Engineering Mathematics

Bertrand Russell wrote that mathematics can exalt "as surely as poetry". This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity, or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections.

The brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For over a century, a diverse array of researchers have been trying to find a language that can be used to capture the essence of what these neurons do and how they communicate - and how those communications create thoughts, perceptions, and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it.

It is no doubt that engineering has always been one of the most sought-after career opportunities for aspirants, driving them towards a rigorous preparation in order to crack any engineering entrance exams. "Mathematics for IIT-JEE (Mains & Advanced), Vol. 4 of 4" is a Sachan Series of our best-in-class study guides useful for IIT-JEE (Mains and Advanced). It is divided into 20 chapters, accompanying complete text material and practice exercises, along with workbook exercises coupled with each theory. It is housed with more than 5000 MCQs and a brilliant collection of previous years’ ...

Math has a reputation for being inaccessible. People think that it requires a special gift or that comprehension is a matter of genes. Yet, the greatest mathematicians throughout history, from Rene Descartes to Alexander Grothendieck, have insisted that this is not the case.

Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler - Stanford researcher, professor of math education, and expert on math learning - has studied why students don't like math and often fail in math classes. She's followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students.

A brilliant research mathematician reveals math to be a creative art form on par with painting, poetry, and sculpture, and rejects the standard anxiety-producing teaching methods used in most schools today. Witty and accessible, Paul Lockhart's controversial approach will provoke spirited debate among educators and parents alike, altering the way we think about math forever.

Thomas Bayes was an eighteenth-century Presbyterian minister and amateur mathematician whose obscure life belied the profound impact of his work. Like most research into probability at the time, his theorem - independently discovered a few years later by Pierre-Simon Laplace, the great French mathematician - was mainly seen as relevant to games of chance, like dice and cards. But its implications soon became clear, affecting fields as diverse as medicine, law and artificial intelligence.

Are the secrets of the universe written in words - or is it all about the digits? K. C. Cole follows up her paean to the power of physics, Sympathetic Vibrations, with this engaging and accessible guide to the might and majesty of mathematics. The Universe and the Teacup uses relatable examples and humorous prose to demonstrate math's ability to "translate the complexity of the world into manageable patterns".

Life is uncertain. We are all the result of an unforeseen and unforeseeable sequence of small occurrences. But what underlies this fragile chain of events? Is it random or just complex? And what role does luck play in our lives? David Spiegelhalter has spent his career crunching data in order to help understand uncertainty and assess the chances of what might happen. In The Art of Uncertainty, he gives listeners a window onto how we can all do this better.

Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the 17th-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it.

In the bestselling The Signal and the Noise, Nate Silver showed how forecasting would define the age of Big Data. Now, in this timely and riveting new book, Silver investigates "The River," or those whose mastery of risk allows them to shape—and dominate—so much of modern life. These professional risk takers—poker players and hedge fund managers, crypto true-believers and blue-chip art collectors—can teach us much about navigating the uncertainty of the 21st century.

Stop making bad decisions because of misunderstood numbers. Learn the math essentials that give you the clarity you've missed. Your future is a sum of your decisions. Transform your life's trajectory—one calculation at a time. From budgets to big dreams, unlock the math standing between you and the life you want to lead.

The techniques of Vedic Mathematics have helped millions of students all over the world get rid of their fear of numbers and improve their scores in quantitative subjects.

This 10-part history of mathematics reveals the personalities behind the calculations: the passions and rivalries of mathematicians struggling to get their ideas heard. Professor Marcus du Sautoy shows how these masters of abstraction find a role in the real world and proves that mathematics is the driving force behind modern science.

We are living through a revolution in machine learning-powered AI that shows no signs of slowing down. This technology is based on relatively simple mathematical ideas, some of which go back centuries, including linear algebra and calculus, the stuff of seventeenth- and eighteenth-century mathematics. It took the birth and advancement of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we see today. In this enlightening book, Anil Ananthaswamy explains the fundamental math behind machine learning.

Trigonometry is perhaps the most essential concept humans have ever devised. The simple yet versatile triangle allows us to record music, map the world, launch rockets into space, and be slightly less bad at pool. Triangles underpin our day-to-day lives and civilization as we know it. In Love Triangle, Matt Parker argues we should all show a lot more love for triangles, along with all the useful trigonometry and geometry they enable.

At its simplest, Bayes’s theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. But in Everything Is Predictable, Tom Chivers lays out how it affects every aspect of our lives. He explains why highly accurate screening tests can lead to false positives and how a failure to account for it in court has put innocent people in jail. A cornerstone of rational thought, many argue that Bayes’s theorem is a description of almost everything. But who was the man who lent his name to this theorem?

For particularly brilliant theoretical physicists like James Clerk Maxwell, Paul Dirac, or Albert Einstein, the search for mathematical truths led to strange new understandings of the ultimate nature of reality. But what are these truths? What are the mysterious numbers that explain the universe? In Fantastic Numbers and Where to Find Them, the leading theoretical physicist and YouTube star Antonio Padilla takes us on an irreverent cosmic tour of nine of the most extraordinary numbers in physics, offering a startling picture of how the universe works.

Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: Observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria.

Should you watch public television without pledging? Exceed the posted speed limit? Hop a subway turnstile without paying? These questions illustrate the "prisoner's dilemma", a social puzzle that we all face every day. Though the answers may seem simple, their profound implications make the prisoner's dilemma one of the great unifying concepts of science. Watching poker players bluff inspired John von Neumann to construct game theory, a mathematical study of conflict and deception.