'Generating functions' diaporamas de présentation

Chapter 9 Generating functions

Chapter 9 Generating functions. Yen-Liang Chen Dept of Information Management National Central University. 9.1. Introductory examples. Ex 9.1. 12 oranges for three children, Grace, Mary, and Frank.

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Discrete Mathematics

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Chapter 10 Infinite Series

Chapter 10 Infinite Series. Early Results Power Series An Interpolation on Interpolation Summation of Series Fractional Power Series Generating Functions The Zeta Function Biographical Notes: Gregory and Euler. 10.1 Early Results.

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12. Further Topics in Analysis

12. Further Topics in Analysis. Orthogonal Polynomials Bernoulli Numbers Euler-Maclaurin Integration Formula Dirichlet Series Infinite Products Asymptotic Series Method of Steepest Descent Dispersion Relations. 1. Orthogonal Polynomials. Rodrigues Formulas :.

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Developing a Mathematical Model of River Travel

Developing a Mathematical Model of River Travel. Gavin Stewart and Benjamin Spitz under Charles Stoddard. Definitions. k - The least number of possible next moves for a boat, unless the boat can reach the end of the river from an earlier campsite Y - The number of campsites on the river.

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? Introduction to Set Theory 1. Sets and Subsets Representation of set:

? Introduction to Set Theory 1. Sets and Subsets Representation of set: Listing elements, Set builder notion, Recursive definition ?, ?, ? P(A) 2 . Operations on Sets Operations and their Properties A=?B A?B, and B ?A Properties Theorems, examples, and exercises.

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HOW TO BE MORE PRODUCTIVE

HOW TO BE MORE PRODUCTIVE. Graham Hutton and Mauro Jaskelioff. Streams. A stream is an infinite sequence of values:. 0 ? 1 ? 2 ? 3 ? 4 . The type of streams is co-inductively defined:. codata Stream A = A ? Stream A . Defining Streams.

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Poisson processes

Poisson processes. Stochastic Process By TMJA Cooray. Introduction. The probability models we have discussed so far involves random variables occurring in discrete sequence. That is both the random variable and the time parameter have been discrete.

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? Introduction to Set Theory 1. Sets and Subsets Representation of set:

? Introduction to Set Theory 1. Sets and Subsets Representation of set: Listing elements, Set builder notion, Recursive definition ?, ?, ? P(A) 2 . Operations on Sets Operations and their Properties A=?B A?B, and B ?A Properties Theorems, examples, and exercises.

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Outline

Outline. The need for transforms Probability-generating function Moment-generating function Characteristic function Applications of transforms to branching processes. Definition of transform.

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Some facts about Power Series

Some facts about Power Series. Consider the power series with non-negative coefficients a k . If converges for any positive value of t , say for t = r , then it converges for all t in the interval [ -r, r ] and thus defines a function of t on that interval.

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Tutorial 5

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MATH 350: Probability

MATH 350: Probability. Fall 2017 Syllabus & Class Policies. Course topics. Introduction to Probability; Discrete and Continuous Distributions; Simulations Combinatorics Conditional Probability Basic distributions and Densities Expected Value; Variance; Moments Sums of Random Variables

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Chapter 7

Chapter 7. 7.1 Recurrence Relations 7.2 Solving Linear Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.4 Generating Functions 7.5 Inclusion- Exclusion 7.6 Applications of Inclusion-Exclusion. 7.1 Recurrence Relations .

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Chapter 7

Chapter 7. 7.1 Recurrence Relations 7.2 Solving Linear Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.4 Generating Functions 7.5 Inclusion- Exclusion 7.6 Applications of Inclusion-Exclusion. 7.1 Recurrence Relations .

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Tutorial 5

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Mathematical Tasks: educating awareness

The Open University Maths Dept. University of Oxford Dept of Education. Promoting Mathematical Thinking. Mathematical Tasks: educating awareness. John Mason & Anne Watson Toulouse June 2010. Combining Functions. Making mathematical sense of phenomena. Using coordinates to read graphs.

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