Title
Foundations of Modern Analysis,New
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In this text, the whole structure of analysis is built up from the foundations. The only things assumed at the outset are the rules of logic and the usual properties of the natural numbers, and with these two exceptions all the proofs in the text rest on the axioms and theorems proved earlier. Nevertheless this treatise (including the first volume) is not suitable for students who have not yet covered the first two years of an undergraduate honours course in mathematics. A striking characteristic of the elementary parts of analysis is the small amount of algebra required. Effectively all that is needed is some elementary linear algebra (which is included in an appendix at the end of the first volume, for the reader's convenience). However, the role played by algebra increases in the subsequent volumes, and we shall finally leave the reader at the point where this role becomes preponderant, notably with the appearance of advanced commutative algebra and homological algebra. As reference books in algebra we have taken R. Godement's 'Abstract Algebra,' and S. A. Lang's 'Algebra' which we shall possibly augment in certain directions by means of appendices. As with the first volume, I have benefited greatly during the preparation of this work from access to numerous unpublished manuscripts of N. Bourbaki and his collaborators. To them alone is due any originality in the presentation of certain topics.
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- Q: How many pages does this book have? A: This book has four hundred pages. It provides a comprehensive exploration of modern analysis.
- Q: What is the binding type of this book? A: The book is paperback bound. This makes it lightweight and portable for easy reading.
- Q: What are the dimensions of this book? A: The book measures five point five one inches in length, zero point nine one inches in width, and eight point five inches in height.
- Q: Who is the author of this book? A: The author is J. Dieudonné. He is known for his contributions to mathematics and analysis.
- Q: What subject does this book cover? A: This book covers the subject of mathematics. It focuses on the foundations of modern analysis.
- Q: What level of mathematics is required to understand this book? A: A solid understanding of undergraduate honors mathematics is required. It is not suitable for students without this background.
- Q: Is this book suitable for beginners in mathematics? A: No, this book is not suitable for beginners. It is designed for those with prior knowledge of advanced mathematics.
- Q: Can I read this book without prior knowledge of algebra? A: No, prior knowledge of algebra is necessary. The role of algebra increases as you progress through the text.
- Q: How is this book structured? A: The book is structured to build concepts from foundational axioms and theorems. Each section relies on previous proofs.
- Q: What is the recommended audience for this book? A: The recommended audience is undergraduate mathematics students. It is aimed at those pursuing advanced studies.
- Q: How should I care for this book? A: To keep this book in good condition, store it in a cool, dry place. Avoid exposure to moisture to prevent damage.
- Q: Is this book safe for young readers? A: No, this book is not safe for young readers. It is intended for advanced students in mathematics.
- Q: What if my book arrives damaged? A: If your book arrives damaged, contact customer support for a return or exchange. They will guide you through the process.
- Q: Can I return this book if I don't like it? A: Yes, you can return the book if it is in original condition. Check the return policy for specific time frames.
- Q: Where can I find additional resources related to this book? A: Additional resources can be found in the appendices and references provided in the book. They include suggested readings.
- Q: What other books relate to the themes in this book? A: Related books include R. Godement's 'Abstract Algebra' and S. A. Lang's 'Algebra.' These texts complement the material covered.