Discrete Mathematics for Computer Science
6 CS 441 Discrete mathematics for CS M. Hauskrecht Course syllabus Tentative topics: • Logic and proofs • Sets • Functions • Integers and modular arithmetic • Sequences and summations • Counting • Probability • Relations • Graphs CS 441 Discrete mathematics for CS M. Hauskrecht Course syllabus
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CS 1652: Data Communication and Computer Networks …
people.cs.pitt.edufrom the application layer to the data-link layer. Concurrent with the lectures, you (in groups of two) will be building a functional TCP/IP stack and a small web server that will run on it.
Informal proofs - University of Pittsburgh
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MIPS Floating Point Instructions
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Foundations of Artificial Intelligence
people.cs.pitt.edu“The branch of computer science that is concerned with the automation of in-telligent behavior” (Luger+Stubblefield, 1993) Views of AI fall into four categories: Thinking humanly Thinking rationally Acting humanly Acting rationally Examining these, we will plump for acting rationally (sort of) AIMA Chapter 1 (after Russell and Norvig) 3
Propositional logic: Horn clauses
people.cs.pitt.edu• Horn form (Horn normal form) • Two inference rules that are sound and complete with respect to propositional symbols for KBs in the Horn normal form: – Resolution (positive unit resolution) – Modus ponens (A∨¬B) ∧(¬A∨¬C ∨D) Can be written also as: (B ⇒ A) ∧(( A ∧C) ⇒ D) CS 2740 Knowledge Representation M. Hauskrecht ...
Sequences and summations
people.cs.pitt.eduSequences and summations CS 441 Discrete mathematics for CS M ... Arithmetic progression Definition: An arithmetic progression is a sequence of the ... -1, 3, 7, 11, … 3 CS 441 Discrete mathematics for CS M. Hauskrecht Geometric progression Definition A geometric progression is a sequence of the form: a, ar, ar2, ..., ark, where a is the ...
Time Series: Autoregressive models AR, MA, ARMA, ARIMA
people.cs.pitt.eduGaussian White Noise {A particular useful white noise is Gaussian white noise, wherein the w ... -20 0 20 40 60 80 12/77. Time Series Analysis The procedure of using known data values to t a time series ... Measures of Dependence A complete description of a time series, observed as a
Introduction to Kernel Methods
people.cs.pitt.edu1 Introduction to Kernel Methods Dave Krebs CS 3750 Fall 2007 ... Paradigm for Pattern Analysis. Kernel Methods in Bioengineering, Signal and Image Processing. 2007. ... 9 Mercer’s Condition (continued) if and only if, for any g(x) such that is finite, then It can be ...
Probabilities: Expected value
people.cs.pitt.eduExpected value Investment problem: • You have 100 dollars and can invest into a stock. The returns are volatile and you may get either $120 with probability of 0.4, or $90 with probability 0.6. • What is the expected value of your investment? • M. Hauskrecht Expected value Investment problem: • You have 100 dollars and can invest into a ...
Sets and set operations - University of Pittsburgh
people.cs.pitt.edu• Ordered-n tuples are used to represent an ordered collection. Definition: An ordered n-tuple (x1, x2, ..., xN) is the ordered collection that has x1 as its first element, x2 as its second element, ..., and xN as its N-th element, N 2. Example: • Coordinates of a point in the 2-D plane (12, 16) x y
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justmaths.co.uk5. Here are the first four terms of an arithmetic sequence. 10 14 18 8un + 17. [2] IQ (a) Write an expression, in terms of n, for the nth term of this sequence. The nth term of a different arithmetic sequence is 3n + 5 (b) Is 108 a term of this sequence? Show how you get your answer. 6. Here are the first six terms of a Fibonacci sequence.
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www.usu.edusequences. For an arithmetic sequence we get thenth term by adding d to the first term n 2 1 times; for a geometric sequence, we multiply the first term byr, n 2 1 times. Formulas for the nth terms of arithmetic and geometric sequences For an arithmetic sequence, a formula for thenth term of the sequence is a n 5 a 1 ~n 2 1!d. (1)