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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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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 publication-ready 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: 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: 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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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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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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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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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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Published by: Massachusetts Institute of Technology | Language: English
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This course explores the following topics: derivation of elastic and plastic stress-strain relations for plate and shell elements; the bending and buckling of rectangular plates; nonlinear geometric effects; post-buckling and ultimate strength of cold formed sections and typical stiffened panels used in naval architecture; the general theor
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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
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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: Massachusetts Institute of Technology | Language: English
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This is a graduate-level 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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Published by: Massachusetts Institute of Technology | Language: English
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Data structures play a central role in modern computer science. You interact with data structures much more often than with algorithms (think of Google, your mail server, and even your network routers). In addition, data structures are essential building blocks in obtaining efficient algorithms. This course will cover major results and curr
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Published by: Massachusetts Institute of Technology | Language: English
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This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality
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Published by: Massachusetts Institute of Technology | Language: English
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This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimu
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