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Paul J. Nahin

The Mathematical Radio: Inside the Magic of AM, FM, and Single-Sideband Kindle Edition

by Paul J. Nahin (Author) Format: Kindle Edition

21 ratings

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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.

Print length

370 pages
Language

English
Publisher

Princeton University Press
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Publication date

Sept. 16 2025
File size

34.5 MB
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Review

"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

"[The book's] challenges are worthwhile."---N. W. Schillow, Choice --This text refers to the hardcover edition.

Review

“In this engaging and substantive book intended to demonstrate the beauty of applied mathematics to mathematicians both applied and pure—take that, G. H. Hardy!—Paul Nahin skillfully explains the mathematics, technology, and social impact of radio.”—Judith V. Grabiner, Pitzer College

“Radio waves—from our cell phones, AM/FM radio, and wireless devices—are zinging all around us, yet few of us have any idea how engineers came to understand these waves and how they invented new electronic devices. In this erudite book, Paul Nahin draws on his brilliant knowledge of electrical engineering to help us appreciate the elegant mathematics that engineers use to design the electronic marvels that enrich our lives.”—W. Bernard Carlson, University of Virginia --This text refers to the hardcover edition.

ASIN ‏ : ‎ B0F64HKLQ3
Publisher ‏ : ‎ Princeton University Press
Accessibility ‏ : ‎ Learn more
Publication date ‏ : ‎ Sept. 16 2025
Language ‏ : ‎ English
File size ‏ : ‎ 34.5 MB
Screen Reader ‏ : ‎ Supported
Enhanced typesetting ‏ : ‎ Enabled
X-Ray ‏ : ‎ Not Enabled
Word Wise ‏ : ‎ Not Enabled
Print length ‏ : ‎ 370 pages
ISBN-13 ‏ : ‎ 978-0691278964
Page Flip ‏ : ‎ Enabled
�鶹�� Rank: #269,224 in Kindle Store (See Top 100 in Kindle Store)
- #21 in Electrical Circuits eBooks
- #22 in Radio & Wireless Telecommunications eBooks
- #43 in Radio Communications
Customer Reviews:
21 ratings

About the author

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Paul J. Nahin

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Paul Nahin was born in California, and did all his schooling there (Brea-Olinda High 1958, Stanford BS 1962, Caltech MS 1963, and - as a Howard Hughes Staff Doctoral Fellow - UC/Irvine PhD 1972, with all degrees in electrical engineering). He worked as a digital logic designer and radar systems engineer in the Southern California aerospace industry until 1971, when he started his academic career. He has taught at Harvey Mudd College, the Naval Postgraduate School, and the Universities of New Hampshire (where he is now emeritus professor of electrical engineering) and Virginia. In between and here-and-there he spent a post-doctoral year at the Naval Research Laboratory, and a summer and a year at the Center for Naval Analyses and the Institute for Defense Analyses as a weapon systems analyst, all in Washington, DC. He has published a couple dozen short science fiction stories in ANALOG, OMNI, and TWILIGHT ZONE magazines, and has written 24 books on mathematics and physics, published by IEEE Press, Springer, and the university presses of Johns Hopkins and Princeton. Translations of his books in Chinese, Russian, Arabic, Greek, Korean, Spanish, Romanian, and Japanese have appeared. The book THE MATHEMATICAL RADIO was published by Princeton in January 2024 and the book THE PROBABILITY INTEGRAL was published by Springer in October 2023. He has given invited talks on mathematics at the Anja Greer Math and Technology Conference at Phillips Exeter Academy (twice, in 2008 and 2018), as well as at Bowdoin College, the Claremont Graduate School, the University of Tennessee, and Caltech, has appeared on National Public Radio's "Science Friday" show (discussing time travel) as well as on New Hampshire Public Radio's "The Front Porch" show (discussing imaginary numbers), and advised Boston's WGBH Public Television's "Nova" program on the script for their time travel episode. He gave the invited Sampson Lectures for 2011 in Mathematics at Bates College (Lewiston, Maine). He received the 2017 Chandler Davis Prize for Excellence in Expository Writing in Mathematics.

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CFortC
Revealed, the detailed math of AM, FM, and SSB
Reviewed in the United States on January 7, 2025
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The author's style is so readable that I completed an initial pass through this book in two evenings. This first pass was just appreciating the worked-out formulations without trying to follow every symbol and transformation in detail. But it is the kind of stuff that I've wondered about ever since my initial college exposure decades ago.

The author also has out a similarly named book "The Science of Radio". I got a hold of a copy of that at the same time. If you are thinking, as I did, that the two books complement each other, I can now state that they do not. It appears to me that the 2001 "The Science of Radio" is an earlier, simplified coverage of the same material. In this 2024 "The Mathematical Radio", the author has created the perfected, "full strength" book covering this material. So, if you were wondering as I did, which book (or both) to get, definitely just get this one "The Mathematical Radio".

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Lawrence Jones
Great for this old EE
Reviewed in the United States on March 21, 2025
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As a retired Electrical Engineer who specialized in digital wireless, I recognized all the topics and math. Book took me down memory lane.

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K. Christie
Good books with LOTS of math
Reviewed in the United States on December 4, 2024
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I should have known from the title that there would be much math to get through. I just wasn't prepared for THIS much at such an advanced level. But I like the author and the coverage is good.

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A. Lee
Useless "Kindle" version
Reviewed in the United States on February 27, 2024
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$14+ for an e-book that you can't read with an e-reader! After viewing it using the Kindle app on a phone, I can confirm it's just a book with text and pictures. There's no good reason for this book to be unavailable on Kindle e-book readers.

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yahoomarine
Great info and math heavy!
Reviewed in the United States on March 10, 2024
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Really good book. A lot of history. Also, a lot of higher level math, more than advertised. Be prepared to put your thinking cap on for this. Not really for your casual radio operator.

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