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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. Apart from this, the two versions are identical.
The Dover version is very affordable; buy copies for all your friends! Pathways from the Past is an offshoot from Math through the Ages. There are two volumes. Each contains historically-based worksheets that teachers can use to teach mathematics.
There are two sets of worksheets. Both sets are available from Oxton House. Math through the Ages has been translated into five other languages; you can see the covers of those editions above. A Guide to Groups, Rings, and Fields is a survey of graduate algebra, aimed principally at those who want to review the subject. Aside from a couple of broadly introductory chapters, the book looks at groups, group actions, and group representation; rings and their modules; fields, skew fields, and Galois theory.
There are no proofs, but I hope readers will find it a useful overview of the material. The link takes you to the main page for the book, where I also keep a list of currently-known errors and misprints. P-adic Numbers: the corrected third printing of the second edition of my book p-adic Numbers: An Introduction came out in mid The book is an introduction to p-adic numbers and p-adic analysis aimed at mathematics undergraduates. It tries to be open up the theory to the reader in a friendly and accessible way.
Check here for a few errata, notes, and other comments about the book. Arithmetic of p-adic Modular Forms was my first book, based on my PhD thesis.
It is desperately out-of-date, since the field has progressed a lot since I wrote it in the late s. Here is the full list. Interests: My research interests are: History of Mathematics, especially the history of algebra and number theory, and Number Theory and Arithmetic Geometry, with a special focus on modular forms and Galois representations.
As a spectator, rather than as an active player, I also try to keep in touch with lots of other fields in mathematics.
Outside mathematics, I am interested in Christian theology, patristics, fountain pens, modern science fiction, literature and poetry, politics, wine, perfume, comic books, and lots of other things. Fernando Q.
About this book Introduction p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely.
Fernando Q. Gouvêa
The p-adic numbers are not as well known as the others, but they play a fundamental role in number theory and in other parts of mathematics, capturing information related to a chosen prime number p. They also allow us to use methods from calculus and analysis to obtain results in algebra and number theory. This book is an elementary introduction to p-adic numbers. Most other books on the subject are written for more advanced students; this book provides an entryway to the subject for students with an undergraduate mathematics education. Readers who want to have an idea of and appreciation for the subject will probably find what they need in this book. Readers on the way to becoming experts can begin here before moving on to more advanced texts.