Acquire a good knowledge of the concepts and methods of the elementary number theory, with particular reference to the study of the Diophantine equations and congruence equations. Provide prerequisites for more advanced courses of algebraic and analytical number theory.
Curriculum
teacher profile teaching materials
ARITHMETIC FUNCTIONS: The Divisor Function. The Moebius Function. The Euler Function. Dirichlet Convolution
CONGRUENCES: Sets of Residues,Some Interesting Congruences, Some Linear Congruences, Some Polynomial Congruences, Primitive Roots, the Theorem of Gauss.
QUADRATIC RESIDUES: The Legendre Symbol. Quadratic Reciprocity. The Jacobi Symbol.The Distribution of Quadratic Residues.
SUMS OF INTEGER SQUARES: Sums of Two Squares. Number of Representations. Sums of Four Squares. Sums of Three Squares.
ELEMENTARY PRIME NUMBER THEORY: Euclid's Theorem Revisited. The Von Mangoldt Function. Tchebycheff's Theorem. Some Results of Mertens
Chowdhury, F.; Chowdhury, M. R. Essentials of Number Theory. Pi Publications, Dhaka, Bangladesh, 2005. ISBN 984-32-2836-7
Hardy, G. H.; Wright, E. M. An introduction to the theory of numbers. Fifth edition. The Clarendon Press, Oxford University Press, New York, 1979. xvi+426 pp. ISBN: 0-19-853170-2; 0-19-853171-0
Davenport, H. Aritmetica superiore. Un'introduzione alla teoria dei numeri. Editore: Zanichelli, 1994. 199 pp. ISBN: 8808091546
Mutuazione: 20410627 TN410 - INTRODUZIONE ALLA TEORIA DEI NUMERI in Matematica LM-40 PAPPALARDI FRANCESCO, TALAMANCA VALERIO
Programme
Division, Factorization, Some Elementary Properties of Primes, Some Results and Problems Concerning Primes.ARITHMETIC FUNCTIONS: The Divisor Function. The Moebius Function. The Euler Function. Dirichlet Convolution
CONGRUENCES: Sets of Residues,Some Interesting Congruences, Some Linear Congruences, Some Polynomial Congruences, Primitive Roots, the Theorem of Gauss.
QUADRATIC RESIDUES: The Legendre Symbol. Quadratic Reciprocity. The Jacobi Symbol.The Distribution of Quadratic Residues.
SUMS OF INTEGER SQUARES: Sums of Two Squares. Number of Representations. Sums of Four Squares. Sums of Three Squares.
ELEMENTARY PRIME NUMBER THEORY: Euclid's Theorem Revisited. The Von Mangoldt Function. Tchebycheff's Theorem. Some Results of Mertens
Core Documentation
Chen, W; ELEMENTARY NUMBER THEORY. https://rutherglen.science.mq.edu.au/wchen/lnentfolder/lnent.htmlChowdhury, F.; Chowdhury, M. R. Essentials of Number Theory. Pi Publications, Dhaka, Bangladesh, 2005. ISBN 984-32-2836-7
Hardy, G. H.; Wright, E. M. An introduction to the theory of numbers. Fifth edition. The Clarendon Press, Oxford University Press, New York, 1979. xvi+426 pp. ISBN: 0-19-853170-2; 0-19-853171-0
Davenport, H. Aritmetica superiore. Un'introduzione alla teoria dei numeri. Editore: Zanichelli, 1994. 199 pp. ISBN: 8808091546
Type of delivery of the course
60 frontal classesAttendance
Attendance is optional and the understanding of the text adopted is sufficient for the full use of the course. Of course, attendance is desirable and STRONGLY recommended, as the interaction between teacher and students is a fundamental and unrepeatable teaching tool.Type of evaluation
two hours written exam with practical and theory problems teacher profile teaching materials
Mutuazione: 20410627 TN410 - INTRODUZIONE ALLA TEORIA DEI NUMERI in Matematica LM-40 PAPPALARDI FRANCESCO, TALAMANCA VALERIO
teacher profile teaching materials
ARITHMETIC FUNCTIONS: The Divisor Function. The Moebius Function. The Euler Function. Dirichlet Convolution
CONGRUENCES: Sets of Residues,Some Interesting Congruences, Some Linear Congruences, Some Polynomial Congruences, Primitive Roots, the Theorem of Gauss.
QUADRATIC RESIDUES: The Legendre Symbol. Quadratic Reciprocity. The Jacobi Symbol.The Distribution of Quadratic Residues.
SUMS OF INTEGER SQUARES: Sums of Two Squares. Number of Representations. Sums of Four Squares. Sums of Three Squares.
ELEMENTARY PRIME NUMBER THEORY: Euclid's Theorem Revisited. The Von Mangoldt Function. Tchebycheff's Theorem. Some Results of Mertens
Chowdhury, F.; Chowdhury, M. R. Essentials of Number Theory. Pi Publications, Dhaka, Bangladesh, 2005. ISBN 984-32-2836-7
Hardy, G. H.; Wright, E. M. An introduction to the theory of numbers. Fifth edition. The Clarendon Press, Oxford University Press, New York, 1979. xvi+426 pp. ISBN: 0-19-853170-2; 0-19-853171-0
Davenport, H. Aritmetica superiore. Un'introduzione alla teoria dei numeri. Editore: Zanichelli, 1994. 199 pp. ISBN: 8808091546
Mutuazione: 20410627 TN410 - INTRODUZIONE ALLA TEORIA DEI NUMERI in Matematica LM-40 PAPPALARDI FRANCESCO, TALAMANCA VALERIO
Programme
Division, Factorization, Some Elementary Properties of Primes, Some Results and Problems Concerning Primes.ARITHMETIC FUNCTIONS: The Divisor Function. The Moebius Function. The Euler Function. Dirichlet Convolution
CONGRUENCES: Sets of Residues,Some Interesting Congruences, Some Linear Congruences, Some Polynomial Congruences, Primitive Roots, the Theorem of Gauss.
