Davis is a member of the American Association of Artificial Intelligence and is a reviewer for many journals. His research primarily focuses on spatial and physical reasoning.
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Condition: New. Seller Inventory Brand new book, sourced directly from publisher. Dispatch time is working days from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Language: English. Brand new Book. Based on the author's course at NYU, Linear Algebra and Probability for Computer Science Applications gives an introduction to two mathematical fields that are fundamental in many areas of computer science.
The course and the text are addressed to students with a very weak mathematical background.
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The section on linear algebra gives an introduction to the theory of vectors, matrices, and linear transformations over the reals. It includes an extensive discussion on Gaussian elimination, geometric applications, and change of basis. It also introduces the issues of numerical stability and round-off error, the discrete Fourier transform, and singular value decomposition. The section on probability presents an introduction to the basic theory of probability and numerical random variables; later chapters discuss Markov models, Monte Carlo methods, information theory, and basic statistical techniques.
The focus throughout is on topics and examples that are particularly relevant to computer science applications; for example, there is an extensive discussion on the use of hidden Markov models for tagging text and a discussion of the Zipf inverse power law distribution. Examples and Programming AssignmentsThe examples and programming assignments focus on computer science applications.
The applications covered are drawn from a range of computer science areas, including computer graphics, computer vision, robotics, natural language processing, web search, machine learning, statistical analysis, game playing, graph theory, scientific computing, decision theory, coding, cryptography, network analysis, data compression, and signal processing.
Homework ProblemsComprehensive problem sections include traditional calculation exercises, thought problems such as proofs, and programming assignments that involve creating MATLAB functions. Seller Inventory AA Condition: NEW.
Linear Algebra and Probability for Computer Science Applications
Emphasis will be given to the use of graphing calculators and on the use of mathematics as a problem-solving tool. Applications in natural science, social science and business will be discussed. This course also serves as a preparation for calculus. Well-prepared students who already have a strong working knowledge of algebra, trigonometry, and logarithms should elect Mathematics in place of Mathematics A graphing calculator is required. Mathematics and constitute a thorough introduction to calculus for students who intend to continue in mathematics and for those who will use calculus in other fields such as science and engineering.
Mathematics covers limits, continuity, derivatives and a brief introduction to integration. Applications to problems in related rates, optimization, solid geometry and elementary mechanics are covered. Requires a strong working knowledge of algebra and trigonometry.
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Students who are weak in these areas should elect Mathematics Second half of the standard one-year calculus sequence see Mathematics above. Mathematics covers techniques of integration, applications of the integral, simple differential equations with their associated mathematical models, sequences, and series. Requires a strong working knowledge of algebra, trigonometry, derivatives, and some familiarity with integration, including Riemann sums and the Fundamental Theorem of Calculus.
soft question - How does linear algebra help with computer science? - Mathematics Stack Exchange
Students with a calculus background who are weak in these areas should elect Mathematics Topics include descriptive statistics, principles of probability, random variables, sampling distributions, point and internal estimation, hypothesis testing, analysis of variance, regression and non-parametric statistics.
Substantial use is made of Minitab statistics program on the computer. Vector spaces, matrices, Gauss-Jordan reduction, products, dimension, linear transformations, eigenvalues and eigenvectors, and a selection of applications of linear algebra to other disciplines. Throughout this course, students will develop their skills at mathematical writing and their ability to create mathematical proofs. Properties of equality, logical implication, proof by contradiction, quantification and proof by induction will be illustrated in context.
A survey of discrete mathematics with topics selected from set theory, functions and relations, number theory, combinatorics, graph theory, logic predicate calculus, quantifiers , introduction to proof techniques, and probability. Vectors, inner and cross products, and vector-valued functions including parametric representations of curves and surfaces in space.
Partial differentiation, the chain rule, function gradients, implicit differentiation, multivariate optimization, and Lagrange multipliers. Multiple integrals and vector analysis, including divergence and curl of vector fields, as well as the theorems of Green, Stokes, and Gauss. First-order differential equations and numerical algorithms of Euler and Runge-Kutta. Linear algebraic systems, Gaussian elimination, row-echelon form, matrix algebra, inverses and determinants. Vector spaces, subspaces, linear independence, bases, span, dimension, linear mappings, and function spaces.
Second and higher-order linear differential equations. Eigenvectors, eigenvalues, and spectral decomposition methods. First order linear differential systems, including solutions methods using matrix exponentials. Applications focus on problems in physics, chemistry, biology, economics and engineering.
Time permitting, additional topics include nonlinear dynamical systems, stability theory, transform theory, and power series solutions. Prerequisite: Mathematics or Computer Science Selected topics in mathematics and computer science as presented by students, departmental faculty and visiting speakers. A mathematical study of probability distributions, random sampling, and topics selected from statistical theory: estimation, hypothesis testing, and regression. A continuation of Mathematics In-depth studies of regression analysis, analysis of variance, experimental design, and nonparametric statistics are included.
Topics pertinent to actuarial mathematics are also covered. Methods of obtaining numerical solutions to mathematical problems. The implementation and error analysis of algorithms are stressed. Topics include: solution of non-linear equations, systems of equations, interpolating polynomials, numerical integration and differentiation, numerical solution to ordinary differential equations, and curve fitting. An introduction to computational methods in mathematical modeling, including linear programming and Markov chains.
Applications in business, economics, and systems engineering. Knowledge of probability will be helpful. A study of the concepts underlying calculus of a single variable: the completeness property of the real number system, convergence, continuity, properties of elementary functions, the derivative, and the Riemann integral. Properties of the integers, real number system and other familiar algebraic entities are viewed abstractly in structures such as groups, semigroups, rings, and fields.
Homomorphisms and isomorphisms functions compatible with the algebraic operations illuminate the underlying similarities among these structures. Students will develop their skills in mathematical writing and presentations. The logical foundations of Euclidean geometry, including the axiom systems of Euclid and Hilbert, and their philosophical implications. An introduction to hyperbolic, elliptic, and projective geometry.
Students will use software such as Geometer's Sketchpad to illustrate and motivate course topics. A study of the history and evolution of mathematical ideas and their significance, from approximately BCE to the present.
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