1. Number theory [electronic resource] : an approach through history from Hammurapi to Legendre [1984]
- Book
- 1 online resource (375 pages) : illustrations.
- Preface
- Table of illustrations
- Abbreviations, basic references and notations
- Protohistory
- Fermat and his Correspondents
- Euler
- An Age of Transition: Lagrange and Legendre
- Additional bibliography and references
- Index nominum
- Index rerum.
- Preface
- Table of illustrations
- Abbreviations, basic references and notations
- Protohistory
- Fermat and his Correspondents
- Euler
- An Age of Transition: Lagrange and Legendre
- Additional bibliography and references
- Index nominum
- Index rerum.
2. Analytic number theory [2002]
- Book
- 1 online resource (xv, 408 pages).
The book includes several survey articles on prime numbers, divisor problems, and Diophantine equations, as well as research papers on various aspects of analytic number theory such as additive problems, Diophantine approximations and the theory of zeta and L-function. Audience: Researchers and graduate students interested in recent development of number theory.
The book includes several survey articles on prime numbers, divisor problems, and Diophantine equations, as well as research papers on various aspects of analytic number theory such as additive problems, Diophantine approximations and the theory of zeta and L-function. Audience: Researchers and graduate students interested in recent development of number theory.
3. The emergence of number [1987]
- Book
- x, 222 p. : ill. ; 23 cm.
SAL3 (off-campus storage)
SAL3 (off-campus storage) | Status |
---|---|
Stacks | Request |
QA241 .C88 1987 | Available |
4. The emergence of number [1980]
- Book
- 376 p. : ill. ; 25 cm.
SAL3 (off-campus storage)
SAL3 (off-campus storage) | Status |
---|---|
Stacks | Request |
QA241 .C95 | Available |
5. Introduction to number theory [2018]
- Book
- xiv, 247 pages ; 23 cm.
Textbook, with answers to some exercises.
(source: Nielsen Book Data)9781786344717 20180319
(source: Nielsen Book Data)9781786344717 20180319
Textbook, with answers to some exercises.
(source: Nielsen Book Data)9781786344717 20180319
(source: Nielsen Book Data)9781786344717 20180319
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | |
QA241 .H4845 2018 | Unknown |
- Book
- xix, 191 pages ; 24 cm.
- On Modular Relations (T Arai, K Chakraborty and S Kanemitsu)-- Figurate Primes and Hilbert's 8th Problem (T-X Cai, Y Zhang and Z-G Shen)-- Statistical Distribution of Roots of a Polynomial Modulo Prime Powers (Y Kitaoka)-- A Survey on the Theory of Universality for Zeta and L-Functions (K Matsumoto)-- Complex Multiplication in the Sense of Abel (K Miyake)-- Problems on Combinatorial Properties of Primes (Z-W Sun)--.
- (source: Nielsen Book Data)9789814644921 20160618
(source: Nielsen Book Data)9789814644921 20160618
- On Modular Relations (T Arai, K Chakraborty and S Kanemitsu)-- Figurate Primes and Hilbert's 8th Problem (T-X Cai, Y Zhang and Z-G Shen)-- Statistical Distribution of Roots of a Polynomial Modulo Prime Powers (Y Kitaoka)-- A Survey on the Theory of Universality for Zeta and L-Functions (K Matsumoto)-- Complex Multiplication in the Sense of Abel (K Miyake)-- Problems on Combinatorial Properties of Primes (Z-W Sun)--.
- (source: Nielsen Book Data)9789814644921 20160618
(source: Nielsen Book Data)9789814644921 20160618
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | |
QA241 .C645 2013 | Unknown |
- Book
- xiv, 603 p. ; 24 cm.
- Numbers.- Numbers.- Induction.- Euclid's Algorithm.- Unique Factorization.- Congruence.- Congruence classes and rings.- Congruence Classes.- Rings and Fields.- Matrices and Codes.- Congruences and Groups.- Fermat's and Euler's Theorems.- Applications of Euler's Theorem.- Groups.- The Chinese Remainder Theorem.- Polynomials.- Polynomials.- Unique Factorization.- The Fundamental Theorem of Algebra.- Polynomials in ?[x].- Congruences and the Chinese Remainder Theorem.- Fast Polynomial Multiplication.- Primitive Roots.- Cyclic Groups and Cryptography.- Carmichael Numbers.- Quadratic Reciprocity.- Quadratic Applications.- Finite Fields.- Congruence Classes Modulo a Polynomial.- Homomorphisms and Finite Fields.- BCH Codes.- Factoring Polynomials.- Factoring in ?[x].- Irreducible Polynomials.
