concrete mathematics a foundation for computer science phần 3 ppsx

... 5-9 28 Practice Makes Perfect: English Grammar for ESL Learners 02 (017-0 43) Unit 5 11 /3/ 04 1:41 PM Page 28 24 Practice Makes Perfect: English Grammar for ESL Learners 8. You buy flowers every ... class? exercise 5-14 34 Practice Makes Perfect: English Grammar for ESL Learners 02 (017-0 43) Unit 5 11 /3/ 04 1:41 PM Page 34 Give an emphatic response to each...

Ngày tải lên: 24/07/2014, 07:21

... is a pattern of ones and zeros stored in a word of computer memory. By the way, a “word” of memory is the basic unit of storage for a computer. A 16-bit computer has a word size of 16 bits, or ... *, 6 ) J, ID, AV 6 FORMAT( I6, 3X, 'SUBJECT ', I6, 3X, 'AV= ', F9.2 ) STOP END Example input cards: 55 821 3 7 9 4 7 812 1 4 3 3 2 8 13 3 2 3 1 1 824 7 9 9...

Ngày tải lên: 12/08/2014, 21:22

... as part of the state of each individual car (part of the state of each instance). On the other hand, we would maintain a count of the total number of Automobiles as part of the state of the class ... expression / | \ / | \ (9 - 4) - 2 expression add_op term CHAP. 4] SOFTWARE 63 The state of an object is provided by variables. As the values of variables change, the state...

Ngày tải lên: 12/08/2014, 21:22

... recurrence makes it possible to build a table of small values very quickly. Perhaps we’ll be able to spot a pattern and guess the answer. n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 J(n) 1 1 3 1 3 5 7 1 3 ... index. ISBN o-2 01- 14236-8 1. Mathematics 19 61- 2. Electronic data processing Mathematics. I. Knuth, Donald Ervin, 19 38- . II. Patashnik, Oren, 19 54- . I...

Ngày tải lên: 14/08/2014, 04:21

... as a binary operation, just as addition and subtraction are binary operations. Mathematicians have used mod this way informally for a long time, taking various quantities mod 10, mod 27 7, and ... 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-fra...

Ngày tải lên: 14/08/2014, 04:21

... 87 106 1 93 299 492 685 878 1071 1264 1'1'1'2&apos ;3& apos; 4' 7'11'18'25&apos ;32 ' 39 ' 71'110'181'252&apos ;32 3' 39 4' 465"" are ... lo 1'10'9'8'7'b'5'4&apos ;3& apos;5'2&apos ;3& apos;1'2'1'2'1'2'1'1'~'1'1'1&a...

Ngày tải lên: 14/08/2014, 04:21

... n fans. How many ways h(n, k) are there for exactly k fans to get their own hats back? For example, if n = 4 and if the hats and fans are named A, B, C, D, the 4! = 24 possible ways for hats ... 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 CDA...

Ngày tải lên: 14/08/2014, 04:21

... 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

... because 2 - & z 0. 268 . This needs to be taken into account if we try to use formula (7.38) in numerical calculations. For example, a fairly expensive name-brand hand Icalculator comes ... 0;) as n -+ 00, un:less z = 0. This shows that formal power series can be manipulated algebraically without worrying about convergence. Example 6: A recurrence that goes ail the way...

Ngày tải lên: 14/08/2014, 04:21

... 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

... “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 ... actually 15 485 863. Exercise 21 shows that a still more accurate approximation to P, results if we begin with a still more accurate approximation to n(n) in place of (9.46). 9.6...

Ngày tải lên: 14/08/2014, 04:21

... results about Fermat’s Last Theorem; see Ribenboim j249j.j A ANSWERS TO EXERCISES 527 If the harmonic aa and a bb. Thus each bb behaves like a drone in the bee tree and each aa behaves like a ... thereby eliminating an upper parameter and a lower parameter. Thus, for example, we get closed forms for F( a, b; a - 1; z), F( a, b; a - 2; z), etc. Gauss [116, $71...

Ngày tải lên: 14/08/2014, 04:21

... V. Waugh and Margaret W. Maxfield, “Side-and-diagonal num- bers,” Mathematics Magazine 40 (1967), 74-83. 298 Warren Weaver, “Lewis Carroll and a geometrical paradox,” American Mathematical Monthly ... Mark Haiman Andrei Broder, Jim McGrath Oren Patashnik Joan Feigenbaum, Dave Helmbold Anna Karlin Oren Patashnik, Alex Schaffer Pang Chen, Stefan Sharkansky Arif Merchant, Stefan Sharkansky...

Ngày tải lên: 14/08/2014, 04:21

... end for 30 : x ← w 31 : for i ← 0 (c− 1) do  Middle vertical. 32 : y ← m 33 : for j ← 0 (c− 2) do 34 : H x,y ← Displacement(H, x, y, −w, 0, +w, 0, 0, −w, 0, +w,d) 35 : y ← y + m 36 : end for 37 : ... information can be used, for instance, in game balancing (e.g. adjusting point rewarding schemes, or testing synthetic players by making them engage in Algorithms and Ne...

Ngày tải lên: 14/08/2014, 11:21