math for computer science amazon
Tài liệu Discrete Math for Computer Science Students doc
Ngày tải lên :
21/02/2014, 09:20
... 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, ... the
product in the denominator of the formula in Exercise 1.4-5 for the number of labellings with
three labels is what it is, and could generalize this formula to four or more labels.
Equivalence...
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Mathematics for Computer Science pot
Ngày tải lên :
05/03/2014, 23:20
... elegant way to model a computer in
mathematical terms. This was a breakthrough, because it allowed the tools of mathemat-
ics to be brought to bear on questions of computation. For example, with his ... truth of mathematics.
2.3 Using Induction
Induction is by far the most important proof technique in computer science. Generally,
induction is used to prove that some statement holds for all natural ... 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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Vic broquard c++ for computer science and engineering
Ngày tải lên :
19/03/2014, 14:14
... 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 ... However, for a mathematician, there are more complex math
operations as well, such as finding the trigonometric sine of an angle or the square root of a
number. Comparison instructions permit the computer ... 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...
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Mathematics for Computer Science pptx
Ngày tải lên :
23/03/2014, 23:20
... — page i — #1
Mathematics for Computer Science
revised Thursday 10
th
January, 2013, 00:28
Eric Lehman
Google Inc.
F Thomson Leighton
Department of Mathematics
and the Computer Science and AI ... proposition for each
possible set of truth values for the variables. For example, the truth table for the
proposition “P AND Q” has four lines, since there are four settings of truth values
for the ... before we
start into mathematics, we need to investigate the problem of how to talk about
mathematics.
To get around the ambiguity of English, mathematicians have devised a spe-
cial language for...
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Logic For Computer Science Foundations of Automatic Theorem Proving potx
Ngày tải lên :
29/03/2014, 09:20
... introduction to mathematical logic, with an em-
phasis on proof theory and procedures for constructing formal proofs of for-
mulae algorithmically.
This book is designed primarily for computer scientists, ... proposition is a Horn
formula iff it is a conjunction of basic Horn formulae.
(a) Show that every Horn formula A is equivalent to a conjunction of
distinct formulae of the form,
P
i
, or
¬P
1
∨ ... Sharpened Hauptsatz for G2
nnf
, 330
7.4.4 The Gentzen System G2
nnf
=
, 336
7.4.5 A Gentzen-like Sharpened Hauptsatz for G2
nnf
=
, 337
PROBLEMS, 337
7.5 Herbrand’s Theorem for Prenex Formulae, 338
7.5.1...
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discrete math in computer science - bogart , stein
Ngày tải lên :
31/03/2014, 15:58
... −r
= r
n
b + a
1 −r
n
1 −r
.
Therefore by the principle of mathematical induction, our formula holds for all integers n greater
than 0.
Corollary 4.2.2 The formula for the sum of a geometric series ... integers for your universe.)
12. Each expression below represents a statement about the integers. Using p(x) for “x is
prime,” q(x, y) for “x = y
2
,” r(x, y) for “x ≤ y,” s(x, y, z) for “z = ... mathematics and the computer science literature,
inductive proofs are written with multiple base cases and multiple implications with no effort to
reduce them to one of the standard forms of mathematical...
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concrete mathematics a foundation for computer science phần 1 pdf
Ngày tải lên :
14/08/2014, 04:21
... defined for
SO
= ao;
all n 3 0
.)
S,
=
S-1
+ a,,
for n > 0.
(2.6)
Therefore we can evaluate sums in closed form by using the methods we
learned in Chapter 1 to solve recurrences in closed form.
For ... were mathematical
tools missing from his repertoire; the mathematics he needed for a thorough,
well-grounded understanding of computer programs was quite different from
what he’d learned as a mathematics ... ideally set up for mathematical induction. In our case,
for example, (1.2) follows easily from (1.1): The basis is trivial, since
TO
=
2’
-
1 = 0. And the induction follows for n > 0 if...
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concrete mathematics a foundation for computer science phần 2 pptx
Ngày tải lên :
14/08/2014, 04:21
... exponents for rising factorial powers, analogous to
(2.52)? Use this to define
XC”.
10
The text derives the following formula for the difference of a product:
A(uv)
= uAv + EvAu.
How can this formula ...
-
yLx/yJ,
for y # 0.
(3.21)
This defines ‘mod’ as a binary operation, just as addition and subtraction are
binary operations. Mathematicians have used mod this way informally for a
long time, ... circle.
34 Let f(n) =
Et=,
[lgkl.
Find a closed form for f(n) , when n 3 1.
L
Provethatf(n)=n-l+f([n/2~)+f(~n/Z])foralln~l.
35
Simplify the formula \(n + 1
)‘n!
e]
mod n.
Simplify it,
but
36...
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Michael Emmerich Leiden Institute for Advanced Computer Science, Leiden University pptx
Ngày tải lên :
16/03/2014, 16:20
... 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 ... course
Historical development of databases
Databases
Introduction
Michael Emmerich
Leiden Institute for Advanced Computer Science, Leiden
University
January 17, 2012
Michael T. M. Emmerich Databases
Preliminaries
Introductory ... 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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vector math for 3d computer graphics - interactive tutorial
Ngày tải lên :
31/03/2014, 15:07
...
file:///C|/InetPub/wwwroot/VectorLessons/vch04/vch04_3.html (2 of 2) [10/9/01 2:23:49 PM]
Vector Math Tutorial for 3D Computer Graphics
Vector Math for 3D Computer Graphics
An Interactive Tutorial
Second Revision, July 2000
This ... PM]
Symbol for Vector Length
A good answer might be:
The length is 5.0. You could use the formula, or by realize that this is another 3-4-5 right triangle.
Symbol for Vector Length
The formula works for ... Inverse
·
Index
Although primarily aimed at computer science students, this tutorial is useful to all
programmers interested in 3D computer graphics or 3D computer game programming. In spite
file:///C|/InetPub/wwwroot/VectorLessons/vectorIndex.html...
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