Introduction to Pure Mathematics - Lesson 5 - Real Analysis - Field of Reals

Introduction to Pure Mathematics - Lesson 5 - Real Analysis - Field of Reals
Introduction to Pure Mathematics - Lesson 5 - Real Analysis - Field of Reals
Introduction to Pure Mathematics - Lesson 5 - Real Analysis - Field of Reals
Introduction to Pure Mathematics - Lesson 5 - Real Analysis - Field of Reals
Introduction to Pure Mathematics - Lesson 5 - Real Analysis - Field of Reals
Introduction to Pure Mathematics - Lesson 5 - Real Analysis - Field of Reals
Introduction to Pure Mathematics - Lesson 5 - Real Analysis - Field of Reals
Introduction to Pure Mathematics - Lesson 5 - Real Analysis - Field of Reals
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Product Description
Introduction to Pure Mathematics for Advanced High School Students consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra.

Lesson 5 from this series focuses on properties of the real numbers. In this lesson we will learn about ordered fields, why the rational numbers are not enough for real world applications, upper and lower bounds, the completeness property of the reals, the Archimedean property, and the density theorem.

The author recommends covering lessons 2, 3, and 4 before beginning this lesson.

Two PDF files are included with your purchase. The first PDF file consists of notes followed by a problem set. The problems are broken down into five levels of difficulty. The second PDF file consists of solutions to all the problems.

This series is intended to give high school students who are advanced in math an honest and rigorous introduction to pure mathematics. It is unfortunate that most students will not be exposed to real theoretical mathematics until their sophomore year of college and after they have already declared themselves math majors. My hope is that students wishing to explore real theoretical mathematics before committing to becoming a math major will now have the opportunity to do so. And of course I hope that they enjoy experiencing pure mathematics as much as I enjoy writing about it.

Terms of use: This product may be used by the purchaser for their classroom use only. All rights reserved. No part of this publication may be reproduced, distributed, or transmitted without written permission from the author. This includes posting this product on the internet in any form, including classroom/personal websites or network drives. If you wish to share this product with colleagues, please contact the author for a discount on multiple licenses.
Total Pages
22 pages
Answer Key
Included
Teaching Duration
4 days
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