Foundations Of Mathematics

This course aims to develop and equip you with the necessary skills for a mathematically related job. You should demonstrate a basic understanding of fundamental mathematical concepts and processes such as such as formal mathematical proofs. You should also learn the rigorous way to approach mathematical problems and to be familiar with the process of abstracting from examples, as these skills are essential for all future mathematics courses. You should develop critical analytical skills for a career in a mathematical related job. You will acquire the communication skills necessary to communicate technical ideas, both written and verbal, to a broad audience.

Content

1. Elementary logic, mathematical statements, quantified statements
2. Sets, operations on sets, Cartesian products, properties of sets
3. Natural numbers, integers, rational numbers, real numbers, complex numbers
4. Relations, equivalence relations, equivalence classes
5. Functions, injective and surjective functions, inverse functions, composition of functions
6. Division algorithm, greatest common divisor, Euclidean algorithm, fundamental theorem of arithmetic, modulo arithmetic