discrete mathematics for computer science with student solutions manual cdrom
Tài liệu Discrete Math for Computer Science Students doc
Ngày tải lên :
21/02/2014, 09:20
... numbers than most of us can
imagine. However in discrete mathematics we often work with functions from a finite set
S with s elements to a finite set T with t elements. Then there are only a finite ... 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 ... the formula was correct. With this idea in hand, we could now explain why the
product in the denominator of the formula in Exercise 1.4-5 for the number of labellings with
three labels is what...
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Mathematics for Computer Science pot
Ngày tải lên :
05/03/2014, 23:20
... n:
• If student 0 gets candy, then student 1 also gets candy.
• If student 1 gets candy, then student 2 also gets candy.
• If student 2 gets candy, then student 3 also gets candy, and so forth.
Now ... are student 17. By these rules, are you entitled to a miniature candy
bar? Well, student 0 gets candy by the first rule. Therefore, by the second rule, student
1 also gets candy, which means student ... proof to
anyone who disagrees with you.
Intimidation. Truth is asserted by someone with whom disagrement seems unwise.
Mathematics its own notion of “proof”. In mathematics, a proof is a verification...
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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 ... or not
a T ever appears, but as with testing validity, this approach quickly bogs down
for formulas with many variables because truth tables grow exponentially with the
number of variables.
Is...
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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 ... 3
These two inequalities, together with the trivial solution for n = 0, yield
To
=O;
T,
=
2T+1
+l
,
for n > 0.
(1.1)
(Notice that these formulas are consistent with the known values
TI
= ... much happier. That is, we’d like a nice, neat,
“closed form” for
T,,
that lets us compute it quickly, even for large n. With
a closed form, we can understand what
T,,
really is.
So how do...
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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 ... different form, n = [n/21 +
[n/2].
If we had wanted the parts to be in nondecreasing order, with the small
groups coming before the larger ones, we could have proceeded in the same
way but with
[n/mJ
... 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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concrete mathematics a foundation for computer science phần 3 ppsx
Ngày tải lên :
14/08/2014, 04:21
... (mod 4).
QED for the case m = 12.
QED: Quite
Easily
So far we’ve proved our congruence for prime m, for m = 4, and for m =
Done.
12. Now let’s try to prove it for prime powers. For concreteness ... fractions
m/n with m > 0 and n 6 N (including fractions that are not reduced).
It is defined recursively by starting with
For N > 1, we form ?$,+I by inserting two symbols just before the kNth
symbol ... with entire equations, for which a slightly different
notation is more convenient:
a
s
b (mod m)
amodm = bmodm.
(4.35)
For example, 9 = -16 (mod 5), because 9 mod 5 = 4 = (-16) mod 5. The
formula...
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concrete mathematics a foundation for computer science phần 4 ppsx
Ngày tải lên :
14/08/2014, 04:21
... harder to start with f(k)
and to figure out its indefinite sum
x
f(k)
6k
= g(k) + C; this function g
might not have a simple form. For example, there is apparently no simple
form for
x
(E)
... every closed form for hypergeometrics
leads to additional closed forms and to additional entries in the database. For
example, the identities in exercises 25 and 26 tell us how to transform one
hypergeometric ... > 2m. Therefore this limit gives us exactly the
sum (5.20) we began with.
5.6 HYPERGEOMETRIC TRANSFORMATIONS
It should be clear by now that a database of known hypergeometric
closed forms is a...
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concrete mathematics a foundation for computer science phần 5 pps
Ngày tải lên :
14/08/2014, 04:21
... haven’t come up with a closed formula for them. We haven’t found
closed forms for Stirling numbers, Eulerian numbers, or Bernoulli numbers
either; but we were able to discover the closed form
H,
... NUMBERS
Before we stop to marvel at our derivation, we should check its accuracy.
For n = 0 the formula correctly gives
Fo
= 0; for n = 1, it gives
F1
=
(+
-
9)/v%, which is indeed 1. For higher ...
(-l).",
for n > 0.
(6.103)
When n = 6, for example, Cassini’s identity correctly claims that 1
3.5-tS2
=
1.
A polynomial formula that involves Fibonacci numbers of the form
F,,+k
for small...
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Owen l astrachan a computer science tapestry exploring programming and computer science with c++ 2nd
Ngày tải lên :
19/03/2014, 14:12
... consider the subfields within an area of study than it is to define the area of
study. So it is with computer science.
1.1 What Is Computer Science?
In some respects, computer science is a new discipline; ... of computer science is computer programming.
Some people prefer the term used in many European languages, informatics, over
what is called computer science in the United States. Computer science ... departments of computer science. But computer science
has benefited from work done in such older disciplines as mathematics, psychology,
electricalengineering, physics, andlinguistics. Computer science...
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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 ... 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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Logic For Computer Science Foundations of Automatic Theorem Proving potx
Ngày tải lên :
29/03/2014, 09:20
... 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, and ... 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
∨ ... Sets (Languages Without Equality), 194
5.4.7 Completeness: Special Case of Languages Without Func-
tion Symbols and Without Equality, 197
PROBLEMS, 205
5.5 Completeness for Languages with Function...
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discrete math in computer science - bogart , stein
Ngày tải lên :
31/03/2014, 15:58
... such that n>0 and for all integers m>n, for every polynomial equation
p(x)=0ofdegree m there are no real numbers for solutions.
11. Let p(x) stand for “x is a prime,” q(x) for “x is even,” ... −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 with r =1is
n−1
i=0
r
i
=
1 ... dreary)
proof of this formula by plugging in our earlier formula for binomial coefficients into all three
terms and verifying that we get an equality. A guiding principle of discrete mathematics is that
when...
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discrete mathematics for new technology second edition - garnier , taylor
Ngày tải lên :
31/03/2014, 15:58
... of undergraduate
computer science curricula and the mathematics which underpins it. Indeed, the
whole relationship between mathematics and computer science has changed so
that mathematics is now ... rigorous way the core mathematics
requirement for undergraduate computer science students at British universities
and polytechnics. Selections from the material could also form a one- or two-
semester ... Therefore
Jack is not a reasonable man.
4. All gamblers are bound for ruin. No one bound for ruin is happy.
Therefore no gamblers are happy.
5. All computer scientists are clever or wealthy. No computer...
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Mathematics for Life Science and Medicine docx
Ngày tải lên :
27/06/2014, 10:20
... Li
Department of Mathematics and
Physics,
Air Force Engineering University,
China
jianq_li@263.net
Wanbiao Ma
Department of Mathematics and
Mechanics,
School of Applied Science,
University of Science ... according to the ideas of
constructing population models with discrete age structure and the epidemic
compartment model, we form an SIS model with discrete age structure as
follows:
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
S
0
(t ... models with bilinear, standard
or quarantine-adjusted incidence, and found that for the SIQR model with
quarantine-adjusted incidence, the periodic solutions may arise by Hopf bi-
furcation, but for...
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