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.
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.
http://www.williamchen-mathematics.info/lnentfolder/lnent.html
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: 20402091 TN410 - INTRODUZIONE ALLA TEORIA DEI NUMERI in Matematica LM-40 N0 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
Script by W. Chenhttp://www.williamchen-mathematics.info/lnentfolder/lnent.html
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 classesType of evaluation
Written and oral exam. The written exam contains six non-theoretical exercises to be solved in two and a half hours. Two tests during the semester can replace the written exam.