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Continuation of modern geometric descriptions of polyhedrons. Included are definitions of convex polyhedron, half spaces, hyperplanes, affine dimension, and some connections to Linear Programming.
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Introduction to (modern) Polyhedral Geometry. This lecture defines convex sets and polyhedra and proves a few statements about convex sets and polyhedra.
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This lecture covers integer variables and modeling of combinatorial problems with integer variables. The example used GRAPH MATCHING.
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MAT-215A Lecture 2024-01-19 at 09:57
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Math 168 Lecture 1, Given on Jan 8th 2024. This lecture gives an introduction to optimization problems and the field of optimization.
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Lecture 2022-02-08. Equinumerous sets. Another proof that the rationals are countable. Uncountability of the set of all languages over {0,1}. When do things become impractical? Concrete dividing…
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Injective, surjective, and bijective functions. Examples. Two methods to shuffle cards. Countably infinite sets.
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Review of strings and languages. Closing a set of languages using some operators. Regular languages. Examples. BYTE, WORD32, and WORD64 as languages computers "like", and how we…
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More about sets. Powerset of a set. Cross product of sets. The axiomatic approach to set theory. Languages (sets of strings).
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NOTE: "Typo" in what I wrote on one slide: R={x: x \not\in x}. Basics of sets. The only basic vocabulary is \in and \emptyset. Defining other relations: union, intersection complement,…
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Basics of sets. The only basic vocabulary is \in and \emptyset. Defining other relations: union, intersection complement, set difference, symmetric difference. Identities and their proofs, including…
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