- (source: Nielsen Book Data)9780387745275 20160605
(source: Nielsen Book Data)9780387745275 20160605
- Numbers.- Numbers.- Induction.- Euclid's Algorithm.- Unique Factorization.- Congruence.- Congruence classes and rings.- Congruence Classes.- Rings and Fields.- Matrices and Codes.- Congruences and Groups.- Fermat's and Euler's Theorems.- Applications of Euler's Theorem.- Groups.- The Chinese Remainder Theorem.- Polynomials.- Polynomials.- Unique Factorization.- The Fundamental Theorem of Algebra.- Polynomials in ?[x].- Congruences and the Chinese Remainder Theorem.- Fast Polynomial Multiplication.- Primitive Roots.- Cyclic Groups and Cryptography.- Carmichael Numbers.- Quadratic Reciprocity.- Quadratic Applications.- Finite Fields.- Congruence Classes Modulo a Polynomial.- Homomorphisms and Finite Fields.- BCH Codes.- Factoring Polynomials.- Factoring in ?[x].- Irreducible Polynomials.
- (source: Nielsen Book Data)9780387745275 20160605
(source: Nielsen Book Data)9780387745275 20160605
dx.doi.org SpringerLink
- dx.doi.org SpringerLink
- Google Books (Full view)
- Book
- xviii, 384 p. ; 25 cm.
- Fundamentals.- Divisibility.- Powers of Integers.- Floor Function and Fractional Part.- Digits of Numbers.- Basic Principles in Number Theory.- Arithmetic Functions.- More on Divisibility.- Diophantine Equations.- Some Special Problems in Number Theory.- Problems Involving Binomial Coefficients.- Miscellaneous Problems.- Solutions to Additional Problems.- Divisibility.- Powers of Integers.- Floor Function and Fractional Part.- Digits of Numbers.- Basic Principles in Number Theory.- Arithmetic Functions.- More on Divisibility.- Diophantine Equations.- Some Special Problems in Number Theory.- Problems Involving Binomial Coefficients.- Miscellaneous Problems.
- (source: Nielsen Book Data)9780817632458 20160605
(source: Nielsen Book Data)9780817632458 20160605
- Fundamentals.- Divisibility.- Powers of Integers.- Floor Function and Fractional Part.- Digits of Numbers.- Basic Principles in Number Theory.- Arithmetic Functions.- More on Divisibility.- Diophantine Equations.- Some Special Problems in Number Theory.- Problems Involving Binomial Coefficients.- Miscellaneous Problems.- Solutions to Additional Problems.- Divisibility.- Powers of Integers.- Floor Function and Fractional Part.- Digits of Numbers.- Basic Principles in Number Theory.- Arithmetic Functions.- More on Divisibility.- Diophantine Equations.- Some Special Problems in Number Theory.- Problems Involving Binomial Coefficients.- Miscellaneous Problems.
- (source: Nielsen Book Data)9780817632458 20160605
(source: Nielsen Book Data)9780817632458 20160605
dx.doi.org SpringerLink
- dx.doi.org SpringerLink
- Google Books (Full view)
10. Number theory with computer applications [1998]
- Book
- xiii, 543 p. : ill. ; 24 cm.
- 1. Introduction. 2. Divisibility and Primes. 3. Modular Arithmetic. 4. Fundamental Theorems of Modular Arithmetic. 5. Cryptography. 6. Primality Testing and Factoring. 7. Primitive Roots. 8. Applications. 9. Quadratic Congruences. 10. Applications. 11. Continued Fractions. 12. Factoring Methods. 13. Diophantine Approximations. 14. Diophantine Equations. 15. Arithmetical Functions and Dirichlet Series. 16. Distribution of Primes. 17. Quadratic Reciprocity Law 18. Binary Quadratic Forms. 19. Elliptic Curves. Appendix A: Mathematical Induction. Appendix B: Binomial Theorem. Appendix C: Algorithmic Complexity and O-notation. Answers and Hints. Index of Notation. Index.
- (source: Nielsen Book Data)9780138018122 20160528
(source: Nielsen Book Data)9780138018122 20160528
- 1. Introduction. 2. Divisibility and Primes. 3. Modular Arithmetic. 4. Fundamental Theorems of Modular Arithmetic. 5. Cryptography. 6. Primality Testing and Factoring. 7. Primitive Roots. 8. Applications. 9. Quadratic Congruences. 10. Applications. 11. Continued Fractions. 12. Factoring Methods. 13. Diophantine Approximations. 14. Diophantine Equations. 15. Arithmetical Functions and Dirichlet Series. 16. Distribution of Primes. 17. Quadratic Reciprocity Law 18. Binary Quadratic Forms. 19. Elliptic Curves. Appendix A: Mathematical Induction. Appendix B: Binomial Theorem. Appendix C: Algorithmic Complexity and O-notation. Answers and Hints. Index of Notation. Index.
