discrete mathematics for computer scientists solution manual pdf

... Trang 1Mathematics for Computer  Scientists  Trang 2Gareth J Janacek & Mark Lemmon CloseMathematics for Computer Scientists Trang 3Mathematics for Computer Scientists© 2011 Gareth ... are looking forward to getting your application! Trang 19Mathematics for Computer Scientists NumbersTrang 20Mathematics for Computer Scientists The statement calculus and logicChapter 2 The statement ... from the crowd. Trang 5Mathematics for Computer Scientists IntroductionIntroduction The aim of this book is to present some the basic mathematics that is needed by computer scientists The reader

Ngày tải lên: 01/04/2021, 12:40

... “works-for-depart-We hold additional information for all sales representatives in a separate table (SREP) “works-for-depart-Wehold additional information for employees who no longer work for the ... mapping from the informal natural language to the formal world of a database design This data integrity constraint problem is inevitable unless we adopt a formal methodology With a formal language, ... DB_S for the sample database A database skeleton defines our vocabulary; for each table we introduce a table alias, and for each table we introduce the names of the involved attributes for that

Ngày tải lên: 08/08/2014, 18:21

... Conference on Computers and Games, Forthcoming in Lecture Notes in Computer Science Springer-Verlag. Hellekalek P 1998 Good random number generators are (not so) easy to find Mathematics and Computers ... ACM-SIAM Symposium on Discrete Algorithms (SODA’97), pp 53–62 Society for Industrial and Applied Mathematics, Philadelphia, PA, USA. Ballard BW 1983 The ∗-minimax search procedure for trees containing ... critical vocabulary for games In Computer Games and Digital Cultures Conference Proceedings (ed M¨ayr¨a F), pp 9–33, Tampere University Press, Tampere, Finland Crawford C 1984 The Art of Computer Game

Ngày tải lên: 14/08/2014, 11:21

... CloseMathematics for Computer Scientists Trang 2Download free eBooks at bookboon.com2 Gareth J Janacek & Mark Lemmon Close Mathematics for Computer Scientists Trang 3Mathematics for Computer Scientists© ... Light is OSRAM Trang 5Mathematics for Computer Scientists IntroductionIntroduction The aim of this book is to present some the basic mathematics that is needed by computer scientists The reader ... code by just reading a manual - you have to do it! Mathematics is exactly the same, you need to do it Trang 6Download free eBooks at bookboon.comMathematics for Computer Scientists 6 Numbers Chapter

Ngày tải lên: 24/10/2014, 17:32

... David M Keil Framingham State University CSCI 317 Discrete Structures 2/14 Study questions on Discrete Structures for Computer Science The intention in providing these questions is ... table contains (a) variables; (b) formulas; (c) values of formulas under one interpretation; (d) values of formulas under all interpretations; (e) operations If formulas  and  have the same truth ... (d) variables; (e) quantifiers A formula in logic is valid if (a) it is true for some interpretation; (b) it is true for all interpretations; (c) it is true for no interpretation; (d) it is an

Ngày tải lên: 17/11/2016, 22:23

... silicate solution-to-sodium hydroxide solution by mass as 2.5; the mass of sodium hydroxide solution = 144/ (1+2.5) = 41 kg/m3; the mass of sodium silicate solution = 144 – 41 =103 kg/m3 Therefore, ... steam-curing at 60oC for 24 hours In order to optimize the usage of formwork, the products were cast and steam-cured initially for about hours The steam-curing was then stopped for some time to allow ... used in the case of reinforced Portland cement concrete columns and beams are applicable for reinforced geopolymer concrete columns Mid-span deflection at service load of reinforced geopolymer concrete

Ngày tải lên: 09/12/2016, 07:56

... semester • Function is extremely important in mathematics and computer science • linear, polynomial, exponential, logarithmic, • Don’t worry! For discrete mathematics, we need to understand functions ... and Onto Functions Sequences and Summation Recursion 4.1 Chapter 4 Sets and Functions Discrete Structures for Computer Science (CO1007) on Ngày Trang 2Nguyen An Khuong, Huynh Tuong NguyenContents ... which often have thesame properties Example • Set of all the students who are currently taking Discrete Mathematics 1 course • Set of all the subjects that K2011 students have to take in the first

