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Applied Algebra

Code: M3001     Acronym: M3001     Level: 300

Keywords
Classification Keyword
OFICIAL Mathematics

Instance: 2017/2018 - 1S Ícone do Moodle

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

Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
L:B 0 Official Study Plan 3 - 6 56 162
L:CC 0 Plano de estudos a partir de 2014 2 - 6 56 162
3
L:F 0 Official Study Plan 2 - 6 56 162
3
L:G 0 study plan from 2017/18 3 - 6 56 162
L:M 38 Official Study Plan 2 - 6 56 162
3
L:Q 0 study plan from 2016/17 3 - 6 56 162
Mais informaçõesLast updated on 2017-11-18.

Fields changed: Calculation formula of final grade, Componentes de Avaliação e Ocupação, Provas e trabalhos especiais

Teaching language

Suitable for English-speaking students

Objectives

The aim of this course is to show some of the applications of abstract algebra, e.g. applications of the theory of groups, rings and fields.

Learning outcomes and competences

It is expected that students learn that some of abstract concepts of algebra have applications within the field of natural sciences.

Working method

Presencial

Program



The program follows the book by Lidl and Pilz "Applied Abstract Algebra"

§01 Lattice
§02 Distributive lattices
§03 Boolean Algebras
§04 Boolean Polynomials
§05 Minimal forms of polynomials (Quine-McCluskey algorithm)
§06 Applications to logic, switching circuits, topology and probability spaces
§07 Rings and polynomials
§08 Fields
§09 Finite Fields
§10 Irreducible polynomials
§11 Fatorization of polynomials over finite fields
§12 Coding theory
§13 Linear codes
§14 Cyclic codes
§15 BCH codes


Mandatory literature

Lidl Rudolf; Applied abstract algebra. ISBN: 978-1-4419-3117-7 (we will use the 2nd edition of this book.)

Complementary Bibliography

S.Givant and P.Halmos; Introduction to Boolean Algebras, Springer, 2009. ISBN: 978-0-387-40293-2
Lidl Rudolf; Finite fields. ISBN: 0-521-30240-4

Teaching methods and learning activities

The course material will be lectured using traditional chalk-board talks.

Software

http://www.sagemath.org/
http://www.python.org

keywords

Physical sciences > Mathematics > Algebra

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation Weight (%)
Exame 100,00
Total: 100,00

Calculation formula of final grade

The final grade (CF) is calculated as 

CF =(T1+T2)/2

where Ti is the grade of the ith quiz (i=1,2).

Examinations or Special Assignments

Two quizzes and one makeup exam.
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