mathematics for computer science mit fall 2012

... important proof technique in computer science. Generally, induction is used to prove that some statement holds for all natural values of a variable. For example, here is a classic formula: 46 Number Theory ... 1) for all n ∈ N. By the principle of induction, P (n) is true for all n ∈ N, which proves the claim. This proof would look quite mysterious to anyone not privy to the scratchwork we did beforehand. ... divisibility hold. 1. If a | b, then a | bc for all c. 2. If a | b and b | c, then a | c. 3. If a | b and a | c, then a | sb + tc for all s and t. 4. For all c = 0, a | b if and only if ca | cb. Proof....

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... original formula for q. Recall that our proof of the formula we had in Exercise 1.4-5 did not explain why the product of three factorials appeared in the denominator, it simply proved the formula ... distinct elements. There are n choices for the first number in the list. For each way of choosing the first element, there are n −1choices for the second. For each choice of the first two elements, ... members (assuming that the president is not on the advisory board)? 10. By using the formula for  n 2  is is straightforward to show that n  n − 1 2  =  n 2  (n − 2). However this proof just uses...

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... 170 Introduction to Programming 3 Computers have a fixed set of instructions that they can perform for us. The specific instruction set depends upon the make and model of a computer. However, these instructions ... that the computer always attempts to do precisely what you tell it to do. Say, for example, you tell the computer to divide ten by zero, it tries to do so and fails at once. If you tell the computer ... instructions that tell the computer every step to take in the proper sequence in order to solve a problem for a user. A programmer is one who writes the computer program. When the computer produces a...

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... databases Databases Introduction Michael Emmerich Leiden Institute for Advanced Computer Science, Leiden University January 17, 2012 Michael T. M. Emmerich Databases Preliminaries Introductory ... telephone)?  Which informations we may consider for the future (e.g. email, birthday, bankaccount, webpage, ip, image, holographic picture, etc )?  By means of which information should we sort ... Paradox, Dbase-III (later FoxPro), System R/R+, IBM-DB2, Watcom SQL, etc.  Simple databases for personal computer arise, such as Excel/Access  1990ties: The internet emerges and with it web-based database...

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... In this problem, we will be reading in formatted data and generating a report. One of the common formats for interchange of formatted data is ’tab delimited’ where each line corresponds to ... } 6 MIT OpenCourseWare http://ocw .mit. edu 6.087 Practical Programming in C January (IAP) 2010 For information about citing these materials or our Terms of Use, visit: http://ocw .mit. edu/terms . ... characters. 4 Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.087: Practical Programming in C IAP 2010 Problem Set 3 Control flow. Functions....

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... degree-of-freedom pose space for a 3D object and also does not account for any non- rigid deformations. Therefore, we use broad bin sizes of 30 degrees for orientation, a factor of 2 for scale, and 0.25 ... Squares, perform poorly when the percent of inliers falls much below 50%. Fortunately, much better performance can be obtained by clustering features in pose space using the Hough transform (Hough, ... while allowing for shifts in their position results in much better classification under 3D rotation. For example, recognition accuracy for 3D objects rotated in depth by 20 degrees increased from 35% for...

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... values in common to both sets. 17 49 COMPUTER SCIENCE TEST PRACTICE BOOK Score Conversions and Percents Below* For GRE Computer Science Test, Form GR0329 Only TOTAL SCORE Raw Score Scaled ... to compare your performance with the performance of others who took this test. Both the worksheet on page 48 and the table on page 49 use performance data from GRE Computer Science Test examinees. The ... Scores* Needed to Earn Selected Scaled Scores on Three Computer Science Test Editions That Differ in Difficulty Raw Scores Scaled Score Form A Form B Form C Number of Questions Used to Compute Raw Score *Raw...

Ngày tải lên: 17/01/2014, 05:20

... book is an introduction to computer science. Computer science is the study of computer hardware, algorithms, and data structures and how they fit together to provide information systems. Each of ... sum- maries, and animations. Computers are therefore information- processing machines, and the computer programs are information-processing systems. 1.1 A BRIEF HISTORY OF COMPUTING Computers as we know ... widespread use was FORTRAN (short for formula translation system). Released in 1954 by IBM, FORTRAN was designed for scientific (mathematical) pro- gramming and allowed mathematical formulas to be...

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... Faculty of Computer Science and Engineering Department of Computer Science 4/4 Part 2. Binary Tree Required Questions Question 8. For each of the following key sequences ... recursive_Insert Faculty of Computer Science and Engineering Department of Computer Science 2/4 Return element of s is appended into q with the same order. For example if q = {1,2,3}, ... (compute(a,n)>compute(a,n-1))?compute(a,n):compute(a,n-1) 3233 6,5,4 4,5,6 Faculty of Computer Science and Engineering Department of Computer Science 1/4 DATA STRUCTURES & ALGORITHMS Tutorial 3 Questions...

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... Faculty of Computer Science and Engineering Department of Computer Science 2/3 Question 6. Suggest a data structure that supports ... for the problem that follow: public class BinaryTree <E extends Comparable<E>> { private class Node { E data; Node left, right; } Node root; } Faculty of Computer Science ... left, right; } Node root; } Faculty of Computer Science and Engineering Department of Computer Science 3/3 Write a recursive method called isCompleteBinaryTree() that returns true if...

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