This text combines elementary number theory with algebraic number theory and applications. Beginning with the arithmetic of the rational intergers and proceeding to an introduction of algebraic number theory via quadratic orders, this text describes new applications of number theory.
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Most Helpful Customer Reviews
8 of 9 people found the following review helpful:
2.0 out of 5 stars
Unimpressed,
By Josh Thorp (Canada) - See all my reviews
This review is from: Fundamental Number Theory with Applications (Discrete Mathematics and Its Applications) (Hardcover)
This book is a confusing mess. If your considering this for an introductory number theory course, stay away. There are several big problems I see with this book. The first being references. Many of the proofs contain references of the essential parts to exersizes (earlier or later) in the book. Add to the fact that none of the exersizes have full solutions, this book is in fact full of incomplete proofs. Also, there are many errors and exersizes which are plain wrong ( I can think of a few exersizes that we used to find infinite counterexamples to) The second problem is notation. The author seems to take full advantage of making everything as short and notation heavy as possible. Unless you really know all your mathematical and logical symbols, this becomes a tedious read. Finally, it's much more of annoyance, the footnotes are huge. Sometimes filling up half the page. I do enjoy reading about mathematical history, but I feel a footnote does not do a biography justice. Either have an appendix, or follow the style in Nicholson's "Abstract Algebra" with a page or two near the endo of every chapter dedicated to the biographies. If you can put up with all these problems, you may find this text useful. It does provide a good basis for number theory and a good introduction to cryptography using the material in the book.
10 of 12 people found the following review helpful:
5.0 out of 5 stars
The basis of cryptography,
By
This review is from: Fundamental Number Theory with Applications (Discrete Mathematics and Its Applications) (Hardcover)
A very solid, rigorous introduction to its subject. Scads of exercises, which is utterly essential for you to gain fluency. As a nice touch, the author also provides answers to half the questions. Alternatively, if you are a lecturer casting around for a suitable text for your class, then this may be useful. You can assign many problems for which your students cannot blithely look up the answers.The book covers topics like Euler's Totient, Quadratic residues, Chinese Remainder Theorem and Diophantine equations. The breadth of number theory. The book has another merit. Pure number theory texts are suitable for those majoring in the field. But even amongst mathematicians, this is a small set. These days, number theory forms the foundations of cryptography. The continued rise of the Internet, especially for commercial applications, including the still incipient web services, has spawned a critical need for better encryption. A major theme of the book is its usefulness to cryptographers. To this end, public keys, elliptic curves and other related topics are prominently described.
4 of 7 people found the following review helpful:
1.0 out of 5 stars
Terrible Book, and Terrible Author,
This review is from: Fundamental Number Theory with Applications (Discrete Mathematics and Its Applications) (Hardcover)
I had the luxory of using this book, and also the great honor of being taught by the "great man" himself, who has written this 120 dollar peace of trash. The book is terrible, when trying to read through the proofs in each section, halfway through the proof it says "this part is left as an exercise"
and an even excersise none the less, I mean if your gonna go through a proof make it COMPLETE, don't tell me its an easy exercise, thats BS, now thats the book, now ill leave you to imagine how terrible of a proffesor he was, let me just say this, i love mathematics, and im planning on concentrating in crpytography, but that SOB Mollin, has me reconsidering the hole thing all together, i'd rather quit the concentration than to have to even open that textbook again and sit through one of his lectures. Whatever you do, don't buy this book, and stay away from Mollin, and if you have to take a class with Mollin, i would deffinitely buy a secondary textbook
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Inside This Book
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First Sentence:
Any logical system must begin with some statements that are assumed to be true. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
complex quadratic orders, canonical prime factorization, imprimitive representations, least multiplicative inverse, simple continued fraction expansion, least residue system modulo, fundamental number theory, incongruent solutions, fundamental discriminant, kth convergent, absolute pseudoprime, multiplication formulae, quadratic sieve method, quadratic irrational, continued fraction algorithm, computational number theory, primitive root modulo, integral polynomial, quadratic reciprocity law, odd prime divisors, polynomial congruences, invertible ideals, integer squares, assume the induction hypothesis, primality test Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fermat's Little Theorem, Arithmetic of the Integers, Chinese Remainder Theorem, Lagrange's Theorem, Gauss's Lemma, Section Six of Chapter One, Well-Ordering Principle, Euler's Criterion, University of Berlin, Thue's Theorem, Law of Order, Axiom Five, Bertrand Russell, Cubic Reciprocity Law, Dirichlet's Theorem, Royal Society, Section Five of Chapter One, Section Six of Chapter Two, Bachet's Theorem, Ecole Normale, Goldbach's Conjecture, Hasse's Theorem, John Selfridge, Julius Caesar, Prove Corollary New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Any logical system must begin with some statements that are assumed to be true. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
complex quadratic orders, canonical prime factorization, imprimitive representations, least multiplicative inverse, simple continued fraction expansion, least residue system modulo, fundamental number theory, incongruent solutions, fundamental discriminant, kth convergent, absolute pseudoprime, multiplication formulae, quadratic sieve method, quadratic irrational, continued fraction algorithm, computational number theory, primitive root modulo, integral polynomial, quadratic reciprocity law, odd prime divisors, polynomial congruences, invertible ideals, integer squares, assume the induction hypothesis, primality test Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fermat's Little Theorem, Arithmetic of the Integers, Chinese Remainder Theorem, Lagrange's Theorem, Gauss's Lemma, Section Six of Chapter One, Well-Ordering Principle, Euler's Criterion, University of Berlin, Thue's Theorem, Law of Order, Axiom Five, Bertrand Russell, Cubic Reciprocity Law, Dirichlet's Theorem, Royal Society, Section Five of Chapter One, Section Six of Chapter Two, Bachet's Theorem, Ecole Normale, Goldbach's Conjecture, Hasse's Theorem, John Selfridge, Julius Caesar, Prove Corollary 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 18
books:
See all 18 books this book cites
22
books
cite this book:
See all 22 books citing this book
- Disquisitiones Arithmeticae by Carl F. Gauss on page 75, page 193, and Back Matter
- Cryptography : Theory and Practice by Douglas R. Stinson in Front Matter, and Back Matter
- Diophantine Equations (Pure & Applied Mathematics) by L.J. Mordell on page 309, and Back Matter
- The Gutenberg Galaxy: The Making of Typographic Man by Marshall McLuhan on page 11
- Introduction to Number Theory by Loo-Keng Hua in Back Matter
See all 18 books this book cites
- Codes: The Guide to Secrecy From Ancient to Modern Times (Discrete Mathematics and Its Applications) by Richard A. Mollin in Front Matter, and Back Matter
- RSA and Public-Key Cryptography (Discrete Mathematics and Its Applications) by Richard A. Mollin in Front Matter, and Back Matter
- An Introduction to Cryptography (Discrete Mathematics and Its Applications) by Richard A. Mollin in Front Matter, and Back Matter
- Algebraic Number Theory (Discrete Mathematics and Its Applications) by Richard A. Mollin in Front Matter, and Back Matter
- Verification of Computer Codes in Computational Science and Engineering by Patrick Knupp in Front Matter
See all 22 books citing this book
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