Understanding Analysis

This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.

This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.

Exam Board: SQA Level: Higher Subject: English First Teaching: September 2014 First Exam: June 2015 This book (which is photocopiable within the purchasing institution) provides detailed suggested marking instructions to use alongside the student book of the same name, which offers practice in the Higher element of Reading for Understanding, Analysis and Evaluation - worth 30% of marks in the final exam. Written by two highly experienced authors, the student book introduces the terms and concepts that lie behind success and offers guidance on the interpretation of questions and targeting answers. - Acquire and improve the skills needed for success in this area of CfE Higher - Detailed marking instructions to reflect the style of assessments in this section of the paper - Revise for the exam using the practice papers in the accompanying student book

This Eighth Edition of Social Statistics for a Diverse Society continues to emphasize intuition and common sense, while demonstrating that social science is a constant interplay between methods of inquiry and important social issues. Recognizing that today’s students live in a world of growing diversity and richness of social differences, authors Chava Frankfort-Nachmias and Anna Leon-Guerrero use research examples that show how statistics is a tool for understanding the ways in which race, class, gender, and other categories of experience shape our social world and influence social behavior. In addition, guides for reading and interpreting the research literature help students acquire statistical literacy, while SPSS demonstrations and a rich variety of exercises help them hone their problem-solving skills.