# Math 201 - Introduction to Proofs

## Course Coordinator

Sung Y. Song (sysong@iastate.edu)

## Catalog Description

MATH 201. Introduction to Proofs.
(3-0) Cr. 3. F.S. Prereq: MATH 166 or MATH 166H
Logic and techniques of proof including induction. Communicating mathematics. Writing proofs about sets, functions, real numbers, limits, sequences, infinite series and continuous function.

## Textbook

Hammack
Book of Proof
ISBN: 9780989472104

Lebl
Basic Analysis: Introduction to Real Analysis
ISBN: 9780161400000

## Syllabus

[BP] refers to the book Book of Proof. [BA] refers to the book Basic Analysis.

Chapter & Sections Topics Time
Sets 3-4 days
[BP] §§1.1-8: Sets
([BA] §0.3: Basic Set Theory)

Logic 4-7 days
[BP] Chapter 2: Logic
Direct Proof 1-3 days
[BP] Chapter 4: Direct Proof
Proof by Contrapositive 1-2 days
[BP] Chapter 5: Proof by Contrapositive
[BP] Chapter 6: Proof by Contradiction
Proving Non-Conditional Statements 1-2 days
[BP] Chapter 7: Proving Non-Conditional Statements
Proofs Involving Sets 1-3 days
[BP] Chapter 8: Proofs Involving Sets
Disproof 1-2 days
[BP] Chapter 9: Disproof
Mathematical Induction 2-4 days
[BP] Chapter 10: Mathematical Induction
Chapters 11-12: Functions and Relations 2-4 days
[BP] §11.0: Relations Between Sets
[BP] Chapter 12: Functions

Cardinality 1-2 days
[BP] Chapter 13: Cardinality
Real Numbers 2-4 days
[BA] § 1.1: Ordered Sets, Fields, Ordered Fields
[BA] § 1.2: Completeness, Archimedean Property
[BA] §1.3: Uncountability of ℝ

Sequences and Series 4-7 days
[BA] Chapter 2: Sequences and Series
Limits and Continuity 1-3 days
[BA] §§3.1-2: Limits of Functions, Continuous Functions

## Objectives with THREE midterms

The following links point to external PDF files:

## Objectives with TWO Midterms

The following links point to external PDF files:

None available.

## Official Math Department Policies

The Math Department Class Policies page describes the official policies that all instructors have to follow. It covers rules on make-up exams, cheating, student behavior, etc.

## Students With Disabilities

If you have a documented disability and require accommodations, you should obtain a Student Academic Accommodation Request (SAAR) from the Disability Resources office (Student Services Building, Room 1076, 294-6624 or TDD 294-6335, disabilityresources@iastate.edu or accommodations@iastate.edu). Please contact your instructor early in the semester so that your learning needs may be appropriately met.