# Mathematics for computer networking

• 153
• 130
• 0

## concrete mathematics a foundation for computer science phần 1 pdf

... the concrete ” -Z A Melzak 12 1 41 Concrete Ma the- matics is a bridge to abstract mathematics “The advanced reader who skips parts that appear too elementary may miss more than the less advanced ... Cataloging-in-Publication Data Graham, Ronald Lewis, 19 3 5Concrete mathematics : a foundation for computer science / Ronald L Graham, Donald E Knuth, Oren Patashnik xiii,625 p 24 cm Bibliography: ... time: n 10 11 12 13 14 S, 10 15 21 28 36 45 55 66 78 91 105 These values are also called the triangular numbers, because S, is the number of bowling pins in an n-row triangular array For example,...
• 64
• 145
• 0

## concrete mathematics a foundation for computer science phần 2 pptx

... generality, we can assume that < a < 1; let us write a = ~ap’J , b = [va-‘l , a- ’ = a+ a’; va-’ = b -v’ Thus a = {a ‘} is the fractional part of a- ‘, and v’ is the mumble-fractional part of va-‘ ... zero, and the first can be evaluated by our usual routine: k,m>O = tm((m+l)‘-m2)[m+16al ll@O = ~m(2m+l)[m...
• 64
• 178
• 0

## concrete mathematics a foundation for computer science phần 3 ppsx

... BBBB Each of the nm possible patterns appears at least once in this array of mN(m,n) strings, and some patterns appear more than once How many times does a pattern a~ a, ,-, appear? That’s easy: ... mathematical formulas that are easy to deal with? A bit of experimentation suggests that the best way is to maintain a x matrix that holds the four quantities involved in the ancestral fractions ... congruences are almost like equations For example, congruence is an equivalence relation; that is, it satisfies the reflexive law a = a , the symmetric law a b =\$ b E a , and the transitive law a E...
• 64
• 179
• 0

## concrete mathematics a foundation for computer science phần 4 ppsx

... named A, B, C, D, the 4! = 24 possible ways for hats to land generate the following numbers of rightful owners: ABCD ABDC ACBD ACDB ADBC ADCB 2 1 BACD BADC BCAD BCDA BDAC BDCA 0 CABD CADB CBAD ... the air The hats come back randomly, one hat to each of the n fans How many ways h(n, k) are there for exactly k fans to get their own hats back? For example, if n = and if the hats and fans are ... b;k! We can now combine all these operations and make a mathematical “pun” by expressing the same quantity in two different ways Namely, we have (9 +a, ) (4 +a, )F q = al a, F altl, a, +1 (8 +...
• 64
• 181
• 0

## concrete mathematics a foundation for computer science phần 5 pps

... drone has one grandfather and one grandmother; he has one greatgrandfather and two great-grandmothers; he has two great-great-grandfathers and three great-great-grandmothers In general, it is easy ... name We have, for example, a0 + 1 a1 + ~ a2 + G = K(ao,al,az ,a3 ) -K(al,az ,a3 ) ' (6.1 35) The same pattern holds for continued fractions of any depth It is easily proved by induction; we have, for ... correctly claims that 3 .5- tS2 = A polynomial formula that involves Fibonacci numbers of the form F,,+k for small values of k can be transformed into a formula that involves only F, and F,+I , because...
• 64
• 207
• 0

## concrete mathematics a foundation for computer science phần 6 doc

... following problem: How many sequences (al ,a2 , al,,) of +1's and -1's have the property that al + a2 + + azn = and have all their partial sums al, al +a2 , al +a2 + +aZn nonnegative? There must be ... the pattern.) There is no closed form for p(n), but the theory of partitions is a fascinating branch of mathematics in which many remarkable discoveries have been made For example, Ramanujan proved ... for rational functions tells us that the answer can be obtained from a partial fraction representation We can use the general expansion theorem (7.30) and grind away; or we can use the fact that...
• 64
• 225
• 0

## concrete mathematics a foundation for computer science phần 7 pot

... space, and we want to estimate the mean of a random variable X by sampling its value repeatedly (For exa.mple, we might want to know the average temperature at noon on a January day in San Francisco; ... special case p = i we can interpret these formulas in a particularly simple way Given a pattern A of m heads and tails, let A: A = fIkpl [Ack’ =A( kj] (8 .76 ) k=l We can easily find the binary representation ... information inside a computer are based on a technique called “hashing!’ The general problem is to maintain a set of records that each contain a “key” value, K, and some data D(K) about that...
• 64
• 233
• 0

Xem thêm