A View of Mathematics
نویسنده
چکیده
1. The Unity of Mathematics 2. The concept of Space 2.1. Projective Geometry 2.2. The Angel of Geometry and the Devil of Algebra 2.3. Non-Euclidean Geometry 2.4. Symmetries 2.5. Line element and Riemannian geometry 2.6. Noncommutative Geometry 2.7. Grothendieck’s Motives 2.8. Topos theory 3. Fundamental Tools 3.1. Positivity 3.2. Cohomology 3.3. Calculus 3.4. Trace and Index Formulas 3.5. Abelian Categories 3.6. Symmetries 4. The input from Quantum Field Theory 4.1. The Standard Model 4.2. Renormalization 4.3. Symmetries Bibliography Biographical Sketch
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