Ngày tải lên: 29/03/2017, 18:30

... Partial Order Relations • Order words such that x comes before y in the dictionary • Schedule projects such that x must be completed before y • Order set of integers, where x < y Definition ... If u is an element of S such that a 4 u for all elements a ∈ A, then u is called anupper bound (cận trên) of A • If l is an element of S such that l 4 a for all elements a ∈ A, then l is called ... Equivalence Relations and Partitions Theorem Let R be an equivalence relation on a set A These statements for elements a and b of A are equivalent: i aRb ii [a] = [b] iii [a] ∩ [b] 6= ∅ Trang 31Nguyen An

Ngày tải lên: 29/03/2017, 18:30

... one of three fields: Information system (32 projects), Software Engineering (12 projects) and Computer Science (15 projects) How many ways are there for a student to choose? Solution: 32 + 12 + ... Combinations Product Rule Example There are32routers in a computer center Each router has24 ports How many different ports in the center? Solution There are two tasks to choose a port: 1 picking ... playing card, gambling, dices, • How many allowable passwords on a computer system? • How many ways to choose a starting line-up for a football Trang 4Nguyen An Khuong, Huynh Tuong NguyenContents

Ngày tải lên: 29/03/2017, 18:30

... Guerino Mazzola · Gérard Milmeister Jody Weissmann Comprehensive Mathematics for Computer Scientists Calculus and ODEs, Splines, Probability, Fourier and Wavelet Theory, Fractals ... core subjects for computer scientists completes the first volume in two regards: Part III first adds topology, differential, and integral calculus to the topics of sets, graphs, algebra, formal logic, ... vector c ∈ Rn such that for every ε > 0, there is an index N with ci ∈ Bε (c) for i > N Equivalently, we may require that for every ε > 0, there is an index M with ci ∈ Kε (c) for i > M If (ci )i

Ngày tải lên: 26/07/2017, 21:40

... Gareth J Janacek & Mark Lemmon Close Mathematics for Computer Scientists Download free ebooks at bookboon.com Mathematics for Computer Scientists © 2011 Gareth J Janacek, Mark Lemmon ... at bookboon.com Mathematics for Computer Scientists Introduction Introduction The aim of this book is to present some the basic mathematics that is needed by computer scientists The reader is not ... write code by just reading a manual - you have to it! Mathematics is exactly the same, you need to it Download free ebooks at bookboon.com Mathematics for Computer Scientists Numbers Chapter Numbers

Ngày tải lên: 26/07/2017, 21:40

... ιντεγερκ 2 ⇒ ν = κ , ωηιχη ισεϖεν 1/25/12 More slowly … • Thm For any integer n, n2 is odd if and only if n is odd • To prove a statement of the form “P iff Q,” two separate proofs are needed: – If P ... the assertions together are abbreviated “P iff Q” or “P⇔Q” or “P ≡Q” 1/25/12 More slowly … • Thm For any integer n, n2 is odd if and only if n is odd () “If n2 is odd then n is odd” is equivalent ... (“contrapositive”) which is the same as “if n is even then n2 is even” (since n is an integer) … then n=2k for some k and n2=4k2, which is even 1/25/12 Contrapositive and converse • The contrapositive of

Ngày tải lên: 22/03/2019, 10:35

... bottom pancake Trang 9Why does this take 2n-3 flips? • For n≥2, let P(n) := “n pancakes can be sorted using 2n-3 flips” • Suppose this is false for some n • Let C = {n: P(n) is false} • C has a least ... arguing that a fraction can be reduced to “lowest terms” integer is nonempty Trang 6To prove P(n) for every nonnegative n: • Let C = {n: P(n) is false} (the set of “counterexamples”) • Assume C ... by WOP Call it m • So m pancakes cannot be sorted using 2m-3 flips and m is the smallest number for which that is the case Trang 10Why does this take 2n-3 flips? • m≠2 since one flip sorts 2 pancakes

