Algebra Didactic

Recommended Prerequisites

3 semesters of Algebra, 2 semesters of Geometry.

Teaching Methods

TP classes are expositive where a rigorous treatment of subject is presented with concepts and proofs. In P classes an active participation of students in class discussions, and  individual and team work is encouraged.      

Learning Outcomes

The program is designed to strengthen concepts of algebra in view of teaching in an elementary course. One begins with an overview of historic evolution. The aim is to avoid omissions or logic errors in mathematic ´s reading and writing. Since the student already have basic knowledge in theory set, we introduce the Zermelo-Fraenkel theory. Also, since he is acquainted with algebraic elementary structures, we study the symmetry groups of regular polygons and polyhedrons. Then he will learn about ordered complete fields, mainly the field of reals. Finally the divisibility and non reducibility and solvability of polynomials with real or complex coefficients will be studied.

Work Placement(s)

No

Syllabus

- Origin and historic development  of algebra.

- Set theory: Zermelo-Fraenkel axioms. cardinality.

- Groups and symmetries:  symmetric and dihedral groups. Permutations. Polyhedrons.

- Ordered rings and complete ordered fields. Polynomial rings. 

- Polynomials: Euclides alghoritm, factorization, irreduciblety criterions

- Equations- radical resolution

- Didatical principles in the teaching of Algebra

- Analysis of the oficial syllabus and scholar books.

Head Lecturer(s)

Natália Isabel Quadros Bebiano Pinheiro da Providência e Costa

Assessment Methods

Final evaluation
Frequency: 50.0%
Exam: 50.0%

Continuous evaluation
Laboratory work or Field work: 5.0%
Project: 15.0%
Research work: 30.0%
Frequency: 50.0%

Bibliography

Amstrong, M.A., Groups and Symmetry, Springer-Verlag, 1988.

Gouveia, M.C.- Àlgebra e Teoria de Galois, Textos de apoio ao Mestrado de Ensino, 2002.

Jech, Thomas, Set Theory:the 3th millenium ed., revised and expanded, Springer Monographs in Mathematics, 2002.

Maio,Waldemar de, and Chiummo, Ana, Fundamentos de matemática:Didática de matemática, LTC, 2012.

Oliveira, A.J.Franco, Teoria dos Conjuntos, Escolar Ed., 1982.

Smith, James T., Zermelo-Fraenkel Set Theory, S. Francisco State University, 2008.

Stewart & I.Tall, The Foudations of Mathematics, Oxford University Press, 1999.

Vlassis, Joelle and Demonty, Isabelle, A Álgebra ensinada por situações-problemas, Instituto Piaget, 2011.