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book: The Mathematical Radio
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The Mathematical Radio

Inside the Magic of AM, FM, and Single-Sideband
Language: English
Published/Copyright: 2025

About this book

How a modern radio works, told through mathematics, history, and selected puzzles

The modern radio is a wonder, and behind that magic is mathematics. In The Mathematical Radio, Paul Nahin explains how radios work, deploying mathematics and historical discussion, accompanied by a steady stream of intriguing puzzles for math buffs to ponder. Beginning with oscillators and circuits, then moving on to AM, FM, and single-sideband radio, Nahin focuses on the elegant mathematics underlying radio technology rather than the engineering. He explores and explains more than a century of key developments, placing them in historical and technological context.

Nahin, a prolific author of books on math for the general reader, describes in fascinating detail the mathematical underpinnings of a technology we use daily. He explains and solves, for example, Maxwell’s equations for the electromagnetic field. Readers need only a familarity with advanced high school–level math to follow Nahin’s mathematical discussions. Writing with the nonengineer in mind, Nahin examines topics including impulses in time and frequency, spectrum shifting at the transmitter, the superheterodyne, the physics of single-sideband radio, and FM sidebands. Chapters end with “challenge problems” and an appendix offers solutions, partial answers, and hints. Readers will come away with a new appreciation for the beauty of even the most useful mathematics.

Reviews

"[The book's] challenges are worthwhile."---N. W. Schillow, Choice --- "Mr. Nahin's fascinating historical guide to the science of how words are transformed into electricity and back again contains a lot of [mathematics]. Luckily, Mr. Nahin . . . is also a warm and infectiously enthusiastic guide in prose."---Steven Poole, Wall Street Journal

Topics

  • Publicly Available

    Frontmatter

    i
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    A Note to the Reader of the Paperback Edition

    vii
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  • Publicly Available

    Contents

    xi
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  • Publicly Available

    Foreword to The Mathematical Radio

    xiii
    Andrew J. Simoson
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  • Publicly Available

    Preface

    xxxiii
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    Chapter 1 Radio Mathematics, Oscillators, and Transmitters

    1
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    Chapter 2 More Radio Mathematics: Circuits That Multiply

    73
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    Chapter 3 The AM Radio Receiver

    133
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    Chapter 4 SSB Radio

    166
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    Chapter 5 FM Radio

    203
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    Chapter 6 American AM Broadcast Radio: A Historical Postscript

    248
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    A Final Author’s Note to the Reader

    263
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    Appendix. Maxwell’s Theory, the Poynting Vector, and a Simple Radio Transmitting Antenna

    265
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    Solutions, Partial Answers, and More Hints to Most of the End-of-Chapter Challenge Problems in The Mathematical Radio

    287
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    Acknowledgments

    303
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    Illustration Credits

    307
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    Index

    309
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
September 16, 2025
eBook ISBN:
9780691278964
Pages and Images/Illustrations in book
View content
https://doi.org/10.1515/9780691278964
eBook ISBN: 9780691278964
Keywords for this book
AM/FM radio theory; applied mathematics; broadcast radio history; G. H. Hardy; The Mathematical Radio: Inside the Magic of AM; FM; Single-Sideband; and Wifi; Paul J. Nahin; princeton university press; math; mathematics; radio; history of knowledge; history of mathematics; singleband; wifi; electronic inventions; math behind radio; how does radio work; radio engineering; oscillators; circuits; pivotal technology; history important technology; mathematical underpinnings
Audience(s) for this book
For an expert adult audience, including professional development and academic research
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Winner of the OpenAthens UX Award 2026
Winner of the OpenAthens UX Award 2026
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