- (source: Nielsen Book Data)9780138018122 20160528
(source: Nielsen Book Data)9780138018122 20160528
SAL3 (off-campus storage)
SAL3 (off-campus storage) | Status |
---|---|
Stacks | Request |
QA241 .K85 1998 | Available |
11. An illustrated theory of numbers [2017]
- Book
- xv, 323 pages ; 29 cm
- Seeing arithmeticFoundations: The Euclidean algorithmPrime factorizationRational and constructible numbersGaussian and Eisenstein integersModular arithmetic: The modular worldsModular dynamicsAssembling the modular worldsQuadratic residuesQuadratic forms: The topographDefinite formsIndefinite formsIndex of theoremsIndex of termsIndex of namesBibliography.
- (source: Nielsen Book Data)9781470434939 20171009
(source: Nielsen Book Data)9781470434939 20171009
- Seeing arithmeticFoundations: The Euclidean algorithmPrime factorizationRational and constructible numbersGaussian and Eisenstein integersModular arithmetic: The modular worldsModular dynamicsAssembling the modular worldsQuadratic residuesQuadratic forms: The topographDefinite formsIndefinite formsIndex of theoremsIndex of termsIndex of namesBibliography.
- (source: Nielsen Book Data)9781470434939 20171009
(source: Nielsen Book Data)9781470434939 20171009
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | |
QA241 .W354 2017 | Unknown |
- Book
- x, 240 pages ; 24 cm.
- Part I. Elementary Number Theory: 1. Prelude-- 2. Arithmetic functions and integer points-- 3. Congruences-- 4. Quadratic reciprocity and Fourier series-- 5. Sums of squares-- Part II. Fourier Analysis and Geometric Discrepancy: 6. Uniform distribution and completeness of the trigonometric system-- 7. Discrepancy and trigonometric approximation-- 8. Integer points and Poisson summation formula-- 9. Integer points and exponential sums-- 10. Geometric discrepancy and decay of Fourier transforms-- 11. Discrepancy in high dimension and Bessel functions-- References-- Index.
- (source: Nielsen Book Data)9781107619852 20160616
(source: Nielsen Book Data)9781107619852 20160616
- Part I. Elementary Number Theory: 1. Prelude-- 2. Arithmetic functions and integer points-- 3. Congruences-- 4. Quadratic reciprocity and Fourier series-- 5. Sums of squares-- Part II. Fourier Analysis and Geometric Discrepancy: 6. Uniform distribution and completeness of the trigonometric system-- 7. Discrepancy and trigonometric approximation-- 8. Integer points and Poisson summation formula-- 9. Integer points and exponential sums-- 10. Geometric discrepancy and decay of Fourier transforms-- 11. Discrepancy in high dimension and Bessel functions-- References-- Index.
- (source: Nielsen Book Data)9781107619852 20160616
(source: Nielsen Book Data)9781107619852 20160616
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | |
QA241 .T68 2014 | Unknown |
- Book
- xv, 256 pages : illustrations ; 25 cm.
- * On the greatest prime factor of some divisibility sequences by A. Akbary and S. Yazdani* A number field extension of a question of Milnor by T. Chatterjee, S. Gun, and P. Rath* Mixing rates of random walks with little backtracking by S. M. Cioaba and P. Xu* Additive and multiplicative functions with similar global behavior by J.-M. De Koninck and N. Doyon* Multidimensional sequences uniformly distributed modulo 1 created from normal numbers by J.-M. De Koninck and I. Katai* The index of $a$ modulo $p$ by A. T. Felix* Determining optimal test functions for bounding the average rank in families of $L$-functions by J. Freeman and S. J. Miller* Familles d'equations de Thue associees a un sous-groupe de rang 1 d'unites totalement reelles d'un corps de nombres by C. Levesque and M. Waldschmidt* Cyclicity of quotients of non-CM elliptic curves modulo primes by G. Meleleo* On the Euler Kronecker constant of a cyclotomic field, II by M. Mourtada and V. K. Murty* The generalized Dedekind determinant by M. R. Murty and K. Sinha* A remark on elliptic curves with a given number of points over finite fields by J. Parks* Recovering cusp forms on GL(2) from symmetric cubes by D. Ramakrishnan* Arithmetic nature of some infinite series and integrals by N. Saradha and D. Sharma* Points on varieties over finite fields in small boxes by I. E. Shparlinski* Bounds for the Lang-Trotter conjectures by D. Zywina.
