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. Paul J. Nahin is emeritus professor of electrical engineering at the University of New Hampshire. He is the author of many popular math books, including most recently In Pursuit of Zeta-3: The World's Most Mysterious Unsolved Math Problem; Hot Molecules, Cold Electrons: From the Mathematics of Heat to the Development of the Trans-Atlantic Telegraph Cable; and How to Fall Slower Than Gravity: And Other Everyday (and Not So Everyday) Uses of Mathematics and Physical Reasoning (all Princeton). "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 "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
