebra best when these ideas are grounded in the familiar geometry of two and three dimensions. Many important notions of linear algebra already occur in these dimensions in a non-trivial way, and a student with a confident grasp of these ideas will encounter little difficulty in extending them to higher dimensions and to more abstract algebraic systems. Moreover, we feel that this geometric approach provides a solid basis for the linear algebra needed in engineering, physics, biology, and chemistry, as well as in economics and statistics. The great advantage of beginning with a thorough study of the linear algebra of the plane is that students are introduced quickly to the most important new concepts while they are still on the familiar ground of two-dimensional geometry. In short order, the student sees and uses the notions of dot product, linear transformations, determinants, eigenvalues, and quadratic forms. This is done in Chapters 2.0-2.7. Then the very same outline is used in Chapters 3.0-3.7 to present the linear algebra of three-dimensional space, so that the former ideas are reinforced while new concepts are being introduced.
Linear Algebra Through Geometry
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Author : T. Banchoff
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Algebra Through Geometry written by T. Banchoff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In this book we lead the student to an understanding of elementary linear algebra by emphasizing the geometric significance of the subject. Our experience in teaching beginning undergraduates over the years has convinced us that students learn the new ideas of linear algebra best when these ideas are grounded in the familiar geometry of two and three dimensions. Many important notions of linear algebra already occur in these dimensions in a non-trivial way, and a student with a confident grasp of these ideas will encounter little difficulty in extending them to higher dimensions and to more abstract algebraic systems. Moreover, we feel that this geometric approach provides a solid basis for the linear algebra needed in engineering, physics, biology, and chemistry, as well as in economics and statistics. The great advantage of beginning with a thorough study of the linear algebra of the plane is that students are introduced quickly to the most important new concepts while they are still on the familiar ground of two-dimensional geometry. In short order, the student sees and uses the notions of dot product, linear transformations, determinants, eigenvalues, and quadratic forms. This is done in Chapters 2.0-2.7. Then the very same outline is used in Chapters 3.0-3.7 to present the linear algebra of three-dimensional space, so that the former ideas are reinforced while new concepts are being introduced.
Groups And Symmetry
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Author : Mark A. Armstrong
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Groups And Symmetry written by Mark A. Armstrong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory. Written in an informal style, the material is divided into short sections each of which deals with an important result or a new idea. Throughout the book, the emphasis is placed on concrete examples, many of them geometrical in nature, so that finite rotation groups and the seventeen wallpaper groups are treated in detail alongside theoretical results such as Lagrange's theorem, the Sylow theorems, and the classification theorem for finitely generated abelian groups. A novel feature at this level is a proof of the Nielsen-Schreier theorem, using group actions on trees. There are more than three hundred exercises and approximately sixty illustrations to help develop the student's intuition.
Introduction To Cryptography
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Author : Johannes Buchmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Cryptography written by Johannes Buchmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control, etc. Therefore, users should not only know how its techniques work, but they must also be able to estimate their efficiency and security. For this new edition, the author has updated the discussion of the security of encryption and signature schemes and recent advances in factoring and computing discrete logarithms. He has also added descriptions of time-memory trade of attacks and algebraic attacks on block ciphers, the Advanced Encryption Standard, the Secure Hash Algorithm, secret sharing schemes, and undeniable and blind signatures. Johannes A. Buchmann is a Professor of Computer Science and Mathematics at the Technical University of Darmstadt, and the Associate Editor of the Journal of Cryptology. In 1985, he received the Feodor Lynen Fellowship of the Alexander von Humboldt Foundation. Furthermore, he has received the most prestigious award in science in Germany, the Leibniz Award of the German Science Foundation. About the first edition: It is amazing how much Buchmann is able to do in under 300 pages: self-contained explanations of the relevant mathematics (with proofs); a systematic introduction to symmetric cryptosystems, including a detailed description and discussion of DES; a good treatment of primality testing, integer factorization, and algorithms for discrete logarithms; clearly written sections describing most of the major types of cryptosystems....This book is an excellent reference, and I believe it would also be a good textbook for a course for mathematics or computer science majors..." -Neal Koblitz, The American Mathematical Monthly
Mathematical Masterpieces
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Author : Art Knoebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-16
Mathematical Masterpieces written by Art Knoebel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-16 with Mathematics categories.
Intended for juniors and seniors majoring in mathematics, as well as anyone pursuing independent study, this book traces the historical development of four different mathematical concepts by presenting readers with the original sources. Each chapter showcases a masterpiece of mathematical achievement, anchored to a sequence of selected primary sources. The authors examine the interplay between the discrete and continuous, with a focus on sums of powers. They then delineate the development of algorithms by Newton, Simpson and Smale. Next they explore our modern understanding of curvature, and finally they look at the properties of prime numbers. The book includes exercises, numerous photographs, and an annotated bibliography.
Undergraduate Algebra
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-03-21
Undergraduate Algebra written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-21 with Mathematics categories.
The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group
The Pleasures Of Probability
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Author : Richard Isaac
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
The Pleasures Of Probability written by Richard Isaac and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
The ideas of probability are all around us. Lotteries, casino gambling, the al most non-stop polling which seems to mold public policy more and more these are a few of the areas where principles of probability impinge in a direct way on the lives and fortunes of the general public. At a more re moved level there is modern science which uses probability and its offshoots like statistics and the theory of random processes to build mathematical descriptions of the real world. In fact, twentieth-century physics, in embrac ing quantum mechanics, has a world view that is at its core probabilistic in nature, contrary to the deterministic one of classical physics. In addition to all this muscular evidence of the importance of probability ideas it should also be said that probability can be lots of fun. It is a subject where you can start thinking about amusing, interesting, and often difficult problems with very little mathematical background. In this book, I wanted to introduce a reader with at least a fairly decent mathematical background in elementary algebra to this world of probabil ity, to the way of thinking typical of probability, and the kinds of problems to which probability can be applied. I have used examples from a wide variety of fields to motivate the discussion of concepts.
Calculus Ii
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Author : Jerrold Marsden
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Calculus Ii written by Jerrold Marsden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The second of a three-volume work, this is the result of the authors'experience teaching calculus at Berkeley. The book covers techniques and applications of integration, infinite series, and differential equations, the whole time motivating the study of calculus using its applications. The authors include numerous solved problems, as well as extensive exercises at the end of each section. In addition, a separate student guide has been prepared.
Factorization And Primality Testing
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Author : David M. Bressoud
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Factorization And Primality Testing written by David M. Bressoud and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
"About binomial theorems I'm teeming with a lot of news, With many cheerful facts about the square on the hypotenuse. " - William S. Gilbert (The Pirates of Penzance, Act I) The question of divisibility is arguably the oldest problem in mathematics. Ancient peoples observed the cycles of nature: the day, the lunar month, and the year, and assumed that each divided evenly into the next. Civilizations as separate as the Egyptians of ten thousand years ago and the Central American Mayans adopted a month of thirty days and a year of twelve months. Even when the inaccuracy of a 360-day year became apparent, they preferred to retain it and add five intercalary days. The number 360 retains its psychological appeal today because it is divisible by many small integers. The technical term for such a number reflects this appeal. It is called a "smooth" number. At the other extreme are those integers with no smaller divisors other than 1, integers which might be called the indivisibles. The mystic qualities of numbers such as 7 and 13 derive in no small part from the fact that they are indivisibles. The ancient Greeks realized that every integer could be written uniquely as a product of indivisibles larger than 1, what we appropriately call prime numbers. To know the decomposition of an integer into a product of primes is to have a complete description of all of its divisors.