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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This course offers an introduction to discrete and computational geometry. Emphasis is placed on teaching methods in combinatorial geometry. Many results presented are recent, and include open (as yet unsolved) problems.
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 mathematics
 discrete geometry
 computational geometry
 convex partitions
 binary space partitions
 art gallery problems
 planar graphs
 pseudotriangulations
 encompassing graphs
 geometric graphs
 crossing numbers
 extremal graph theory
 gallaisylvester problems
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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László Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course "Applied Geometric Algebra" taught by Professor Tisza in the Spring of 1976.
Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza's attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems.
The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, '77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publicationready PDFs. You can read about his motivation for wanting to see these notes published in his Preface. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This course covers a collection of geometric techniques that apply broadly in modern algorithm design.
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 mathematics
 spectral graph theory
 iterative methods for linear algebra
 convex geometry
 lattices and basis reduction
 lps and sdps for approximating nphard problems
 graph laplacians
 cheeger inequalities
 fritz john?s theorem
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Published by: Capilano University  Language: English
Published by: Capilano University  Language: English
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To develop an understanding of single variable differential calculus with emphasis on geometric interpretation, and the appropriate use of the graphing calculator technology
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Published by: Universitat Politècnica de Catalunya  Language: Spanish
Published by: Universitat Politècnica de Catalunya  Language: Spanish
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L'objectiu general de l'assignatura es pot descriure com:
Estudi de les propietats de la llum. Establir el model geomètric per explicar la propagació de la llum. Conèixer les lleis de l'Òptica Geomètrica. Descriure els diferents elements constitutius del sistema òptic (dioptres, miralls, lents i diafragmes). Aplicar del model geomètric per
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software.
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 mathematics
 phase plane
 limit cycles
 poincarebendixson theory
 timedependent systems
 floquet theory
 poincare maps
 averaging
 stability of equilibria
 nearequilibrium dynamics
 center manifolds
 elementary bifurcations
 normal forms
 chaos
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This course will focus on fundamental subjects in (deterministic) optimization, connected through the themes of convexity, geometric multipliers, and duality. The aim is to develop the core analytical and computational issues of continuous optimization, duality, and saddle point theory using a handful of unifying principles that can be easi
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 electrical engineering and computer science
 convexity
 optimization
 geometric duality
 lagrangian duality
 fenchel duality
 cone programming
 semidefinite programming
 subgradients
 constrained optimization
 gradient projection
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the course Analysis I (18.100B) is a prerequisite, topological notions like compactness, connectedness, and related properties of continuous functions are taken for granted.
This course offers biweekly problem sets with sol
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 mathematics
 functions of one complex variable
 cauchy's theorem
 holomorphic functions
 meromorphic functions
 residues
 contour integrals
 conformal mapping
 infinite series and products
 the gamma function
 the mittagleffler theorem
 harmonic functions
 dirichlet's problem
 the riemann mapping theorem
 the riemann zeta function
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This course will focus on various aspects of mirror symmetry. It is aimed at students who already have some basic knowledge in symplectic and complex geometry (18.966, or equivalent). The geometric concepts needed to formulate various mathematical versions of mirror symmetry will be introduced along the way, in variable levels of detail and
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 mathematics
 mirror symmetry
 deformation
 hodge theory
 pseudoholomorphic
 gromovwitten
 cohomology
 yukawa
 monodromy
 picardfuchs
 lagrangian floer theory
 homology
 syz conjecture
 submanifolds
 k3 surfaces
 matrices
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This course provides an introduction to the mechanics of solids with applications to science and engineering. We emphasize the three essential features of all mechanics analyses, namely: (a) the geometry of the motion and/or deformation of the structure, and conditions of geometric fit, (b) the forces on and within structures and assemblage
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 mechanical engineering
 statics
 pressure
 deformation
 deformable solid
 equilibrium
 geometric compatibility
 material behavior
 stress
 strain
 shear
 elasticity
 thermal expansion
 failure modes
 biomechanics
 natural materials
 motion
 structure
 force
 moment
 member
 truss
 friction
 torsion
 bending
 displacement
 beam
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This course explores the following topics: derivation of elastic and plastic stressstrain relations for plate and shell elements; the bending and buckling of rectangular plates; nonlinear geometric effects; postbuckling and ultimate strength of cold formed sections and typical stiffened panels used in naval architecture; the general theor
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 mechanical engineering
 plates
 shells
 engineering strain
 strain measure
 bending moment
 structural plasticity
 membrane energy
 greenlagrangian strain
 bending theory of plates
 buckling theory of plates
 raleighritz quotient
 local buckling
 plastic buckling
 cylindrical shells
 axial load
 lateral pressure
 hydrostatic pressure
 torsion
 bending boundary c
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Published by: The Open University  Language: English
Published by: The Open University  Language: English
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This unit looks at complex numbers. You will learn how they are defined, examine their geometric representation and then move on to looking at the methods for finding the nth roots of complex numbers and the solutions to simple polynominal equations.
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Published by: The Open University  Language: English
Published by: The Open University  Language: English
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In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as sho
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Published by: Universitat Politècnica de Catalunya  Language: Spanish
Published by: Universitat Politècnica de Catalunya  Language: Spanish
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L'assignatura es basa en l'òptica geomètrica, electromagnètica i quàntica per a l'estudi dels fenòmens lluminosos relacionats amb la naturalesa de la llum, la seva producció, propagació i interacció amb la matèria. Aplicacions a la fotometria i instruments òptics.
Objectiu 1. Saber utilitzar els models geomètric i ondulatori de la llum per
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Published by: Universitat Politècnica de Catalunya  Language: Spanish
Published by: Universitat Politècnica de Catalunya  Language: Spanish
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Estudi de les propietats de la llum. Establir els models que permeten explicar les trajectòries lluminoses i la formació de les imatges. Aprofundir en el model geomètric de la llum descrit pel concepte de raig. Descriure els diferents elements constitutius del sistema òptic (dioptres, miralls, lents i diafragmes) en aproximació paraxial. Co
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Published by: Massachusetts Institute of Technology  Language: English
Published by: Massachusetts Institute of Technology  Language: English
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This is a graduatelevel course in combinatorial theory. The content varies year to year, according to the interests of the instructor and the students. The topic of this course is hyperplane arrangements, including background material from the theory of posets and matroids.
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Tag(s):
 mathematics
 combinatorial theory
 hyperplane arrangements
 intersection poset
 matroids
 geometric lattices
 broken circuits
 modular elements
 supersolvability
 finite fields
 hyperplane
 arrangements
 intersection poset
 geometric lattices
 broken circuits
 modular elements
 supersolvability
 finite fields
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