Applied Algebra
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2017/2018 - 1S 
Cycles of Study/Courses
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.