Can You Divide Anything By Zero
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Analysis I
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
Finding Zero
“A captivating story, not just an intellectual quest but a personal one . . . gripping [and] filled with the passion and wonder of numbers.” —The New York Times Virtually everything in our lives is digital, numerical, or quantified. But the story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. Finding Zero is the saga of Amir Aczel’s lifelong obsession: to find the original sources of our numerals, perhaps the greatest abstraction the human mind has ever created. Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross-examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the ride. The history begins with Babylonian cuneiform numbers, followed by Greek and Roman letter numerals. Then Aczel asks: Where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero—the keystone of our entire system of numbers—on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves—who finally reveal where our numbers come from. “A historical adventure that doubles as a surprisingly engaging math lesson . . . rip-roaring exploits and escapades.” —Publishers Weekly
Divide Me By Zero
A New York Times Editor’s Choice As a young girl, Katya Geller learned from her mother that math was the answer to everything. Now, approaching forty, she finds this wisdom tested: she has lost the love of her life, she is in the middle of a divorce, and has just found out that her mother is dying. Nothing is adding up. With humor, intelligence, and unfailing honesty, Katya traces back her life’s journey: her childhood in Soviet Russia, her parents’ great love, the death of her father, her mother’s career as a renowned mathematician, and their immigration to the United States. She is, by turns, an adrift newlywed, an ESL teacher in an office occupied by witches and mediums, a restless wife, an accomplished writer, a flailing mother of two, a grieving daughter, and, all the while, a woman caught up in the most common misfortune of all—falling in love. Award-winning author Lara Vapnyar delivers an unabashedly frank and darkly comic tale of coming of age in middle age. Divide Me by Zerois almost unclassifiable—a stylistically original, genre-defying mix of classic Russian novel, American self-help book, Soviet math textbook, sly writing manual, and, at its center, a universal story with unforgettable lessons for us all.