## Mathematical Induction

First principal of mathematical Induction.

## Sequence, summations, Infinite sets

Sequence, summations, Infinite sets.

## Functions

Functions; Types of Functions; Inverse and Composition Functions.

## Sets operations

Set Operations; Set Identities; Generalized Unions and Intersections; Computer Representation of Sets; The cardinality of the union of sets.

## Sets

Sets, Equal Sets, Subsets; Cardinality of Finite Sets; Power Sets; Cartesian Products.

## Proof Strategy

Proof Strategy; Forward and Backward Reasoning; Leveraging Proof by Cases; Conjecture; Uniqueness Proofs; Additional Proof Methods.

## Methods of Proof

General Philosophy; Rules of Inference; Rules of Inference for Quantifiers; Fallacies; Types of Proof.

## Predicate Logic

Predicates and Quantifiers; Existential and Universal Quantification; Translating Sentences using Quantifiers; Numerical Quantification.

## Propositional Logic 2

Validity and Propositional Equivalences; Showing Equivalence using Truth Tables; Showing Equivalence using Symbolic Manipulations.

## Propositional Logic

Introduction to Propositional Logic; Operations on Propositions; Truth Tables; Translating Sentences into Logical Expressions.