Ngày tải lên: 22/03/2019, 10:37

... may be hard to simplify formulas as much as possible – Any tautology is equivalent to p ⋁ ¬p so if we could easily simplify formulas we could easily determine whether a formula is a tautology ... Trang 1Logic and computersTrang 2Binary Arithmetic0 +0 0 0 +1 1 1 +0 1 1 +1 10 Only two digits: the bits 0 and 1 (Think: 0 = F, 1 = T) Trang 3Logic and Computers A half adder: ... number of bits to be added? 0 a2 b2 a1 b1 c2 c1 carryout Trang 12Simplifying Circuits• Simpler formulas turn into circuits that use less hardware! • E.g p ⋁ q ⋁ (p⋀q) is equivalent to p ⋁ q

Ngày tải lên: 22/03/2019, 10:41

... is contained in B” • (∀x) (x∈A ⇒ x∈B) • N ⊆ Z, {7} ⊆ {7, “Sunday”, π} • ∅ ⊆ A for any set A (∀x) (x∈∅ ⇒ x∈A) • A ⊆ A for any set A • To be clear that A ⊆ B but A ≠ B, write A ⊊ B • “Proper subset” ... Trang 1SetsTrang 2What is a Set?• Informally, a collection of objects, determined by its members, treated as a single mathematical object

Ngày tải lên: 22/03/2019, 10:45

... → R f(x,y) = x/y Defined for all pairs (x,y) except when y=0! 2/13/12 A Function that is “Partial,” Not Total domain f R×R codomain R f: R ×R → R f(x,y) = x/y Defined for all pairs (x,y) except ... “Size” For finite sets, a bijection exists iff A and B have the same number of elements domain A 2/13/12 f codomain B 10 Cardinality or “Size” Use the same as a definition of “same size” for infinite

Ngày tải lên: 22/03/2019, 10:47

... 1 1 Trang 11Cantor’s TheoremFor every set, A (finite or infinite) , there is no bijection A↔P(A) Trang 12There is no bijection A↔P(A)W::= {a A | a  f(a)} , so for any a, a W iff a  f(a) ... , for some a0 A (∀a) a f(a0) iff a  f(a ) Pf by contradiction: suppose f:A↔P(A) is a bijection Let Pf by contradiction: Trang 13There is no bijection A↔P(A)W::= {a A | a  f(a)} , so for ... A↔P(A)W::= {a A | a  f(a)} , so for any a , a W iff a  f(a) f is a bijection, so W=f(a0) , for some a0 A a f(a ) iff a  f(a ) Pf by contradiction: suppose f:A↔P(A) is a bijection Let

Ngày tải lên: 22/03/2019, 10:49

... level Fifth level Trang 5Example Induction ProofLet’s prove: r-1 (for r ≠ 1) Trang 6Statements in magenta form atemplate for inductive proofs: • Proof: (by induction on n ) • The induction ... 1+r +r + +r = r-1 L (for r ≠ 1) Trang 7Base Case (n = 0):r - 1 = = r - 1 1 L 0+1 1+r +r + +r = r - 1 Example Induction Proof 1 OK! Trang 8• Inductive Step: Assume P ( n ) for some n ≥ 0 and prove

Ngày tải lên: 22/03/2019, 10:51

... Theorem on D+C recurrences • T(1) = 1 • T(n) = aT(n/b) + cn e • Let L = logba • Recurrence has the solution: 1 T(n) = Θ(n e ) if e > L 2 T(n) = Θ(n e log n) if e = L 3 T(n) = Θ(n L ) if e < ... n-1 multiplications • Method 2: use successive squaring – How many times can you divide n by 2 before it is reduced to 1? – Repeated squaring requires between – Huge savings! n = 1000 => at ... multiplications • Method 2: use successive squaring – Requires about log2n multiplications • Same idea works for multiplication modulo p • Example: If n is a 500-digit number, we can compute q n (mod p) in

Ngày tải lên: 22/03/2019, 10:55

... Functions3/26/12 Trang 2Asymptotic Equivalence• Def: For example, Note that n2 +1 is being used to name the function f such that f(n) = n2 +1 for every n f (n) : g(n) iff limn        ... example: Stirling’s formula n! : n e ⎛ ⎝⎜ ⎞ ⎠⎟    3/26/12 Trang 4Little-Oh: f = o(g)• Def: f(n) = o(g(n)) if lim n           • For example, n2 ...                So, for example, 3n2       Trang 11Rough Paraphrase• f∼g: f and g grow to be roughly equal •

Ngày tải lên: 22/03/2019, 10:59