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
-Definition and Dirichlet convolution.
-Number and sum of divisors function.
-Möbius function.
-Euler function.
Congruences:
-Sets of residues.
-Polynomial congruences.
-Primitive roots.
Quadratic residues:
-Legendre symbol.
-Quadratic reciprocity.
-Jacobi symbol.
Sums of squares:
-Sums of two squares.
-Number of representations.
-Sums of four squares.
-Sums of three squares.
Continued fractions and diophantine approximation:
-Simple continued fractions.
-Continued fractions and diophantine approximation.
-Infinite simple continued fractions.
-Periodic continued fractions.
-Pell's equation.
-Liouville's Theorem.
Note di W. Chen
http://www.williamchen-mathematics.info/lnentfolder/lnent.html
An Introduction to the Theory of Numbers by G. H. Hardy, E. M. Wright
M. Fontana, Appunti del corso TN1 (Argomenti della teoria classica dei numeri), http://www.mat.uniroma3.it/users/fontana/didattica/fontana_didattica.html#dispense
Mutuazione: 20410627 TN410 - INTRODUZIONE ALLA TEORIA DEI NUMERI in Matematica LM-40 BARROERO FABRIZIO
Programme
Arithmetic functions and their properties:-Definition and Dirichlet convolution.
-Number and sum of divisors function.
-Möbius function.
-Euler function.
Congruences:
-Sets of residues.
-Polynomial congruences.
-Primitive roots.
Quadratic residues:
-Legendre symbol.
-Quadratic reciprocity.
-Jacobi symbol.
Sums of squares:
-Sums of two squares.
-Number of representations.
-Sums of four squares.
-Sums of three squares.
Continued fractions and diophantine approximation:
-Simple continued fractions.
-Continued fractions and diophantine approximation.
-Infinite simple continued fractions.
-Periodic continued fractions.
-Pell's equation.
-Liouville's Theorem.
Core Documentation
Lecture notesNote di W. Chen
http://www.williamchen-mathematics.info/lnentfolder/lnent.html
An Introduction to the Theory of Numbers by G. H. Hardy, E. M. Wright
M. Fontana, Appunti del corso TN1 (Argomenti della teoria classica dei numeri), http://www.mat.uniroma3.it/users/fontana/didattica/fontana_didattica.html#dispense
Type of delivery of the course
Lectures in class on blackboard and exercise classes. In the case of an extension of the health emergency from COVID-19, all the provisions that regulate the methods of carrying out the teaching activities and student assessment will be implemented. In particular, the following methods will apply: streaming lectures on the platform Microsoft Teams.Type of evaluation
Written and oral exam. The written exam contains six non-theoretical exercises to be solved in two hours. Two tests during the semester can replace the written exam. teacher profile teaching materials
-Definition and Dirichlet convolution.
-Number and sum of divisors function.
-Möbius function.
-Euler function.
Congruences:
-Sets of residues.
-Polynomial congruences.
-Primitive roots.
Quadratic residues:
-Legendre symbol.
-Quadratic reciprocity.
-Jacobi symbol.
Sums of squares:
-Sums of two squares.
-Number of representations.
-Sums of four squares.
-Sums of three squares.
Continued fractions and diophantine approximation:
-Simple continued fractions.
-Continued fractions and diophantine approximation.
-Infinite simple continued fractions.
-Periodic continued fractions.
-Pell's equation.
-Liouville's Theorem.
Note di W. Chen
http://www.williamchen-mathematics.info/lnentfolder/lnent.html
An Introduction to the Theory of Numbers by G. H. Hardy, E. M. Wright
M. Fontana, Appunti del corso TN1 (Argomenti della teoria classica dei numeri), http://www.mat.uniroma3.it/users/fontana/didattica/fontana_didattica.html#dispense
Mutuazione: 20410627 TN410 - INTRODUZIONE ALLA TEORIA DEI NUMERI in Matematica LM-40 BARROERO FABRIZIO
Programme
Arithmetic functions and their properties:-Definition and Dirichlet convolution.
-Number and sum of divisors function.
-Möbius function.
-Euler function.
