Analysis I


Terence Tao - 2006
    

The Calculus Story: A Mathematical Adventure


David Acheson - 2017
    It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is also something of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn...In The Calculus Story David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step by step treatment, he demonstrates how to start doing calculus, from the very beginning.

Amateur: An inexpert, inexperienced, unauthoritative, enamored view of life. (How To Be Ferociously Happy Book 2)


Dushka Zapata - 2016
     It's meant to be a very easy read; not a book you read systematically from beginning to end but rather a book to read during those times you find reading a book overwhelming. How we choose to look at something is essential to our happiness, and the author, Dushka Zapata, hopes to leave readers with a little of that.

Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else


Jordan Ellenberg - 2021
    For real.If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel.Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry," from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World


Edward Dolnick - 2011
    A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

Ayodhya: The Dark Night


Krishna Jha - 2012
    Before the adversaries could discover his presence, he dashed straight towards Abhiram Das, the vairagi who was holding the idol in his hands and leading the group of intruders. […] The sadhu quickly freed himself and, together with his friends, retaliated fiercely. Heavy blows began raining from all directions. Soon, the muezzin realized that he was no match for the men and that he alone would not be able to stop them.22 December 1949: A conspiracy that began with the assassination of Mahatma Gandhi culminated in the execution of the Ayodhya strategy. Late that night, a little-known sadhu, Abhiram Das, and his followers entered the Babri Masjid and planted an idol of Rama inside it. While it is known that the Hindu Mahasabha had a role in placing the idol in the mosque, the larger plot and the chain of events that led to that act have never been subject to rigorous scrutiny. Through intrepid research and investigation, Krishna Jha and Dhirendra K. Jha bring together the disparate threads of the buried narrative for the first time.Through a series of first-hand interviews with eyewitnesses and the unearthing of archival material, the authors take us behind the scenes to examine the motivations and workings of the Mahasabha members who pulled the strings. They also examine the liaison between Mahasabhaites and Hindu traditionalists in the Congress – an association that Jawaharlal Nehru sought to break in his cautious battle with Sardar Vallabhbhai Patel and the right-wing forces. Ayodhya: The Dark Night uncovers, in vivid detail, what really transpired on the fateful night that was to leave a permanent scar on the Indian polity.

Methods of Logic


Willard Van Orman Quine - 1950
    Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate-functor logic and the affinities between higher set theory and the elementary logic of terms, W. V. Quine's new edition will serve admirably for both classroom and independent use.

The Art of Mathematics


Jerry P. King - 1992
    Jerry King is no exception. His informal, nontechnical book, as its title implies, is organized around what Bertrand Russell called the 'supreme beauty' of mathematics--a beauty 'capable of a stern perfection such as only the greatest art can show.'NATUREIn this clear, concise, and superbly written volume, mathematics professor and poet Jerry P. King reveals the beauty that is at the heart of mathematics--and he makes that beauty accessible to all readers. Darting wittily from Euclid to Yeats, from Poincare to Rembrandt, from axioms to symphonies, THE ART OF MATHEMATICS explores the difference between real, rational, and complex numbers; analyzes the intellectual underpinnings of pure and applied mathematics; and reveals the fundamental connection between aesthetics and mathematics. King also sheds light on how mathematicians pursue their research and how our educational system perpetuates the damaging divisions between the two cultures.

Number: The Language of Science


Tobias Dantzig - 1930
    Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

Relativity: The Special and the General Theory


Albert Einstein - 1916
    Having just completed his masterpiece, The General Theory of Relativity—which provided a brand-new theory of gravity and promised a new perspective on the cosmos as a whole—he set out at once to share his excitement with as wide a public as possible in this popular and accessible book.Here published for the first time as a Penguin Classic, this edition of Relativity features a new introduction by bestselling science author Nigel Calder.

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics


John Derbyshire - 2003
    Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.

Raptured: A Novel on the Second Coming of the Lord


Ernest Angley - 1950
    RAPTURED Additional Information Will sinful humanity have to endure the reign of the beast before the full wrath of God falls upon them?

My Brain is Open: The Mathematical Journeys of Paul Erdős


Bruce Schechter - 1998
    Hungarian-born Erdős believed that the meaning of life was to prove and conjecture. His work in the United States and all over the world has earned him the titles of the century's leading number theorist and the most prolific mathematician who ever lived. Erdős's important work has proved pivotal to the development of computer science, and his unique personality makes him an unforgettable character in the world of mathematics. Incapable of the smallest of household tasks and having no permanent home or job, he was sustained by the generosity of colleagues and by his own belief in the beauty of numbers. Witty and filled with the sort of mathematical puzzles that intrigued Erdős and continue to fascinate mathematicians today, My Brain Is Open is the story of this strange genius and a journey in his footsteps through the world of mathematics, where universal truths await discovery like hidden treasures and where brilliant proofs are poetry.

The Computer and the Brain


John von Neumann - 1958
    This work represents the views of a mathematician on the analogies between computing machines and the living human brain.

The Great Equations: Breakthroughs in Science from Pythagoras to Heisenberg


Robert P. Crease - 2008
    Crease tells the stories behind ten of the greatest equations in human history. Was Nobel laureate Richard Feynman really joking when he called Maxwell's electromagnetic equations the most significant event of the nineteenth century? How did Newton's law of gravitation influence young revolutionaries? Why has Euler's formula been called "God's equation," and why did a mysterious ecoterrorist make it his calling card? What role do betrayal, insanity, and suicide play in the second law of thermodynamics?The Great Equations tells the stories of how these equations were discovered, revealing the personal struggles of their ingenious originators. From "1 + 1 = 2" to Heisenberg's uncertainty principle, Crease locates these equations in the panoramic sweep of Western history, showing how they are as integral to their time and place of creation as are great works of art.