Closer and Closer: Introducing Real Analysis (Hardcover)

~ Carol S. Schumacher (Author) "This book is a first introduction to real analysis..." (more)
Key Phrases: linear spaces, arbitrary indexing set, doubly indexed sequence, Prove Theorem, Use Theorem, Prove Corollary (more...)

Editorial Reviews

Product Description

Closer and Closer is the ideal first introduction to real analysis for upper-level undergraduate mathematics majors. The text takes students on a guided journey through the often challenging world of analysis, providing them with the tools to solve rigorous problems with ease. The author achieves this with a student-friendly writing style, an active learning approach, and rich examples and problem sets, along with a unique two-part format. Core Chapters open the text and introduce the most important tools used in analysis. The Excursions then round out and complement Core chapters, allowing students to explore new problems on their own. This two part approach provides a flexible, interactive introduction to relevant concepts and allows students to truly understand and retain key material presented throughout the text. Closer and Closer offers an unparalleled introduction to the foundations of this important area of mathematics.

Product Details

• Hardcover: 438 pages
• Publisher: Jones & Bartlett Publishers; 1 edition (July 2, 2007)
• Language: English
• ISBN-10: 0763735930
• ISBN-13: 978-0763735937
• Product Dimensions: 9.2 x 7.5 x 1.1 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #841,541 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

2 of 16 people found the following review helpful:

3.0 out of 5 stars It's alright., January 29, 2008

By	A Reader (California USA) - See all my reviews

I picked this book at random from the library. Might deserve more than 3 stars, might deserve less.

Anyway, I'm just getting tired of my own half-*ss understanding of certain mathematical terminology and procedures and exactly which concepts they r refering to.

The nice thing about this text--that i've seen so far--is that u can still understand what's going on, even when the author gets a little crazy. For example, "Thus a function has three ingredients: a set of inputs, a set of outputs, and a procedure by which we associate elements in the first set with elements in the second set."

So much crazy baggage in that statement. Inputs, outputs, and procedures all imply notions of time and causality. I can assure u as a fairly successful equation-slinger that the type of equations that represent systems with inputs and ouputs don't look exactly like mathematical functions of the f(x)=x+1. From the perspective of an hard science, these mathematical functions have no causality (functions based on time-varying or time-invariant differential equations can be justly said to have inputs and outputs and even "procedures"). Anyway, here each pair of points happen at the same time. To think otherwise, is irrational.

Silly Rabbit, trix are for kids. Still, silly rabbits like silly thought moments don't detract from the taste or the text. So i'm pretty happy with the author so far. Hey, I always thought, even if trix r for kids, the Rabbit should get to eat some of the trix too (he's on the box for darn sake!).