General description
The course outlines the basic notions in Abstract Algebra, and aims to provide the student with a clear understanding of elementary algebraic structures and how to build them starting from fundamental concepts based on mere Logic, which would make the student able to carry on logical arguments and reasoning. This course starts with a reminder of fundamental definitions and notations used in Logic, Set theory and Binary Operations, then moves on to study some basic algebraic structures, such as Groups and Rings, and applies the theoretical notions onto the Set of Integers Z.
Intended Learning Outcomes by the end of the course: 1) Understanding the basic principles and notations in Logic and Set Theory. 2) Knowledge of some Counting methods, which would be helpful later when studying the complexity of algorithms. 3) Understanding Binary operations and its properties in the fundamental algebraic structures of Groups, Rings and Fields. 4) Mastering the Euclids Algorithm to compute the Greatest Common Divisor (GCD) and the Least Common Multiple in the Ring of Integers.