Real and complex numbers and the natural laws for addition and multiplication up to the polar form of a complex number and De Moivre's theorem. Addition and multiplication modulo n, laws for these operations, unity, inverses, idempotents, nilpotents, zero-divisors, units, basic theorems. Vector spaces: axioms, vectors in 3 dimensions as an algebra. Laws of matrix operations. Generalization to rings, fields and algebras. Groups: definitions, examples, axioms, basic theorems. Boolean algebras of sets, propositions and switching circuits.
Contact hours:
5 lectures/tutorials per week.Assessment:
2 tests (25%), 3 or 4 assignments (15%) and final exam (60%).