2023
Introduction to Number Theory
Name: Introduction to Number Theory
Code: MAT14237L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial
Presentation
In this curricular unit, the elementary part of number theory, the properties of positive integers, is studied.
Sustainable Development Goals
Learning Goals
The study of the properties of positive integers is the central objective of number theory. Number theory is divided into three main branches: elementary theory, analytical theory and algebraic theory. This course is dedicated to the elementary part of number theory, here the basic results will be studied, not only for the study of the analytical and algebraic parts, but also for the other branches of mathematics.
Contents
1. Divisibility
2. Congruences
3. Combinatorial Number Theory
4. Primitive Roots
5. Quadratic Residues
6. Arithmetic Functions
7. Continuous fractions
2. Congruences
3. Combinatorial Number Theory
4. Primitive Roots
5. Quadratic Residues
6. Arithmetic Functions
7. Continuous fractions
Teaching Methods
Problem-solving sessions, where students are invited to work on their own or in small groups, with some moments of exposition or discussion involving the whole class.
The evaluation may be either continuous, done through between two and six partial tests and quizzes, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam. Students who achieve a grade of 18 or above may have to do an extra oral exam. For these students the final grade is the maximum between 17 and the simple average of the previous grade and the oral exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final mark.
The evaluation may be either continuous, done through between two and six partial tests and quizzes, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam. Students who achieve a grade of 18 or above may have to do an extra oral exam. For these students the final grade is the maximum between 17 and the simple average of the previous grade and the oral exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final mark.
Teaching Staff
- Nuno Maria Gonçalves Soares Franco [responsible]
