Title
lments d'analyse et d'algbre: (et de thorie des nombres),Used
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Cet ouvrage est issu d'un cours en premire anne l'cole Polytechnique.Son format un peu particulier en fait un bon compagnon pour la prparation des concours du taupin ambitieux et de l'agrgatif, ou pour l'tudiant de L3 ou quiconque ayant atteint ce niveau et cherchant saisir le fonctionnement interne des mathmatiques. Le long chapitre 'Vocabulaire Mathmatique', dont le but tait d'offrir aux lves des autres filires le rsum d'un cours des meilleures classes de MP*, regroupe et prcise, sous une forme compacte, l'essentiel des notions de base vues en L1 et L2 ou pendant les classes prparatoires (groupes, anneaux, corps, algbre linaire, matrices, topologie, compacit, connexit, compltude, sries numriques, convergence de fonctions, espaces hermitiens).Il comporte plus d'une centaine d'exercices corrigs. Le cours qui suit offre une introduction trois des thories la racine des mathmatiques : la thorie des reprsentations des groupes finis, qui est la fois une extension naturelle de l'algbre linaire et une premire approche de la transforme de Fourier, l'analyse fonctionnelle classique (espaces de Banach et Hilbert, intgrale de Lebesgue, transforme de Fourier) et la thorie des fonctions holomorphes. Il recouvre une bonne partie du cursus de L3 l'Universit.Les 13 problmes corrigs combinent les thormes du cours pour dmontrer de jolis rsultats comme l'irrationalit de Sigma (3). La principale originalit de l'ouvrage vient de l'accent mis sur l'aspect culturel et l'unit des mathmatiques. De nombreuses notes de bas de page proposent de petites excursions en dehors de l'autoroute des mathmatiques utiles. Sept appendices prsentent des extraits de la littrature mathmatique classique, accessibles avec le contenu du cours, qui montrent comment les thories de base se combinent pour la rsolution de problmes naturels profonds.L'un d'entre eux est consacr au thorme des nombres premiers dont la dmonstration a pris plus de 150 ans ; un autre est une introduction au programme de Langlands, qui occupe les arithmticiens depuis plus de 40 ans, et dont une des retombes les plus spectaculaires est la dmonstration du thorme de Fermat. Entre les deux le lecteur pourra dcouvrir quelques aspects du monde padique ou une formule indiquant des liens encore mystrieux entre les mondes rels et padiques, ou encore un problme millnaire non encore rsolu.
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Shipping & Returns
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We ship your order within 2–3 business days for USA deliveries and 5–8 business days for international shipments. Once your package has been dispatched from our warehouse, you'll receive an email confirmation with a tracking number, allowing you to track the status of your delivery.
Returns
To facilitate a smooth return process, a Return Authorization (RA) Number is required for all returns. Returns without a valid RA number will be declined and may incur additional fees. You can request an RA number within 15 days of the original delivery date. For more details, please refer to our Return & Refund Policy page.
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Warranty
We provide a 2-year limited warranty, from the date of purchase for all our products.
If you believe you have received a defective product, or are experiencing any problems with your product, please contact us.
This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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Frequently Asked Questions
- Q: What is the main focus of 'Éléments d'analyse et d'algèbre'? A: The book focuses on foundational concepts in analysis and algebra, aiming to provide a strong mathematical grounding for students in advanced studies.
- Q: Who is the author of this book? A: The author of 'Éléments d'analyse et d'algèbre' is Pierre Colmez.
- Q: What is the target audience for this book? A: This book is intended for first-year students at École Polytechnique, as well as those preparing for competitive exams and students in their third year of university.
- Q: How many pages does this book contain? A: The book contains a total of 658 pages.
- Q: What type of binding does this book have? A: The book is available in a hardcover binding, which provides durability and a professional appearance.
- Q: When was 'Éléments d'analyse et d'algèbre' published? A: The book was published on November 15, 2011.
- Q: Does the book include exercises and solutions? A: Yes, the book contains over a hundred corrected exercises that help reinforce the concepts discussed.
- Q: What topics are covered in the book? A: The book covers topics such as group theory, linear algebra, functional analysis, and the theory of holomorphic functions, among others.
- Q: Are there any additional resources included in the book? A: Yes, the book includes several appendices that offer excerpts from classical mathematical literature, enhancing the understanding of the theories presented.
- Q: Is this book suitable for self-study? A: Yes, this book can be used for self-study by motivated students who have reached at least a third-year level in mathematics.