Yet Another Introduction to Analysis

Rating:
Summary: Basic Real Analysis unleashed
Review: Bryant builds the basic concepts of a first course in mathematical analysis upon the notion of numerical sequences. This approach gives an unified vision and amazing insights. Infinite series, limits, derivatives, Riemann integral are studied in an integrated vision. Clear ideas, illustrations and humor are found across all its pages. Good and illuminating exercises, too. An excellent introduction to basic real analysis.

Rating:
Summary: Exposes Mathematical Analysis Without Set Theory Background
Review: Mathematical analysis is a refinement of calculus, and a pathway into further branches of mathematics, including topology and advanced topics in algebra. Analysis, however, may not seem to be at all related to calculus at its initial stages. An introductory course on analysis can render an unprepared student, even with experience in other branches of mathematics, perplexed and challenged to an extreme. Only later in the analysis course are even the most basic topics of calculus introduced.

One of the most important considerations prior to taking an analysis course is the level of background and understanding of mathematical logic. Set theory, a branch of mathematical logic, is in fact the basis of calculus as well. Due to an emphasis upon computations, however, the highest grades in calculus are possible without understanding, or even knowing of, this underlying foundation.

This work is unique among those introducing analysis, in that it does not require a background in set theory. It in fact teaches numerous fundamental concepts of set theory, without stating that it is doing so. Examples provided are based on daily concrete experience, yet are altered for purposes of mathematical instruction. These descriptions are sufficiently general as to prepare the reader for when formal set theory is introduced in more rigorous textbooks.

In addition to being an extremely readable and accessible work, solutions and hints are provided for every review question for every section of the book. This is in stark contrast to textbooks on the subject, which, while costing several times more, are typically designed for a classroom setting, and so leave all questions unanswered. This self-testing of the understanding of each section is crucial for subject matter requiring such attention to detail and precision.

The numerous illustrations throughout the book are rendered clearly and with instructional purpose, yet are often drawn by hand, adding to the sense of familiarity with the author. All of the basic subject matter for a course on analysis is provided, yet has been specifically tailored for a reader in the stages of preparation, of review after completion, or one who is simply inquisitive as to what is required to comprehend analysis successfully.

The softcover edition is durable and portable, and the book remains in excellent condition through numerous readings, which it will almost certainly go through.

If you have been required to take an analysis class but left it with only a vague sense of its underpinnings, you may wish to go through this work when time permits. For the price of the book, the information and instruction provided is truly outstanding. This text receives the highest marks in all categories.

Rating:
Summary: Great Introduction
Review: This is a text for Real Analysis at the Junior Level (American university level). It goes to extreme lengths to make analysis understandable to people who have no prior exposure. The organization is good. Completeness is introduced early as (the "piggy in the middle"). Proofs are written in detail with fill-in-the-blank spots to force the reader to follow the argument. It has good exercises making it an easy book to teach out of. Excellent for the absolute beginner. Good candidate for the classroom.

Rating:
Summary: Great Introduction
Review: This is a text for Real Analysis at the Junior Level (American university level). It goes to extreme lengths to make analysis understandable to people who have no prior exposure. The organization is good. Completeness is introduced early as (the "piggy in the middle"). Proofs are written in detail with fill-in-the-blank spots to force the reader to follow the argument. It has good exercises making it an easy book to teach out of. Excellent for the absolute beginner. Good candidate for the classroom.

Rating:
Summary: Outstanding introduction to advanced mathematics
Review: While there have been countless introductions to mathematical analysis (calculus) this is my favorite. The author does a brilliant job of making the subject matter interesting and very understandable with excellent exercises along the way which have solutions in the back ! A must read for bright highschool seniors and college freshman that are taking calculus or will be.