Description

To develop the students' ability to construct a rigorous proof of a mathematical claim. Students will also be made aware of mathematical results that are of interest to those wishing to analyze a particular mathematical model. Topics will be drawn from logic, set theory, structure of the number line, functions, sequences and continuity.

Credit will be granted for only one of the following: MATH 310 or MATH 307.
Math majors may not use this course for one of their upper level mathematics requirements.

Prerequisites

Math141 is a prerequisite. Math241 and Math240/461 (or Math340 and 341) are pre/co-requisites. 

Topics

Introduction to Sets

Set operations
De Morgan's Law

Some Logic

Direct proofs
Contrapositive proofs
Proofs by contradiction
Quantifiers
Impact of change of quantifiers, order of quantifiers and negations on meaning of statements
Disproving statements

Proof techniques applied to:

Divisibility
Real number properties
Set equalities
Equivalence relations

Cardinality

Size of sets
Countability
Bernstein's Theorem

Induction

First principle of finite mathematical induction
Second principle of finite mathematical induction
Applications

Sequences

Definition of limit
Convergence
Monotone convergence theorem
Bolzano-Weierstrass theorem

Completeness

Greatest lower bounds
Least upper bounds
Cauchy sequece

Functions

Injective, Surjective and Bijective functions
Continuous functions with sequence definition
Continuous functions with epsilon/delta definition