عنوان

Linear algebra and probability for computer science applications /

1466501553

9781466501553

dltt

Linear algebra and probability for computer science applications /

[Book]

Ernest Davis

xviii, 413 pages :

illustrations ;

25 cm

Includes bibliographical references and index

1. MATLAB -- Desk calculator operations -- Booleans -- Nonstandard numbers -- Loops and conditionals -- Script file -- Functions -- Variable scope and parameter passing -- Part 1. Linear algebra -- 2. Vectors -- Definition of vectors -- Applications of vectors -- Basic operations on vectors -- Dot product -- Vectors in MATLAB basic operations -- Plotting vectors in MATLAB -- Vectors in other programming languages -- 3. Matrices -- Definition of matrices -- Applications of matrices -- Simple operations on matrices -- Multiplying a matrix times a vector -- Linear transformation -- Systems of linear equations -- Matrix multiplication -- Vectors as matrices -- Algebraic properties of matrix multiplication -- Matrices in MATLAB -- 4. Vector spaces -- Fundamentals of vector spaces -- Proofs and other abstract mathematics (optional) -- Vector spaces in general (very optional) -- 5. Algorithms -- Gaussian elimination : examples -- Gaussian elimination : discussion -- Computing a matrix inverse -- Inverse and systems of equations in MATLAB -- Ill-conditioned matrices -- Computational complexity -- 6. Geometry -- Arrows -- Coordinate systems -- Simple geometric calculations -- Geometric transformations -- 7. Change of basis, DFT, and SVD -- Change of coordinate system -- The formula for basis change -- Confusion and how to avoid it -- Nongeometric change of basis -- Color graphics -- Discrete Fourier transform (optional) -- Singular value decomposition -- Further properties of the SVD -- Applications of the SVD -- MATLAB --

Part 2. Probability -- 8. Probability -- The interpretation of probability theory -- Finite sample spaces -- Basic combinatorial formulas -- The axioms of probability theory -- Conditional probability -- The likelihood interpretation -- Relation between likelihood and sample probability -- Bayes' law -- Independence -- Random variables -- Application : naive Bayes classification -- 9. Numerical random variables -- Marginal distribution -- Expected value -- Decision theory -- Variance and standard deviation -- Random variables over infinite sets of integers -- Three important discrete distributions -- Continuous random variables -- Two important continuous distributions -- 10. Markov models -- Stationary probability distribution -- PageRank and link analysis -- Hidden Markov models and the K-gram model -- 11. Confidence intervals -- The basic formula for confidence intervals -- Application : evaluating a classifier -- Bayesian statistcial inference (optional) -- Confidence intervals in the frequentist viewpoint (optional) -- Hypothesis testing and statistical significance -- Statistical inference and ESP -- 12. Monte Carlo methods -- Finding area -- Generating distributions -- Counting -- Counting solutions to a DNF formula (optional) -- Sums, expected values, and integrals -- Probabilistic problems -- Resampling -- Pseudorandom numbers -- Other probabilistic algorithms -- MATLAB -- 13. Informational and entropy -- Information -- Entropy -- Conditional entropy and mutual information -- Coding -- Entropy of numeric and continuous random variables -- The principle of maximum entropy -- 14. Maximum likelihood estimation -- Sampling -- Uniform distribution -- Gaussian distribution : known variance -- Gaussian distribution : unknown variance -- Least squares estimates -- Principal component analysis -- Applications of principal component analysis

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"Taking a computer scientist's point of view, this classroom-tested text gives an introduction to linear algebra and probability theory, including some basic aspects of statistics. It discusses examples of applications from a wide range of areas of computer science, 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. It includes an extensive discussion of MATLAB, and includes numerous MATLAB exercises and programming assignments"--

Algebras, Linear

Computer science-- Mathematics

Probabilities

Davis, Ernest

20120717114415.0

[Book]

Y