Exploring the Infinite by Jennifer Brooks

Exploring the Infinite by Jennifer Brooks

This is a textbook for an introductory course in analysis, combining topics from a transition course. At some schools, a transition course is combined over one or two semesters to introduce topics from real analysis. This allows students a more gradual approach to the difficult topics of analysis. Beginning with logic and sets, this text gradual

This book consists of two distinct sectionsThe first resembles a traditional introduction to proof (including counterexamples) and standard mathematical topics (sets, functions, number theory, some abstract algebra, etc.). The work could serve as a textbook for a semester course on that alone. The second part focuses on analysis of the real line. The work begins by establishing the existence of an uncountable set followed by the completion of the real line via Cauchy sequences. Next is the topology of the real line (basic point set in a metric space ending with Heine-Borel and the Cantor set). It concludes by examining continuous and uniformly continuous functions, derivatives, and absolutely and conditionally convergent series and rearrangements. The book is well written and accessible to students, with thought-provoking exercises sprinkled throughout and larger exercise sets at the end of each chapter. It could easily be used for a two-semester course after multivariable calculus, preparing students with the fundamentals for upper-division courses, particularly an advanced calculus course. In the appendix, there are also “Programming Projects,†such as a brief course on Python as a suggested language. This book is worthy of consideration.

--J. R. Burke, Gonzaga University, Choice magazine 2016

Jennifer has had a passion for writing and reading ever since her grandfather took her as a young girl to the local Bookmobile and made her get a library card. She wrote her first novel-length book at age 11 and continued to write poetry as well as both short and novel-length stories throughout the rest of her adolescent and adult life. Jennifer has also always loved the outdoors, and she has spent the past several years learning how to grow and preserve her own food as well as live off the land. Facing the Storm is her second published work and combines her appreciation of writing and nature. She lives with her husband, a fluffy cat, and an adorable dog outside of Pittsburgh, Pennsylvania.

SKU	Unavailable
ISBN 13	9781032477046
ISBN 10	1032477040
Title	Exploring the Infinite
Author	Jennifer Brooks
Series	Textbooks In Mathematics
Condition	Unavailable
Binding Type	Paperback
Publisher	CRC Press LLC
Year published	2023-01-21
Number of pages	300
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.