- (source: Nielsen Book Data)9781470414573 20160619
(source: Nielsen Book Data)9781470414573 20160619
- * On the greatest prime factor of some divisibility sequences by A. Akbary and S. Yazdani* A number field extension of a question of Milnor by T. Chatterjee, S. Gun, and P. Rath* Mixing rates of random walks with little backtracking by S. M. Cioaba and P. Xu* Additive and multiplicative functions with similar global behavior by J.-M. De Koninck and N. Doyon* Multidimensional sequences uniformly distributed modulo 1 created from normal numbers by J.-M. De Koninck and I. Katai* The index of $a$ modulo $p$ by A. T. Felix* Determining optimal test functions for bounding the average rank in families of $L$-functions by J. Freeman and S. J. Miller* Familles d'equations de Thue associees a un sous-groupe de rang 1 d'unites totalement reelles d'un corps de nombres by C. Levesque and M. Waldschmidt* Cyclicity of quotients of non-CM elliptic curves modulo primes by G. Meleleo* On the Euler Kronecker constant of a cyclotomic field, II by M. Mourtada and V. K. Murty* The generalized Dedekind determinant by M. R. Murty and K. Sinha* A remark on elliptic curves with a given number of points over finite fields by J. Parks* Recovering cusp forms on GL(2) from symmetric cubes by D. Ramakrishnan* Arithmetic nature of some infinite series and integrals by N. Saradha and D. Sharma* Points on varieties over finite fields in small boxes by I. E. Shparlinski* Bounds for the Lang-Trotter conjectures by D. Zywina.
- (source: Nielsen Book Data)9781470414573 20160619
(source: Nielsen Book Data)9781470414573 20160619
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | |
QA11 .A1 S325 2015 | Unknown |
- Book
- 1 online resource (240 pages). Digital: text file; PDF.
The aim of this book is to serve as an introductory text to the theory of linear forms in the logarithms of algebraic numbers, with a special emphasis on a large variety of its applications. We wish to help students and researchers to learn what is hidden inside the blackbox ‚Baker's theory of linear forms in logarithms' (in complex or in $p$-adic logarithms) and how this theory applies to many Diophantine problems, including the effective resolution of Diophantine equations, the $abc$-conjecture, and upper bounds for the irrationality measure of some real numbers. Written for a broad audience, this accessible and self-contained book can be used for graduate courses (some 30 exercises are supplied). Specialists will appreciate the inclusion of over 30 open problems and the rich bibliography of over 450 references.
The aim of this book is to serve as an introductory text to the theory of linear forms in the logarithms of algebraic numbers, with a special emphasis on a large variety of its applications. We wish to help students and researchers to learn what is hidden inside the blackbox ‚Baker's theory of linear forms in logarithms' (in complex or in $p$-adic logarithms) and how this theory applies to many Diophantine problems, including the effective resolution of Diophantine equations, the $abc$-conjecture, and upper bounds for the irrationality measure of some real numbers. Written for a broad audience, this accessible and self-contained book can be used for graduate courses (some 30 exercises are supplied). Specialists will appreciate the inclusion of over 30 open problems and the rich bibliography of over 450 references.
15. Methods of solving number theory problems [2018]
- Book
- 1 online resource
- Preface.- Numbers: Problems Involving Integers.- Further Study of Integers.- Diophantine Equations and More.- Pythagorean Triples, Additive Problems, and More.- Homework.
- (source: Nielsen Book Data)9783319909141 20180910
(source: Nielsen Book Data)9783319909141 20180910
- Preface.- Numbers: Problems Involving Integers.- Further Study of Integers.- Diophantine Equations and More.- Pythagorean Triples, Additive Problems, and More.- Homework.
- (source: Nielsen Book Data)9783319909141 20180910
(source: Nielsen Book Data)9783319909141 20180910
16. Number fields [2018]
- Book
- 1 online resource (xviii, 203 pages). Digital: text file; PDF.