Congruences:
-Sets of residues.
-Polynomial congruences.
-Primitive roots.
Quadratic residues:
-Legendre symbol.
-Quadratic reciprocity.
-Jacobi symbol.
Sums of squares:
-Sums of two squares.
-Number of representations.
-Sums of four squares.
-Sums of three squares.
Continued fractions and diophantine approximation:
-Simple continued fractions.
-Continued fractions and diophantine approximation.
-Infinite simple continued fractions.
-Periodic continued fractions.
-Pell's equation.
-Liouville's Theorem.
Core Documentation
Lecture notesNote di W. Chen
http://www.williamchen-mathematics.info/lnentfolder/lnent.html
An Introduction to the Theory of Numbers by G. H. Hardy, E. M. Wright
M. Fontana, Appunti del corso TN1 (Argomenti della teoria classica dei numeri), http://www.mat.uniroma3.it/users/fontana/didattica/fontana_didattica.html#dispense
Type of delivery of the course
Lectures in class on blackboard and exercise classes. In the case of an extension of the health emergency from COVID-19, all the provisions that regulate the methods of carrying out the teaching activities and student assessment will be implemented. In particular, the following methods will apply: streaming lectures on the platform Microsoft Teams.Type of evaluation
Written and oral exam. The written exam contains six non-theoretical exercises to be solved in two hours. Two tests during the semester can replace the written exam. teacher profile teaching materials
-Definition and Dirichlet convolution.
-Number and sum of divisors function.
-Möbius function.
-Euler function.
Congruences:
-Sets of residues.
-Polynomial congruences.
-Primitive roots.
Quadratic residues:
-Legendre symbol.
-Quadratic reciprocity.
-Jacobi symbol.
Sums of squares:
-Sums of two squares.
-Number of representations.
-Sums of four squares.
-Sums of three squares.
Continued fractions and diophantine approximation:
-Simple continued fractions.
-Continued fractions and diophantine approximation.
-Infinite simple continued fractions.
-Periodic continued fractions.
-Pell's equation.
-Liouville's Theorem.
Note di W. Chen
http://www.williamchen-mathematics.info/lnentfolder/lnent.html
An Introduction to the Theory of Numbers by G. H. Hardy, E. M. Wright
M. Fontana, Appunti del corso TN1 (Argomenti della teoria classica dei numeri), http://www.mat.uniroma3.it/users/fontana/didattica/fontana_didattica.html#dispense
Mutuazione: 20410627 TN410 - INTRODUZIONE ALLA TEORIA DEI NUMERI in Matematica LM-40 BARROERO FABRIZIO
Programme
Arithmetic functions and their properties:-Definition and Dirichlet convolution.
-Number and sum of divisors function.
-Möbius function.
-Euler function.
Congruences:
-Sets of residues.
-Polynomial congruences.
-Primitive roots.
Quadratic residues:
-Legendre symbol.
-Quadratic reciprocity.
-Jacobi symbol.
Sums of squares:
-Sums of two squares.
-Number of representations.
-Sums of four squares.
-Sums of three squares.
Continued fractions and diophantine approximation:
-Simple continued fractions.
-Continued fractions and diophantine approximation.
-Infinite simple continued fractions.
-Periodic continued fractions.
-Pell's equation.
-Liouville's Theorem.
Core Documentation
Lecture notesNote di W. Chen
http://www.williamchen-mathematics.info/lnentfolder/lnent.html
An Introduction to the Theory of Numbers by G. H. Hardy, E. M. Wright
M. Fontana, Appunti del corso TN1 (Argomenti della teoria classica dei numeri), http://www.mat.uniroma3.it/users/fontana/didattica/fontana_didattica.html#dispense
Type of delivery of the course
Lectures in class on blackboard and exercise classes. In the case of an extension of the health emergency from COVID-19, all the provisions that regulate the methods of carrying out the teaching activities and student assessment will be implemented. In particular, the following methods will apply: streaming lectures on the platform Microsoft Teams.Type of evaluation
Written and oral exam. The written exam contains six non-theoretical exercises to be solved in two hours. Two tests during the semester can replace the written exam.