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Author: Yang-Hui He
Publisher: Springer Nature
ISBN: 3030775623
Category : Mathematics
Languages : en
Pages : 214
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Book Description
Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science. The study of Calabi–Yau manifolds lies at an exciting intersection between physics and mathematics. Recently, there has been much activity in applying machine learning to solve otherwise intractable problems, to conjecture new formulae, or to understand the underlying structure of mathematics. In this book, insights from string and quantum field theory are combined with powerful techniques from complex and algebraic geometry, then translated into algorithms with the ultimate aim of deriving new information about Calabi–Yau manifolds. While the motivation comes from mathematical physics, the techniques are purely mathematical and the theme is that of explicit calculations. The reader is guided through the theory and provided with explicit computer code in standard software such as SageMath, Python and Mathematica to gain hands-on experience in applications of artificial intelligence to geometry. Driven by data and written in an informal style, The Calabi–Yau Landscape makes cutting-edge topics in mathematical physics, geometry and machine learning readily accessible to graduate students and beyond. The overriding ambition is to introduce some modern mathematics to the physicist, some modern physics to the mathematician, and machine learning to both.
Author: Yang-Hui He
Publisher: Springer Nature
ISBN: 3030775623
Category : Mathematics
Languages : en
Pages : 214
Get Book Here
Book Description
Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science. The study of Calabi–Yau manifolds lies at an exciting intersection between physics and mathematics. Recently, there has been much activity in applying machine learning to solve otherwise intractable problems, to conjecture new formulae, or to understand the underlying structure of mathematics. In this book, insights from string and quantum field theory are combined with powerful techniques from complex and algebraic geometry, then translated into algorithms with the ultimate aim of deriving new information about Calabi–Yau manifolds. While the motivation comes from mathematical physics, the techniques are purely mathematical and the theme is that of explicit calculations. The reader is guided through the theory and provided with explicit computer code in standard software such as SageMath, Python and Mathematica to gain hands-on experience in applications of artificial intelligence to geometry. Driven by data and written in an informal style, The Calabi–Yau Landscape makes cutting-edge topics in mathematical physics, geometry and machine learning readily accessible to graduate students and beyond. The overriding ambition is to introduce some modern mathematics to the physicist, some modern physics to the mathematician, and machine learning to both.
Author: George R. McGhee
Publisher: Cambridge University Press
ISBN: 1139459953
Category : Science
Languages : en
Pages : 185
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Book Description
The metaphor of the adaptive landscape - that evolution via the process of natural selection can be visualized as a journey across adaptive hills and valleys, mountains and ravines - permeates both evolutionary biology and the philosophy of science. The focus of this 2006 book is to demonstrate to the reader that the adaptive landscape concept can be put into actual analytical practice through the usage of theoretical morphospaces - geometric spaces of both existent and non-existent biological form - and to demonstrate the power of the adaptive landscape concept in understanding the process of evolution. The adaptive landscape concept further allows us to take a spatial approach to the concepts of natural selection, evolutionary constraint and evolutionary development. For that reason, this book relies heavily on spatial graphics to convey the concepts developed within these pages, and less so on formal mathematics.
Author: William M. Ivins
Publisher: Courier Corporation
ISBN: 0486143589
Category : Art
Languages : en
Pages : 130
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Book Description
This highly stimulating study observes many historical interrelationships between art and mathematics. It explores ancient and Renaissance painting and sculpture, the development of perspective, and advances in projective geometry.
Author: Roberto Alonso González-Lezcano
Publisher:
ISBN: 9781799872801
Category : Buildings
Languages : en
Pages : 312
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Book Description
"The chapters in this book will address issues concerning Indoor Environmental Quality (IEQ), which are described more simply as the conditions inside the building and cover issues such as air quality, access to daylight and views, pleasant acoustic conditions and occupant control over lighting and thermal comfort"--
Author: Bogdan Grechuk
Publisher: Springer Nature
ISBN: 3030806278
Category : Mathematics
Languages : en
Pages : 437
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Book Description
Landscape of 21st Century Mathematics offers a detailed cross section of contemporary mathematics. Important results of the 21st century are motivated and formulated, providing an overview of recent progress in the discipline. The theorems presented in this book have been selected among recent achievements whose statements can be fully appreciated without extensive background. Grouped by subject, the selected theorems represent all major areas of mathematics: number theory, combinatorics, analysis, algebra, geometry and topology, probability and statistics, algorithms and complexity, and logic and set theory. The presentation is self-contained with context, background and necessary definitions provided for each theorem, all without sacrificing mathematical rigour. Where feasible, brief indications of the main ideas of a proof are given. Rigorous yet accessible, this book presents an array of breathtaking recent advances in mathematics. It is written for everyone with a background in mathematics, from inquisitive university students to mathematicians curious about recent achievements in areas beyond their own.