- 1: A Special Case of Fermat's Conjecture.- 2: Number Fields and Number Rings.- 3: Prime Decomposition in Number Rings.- 4: Galois Theory Applied to Prime Decomposition.- 5: The Ideal Class Group and the Unit Group.- 6: The Distribution of Ideals in a Number Ring.- 7: The Dedekind Zeta Function and the Class Number Formula.- 8: The Distribution of Primes and an Introduction to Class Field Theory.- Appendix A: Commutative Rings and Ideals.- Appendix B: Galois Theory for Subfields of C.- Appendix C: Finite Fields and Rings.- Appendix D: Two Pages of Primes.- Further Reading.- Index of Theorems.- List of Symbols.
- (source: Nielsen Book Data)9783319902326 20180910
(source: Nielsen Book Data)9783319902326 20180910
- 1: A Special Case of Fermat's Conjecture.- 2: Number Fields and Number Rings.- 3: Prime Decomposition in Number Rings.- 4: Galois Theory Applied to Prime Decomposition.- 5: The Ideal Class Group and the Unit Group.- 6: The Distribution of Ideals in a Number Ring.- 7: The Dedekind Zeta Function and the Class Number Formula.- 8: The Distribution of Primes and an Introduction to Class Field Theory.- Appendix A: Commutative Rings and Ideals.- Appendix B: Galois Theory for Subfields of C.- Appendix C: Finite Fields and Rings.- Appendix D: Two Pages of Primes.- Further Reading.- Index of Theorems.- List of Symbols.
- (source: Nielsen Book Data)9783319902326 20180910
(source: Nielsen Book Data)9783319902326 20180910
17. Sequences, Groups, and Number Theory [2018]
- Book
- 1 online resource.
- General Framework.- Number Theoretic Aspects of Regular Sequences.- First-order Logic and Numeration System.- Some Applications of Algebra to Automatic Sequences.- Avoiding or Limiting Regularities in Words.- Coloring Problems for Infinite Words.- Normal Numbers and Computer Science.- Normal Numbers and Symbolic Dynamics.- About the Domino Problem for Subshifts on Groups.- Automation (Semi)Groups: Wang Tilings and Schreier Tries.- Amenability of Groups and G-Sets.- Index.- References.
- (source: Nielsen Book Data)9783319691510 20180730
(source: Nielsen Book Data)9783319691510 20180730
- General Framework.- Number Theoretic Aspects of Regular Sequences.- First-order Logic and Numeration System.- Some Applications of Algebra to Automatic Sequences.- Avoiding or Limiting Regularities in Words.- Coloring Problems for Infinite Words.- Normal Numbers and Computer Science.- Normal Numbers and Symbolic Dynamics.- About the Domino Problem for Subshifts on Groups.- Automation (Semi)Groups: Wang Tilings and Schreier Tries.- Amenability of Groups and G-Sets.- Index.- References.
- (source: Nielsen Book Data)9783319691510 20180730
(source: Nielsen Book Data)9783319691510 20180730
18. Invitation to number theory [2017]
- Book
- 1 online resource.
Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, ... and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more.In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.
(source: Nielsen Book Data)9780883856536 20180219
(source: Nielsen Book Data)9780883856536 20180219
Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, ... and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more.In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.
(source: Nielsen Book Data)9780883856536 20180219
(source: Nielsen Book Data)9780883856536 20180219
19. Sequential experiments with primes [2017]
- Book
- xi, 279 pages : illustrations (some color) ; 25 cm
- Forward.- 1. Introduction.- 2. Warming Up: Integers, Sequences, and Experimental Mathematics.- 3. Greatest Prime Factor Sequences.- 4. Conway's Subprime Function and Related Structures with a Touch of Fibonnacci Flavor.- 5. Going All Experimental - More Games and Applications.- Appendix 0.- Visualization.- Appendix 1.- Appendix 2.- Appendix 3.- References.
- (source: Nielsen Book Data)9783319567617 20180530
(source: Nielsen Book Data)9783319567617 20180530
- Forward.- 1. Introduction.- 2. Warming Up: Integers, Sequences, and Experimental Mathematics.- 3. Greatest Prime Factor Sequences.- 4. Conway's Subprime Function and Related Structures with a Touch of Fibonnacci Flavor.- 5. Going All Experimental - More Games and Applications.- Appendix 0.- Visualization.- Appendix 1.- Appendix 2.- Appendix 3.- References.
- (source: Nielsen Book Data)9783319567617 20180530
(source: Nielsen Book Data)9783319567617 20180530
Science Library (Li and Ma)
Science Library (Li and Ma) | Status |
---|---|
Stacks | |
QA241 .C37 2017 | Unknown |
- Book
- 1 online resource.
EBSCOhost Access limited to 1 user
- EBSCOhost Access limited to 1 user
- Google Books (Full view)
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