discrete mathematics for computer scientists solutions manual

... 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...

Ngày tải lên: 21/02/2014, 09:20

... possible, and so the total score for the game is 1(1 − 1)/2 = 0. Therefore, P(1) is true. Inductive step: Now we must show that P (1), . , P (n − 1) imply P (n) for all n ≥ 2. So assume that P ... 1) for all n ∈ N. By the principle of induction, P (n) is true for all n ∈ N, which proves the claim. This proof would look quite mysterious to anyone not privy to the scratchwork we did beforehand. ... 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....

Ngày tải lên: 05/03/2014, 23:20

... 0:28 — 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 ... 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 ... b for some s 2 Sg: For example, if we let Œr; s denote set of numbers in the interval from r to s on the real line, then f 1 .Œ1; 2/ D Œ1=4; 1. For another example, let’s take the “search for...

Ngày tải lên: 23/03/2014, 23:20

... 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 ... 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 ... conjecture. For n = 1, the sum is 1. For n = 2, the sum is 1 + 3 = 4. For n = 3, the sum is 1 + 3 +5 = 9. For n = 4, the sum is 1 + 3 +5 +7 = 16. At this stage we notice that, so far, for each value...

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Ngày tải lên: 24/10/2014, 17:32

... DefiniteIntegralsandUsefulFormulas 287 7.2.3. General Reduction Formulas for the Evaluation of Integrals . . . . . . . . . . . . . . . . 289 7.2.4. General Asymptotic Formulas for the Calculation of ... 666 15.3. Traveling-Wave Solutions, Self-Similar Solutions, and Some Other Simple Solutions. SimilarityMethod 667 15.3.1. PreliminaryRemarks 667 15.3.2. Traveling-Wave Solutions. Invariance of ... Self-Similar Solutions. Invariance of Equations Under Scaling Transformations 669 15.3.4. Equations Invariant Under Combinations of Translation and Scaling Transformations,andTheirSolutions 674 15.3.5....

Ngày tải lên: 08/03/2014, 12:20

... machine ($160,000 + $37,500) does not cover cash outflow for equipment rental. © The McGraw-Hill Companies, Inc., 1997 Solutions Manual, Chapter 2 15 Solutions to Exercises 2–14. (15 min.) Basic concepts. Cost ... units x ($1.30 for materials + $.80 for conversion costs). $44,200 = 17,000 units x ($1.30 + $.80 + $.20 + $.30). $26,000 = $1.30 for materials x 20,000 units. $16,000 = $.80 for conversion ... Companies, Inc., 1997 Solutions Manual, Chapter 2 29 2–27. (15 min.) Components of full costs. a. Product cost per unit: $120 + $70 + $18 + ($72,000/1,200 units) = $268 b. Period costs for the period: $48,000...

Ngày tải lên: 29/03/2014, 20:20

... ISTE Ltd. Mathematics for Informatics and Computer Science Pierre Audibert www.it-ebooks.info PART 1 Combinatorics © 2010 ISTE Ltd. Published 2010 by ISTE Ltd. Mathematics for Informatics ... programmings. For algorithmic enthusiasts in general, see the following books for further detail: [AHO 87], [BER 91], [COR 02], [SED 91]. www.it-ebooks.info Mathematics for Informatics and Computer ... www.it-ebooks.info 14 Mathematics for Informatics and Computer Science 1.6.3. Complete Sudoku grids A calculation that leads to a number of solutions exceeding 10 21 can only be done with the help of a computer. ...

Ngày tải lên: 05/05/2014, 15:02

... called a basis for the vector space. Before we can define exactly what a basis is, we need to know what it means for a set of vectors to be linearly independent. Mathematics for 3D Game ... 62 Exercises for Chapter 3 64 Chapter 4 Transforms 67 4.1 Linear Transformations 67 4.1.1 Orthogonal Matrices 68 4.1.2 Handedness 70 4.2 Scaling Transforms 70 4.3 Rotation Transforms 71 4.3.1 ... product of these transformations is called the model-view transformation. Once a model’s vertices have been transformed into camera space, they un- dergo a projection transformation that has...

Ngày tải lên: 29/05/2014, 17:21

... of view, believed that the information provided by a company’s accounts should help them form judgements concern- ing valuation. In fact the case for accounting reform does not rest simply on ... present value for the individual building or for a particular machine but only for groups of assets which can be identified as a separate income-generating unit. Capital maintenance Let us for a while ... maintenance – Not adjusted for inflation (Money financial capital maintenance) – Adjusted for inflation (Real financial capital maintenance) 68 Part 1 · The framework of financial reporting For certain purposes...

Ngày tải lên: 21/06/2014, 04:20

... cash flows ● Disclosure When to perform an impairment review We have already touched upon the special requirements for goodwill and intangible assets (see p. 121). For the generality of assets a ... use value is based on the additional assumption ‘that the property can be used for the foreseeable future only for the existing use’ (p. 60). The adoption of the proposals set out in FRED 29 ... substantial size given its location that there is no market for such properties. Valuation of specialised properties Because of the lack of a market for such assets they should be valued by reference...

Ngày tải lên: 21/06/2014, 04:20

... required for the year ended 30 November 1998 for each of the above projects. (6 marks) (b) Calculate and disclose the appropriate amounts for the financial statements of Forfar plc for the year ... to be provided for as follows: ● Freehold property – 2.5% p.a. on valuation. The land element is £1.5 million. ● Plant and machinery – 10% p.a. on cost. ● Plant held for rental is for short-term ... for the land and buildings (land element – £2m) and £5m for the plant. Asset lives were estimated at 50 years for the premises and 10 years for the plant; a full year’s depreciation is charged in...

Ngày tải lên: 21/06/2014, 04:20

... to establish principles for the use of hedge accounting when accounting for financial instruments. FRED 23 proposes that, in order for a financial instrument to qualify for hedge account- ing, ... accounted for correctly under FRS 12: ‘Provisions, Contingent Liabilities and Contingent Assets’. World Wide Nuclear Fuels plc disclosed the following information in its financial state- ments for ... the sale agreement, oil has to be supplied for a five year period to the company’s former holding company at an uneconomic rate. As a result a provision for future operating losses has been set...

Ngày tải lên: 21/06/2014, 04:20

... that makes accounting for defined benefit schemes such an interesting and difficult problem for the accountant. Fortunately for many employees, but perhaps unfortunately for accountants, most ... assets Movement of the surplus 22 June 2002 The information relating to the performance statements Information relating to the actuarial loss or gain for the current period only Compliance with ... presented. For example, the predictive value of information provided by the financial performance statement is enhanced if unusual or infrequent items of gains or losses are disclosed and if information...

Ngày tải lên: 21/06/2014, 04:20

Ngày tải lên: 21/06/2014, 04:20

Ngày tải lên: 21/06/2014, 04:20

Ngày tải lên: 21/06/2014, 04:20

Ngày tải lên: 21/06/2014, 04:20