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Department of Mathematics and Applications
"Renato Caccioppoli"


Algebra 1

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Algebra 1

Credits

12

Prerequisites

None

Scientific-disciplinary sector (SSD)

MAT/02 Algebra

Examination method

Oral exam

Learning
objectives

The course aims to provide students with the language, notions and tools shared by the basic courses in mathematics and to introduce them to a critical understanding of the contents and methods of modern algebra. It offers a “semi-naive” treatment of set theory and an introduction to the study of algebraic structures, with particular regard to finite groups and the arithmetical questions related to their order.

Syllabus

Relations on a set, functions, comparison of sets, the set of natural numbers, the principle of induction, the set of integers, algebraic structures and their properties, homomorphisms between algebraic structures, elements of arithmetic in Z and of modular arithmetic, rules of calculation in groups, group homomorphisms, conjugation, automorphisms, permutation groups, Sylow theorems.

Expected learning
outcomes

At the end of the course, students must demonstrate that they:

  • know and understand the topics covered in set theory, arithmetic and group theory, and are able to use the language of set theory;
  • are able to apply the knowledge acquired to link abstract settings easily with the corresponding concrete examples, and to formulate and understand statements;
  • are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
  • are able to identify the most appropriate methods to analyse and solve a problem related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Command of the knowledge acquired, clarity of presentation, rigour in the use of language, confidence in using the notions acquired.