My own first exposure to the book came when I was an undergraduate and one of my friends came back from an REU and gave a talk on p-adic numbers. I was intrigued by one of the counterintuitive results that one gets when working in the p-adic topology — all triangles are isosceles, but none are equilateral! I checked it out of the library and found a book that was mathematically rich while still being clear and lively to read. In the intervening decade and a half, as I have spent much time reading about and working with p-adic numbers in my own research, I have read any number of treatments of the subject, and certainly several other sources come to mind that have various advantages in their different goals and perspectives. But if I had to recommend one book on the subject to a student — or even to a fully grown mathematician who had never played with p-adic numbers before — it would still be this book. It turns out that the p-adic rational numbers are similar to the real numbers in some senses they are locally compact completions of the normal rational numbers, they are not algebraically closed while being very different in other senses the p-adic rationals are totally disconnected and are not ordered, for example.
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Springer; 2nd edition August 5, Language: Customers who viewed this item also viewed. Amazon Advertising Find, attract, and engage customers. Learn more about Amazon Prime. Want to Read saving…. There are few adventures in other territories, p-adlc few opportunities to visit some of the more exotic cor ners of mathematics.
Showing of 3 reviews. There are numbers of all kinds: Explore the Home Gift Guide. Can we conclude that the equation has a solution in? Thiago Dourado marked it as to-read Dec 15, The overall conclusion is simple: Amazon Giveaway allows you to run promotional giveaways in order to mumbers buzz, reward your njmbers, and attract new followers and customers. I really love the way Gouvea writes about math.
Review From the reviews: Get to Know Us. Noah Lichtblau is currently reading it Oct 30, The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. To ask other readers questions about P-Adic Numbersplease sign up. Collection of teaching and learning tools built by Wolfram education experts: This elementary introduction offers a broad understanding of p-adic numbers. The -adic numbers are useful in solving Diophantine equations.
The -adics were probably first introduced by Hensel in a paper which was concerned with the development of algebraic numbers in power series. Trivia About P-Adic Numbers: Hasse subsequently formulated the Hasse principlewhich is one of the chief applications of local field theory.
This is a common argument that is used in solving these types of equations: Seventh International Conference on P-Adic In conclusion, I recommend this book to the set of people interested in p-adic numbers, and its complement. Amazon Restaurants Food delivery from local restaurants. Daniel rated it really liked it Dec 25, Paperbackpages. Learn more about Amazon Giveaway. Perez-GarciaAlain Escassut No preview available — The reader is led into oguvea rich structure of the fields Qp and Cp in a beautiful balance between analytic and algebraic aspects.
The completion of this space can therefore be constructed, and the set of -adic numbers is defined to be this completed space. The goal of this book is to offer such an opportunity, by way of a gluvea to the p-adic universe. Any nonzero rational number can be represented by. Practice online or make a printable study sheet. Suppose we have an equation that does have solutions in and in all numbres for every prime.
Riccardo Giannitrapani added it Oct 31, Another application is the theorem that the harmonic numbers are never integers except for. No trivia or quizzes yet.
GOUVEA P-ADIC NUMBERS PDF
Tthe non-expanded version is now published by Dover. The book is an introduction to the history of mathematics with the needs of mathematics teachers chiefly in mind. The main differences between the expanded second edition and the just-plain second edition are: The expanded edition has a prettier cover. The expanded edition includes problems and projects.
p-adic Numbers: An Introduction
Set up a giveaway. See all 3 reviews. The completion of this space can therefore be constructed, and the set of -adic numbers is defined to be this completed space. If andthen the expansion is unique. The reader is led into the rich structure of the fields Qp and Cp in a beautiful balance between analytic and algebraic aspects. For another example, consider. You already told me what the answer is!
Fernando Q. Gouvêa