ADVANCED ALGEBRA AND MATHEMATICAL LOGIC
University of Camerino
Course Details
Course Content
Basic algebra. groups and fields. Basic number theory, congruences.
The course is divided into two units of 6 credits:
1. Advanced Algebra
2. Advanced Mathematical Logic.
A general aim is to introduce and emphasize the use of algebraic and logical tools in several applications (also regarding computer science).
Educational objectives of 1: becoming familiar with number theory, group theory, finite field theory and their applications to cryptography and network security.
Educational objectives 2: becoming familiar with the development of mathematical logic from Cantor's set theory to Turing and Goedel's incompleteness theorems and with its contribution to algebra, algebraic geometry and theoretical computer science.
Learning Outcomes
The course is divided into two units of 6 credits:
1. Advanced Algebra
2. Advanced Mathematical Logic.
A general aim is to introduce and emphasize the use of algebraic and logical tools in several applications (also regarding computer science).
Educational objectives of 1: becoming familiar with number theory, group theory, finite field theory and their applications to cryptography and network security.
Educational objectives 2: becoming familiar with the development of mathematical logic from Cantor's set theory to Turing and Goedel's incompleteness theorems and with its contribution to algebra, algebraic geometry and theoretical computer science.
Literature and Course Materials
Advanced Algebra: S. Leonesi - C. Toffalori, Numeri e Crittografia, Springer Italia, 2006
Advanced Mathematical Logic: Carlo Toffalori-Patrizio Cintioli, Logica matematica, McGraw-Hill Italia, 2000
Note aggiuntive saranno eventualmente distribuite agli student