Fundamental Algebra

Code:

M501

Acronym:

M501

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2017/2018 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Doctoral Program in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
IUD-M	4	PE do Prog Inter-Univ Dout Mat	1	-	9	60	243

Teaching language

English

Objectives

Introduction ot basic topics of Abstract Algebra.

Learning outcomes and competences

Familiarity with basic concepts and results of Abstract Algebra.

Working method

Presencial

Program

Group actions, Sylow theory. Nilpotent and solvable groups. Free groups and presentations. Lie groups and algebraic groups. Groups with operators. Rings and modules. Hermite, Smith and Jordan normal forms for matrices. Wedderburn theory. Linear representations of groups. Polynomial rings and factorization theory. Field extensions. Galois theory. Norms, traces and discriminants. Ideal theory in commutative rings. Rings of integers. Dedekind domains. Algebraic sets and Hilbert's Nullstellensatz.

The program will cover most of the above topics. Depending on the background and interests of the students, some topics may be developed in considerably more depth than others.

Mandatory literature

Isaacs I. Martin; Algebra. ISBN: 0-534-19002-2

Complementary Bibliography

Pierre Antoine Grillet; Abstract Algebra, Springer, 2007. ISBN: 978-0387715674
Jacobson Nathan; Basic algebra. ISBN: 0-7167-0453-6 (Vol. I)
Nathan Jacobson; Basic Algbra II, Dover, 2009. ISBN: 978-0486471877
Hungerford Thomas W.; Algebra. ISBN: 0-387-90518-9
Serge Lang; Algebra, Springer, 2002. ISBN: 978-1-4612-6551-1

Teaching methods and learning activities

The course material is presented and developed in the lectures.

Software

GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra

keywords

Physical sciences > Mathematics > Algebra

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Trabalho escrito	100,00
Total:	100,00

Eligibility for exams

Course registration is the only requirement.

Calculation formula of final grade

The course grade is obtained by adding the grades of the solutions of the proposed problems, the sum being converted to the 0 to 20 scale.

Classification improvement

An additional problem set may be proposed for which the grades of individual problems may be used to replace lower grades obtained during the semester.