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An Introduction to Noncommutative Spaces and Geometry
This book explains a new kind of geometry called noncommutative geometry. In regular geometry, the order in which you multiply coordinates doesn’t matter (for example, 2 × 3 is the same as 3 × 2). But in noncommutative geometry, this is not true, the . . . READ MORE
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Complex geometry, Calabi-Yau manifolds, Toric Geometry
This book is a helpful guide for anyone studying complex geometry, especially those interested in string theory. It explains difficult ideas in a way that’s easy to understand, and it’s a good resource for students or researchers who want to learn mo . . . READ MORE
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Differential Geometry in Physics by Gabriel Lugo - PDF
This book introduces how the ideas of differential geometry (which is a branch of math dealing with shapes, curves, and spaces). Differential geometry is really important in understanding modern physics. It breaks down complex concepts like manifolds . . . READ MORE
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First Steps Towards a Symplectic Dynamics, Bramham -PDF
A long time ago, these two fields - symplectic geometry (which comes from physics and helps describe the shape of space) and dynamical systems (which studies how things move or evolve) were closely connected. But over the years, they drifted apart. B . . . READ MORE
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Geometry and Topology in Electronic Structure Theory
This is a set of advanced lecture notes by physicist Raffaele Resta. It is best for the graduate physics courses and explains how certain mathematical ideas (like geometry and topology) help us understand the electronic properties of materials—espec . . . READ MORE
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Introduction to Braided Geometry and q-Minkowski Space
This book introduces a special kind of geometry called “braided geometry" which is usefull to twist and “braid” the coordinates of space, which is different from the usual way we think about points in space. His work explores how these braided space . . . READ MORE
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Lectures on Calabi-Yau and Special Lagrangian Geometry
This book is an introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by recent results on singularities of special Lagrangian geometry. Yau Manifolds are special shapes (call . . . READ MORE
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Lectures on the Geometry of Quantization by Sean Bates
This book serves as an introduction to the mathematical concepts behind the transition from classical mechanics to quantum mechanics. It explains some math ideas that help us understand how classical physics changes into quantum physics. The book tal . . . READ MORE
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Noncommutative Geometry by Alain Connes - Free PDF
This math book that explores a new kind of geometry call "Noncommutative Geometry" where the usual rules don’t always apply. Normally, when we think about geometry, we imagine shapes and spaces described by functions that behave nicely meaning if you . . . READ MORE
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Noncommutative Geometry, Quantum Fields and Motives PDF
The book explores some very advanced ideas that connect modern math and physics. It starts with noncommutative geometry, which is a way of studying spaces where the usual rules about how things multiply then, the book looks at quantum field theory, w . . . READ MORE
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The Edinburgh Lectures on Geometry Michael Atiyah - PDF
The Edinburgh Lectures on Geometry, Analysis and Physics by Sir Michael Atiyah are a series of six talks he gave in 2008–2009 at the University of Edinburgh. In these lectures, Atiyah explored how ideas from geometry and analysis connect deeply with . . . READ MORE
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The Geometrization of Physics by Richard Palais - PDF
This short book is based on lectures Palais gave on the general subject of “gauge field theory” in 1981. It explains how we can use geometry (the kind you study in advanced math ) to better understand how forces like gravity and electricity work.
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