A Mathematical Introduction to General Relativity - by Amol Sasane (Hardcover)
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<p/><br></br><p><b> About the Book </b></p></br></br>The World of Discovery Collection is a specially curated selection of children's books that focus on discovering Asia and discovering STEM (Science, Technology, Engineering and Maths). Under the guidance of Dr Ruth Y L Wong, these books aim to promote reading for pleasure, while exciting kids through discovery. With 51 books in this inaugural batch, and with more to come, the books are divided into three levels depending on the child's reading ability: A (Achieving), B (Blooming) and C (Confident). Level B Set 2 features nine titles, exploring themes of science, imagination, nature and global stories. Intended outcomes of Level B include teaching children to be able to: - follow a text when it is being read aloud - turn the page at the right time - sound out at least 70% of the words in the book - read simple sentences - enjoy being read to Each book includes a story-based activity at the end of the books to help parents and educators get children to engage with the story. Includes these 9 titles: Brave Beachley (Sisu Girls series) Brave Beachley tells the tale of Australian Layne Beachley and how she chased her dream to become a world champion surfer. Because tough times are sure to happen. They are part and parcel of life's plan. But don't let those tough times stop you, pick yourself up and say: 'I CAN!' Fearless Frosty (Sisu Girls series) Fearless Frosty tells the story of New Zealander Anna Frost and how she chased her dream to become a professional mountain runner. Whatever it is, go after it. Find the thing that makes you fly! Because one thing is for certain: You'll never know unless you try. Mighty Mira (Sisu Girls series) Mighty Mira tells the tale of Nepali Mira Rai and how she chased her dream to become a professional mountain runner. The moral of my story; Live the moment, live the now. Don't worry if you don't know the path, Have courage, and you'll discover how. Panjang: The Tall Boy Who Became Prime Minister Panjang is the tallest kid around. He hates standing out, but little does he know, he's on his way to greater heights ... This book tells the childhood story of Singapore's second prime minister, Goh Chok Tong, and how he conquered his self-consciousness to become a leader. This tall tale inspires children to embrace the things that make them different. Tun Dr Siti Hasmah Mohd Ali: The Accidental Doctor Meet Siti Hasmah, a little girl, who wanted to be a journalist, in a period when not every girl was sent to school. Find out how she coped when World War II struck. Walk in her footsteps as she graduated from university and went on to save the lives of many Malaysian women and children. See what she finally ended up being. Meme the Monkey: Wins in Life We all like to win and do well. But what does it really mean to win in life? Meme the Monkey wants to do well and tries her very best to. But she soon learns that doing well in life is not just about scoring high marks in her exams - there are other more important things. I Really, Really Don't Like Water! (Wow Wild Asia series) Boleh the otter pup really, really does not like water. Mama starts him on swimming lessons. What should he do? Can he ever get used to the water? Read Boleh's splashy tale of learning new skills and the good surprise that comes with it. I Really, Really Don't Like Heights! (Wow Wild Asia series) Sayang the Leopard cub really, really does not like heights. When Sayang playfully chases after the bird, he ends too high up in a tree. Can Bear, Monkey and Squirrel help Sayang find his footing and courage to climb down the tree? I Really, Really Don't Like Bees! (Wow Wild Asia series) Tahan the bear cub really, really does not like bees. Tahan is nervous when he joins Papa for his first trip to a beehive. Will he succeed in collecting any honey? Can he ever put up with buzzing, swarming bees?<p/><br></br><p><b> Book Synopsis </b></p></br></br>The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.
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