Chapter 1: Introduction

In this chapter we discuss the need for the sort of rigorous development of analysis. Much of this course is occupied with rigorously proving results which you have already learned in Calculus, so we start by examining some of the gaps in our understanding which need patching. The starting point of analysis is the real numbers, so we discuss the difficulties in proving a fairly intuitive result about real numbers.

Chapter Contents

Class 01
- What is Analysis and why study it?
- Mathematical rigor and axioms
- Group exercise: a theorem of Archimedes
- Class discussion: How we think of the real numbers

Analysis WebNotes by John Lindsay Orr.
Comments to the author: jorr@math.unl.edu

All contents copyright (C) 1996 John L. Orr
University of Nebraska--Lincoln
All rights reserved

Last modified: June 1996