Introduction to Elements

**Students must pass qualifying exam to take Introduction to Elements. Two week long course that covers part of the Elements of Mathematics curriculum. Book 0, Chapter 1 Operational Systems covers operational systems and their properties. It begins with finite modular number systems in traditional arithmetic operations and expands to natural and whole numbers. It also includes some non-numerical systems involving permutations and geometry mappings. Each system is analyzed carefully for the properties: commutative, associative, neutral element (identity element) and invertibility. Equations are solved in every system. Logic, Book 1, Chapter 1 introduces propositional calculus. The language includes propositional variables representing sentences with discernible truth values and connectives representing “not”, “and”, “or” (inclusive), “implies”, and the bi-conditional. The truth values of formulas built using variables and connectives are discerned through the use of truth tables. Students are introduced to the ideas of contradiction, tautology, and substitution. They also learn to recognize complex instances of simple tautologies as tautologies, without the use of truth tables.