Learning outcomes |
General Objectives: Assimilate, relate, and apply concepts and results in Group Theory, Ring Theory, and Field Theory. Build upon the elementary aspects of group theory and ring theory covered in Algebra I, where various concrete examples were presented. Provide students with the opportunity to deepen their understanding of abstract mathematical reasoning and proofs initiated in the Algebra I course.
Competencies to be Developed by Students: Capacity for abstraction and generalization. Logical reasoning skills. Proficiency in written and oral communication using mathematical language. Ability to formulate and solve problems related to algebraic structures.
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Main Bibliography |
Dummit, David S.; Foote, Richard M., Abstract algebra. Third edition. John Wiley & Sons, Inc., Hoboken, NJ, 2004. Fraleigh, J.B. A First Course in Abstract Algebra (7th edition), Pearson, 2003 Milne, J.S., Group Theory and Fields and Galois Theory, 2012 (Available from http://www.jmilne.org/math/CourseNotes/FTe6.pdf ) Monteiro, A. J., Matos, I. T., Álgebra: Um Primeiro Curso (2ª edição), Escolar Editora, 2001 Spindler, Karlheinz, Abstract algebra with applications. Vol. II. Rings and Fields. Marcel Dekker, Inc., New York, 1994 Stewart, I, Galois Theory, 4ed, CRC Press, 2015
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Teaching Methodologies and Assessment Criteria |
The classes combine theory with practice. The teacher introduces the concepts, states and proves the fundamental results, provides examples and applications. The students are encouraged to participate in the classes, to interact with their teacher and colleagues and also to work independently, by solving exercises, guided reading, problem formulation and problem solving.
The evaluation carried out during the teaching-learning process consists of homework problems and two written tests. The students may still take a final examination.
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