concrete mathematics a foundation for computer science phần 5 pps

concrete mathematics a foundation for computer science phần 5 pps

concrete mathematics a foundation for computer science phần 5 pps

... same pattern holds for continued fractions of any depth. It is easily proved by induction; we have, for example, K(ao,al,az ,a3 +l /a4 ) := K(ao,al ,a2 ,a3 ,a4 ) K(al, az, a3 + l /a4 1 K(al,az,as,ad) ... arise naturally. Let’s consider the pedigree of a male bee. Each male (also known as a drone) is produced asexually from a female (also known as a queen); each female, how...

Ngày tải lên: 14/08/2014, 04:21

64 366 0
concrete mathematics a foundation for computer science phần 3 ppsx

concrete mathematics a foundation for computer science phần 3 ppsx

... 492 6 85 878 1071 1264 1'1'1'2'3' 4' 7'11'18' 25& apos;32' 39' 71'110'181' 252 '323' 394' 4 65& quot;" are the ... a4 ; al = a9 = as; a2 = alo = o6; and a3 = all = a7 . So the values of ao, al, a2 , and as can be chosen in n4 ways, and the remaining a s depend on them. Does this lo...

Ngày tải lên: 14/08/2014, 04:21

64 361 0
concrete mathematics a foundation for computer science phần 4 ppsx

concrete mathematics a foundation for computer science phần 4 ppsx

... an auxiliary variable z, A( z) = ac +a, z +a2 z2+ = to@“. k>O (5. 52) It’s appropriate to use the letter z as the name of the auxiliary variable, be- cause we’ll often be thinking of z as a ... land generate the following numbers of rightful owners: ABCD 4 BACD 2 CABD 1 DABC 0 ABDC 2 BADC 0 CADB 0 DACB 1 ACBD 2 BCAD 1 CBAD 2 DBAC 1 ACDB 1 BCDA 0 CBDA 1 DBCA 2 ADBC 1 BDAC 0 CDAB 0...

Ngày tải lên: 14/08/2014, 04:21

64 397 0
concrete mathematics a foundation for computer science phần 9 pps

concrete mathematics a foundation for computer science phần 9 pps

... LLLRRRRR = & z .3 158 . Incidentally, an average of .334 implies at least 287 at bats. 51 8 ANSWERS TO EXERCISES and this is the case x = N of exercise 22. 5. 55 Let Q(k) = (k+Al) (k+AM)Zand R(k) ... results about Fermat’s Last Theorem; see Ribenboim j249j.j A ANSWERS TO EXERCISES 52 7 If the harmonic aa and a bb. Thus each bb behaves like a drone in the bee tree and each...

Ngày tải lên: 14/08/2014, 04:21

64 427 0
concrete mathematics a foundation for computer science phần 1 pdf

concrete mathematics a foundation for computer science phần 1 pdf

... intended as an antidote to “Abstract Mathematics, ” since concrete classical results were rap- idly being swept out of the modern mathematical curriculum by a new wave of abstract ideas popularly called ... Ronald Lewis, 19 35- Concrete mathematics : a foundation for computer science / Ron- ald L. Graham, Donald E. Knuth, Oren Patashnik. xiii,6 25 p. 24 cm. Bibliogr...

Ngày tải lên: 14/08/2014, 04:21

64 391 0
concrete mathematics a foundation for computer science phần 2 pptx

concrete mathematics a foundation for computer science phần 2 pptx

... name and conquer. a = ~ap’J , a- ’ = a+ a’; The change of vari- able from k to j is b = [va-‘l , va-’ = b -v’. Thus a = {a ‘} is the fractional part of a- ‘, and v’ is the mumble-fractional part ... notations for rising powers as well as falling powers. Mathematicians have long had both sine and cosine, tangent and cotangent, secant and cosecant, max and min; now we also have both f...

Ngày tải lên: 14/08/2014, 04:21

64 341 0
concrete mathematics a foundation for computer science phần 6 doc

concrete mathematics a foundation for computer science phần 6 doc

... sequences (al ,a2 . , al,,) of +1's and -1's have the property that al + a2 +. . . + azn = 0 and have all their partial sums al, al +a2 , . . . . al +a2 + +aZn nonnegative? There ... many spanning trees f, are in such a graph? A spanning tree is a subgraph containing all the vertices, and containing enough edges to make the subgraph connected yet not so many...

Ngày tải lên: 14/08/2014, 04:21

64 338 0
concrete mathematics a foundation for computer science phần 7 pot

concrete mathematics a foundation for computer science phần 7 pot

... month each person is reassigned to an adjacent state, each adjacent state being equally likely. (Here’s a diagram of the adjacencies: The initial states are circled.) For example, Alice is restationed ... (8.82) that A would probably beat B, that B would probably beat C, and that C would probably beat A; but all three patterns are simultaneously in the game.) What are each player’s cha...

Ngày tải lên: 14/08/2014, 04:21

64 395 1
concrete mathematics a foundation for computer science phần 8 doc

concrete mathematics a foundation for computer science phần 8 doc

... “Eulerian” (eighteenth-century) mathematics. 9.3 0 MANIPULATION 447 This may look worse than the sum we began with, but it’s actually a step for- ward, because we have very good approximations for ... the asymptotic expansion (?) = -&(I-&+j&+&-j&g++ all have denominators that are powers of 2. 61 Exercise 45 proves that the discrepancy D( 01, n) is o(n) for...

Ngày tải lên: 14/08/2014, 04:21

64 310 0
concrete mathematics a foundation for computer science phần 10 docx

concrete mathematics a foundation for computer science phần 10 docx

... sum 602. for 1x1,” American Mathematical Monthly 96 (1989), 52 5 -52 6. 131 Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, Concrete 102. Mathematics: A Foundation for Computer Science. Addison-Wesley, 1989. ... Warren Weaver, “Lewis Carroll and a geometrical paradox,” American Mathematical Monthly 45 (1938), 234-236. 58 2 BIBLIOGRAPHY 51 52 53 54 55 56 57...

Ngày tải lên: 14/08/2014, 04:21

64 459 0
w