QUADRATIC RESIDUES: The Legendre Symbol. Quadratic Reciprocity. The Jacobi Symbol.The Distribution of Quadratic Residues.
SUMS OF INTEGER SQUARES: Sums of Two Squares. Number of Representations. Sums of Four Squares. Sums of Three Squares.
ELEMENTARY PRIME NUMBER THEORY: Euclid's Theorem Revisited. The Von Mangoldt Function. Tchebycheff's Theorem. Some Results of Mertens
Core Documentation
Chen, W; ELEMENTARY NUMBER THEORY. https://rutherglen.science.mq.edu.au/wchen/lnentfolder/lnent.htmlChowdhury, F.; Chowdhury, M. R. Essentials of Number Theory. Pi Publications, Dhaka, Bangladesh, 2005. ISBN 984-32-2836-7
Hardy, G. H.; Wright, E. M. An introduction to the theory of numbers. Fifth edition. The Clarendon Press, Oxford University Press, New York, 1979. xvi+426 pp. ISBN: 0-19-853170-2; 0-19-853171-0
Davenport, H. Aritmetica superiore. Un'introduzione alla teoria dei numeri. Editore: Zanichelli, 1994. 199 pp. ISBN: 8808091546
Type of delivery of the course
60 frontal classesAttendance
Attendance is optional and the understanding of the text adopted is sufficient for the full use of the course. Of course, attendance is desirable and STRONGLY recommended, as the interaction between teacher and students is a fundamental and unrepeatable teaching tool.Type of evaluation
two hours written exam with practical and theory problems teacher profile teaching materials
Mutuazione: 20410627 TN410 - INTRODUZIONE ALLA TEORIA DEI NUMERI in Matematica LM-40 PAPPALARDI FRANCESCO, TALAMANCA VALERIO
teacher profile teaching materials
ARITHMETIC FUNCTIONS: The Divisor Function. The Moebius Function. The Euler Function. Dirichlet Convolution
CONGRUENCES: Sets of Residues,Some Interesting Congruences, Some Linear Congruences, Some Polynomial Congruences, Primitive Roots, the Theorem of Gauss.
QUADRATIC RESIDUES: The Legendre Symbol. Quadratic Reciprocity. The Jacobi Symbol.The Distribution of Quadratic Residues.
SUMS OF INTEGER SQUARES: Sums of Two Squares. Number of Representations. Sums of Four Squares. Sums of Three Squares.
ELEMENTARY PRIME NUMBER THEORY: Euclid's Theorem Revisited. The Von Mangoldt Function. Tchebycheff's Theorem. Some Results of Mertens
Chowdhury, F.; Chowdhury, M. R. Essentials of Number Theory. Pi Publications, Dhaka, Bangladesh, 2005. ISBN 984-32-2836-7
Hardy, G. H.; Wright, E. M. An introduction to the theory of numbers. Fifth edition. The Clarendon Press, Oxford University Press, New York, 1979. xvi+426 pp. ISBN: 0-19-853170-2; 0-19-853171-0
Davenport, H. Aritmetica superiore. Un'introduzione alla teoria dei numeri. Editore: Zanichelli, 1994. 199 pp. ISBN: 8808091546
Mutuazione: 20410627 TN410 - INTRODUZIONE ALLA TEORIA DEI NUMERI in Matematica LM-40 PAPPALARDI FRANCESCO, TALAMANCA VALERIO
Programme
Division, Factorization, Some Elementary Properties of Primes, Some Results and Problems Concerning Primes.ARITHMETIC FUNCTIONS: The Divisor Function. The Moebius Function. The Euler Function. Dirichlet Convolution
CONGRUENCES: Sets of Residues,Some Interesting Congruences, Some Linear Congruences, Some Polynomial Congruences, Primitive Roots, the Theorem of Gauss.
QUADRATIC RESIDUES: The Legendre Symbol. Quadratic Reciprocity. The Jacobi Symbol.The Distribution of Quadratic Residues.
SUMS OF INTEGER SQUARES: Sums of Two Squares. Number of Representations. Sums of Four Squares. Sums of Three Squares.
ELEMENTARY PRIME NUMBER THEORY: Euclid's Theorem Revisited. The Von Mangoldt Function. Tchebycheff's Theorem. Some Results of Mertens
Core Documentation
Chen, W; ELEMENTARY NUMBER THEORY. https://rutherglen.science.mq.edu.au/wchen/lnentfolder/lnent.htmlChowdhury, F.; Chowdhury, M. R. Essentials of Number Theory. Pi Publications, Dhaka, Bangladesh, 2005. ISBN 984-32-2836-7
Hardy, G. H.; Wright, E. M. An introduction to the theory of numbers. Fifth edition. The Clarendon Press, Oxford University Press, New York, 1979. xvi+426 pp. ISBN: 0-19-853170-2; 0-19-853171-0
Davenport, H. Aritmetica superiore. Un'introduzione alla teoria dei numeri. Editore: Zanichelli, 1994. 199 pp. ISBN: 8808091546
Type of delivery of the course
60 frontal classesAttendance
Attendance is optional and the understanding of the text adopted is sufficient for the full use of the course. Of course, attendance is desirable and STRONGLY recommended, as the interaction between teacher and students is a fundamental and unrepeatable teaching tool.Type of evaluation
two hours written exam with practical and theory problems teacher profile teaching materials
Mutuazione: 20410627 TN410 - INTRODUZIONE ALLA TEORIA DEI NUMERI in Matematica LM-40 PAPPALARDI FRANCESCO, TALAMANCA VALERIO