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

book coverHammack
Book of Proof
ISBN: 9780989472104


book coverLebl
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  
Proof by Contradiction 1-2 days
[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:

Old Exams

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.

More information about disability resources in the Mathematics Department can be found at http://www.math.iastate.edu/Undergrad/AccommodationPol.html.