Logic and Proof

This course is designed for students who wish to learn about fundamental logic methods used for proofs.

The objective of this course is to master the fundamentals of mathematical logic and methods of proof. That is, after the course students should be able to construct and write mathematical proofs and be able to apply them in every day life, when they speak and write.

This course is designed as a 2 part course.

Part One: Language of Logic, Demonstrations and Quantified Statements

• Statements, Open Statements, Compound Statements, Truth Tables, Tautologies,
• Valid Arguments, Establish Validity with Demonstration, Equivalence,
• Conditional Demonstrations, Indirect Proofs, Negations Quantified Statements, Universal and Existential Quantfier, Translating
• Quantifed Statements, Restricted Quantifier, Rules of Logic for Quantified Statements.

Part Two: Algebra of Sets, Functions, and Induction

• Equality, Relations among Sets, New Sets from Old, Definitions and Axioms, Theorems, Set Inclusion
• Ordered Pairs, Relations, Functional Notation, Into, Onto, One-to- one, Inverse, Compositions
• Principle of Mathematical Induction, Modified Principle of Mathematical Induction, Second of Mathematical Induction.

Mathematical Proofs: A Transition to Advanced Mathematics, 3rd edition, Gary Chartrand, Albert D. Polimeni, Ping Zhang, (2013), Chapter 1-14