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Carus Mathematical Monographs #11
An Introduction to the Theory of Numbers
Divisibility congruences quadratic reciprocity and quadratic forms some functions of number theory some diophantine equations farey fractions and irrational numbers simple continued fractions primes and multiplicative number theory algebraic numbers the partition function the density of sequences of integers
545 pages, Paperback
First published January 28, 1956
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Displaying 1 - 8 of 8 reviews
February 12, 2020
A tough book. I didn't like the style of the book too much to say the least.
Let's begin with the positives. The book is designed geniously. Each chapter is almost self-contained barring few basic ideas that any college undergrad ought to know. Kudos for that. Each topic is covered in almost excruciating detail- at times a positive, at times not. The author has introduced, to my understanding, every tool and concept any undergrad needs to be aware of after taking a first course in number theory. I cannot stress enough the breadth and depth that this book covers. Marvelous. One star just for that.
My issues with the book, are ironically regarding the writing style. I find the book too scattered. Maybe because I used an e-book but at times the book is extremely unclear. To cite an example, an exercise in the section dealing with elliptic curves left me completely perplexed. I didn't know at what times the author was referring to a particular example and when he made a statement with regards to a theorem. Besides elliptic curve, I found the Farey sequences a bit too difficult to grasp.
Having said all of that, I find it slightly difficult to enumerate every topic covered in the book but you can easily get a table of contents online. I would recommend this book if you're a Math major. This is one book you must have on introductory number theory if you want just one.
Let's begin with the positives. The book is designed geniously. Each chapter is almost self-contained barring few basic ideas that any college undergrad ought to know. Kudos for that. Each topic is covered in almost excruciating detail- at times a positive, at times not. The author has introduced, to my understanding, every tool and concept any undergrad needs to be aware of after taking a first course in number theory. I cannot stress enough the breadth and depth that this book covers. Marvelous. One star just for that.
My issues with the book, are ironically regarding the writing style. I find the book too scattered. Maybe because I used an e-book but at times the book is extremely unclear. To cite an example, an exercise in the section dealing with elliptic curves left me completely perplexed. I didn't know at what times the author was referring to a particular example and when he made a statement with regards to a theorem. Besides elliptic curve, I found the Farey sequences a bit too difficult to grasp.
Having said all of that, I find it slightly difficult to enumerate every topic covered in the book but you can easily get a table of contents online. I would recommend this book if you're a Math major. This is one book you must have on introductory number theory if you want just one.
March 31, 2008
I read this book because a professor of mine, who was retiring, gave me this book because I had displayed an interest in the material. That professor was really good. I became a math major as a direct result of that action.
I learned about the elementary theory of congruences from this book. But it is referenced everywhere. I plan to read through more topics in this book later.
I have heard that it has an awesome discussion of the theory of continued fractions.
I learned about the elementary theory of congruences from this book. But it is referenced everywhere. I plan to read through more topics in this book later.
I have heard that it has an awesome discussion of the theory of continued fractions.
April 20, 2007
the go-to book for undergrad number theory.
October 4, 2016
My favorite book on my shelf, if it ever had occasion to spend much time there.
August 18, 2017
I suppose it was a kind of arrogant, perverse madness that made me order this from the library's web-facility. I managed the Introduction [illuminating!]. Nuf confessed.
October 31, 2019
A very nice introduction to the theory of numbers starting with the fundamental theorem of number theory and then navigating through the basic topics reaching quadratic forms in a very nice treatment in addition to elementary topics in elliptic curves. I would recommend it for those who want to learn the number-theoretic approach to quadratic forms and their properties. The problems are well-thought of and are very beneficial for students to solve.
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January 6, 2024The decimal expansion of 1/p has period p-1 if and only if 10 is a primitive root of p.
September 11, 2015
it's a good book
Displaying 1 - 8 of 8 reviews