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# Applied Algebra

 Code: M3001 Acronym: M3001 Level: 300

Keywords
Classification Keyword
OFICIAL Mathematics

## Instance: 2018/2019 - 1S

 Active? Yes Responsible unit: Department of Mathematics Course/CS Responsible: First Degree 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 study plan from 2016/17 3 - 6 56 162
L:CC 0 Plano de estudos a partir de 2014 2 - 6 56 162
3
L:F 0 study plan from 2017/18 2 - 6 56 162
3
L:G 0 study plan from 2017/18 3 - 6 56 162
L:M 40 Plano estudos a partir do ano letivo 2016/17 2 - 6 56 162
3
L:Q 0 study plan from 2016/17 3 - 6 56 162

### Teaching Staff - Responsibilities

Teacher Responsibility
Christian Edgar Lomp

### Teaching - Hours

 Theoretical and practical : 4,00
Type Teacher Classes Hour
Theoretical and practical Totals 1 4,00
Christian Edgar Lomp 4,00

### 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.

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 Linear Coding theory

### 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 theoretical classes will explain the theory illustrated by  examples. The example classes will serve to solve excercises.

### Software

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

### keywords

Physical sciences > Mathematics > Algebra

### Evaluation Type

Distributed evaluation without final exam

### Assessment Components

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

### Amount of time allocated to each course unit

designation Time (hours)
Estudo autónomo 112,00
Frequência das aulas 50,00
Total: 162,00

### Eligibility for exams

There are no rules concerning the attendance frequency.

### Calculation formula of final grade

1. During the regular time ("época normal") the final grade is obtained by the sum of the grades of two quizzes ("testes"):

Quiz 1: in the first quiz, which will take place during class time and which is still to be scheduled, students can obtain up to 10 points. A student who does not obtain 2 points will automatically obtain a "failed" in the first exam period.

Teste 2: in the second quiz, which will take place in January, students can obtain up to 10 points. A student who does not obtain 2 points will automatically obtain a "failed" in the first exam period.

The final grade is the sum of the scores obtained in both quizzes or "failed" in case one of the scores is below 2 points.

2. The make-up exam consists of only one exam which contains two parts corresponding to Quiz 1 + 2. Students have to have at least 2 points in each of the parts.

### Examinations or Special Assignments

Two quizzes and one makeup exam.