Introductory Analysis An Inquiry Approach

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

John Ross is an Assistant Professor of Mathematics at Southwestern University. He earned his Ph.D. and M.A. in Mathematics from Johns Hopkins University, and his B.A. in Mathematics from St. Mary's College of Maryland. His research is in geometric analysis, answering questions about manifolds that arise under curvature flows. He enjoys overseeing undergraduate research, teaching in an inquiry-based format, biking to work, and hiking in Central Texas. Kendall Richards is a Professor of Mathematics at Southwestern University. He earned his B.S. and M.A. in Mathematics from Eastern New Mexico University and his Ph.D. in Mathematics from Texas Tech University. He is inspired by working with students and the process of learning. His research pursuits have included questions involving special functions, inequalities, and complex analysis. He also enjoys long walks and a strong cup of coffee.