#### 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 principal of finite mathematical induction

Second principal 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