A collection of inter-connected topics in areas of mathematics which particularly interest the author, ranging over the two millennia from the work of Archimedes to the "Werke" of Gauss. The book is intended for those who love mathematics, including undergraduate students of mathematics, more experienced students and the vast unseen host of amateur mathematicians. It is equally a useful source of material for those who teach mathematics.
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Editorial Reviews
Review
"In an ideal university the staff would supplement the standard courses by offering lectures in which they talked about topics which they particularly loved at a level which the students could understand. And, in an ideal university, the students would flock to such lectures.
George Phillips' book consists of five short courses to be given at our ideal university. As the title is intended to suggest, the topics are treated with due respect for their history and all have their roots in the works of Gauss or earlier mathematicians. The level chosen is that of a first or second year student and the exposition uses the relaxed "explanation, theorem, proof"style of the best colloquium talks."
London Mathematical Society Newsletter, October 2001
"In five chapters (From Archimedes to Gauss, Logarithms, Interpolation, Continued fractions, More number theory), the author shows that many interesting and important results in mahtematics have been discovered by ordinary people and not onl by great geniuses. Each chapter includes the history of its topic with an interpretation of the mathematical problems. The book shows how and why some results in mathematics have been discovered or obtained, by following the steps of well-known mathematicians who discovered them. It is a useful source of mathematical material for teachers, undergraduate students, students and the vast numbers of amateurs who love mathematics."
European Mathematical Society Newsletter, Issue 41, September 2001
George Phillips' book consists of five short courses to be given at our ideal university. As the title is intended to suggest, the topics are treated with due respect for their history and all have their roots in the works of Gauss or earlier mathematicians. The level chosen is that of a first or second year student and the exposition uses the relaxed "explanation, theorem, proof"style of the best colloquium talks."
London Mathematical Society Newsletter, October 2001
"In five chapters (From Archimedes to Gauss, Logarithms, Interpolation, Continued fractions, More number theory), the author shows that many interesting and important results in mahtematics have been discovered by ordinary people and not onl by great geniuses. Each chapter includes the history of its topic with an interpretation of the mathematical problems. The book shows how and why some results in mathematics have been discovered or obtained, by following the steps of well-known mathematicians who discovered them. It is a useful source of mathematical material for teachers, undergraduate students, students and the vast numbers of amateurs who love mathematics."
European Mathematical Society Newsletter, Issue 41, September 2001
About the Author
George Phillips, is a Scot who has lectured and researched in mathematics, mainly at the University of St Andrews, Scotland, but also in many other universities in the UK, the USA, Canada, Brazil, Portugal, Italy, the Czech Republic, Greece, Bulgaria, Turkey, Israel, Malaysia, Singapore, China, and Australia.
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Most Helpful Customer Reviews
5 of 5 people found the following review helpful:
5.0 out of 5 stars
Math motivated by history,
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This review is from: Two Millennia of Mathematics: From Archimedes to Gauss (CMS Books in Mathematics) (Hardcover)
You might think this is a history of math book but it isn't, it's a math book where the 5 topics are subjects the author likes and he motivates the math via some history. You can "look inside" to see the topics, but what I believe to be the most important thing in a review of a math book is "who is this appropriate for ?". The answer in this case is a person with a math background like you would receive in a physics, chemistry, or engineering undergrad degree or a math major undergrad student. You will not be able to follow it without a certain mathematical maturity. I loved it because I'm a mathematician with an interest in these subjects which I have seen before. A more advanced book along the same lines is "Pi and the AGM". People looking for interesting math not requiring as much math background might like "Prime Obsession" or "The Golden Ratio".
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Inside This Book
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First Sentence:
Archimedes will be remembered when Aeschylus is forgotten because languages die and mathematical ideas do not. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
divided difference form, repeated extrapolation, repeated square roots, highest common divisor, forward difference formula, circumscribed regular polygons, interpolating polynomial, periodic continued fraction, interpolating points, minimal residues, simple continued fraction, error series, common limit, quadratic residue, triangular set, divided differences Key Phrases - Capitalized Phrases (CAPs): (learn more)
Historical Notes, Isaac Newton, James Gregory, Other Differences, Leonhard Euler, Liú Zhuó, Use the Binet New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Archimedes will be remembered when Aeschylus is forgotten because languages die and mathematical ideas do not. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
divided difference form, repeated extrapolation, repeated square roots, highest common divisor, forward difference formula, circumscribed regular polygons, interpolating polynomial, periodic continued fraction, interpolating points, minimal residues, simple continued fraction, error series, common limit, quadratic residue, triangular set, divided differences Key Phrases - Capitalized Phrases (CAPs): (learn more)
Historical Notes, Isaac Newton, James Gregory, Other Differences, Leonhard Euler, Liú Zhuó, Use the Binet New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 26
books:
See all 26 books this book cites
2
books
cite this book:
- An Introduction to the Theory of Numbers (Oxford Science Publications) by G. H. Hardy in Front Matter, and Back Matter
- Numerical Analysis (Proceedings of Symposia in Applied Mathematics, V. 22) by American Mathematical Society in Back Matter (1), and Back Matter (2)
- An Introduction to the History of Mathematics (Saunders Series) by Howard Eves in Back Matter
- Introduction to Number Theory With Computing by R. B. J. T. Allenby in Back Matter
- Approximation of Functions by George G. Lorentz in Back Matter
See all 26 books this book cites
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