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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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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 ...
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
people.cs.pitt.eduInformal proofs Proving theorems in practice: • The steps of the proofs are not expressed in any formal language as e.g. propositional logic
MIPS Floating Point Instructions
people.cs.pitt.edu11/9/2011 1 MIPS Floating Point Instructions CS/COE 447 Why Floating Point? • Sometimes need very small, or very large numbers? Non-integers?
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 ...
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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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)
North Carolina Math 1 North Carolina Standard Course ... - NC
files.nc.gova. Build linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two ordered pairs (include reading these from a table). b. Build a function that models a relationship between two quantities by combining linear, exponential, or quadratic
Quadratic Sequences GCSE Mark Score (%) Edexcel …
examqa.comQuadratic Sequences, GCSE, Maths, Edexcel, AQA, OCR, WJEC Quadratic Sequences Questions, Quadratic Sequences Practice Questions, Quadratic Sequences Worksheet, Quadratic Sequences GCSE Questions, Quadratic Sequences GCSE Practice Questions, Quadratic Sequences GCSE Worksheet, GCSE Maths Created Date: 4/20/2018 1:17:01 PM
ARITHMETIC SEQUENCES & SERIES WORKSHEET
www.doralacademyprep.orgMar 17, 2015 · ARITHMETIC SEQUENCES & SERIES WORKSHEET The general term of an arithmetic sequence is given by the formula a n = a 1 + (n - 1)d where a 1 is the first term in the sequence and d is the common difference. Finding the sum of a given arithmetic sequence: 1. Identify a 1, n, and d for the sequence. 2. Find a
Arithmetic Sequences and Series Grade 12 CAPS …
brettonwoodhighschool.co.zaProblem 2 on Arithmetic Sequences. Solution The 4th term of an AS is 14 and the 16th term is 50. Calculate the first term and the common difference. 4 term : 3 14. (1) 4 th T a d 16 term : 15 50. (2) 16 th T a d Subtracting equation (1) from equation (2), we get 12dd 36 3 So 3(3) 14 5aa
Creating Phylogenetic Trees with MEGA
barc.wi.mit.edu• Identify and acquire the sequences that are to be included on the tree • Align the sequences (MSA using ClustalW, T‐Coffee, MUSCLE, etc.) • Estimate the tree by one of several methods • Draw the tree and present it From Hall, B.G. (p.3 ‐see Further Reading Slide)
JustMaths - Maths Tutorials, Resources and Support
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.