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Vous aimez le chiffre 7 ? Normal, il est le préféré de la plupart d’entre nous. C’est ainsi, nous avons des sentiments envers ces créations purement humaines que sont les nombres. Les impairs nous séduisent, le chiffre 13 laisse perplexe, les équations nous fascinent... Alex Bellos sait l’exaltation que l’esprit humain peut éprouver en mathématiques. Et c’est cet émerveillement qu’il met à la portée de tous dans Alex et la magie des nombres. Par son humour, il en réconciliera plus d’un avec les cercles, la trigonométrie, les mystérieux nombres imaginaires ou les exponentielles. On y croise les esprits remarquables de la Grèce antique – Pythagore ou Archimède –, mais aussi de la Renaissance et de notre temps, tel Cédric Villani. De sa plume fantasque, Alex Bellos nous entraîne dans une aventure magique au pays des mathématiques, la plus ludique des disciplines scientifiques.

Mathematics

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Fundamentals of Advanced Mathematics, Volume Three, begins with the study of differential and analytic infinite-dimensional manifolds, then progresses into fibered bundles, in particular, tangent and cotangent bundles. In addition, subjects covered include the tensor calculus on manifolds, differential and integral calculus on manifolds (general Stokes formula, integral curves and manifolds), an analysis on Lie groups, the Haar measure, the convolution of functions and distributions, and the harmonic analysis over a Lie group. Finally, the theory of connections is (linear connections, principal connections, and Cartan connections) covered, as is the calculus of variations in Lagrangian and Hamiltonian formulations. This volume is the prerequisite to the analytic and geometric study of nonlinear systems.

Mathematics

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This book is not intended for budding mathematicians. It was created for a math program in which most of the students in upper-level math classes are planning to become secondary school teachers. For such students, conventional abstract algebra texts are practically incomprehensible, both in style and in content. Faced with this situation, we decided to create a book that our students could actually read for themselves. In this way we have been able to dedicate class time to problem-solving and personal interaction rather than rehashing the same material in lecture format.

Mathematics

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Mathematics

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Mathematics.