**AMS/MAA Textbooks**

Volume: 24;
2013;
171 pp;
Softcover

**Print ISBN: 978-1-93951-203-1
Product Code: TEXT/24**

List Price: $56.00

AMS Member Price: $42.00

MAA Member Price: $42.00

**Electronic ISBN: 978-1-61444-613-2
Product Code: TEXT/24.E**

List Price: $56.00

AMS Member Price: $42.00

MAA Member Price: $42.00

# Distilling Ideas: An Introduction to Mathematical Thinking (Graphs, Groups, Calculus)

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*Brian P. Katz; Michael Starbird*

MAA Press: An Imprint of the American Mathematical Society

Mathematics is not a spectator sport; successful students of mathematics grapple with ideas for themselves. Distilling Ideas presents a carefully designed sequence of exercises and theorem statements that challenge students to create proofs and concepts. As students meet these challenges, they discover strategies of proofs and strategies of thinking beyond mathematics. In other words, Distilling Ideas helps its users to develop the skills, attitudes, and habits of mind of a mathematician, and to enjoy the process of distilling and exploring ideas. Distilling Ideas is an ideal textbook for a first proof-based course. The text engages the range of students' preferences and aesthetics through a corresponding variety of interesting mathematical content from graphs, groups, and epsilon-delta calculus. Each topic is accessible to users without a background in abstract mathematics because the concepts arise from asking questions about everyday experience. All the common proof structures emerge as natural solutions to authentic needs. Distilling Ideas or any subset of its chapters is an ideal resource either for an organized Inquiry Based Learning course or for individual study.

# Table of Contents

## Distilling Ideas: An Introduction to Mathematical Thinking (Graphs, Groups, Calculus)

- Cover cover11
- copyright page ii3
- title page iii4
- Contents vii8
- Preface ix10
- Introduction 118
- Graphs 522
- Groups 4360
- Examples Lead to Concepts 4360
- Clock-Inspired Groups 5269
- Symmetry Groups of Regular Polygons 5572
- Subgroups, Generators, and Cyclic Groups 5673
- Sizes of Subgroups and Orders of Elements 6279
- Products of Groups 6481
- Symmetric Groups 6582
- Maps between Groups 6885
- Normal Subgroups and Quotient Groups 7693
- More Examples* 8097
- Groups in Action* 8198
- The Man Behind the Curtain 85102

- Calculus 89106
- Conclusion 149166
- Annotated Index 153170
- List of Symbols 165182
- About the Authors 169186
- Back cover 172189