Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea magistrale in Mathematics - Enrollment from 2025/2026The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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3 courses to be chosen between
To be chosen between
Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Advanced course in foundations of mathematics (2017/2018)
Teaching code
4S001104
Teacher
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/01 - MATHEMATICAL LOGIC
Period
II sem. dal Mar 1, 2018 al Jun 15, 2018.
Learning outcomes
Introducing the students to elementary number theory, one of the cornerstones of discrete computational mathematics as well as of the pertinent branches of cryptography. At the end of the course the student will be able to rigorously argue, carry out proofs and read article and monographs (also advanced ones) regarding elementary number theory and the related parts of cryptography.
Program
1) Construction of the integers from the Peano Axioms.
2) Arithmetic and algebraic operations with integers.
3) The well-ordering principle and proofs by induction.
4) Divisibility and the division algorithm.
5) Representation of integers in different bases.
6) The greatest common divisor and the Euclidean algorithm.
7) Prime numbers and the fundamental theorem of arithmetic.
8) Linear Diophantine equations.
9) Congruences and the Chinese remainder theorem.
10) The Theorems of Fermat, Euler and Wilson.
11) Public Key Cryptography (the RSA Cryptosystem).
12) Quadratic reciprocity.
Author | Title | Publishing house | Year | ISBN | Notes |
---|---|---|---|---|---|
Henri Cohen | A Course in Computational Algebraic Number Theory | Springer | 1993 | ||
William Stein | Elementary Number Theory: Primes, Congruences, and Secrets – A computational approach. | Springer | 2008 |
Examination Methods
Written examination only.