Computation as static measurement: Numbers and types of number: integer, rational, irrational. Structured forms: Vectors and vector operations. Linear transformations. Applications in video games and robot motion planning. (3 lectures) Computation as dynamic measurement: Introduction to calculus; functions and their graphs: geometric interpretation of derivative; standard differentiation formulae and rules; maxima and minima, information obtained from second derivative; basic integral calculus; geometric interpretation of integral; standard integral formulae. (5-6 lectures) Beyond traditional notions of number : Definition of complex number, representation forms (coordinate, polar), properties of complex numbers: conjugates, modulus, standard arithmetic operations. (3 lectures) Computational approaches for hard calculations: Providing support for experimental claims: regression methods (1-2 lectures) Computational models of richer structures: Linear and Matrix
algebra; common computational objects described by matrices; weighted directed graphs; properties and operations on matrices: determinant, singularity and invertibility; eigenvalues and eigenvectors; conditions guaranteeing existence of useful forms - the Perron-Frobenius Theorem: notable applications of the PF-eigenvector: Google page ranking algorithm; ranking of sports leagues. (8-9 lectures) A bit of information theory: Shannon's Fundamental questions: What is information? How is it measured? Shannon's model of communication; information content as reduced uncertainty; the notion of information entropy and the Source Coding Theorem. Dealing with noise and redundancy coding; higher levels: entropy and redundancy in Natural language; very informal introduction to n-gram language models and applications: text prediction, plagiarism/collusion detection (5-7 lectures)
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