Making Sense Of Equations
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Making Sense of Equations
Whether you realize or not, mathematics is actually a language. The purpose of a language is to communicate, and mathematics is how we communicate about quantities and logical relationships. We do so by using signs, symbols, and other mathematical terms. One of the most important communication tools in the language of math is an equation. When students can use equations fluently, it helps them communicate in math more precisely, and it helps them more easily make sense of math. Equations help us solve a variety of problems, from figuring out how many laps a swimmer must complete during her workout to figuring out how much it will cost to go on vacation. Like any communication tool, equations are full of nuances. These countless little details can either cause a great deal of confusion, or they can be opportunities to build precision and fluency. Making Sense of Equations focuses on precision and fluency, and it helps students notice the little details that have a big impact on understanding.
Making Sense of Chaos
‘Doyne Farmer is the world's leading thinker on technological change. For decades he has focused on the question of how we can make sense of the data of today to see where the world is going tomorrow. This wonderful book applies these insights to economics, addressing the big global issues of environmental sustainability, and the well-being and prosperity of people around the world’ Max Roser, Founder of Our World in Data We live in an age of increasing complexity, where accelerating technology and global interconnection hold more promise – and more peril – than any other time in human history. As well as financial crises, issues around climate change, automation, growing inequality and polarization are all rooted in the economy, yet standard economic predictions fail us. Many books have been written about Doyne Farmer and his pioneering work in chaos and complexity theory. Making Sense of Chaos is the first in his own words, presenting a manifesto for doing economics better. In a tale of science and ideas, Farmer fuses his profound knowledge with stories from his life to explain how to harness a scientific revolution to address the economic conundrums facing society. Using big data and ever more powerful computers, we can for the first time apply complex systems science to economic activity, building realistic models of the global economy. The resulting simulations and the emergent behaviour we observe form the cornerstone of complexity economics. This new science, Farmer shows, will allow us to test ideas and make significantly better economic predictions – and, ultimately, create a better world.
Making Sense of Statistical Mechanics
Many people, including physicists, are confused about what the Second Law of thermodynamics really means, about how it relates to the arrow of time, and about whether it can be derived from classical mechanics. They also wonder what entropy really is: Is it all about information? But, if so, then, what is its relation to fluxes of heat? One might ask similar questions about probabilities: Do they express subjective judgments by us, humans, or do they reflect facts about the world, i.e. frequencies. And what notion of probability is used in the natural sciences, in particular statistical mechanics? This book addresses all of these questions in the clear and pedagogical style for which the author is known. Although valuable as accompaniment to an undergraduate course on statistical mechanics or thermodynamics, it is not a standard course book. Instead it addresses both the essentials and the many subtle questions that are usually brushed under the carpet in such courses. As one of the most lucid accounts of the above questions, it provides enlightening reading for all those seeking answers, including students, lecturers, researchers and philosophers of science.