### An Inquiry Approach

### An Inquiry Approach

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** Introductory Analysis: An Inquiry Approach** aims to provide a self-contained, inquiry-oriented approach to undergraduate-level real analysis.

The presentation of the material in the book is intended to be "inquiry-oriented'" in that as each major topic is discussed, details of the proofs are left to the student in a way that encourages an active approach to learning. The book is "self-contained" in two major ways: it includes scaffolding (i.e., brief guiding prompts marked as Key Steps in the Proof) for many of the theorems. Second, it includes preliminary material that introduces students to the fundamental framework of logical reasoning and proof-writing techniques. Students will be able to use the guiding prompts (and refer to the preliminary work) to develop their proof-writing skills.

Features

- Structured in such a way that approximately one week of class can be devoted to each chapter
- Suitable as a primary text for undergraduates, or as a supplementary text for some postgraduate courses
- Strikes a unique balance between enquiry-based learning and more traditional approaches to teaching

**Prerequisites**

Chapter P1: Exploring Mathematical Statements

Chapter P2: Proving Mathematical Statements

Chapter P3: Preliminary Content

**Main Content**

Chapter 1: Properties of R

Chapter 2: Accumulation Points and Closed Sets

Chapter 3: Open Sets and Open Covers

Chapter 4: Sequences and Convergence

Chapter 5: Subsequences and Cauchy Sequences

Chapter 6: Functions, Limits, and Continuity

Chapter 7: Connected Sets and the Intermediate Value Theorem

Chapter 8: Compact Sets

Chapter 9: Uniform Continuity

Chapter 10: Introduction to the Derivative

Chapter 11: The Extreme and Mean Value Theorems

Chapter 12: The Definite Integral: Part I

Chapter 13: The Definite Integral: Part II

Chapter 14: The Fundamental Theorem(s) of Calculus

Chapter 15: Series

**Extended Explorations**

Chapter E1: Function Approximation

Chapter E2: Power Series

Chapter E3: Sequences and Series of Functions

Chapter E4: Metric Spaces

Chapter E5: Iterated Functions and Fixed Point Theorems