A Survey of Math

Survey of mathematics highlights the power of mathematics as a deductive discipline. The course covers four topics in mathematics. Each topic will build upon the next. The use of deductive arguments, both in formal and natural languages, will be emphasized. Topics include Set Theory, Cantor's Diagonalization Argument, countable and uncountable infinite, mathematical induction, cardinal numbers, one to one correspondence, Venn diagrams, sequences, applications in sequences, rational and irrational numbers, geometric proofs involving similar triangles, area, pythagorean theorem, trigonometry. Algebraic proofs involving the quadratic formula, irrationality of the number Phi, mathematical induction, proofs with sequences, proof by contradiction, fibonacci sequence and the golden ratio, continued fractions, fractals with an emphasis on pattern building, sequences, length and area.