Author: Mark Vidler
Publisher: Inner Traditions
ISBN: 9781620554685
Category : Body, Mind & Spirit
Languages : en
Pages : 0
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Book Description
Identifies the patterns of our planet’s design within the natural landscape • Explains the geometry inherent in the mountains and coasts on all continents • Reveals how ancient monuments were built to reflect and enhance the Earth’s design, often connecting sites around the world • Includes detailed maps that show the simple geometrical relationships among the world’s mountains, coastlines, islands, and ancient monuments From continent to continent across the globe, Mark Vidler and Catherine Young reveal that order is everywhere on Earth. On remote islands, soaring summits, and level deltas, they unveil natural topographic patterns related to pi, the golden ratio, and right-triangle geometry. And as the planet’s design emerges, it becomes clear that this hidden order in nature decided the location of ancient monuments the world over. Through detailed maps, Vidler and Young show how the locations of megalithic monuments reflect and enhance a natural pattern on the Earth that connects its major features. The rows of standing stones at Carnac in France, for example, point to the summits of Mount Everest and K2, and Angkor Wat in Cambodia is on a straight line joining Mount Kilimanjaro in Africa and the tip of Cape Comorin in India. The authors examine the geography of many islands and each continent, including Antarctica, to show how the highest peak on each landmass falls on a line connecting coastal extremes. They reveal how circles of standing stones and man-made mounds mark intersections of these lines. They explore the connection between the Nazca lines in Peru and the Amazon, Nile, and Ganges deltas and explain how the locations of the Giza pyramids, Stonehenge, and Machu Picchu are integrated into the natural design on Earth. As they uncover geometric patterns on the Earth line by line, point by point, the authors reveal how the world’s ancient monuments represent a form of transglobal communication that far predates the written word.
Author: Charles R. Kolb
Publisher:
ISBN:
Category : Land use
Languages : en
Pages : 48
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Book Description
A ethod of classifying landscape ba ed on relief, slope, slope occurrence, and plan-profile is presented. The interrelation of these parameters in landscape definition, modification in definition due to scale difference, and synthesis of these parameters in a single semiquantitative landscape symbolization are discussed. Landscape geometry classification is limited to terrain exhibiting more than 10 ft of relief. Terrain feat res ex ibiting less than 10 ft of relief are classified as surface roughness or microrelief. T E GOAL HAS BEEN TO DEVELOP AS COMPLETE A LANDSCAPE GEOMETRY DEFINITION AS POSSIBLE WITHIN AS SIMPLE A FRAMEWORK AS POSSIBLE. (Author.
Author: Lionel March
Publisher: Routledge
ISBN: 100069111X
Category : Architecture
Languages : en
Pages : 492
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Book Description
Originally published in 1971 The Geometry of Environment is a fusion of art and mathematics introducing stimulating ideas from modern geometry, using illustrations from architecture and design. The revolution in the teaching of mathematics and the advent of the computer in design challenge traditional ways of appreciating the space about us, and expand the ‘structural’ understanding of our surroundings through such concepts as transformations, symmetry groups, sets and graphs. This book aims to show the relevance of ‘new maths’ and encourages exploration of the widening intellectual horizons of environmental design and architecture.
Author: Amir R. Alexander
Publisher: Stanford University Press
ISBN: 9780804732604
Category : Science
Languages : en
Pages : 318
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Book Description
This challenging book argues that a new way of speaking of mathematics and describing it emerged at the end of the 16th century. Leading mathematicians began referring to their field in terms drawn from the exploration accounts of Columbus and Magellan. Many of those who promoted the vision of mathematics as heroic exploration also played central roles in developing the most important mathematical innovation of the period?the infinitesimal methods, which the author shows was no coincidence.
Author: Catherine Dee
Publisher: Taylor & Francis
ISBN: 1134577893
Category : Architecture
Languages : en
Pages : 222
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Book Description
This book is an introduction to landscape architecture for students. Landscape architecture is a visual subject so the book is be illustrated with the author's own drawings.
