Foundations of Higher Mathematics Exploration and Proof

by Fendel, Daniel; Resek, Diane

• ISBN13: 9780201125870
• ISBN10: 0201125870
• Edition: 1st
• Format: Paperback
• Copyright: 1990-01-01
• Publisher: Pearson

Summary

Foundations of Higher Mathematics: Exploration and Proof is the ideal text to bridge the crucial gap between the standard calculus sequence and upper division mathematics courses. The book takes a fresh approach to the subject: it asks students to explore mathematical principles on their own and challenges them to think like mathematicians. Two unique featuresan exploration approach to mathematics and an intuitive and integrated presentation of logic based on predicate calculusdistinguish the book from the competition. Both features enable students to own the mathematics they're working on. As a result, your students develop a stronger motivation to tackle upper-level courses and gain a deeper understanding of concepts presented.

Table of Contents

Thinking Mathematically

About Exploration and Proof

Exploration and Proofs about Sets and the Integers

The Language and Logic of Mathematics

Basic Methods of Proof and Exploration

Core Mathematics

Induction and the Integers

Relations and Functions

Further Ideas on Functions and Relations

Topics In Mathematics

Cardinality

Limits and Continuity

Groups

Appendicies

Index

Table of Contents provided by Publisher. All Rights Reserved.