What This Document Is
This is a focused study guide designed to help students prepare for the first test in MATH 337: Elements of Real Analysis, offered at Western Kentucky University. It centers on foundational concepts within real analysis, a rigorous branch of mathematical analysis that delves into the properties of real numbers and functions. The guide aims to solidify understanding of core principles and techniques essential for success in the course.
Why This Document Matters
This resource is invaluable for students currently enrolled in MATH 337 who are looking to systematically review key definitions and theorems before their first assessment. It’s particularly helpful for those who benefit from a structured approach to studying and want to test their ability to recall and apply fundamental concepts. Utilizing this guide can help identify areas needing further review and strengthen overall comprehension of the material. It’s best used in conjunction with lecture notes, textbook readings, and practice problems.
Common Limitations or Challenges
This study guide is *not* a substitute for attending lectures or completing assigned homework. It doesn’t contain fully worked-out examples or step-by-step solutions to problems. Instead, it focuses on the theoretical underpinnings of the course material. It also assumes a base level of mathematical maturity and familiarity with proof-writing techniques. The guide will not cover topics beyond those assessed on the first test.
What This Document Provides
* A review of the formal definition and properties of absolute value, including inequalities related to it.
* Key definitions concerning bounded sets and upper/lower bounds within ordered sets.
* Exploration of the Least Upper Bound Property and its connection to the Well-Ordering Property of integers.
* A focused look at the Nested Interval Property and its implications.
* Guidance on understanding the relationship between a set and its negation in terms of upper and lower bounds.
* Discussion of representing decimal expansions as fractions.
* Considerations for finding rational and irrational numbers between any two real numbers.
