Mathematics Education; Learning; Teaching
Tools to make hard problems easier to solve.In this book, Sanjoy Mahajan shows us that the way to master complexity is through insight rather than precision. Precision can overwhelm us with information, whereas insight connects seemingly disparate pieces of information into a simple picture. Unlike computers, humans depend on insight. Based on the author's fifteen years of teaching at MIT, Camb…
This open access book bridges a gap between introductory Quantum Field Theory (QFT) courses and state-of-the-art research in scattering amplitudes. It covers the path from basic definitions of QFT to amplitudes, which are relevant for processes in the Standard Model of particle physics. The book begins with a concise yet self-contained introduction to QFT, including perturbative quantum gravity…
This open access book provides an essential guide to value sets for anyone working with EQ-5D-5L data. The EQ-5D-5L is one of the most widely used health related quality of life questionnaires around the world, with applications in clinical trials, population health surveys and routine outcomes measurement. In addition to providing a concise, generic way of describing health, the EQ-5D-5L facil…
This text is an introduction to the fields of experimental and theoretical particle physics and cosmology. The book focuses on three principal areas: supersymmetry, string theory, and astrophysics and cosmology. The chapters on supersymmetry introduce the basics of supersymmetry and its phenomenology, and cover dynamics, dynamical supersymmetry breaking, and electric–magnetic duality. The boo…
In recent years, the unprecedented experimental control of the laws of quantum mechanics has led to the so-called quantum technology revolution, a terminology adopted to refer to the applications in which quantum properties play a prominent role. Also the fundamental physics has benefited from these advancements with the development of quantum simulators, controlled quantum platforms engineered…
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a su…
Before Albert Einstein proposed the concept of four-dimensional spacetime, late Victorian scientists, radical philosophers and writers were discussing the possibility of a different kind of fourth dimension. Before Einstein offers the first book-length examination of the impact of pre-Relativity four-dimensional theory on literature and culture at the turn of the twentieth century.
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation.In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems e…