best discrete math book for computer science

... of any of the books already there. (Notice that if book 2 and book 1 are on shelf 7 in that order, putting book 3 to the immediate right of book 2 means putting it between book2 and book 1.) Thus ... may we place k distinct books on n shelves of a bookcase (all books pushed to the left as far as possible) if there must be at least one book on each shelf? 8. The formula for the number of multisets ... put the books on the shelves as follows: put all the books before the first piece of wood on shelf 1, all the books between the first and second on shelf 2, and so on until you put all the books...

Ngày tải lên: 21/02/2014, 09:20

Ngày tải lên: 18/12/2013, 15:37

... elegant way to model a computer in mathematical terms. This was a breakthrough, because it allowed the tools of mathemat- ics to be brought to bear on questions of computation. For example, with his ... truth of mathematics. 2.3 Using Induction Induction is by far the most important proof technique in computer science. Generally, induction is used to prove that some statement holds for all natural ... 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

... 170 Introduction to Programming 3 Computers have a fixed set of instructions that they can perform for us. The specific instruction set depends upon the make and model of a computer. However, these instructions ... However, for a mathematician, there are more complex math operations as well, such as finding the trigonometric sine of an angle or the square root of a number. Comparison instructions permit the computer ... that the computer always attempts to do precisely what you tell it to do. Say, for example, you tell the computer to divide ten by zero, it tries to do so and fails at once. If you tell the computer...

Ngày tải lên: 19/03/2014, 14:14

... — 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 AI ... 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 ... before we start into mathematics, we need to investigate the problem of how to talk about mathematics. To get around the ambiguity of English, mathematicians have devised a spe- cial language for...

Ngày tải lên: 23/03/2014, 23:20

... Edition) This book is intended as an introduction to mathematical logic, with an em- phasis on proof theory and procedures for constructing formal proofs of for- mulae algorithmically. This book is ... primarily for computer scientists, and more gen- erally, for mathematically inclined readers interested in the formalization of proofs, and the foundations of automatic theorem-proving. The book is ... proposition is a Horn formula iff it is a conjunction of basic Horn formulae. (a) Show that every Horn formula A is equivalent to a conjunction of distinct formulae of the form, P i , or ¬P 1 ∨...

Ngày tải lên: 29/03/2014, 09:20

... defined for SO = ao; all n 3 0 .) S, = S-1 + a,, for n > 0. (2.6) Therefore we can evaluate sums in closed form by using the methods we learned in Chapter 1 to solve recurrences in closed form. For ... were mathematical tools missing from his repertoire; the mathematics he needed for a thorough, well-grounded understanding of computer programs was quite different from what he’d learned as a mathematics ... looks as if T, = 2n-1, for n 3 0. (1.2) At least this works for n < 6. Mathematical induction is a general way to prove that some statement about the integer n is true for all n 3 no. First...

Ngày tải lên: 14/08/2014, 04:21

... OR difference/anti-difference pairs useful for summation. page 55. Get it? Despite all the parallels between continuous and discrete math, some continuous notions have no discrete analog. For example, the chain ... - yLx/yJ, for y # 0. (3.21) This defines ‘mod’ as a binary operation, just as addition and subtraction are binary operations. Mathematicians have used mod this way informally for a long time, ... circle. 34 Let f(n) = Et=, [lgkl. Find a closed form for f(n) , when n 3 1. L Provethatf(n)=n-l+f([n/2~)+f(~n/Z])foralln~l. 35 Simplify the formula \(n + 1 )‘n! e] mod n. Simplify it, but 36...

Ngày tải lên: 14/08/2014, 04:21

Ngày tải lên: 14/08/2014, 04:21

Ngày tải lên: 14/08/2014, 04:21

Ngày tải lên: 14/08/2014, 04:21

Ngày tải lên: 14/08/2014, 04:21

Ngày tải lên: 14/08/2014, 04:21

Ngày tải lên: 14/08/2014, 04:21

Ngày tải lên: 14/08/2014, 04:21

Ngày tải lên: 14/08/2014, 04:21

... fundamental one in discrete mathematics. The principle of mathematical induction is usually described in two forms. The one we have talked about so far is called the “weak form.” The Weak Principle of Mathematical ... −r = r n b + a 1 −r n 1 −r . Therefore by the principle of mathematical induction, our formula holds for all integers n greater than 0. Corollary 4.2.2 The formula for the sum of a geometric series ... integers for your universe.) 12. Each expression below represents a statement about the integers. Using p(x) for “x is prime,” q(x, y) for “x = y 2 ,” r(x, y) for “x ≤ y,” s(x, y, z) for “z =...

Ngày tải lên: 31/03/2014, 15:58

... million $150 million for STEM projects Loan Forgiveness $96 million for math and science teachers Loan Forgiveness $106 million TOTAL $522 million $867 million* *Funding total for Department of ... http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0938336; Association for Computing Machinery. (2006). A Model Curriculum for K-12 Computer Science: Final Report of the ACM K-12 Task Force, Second Edition. New York: Association for Computing Machinery; ... AP Computer Science: Principles —Course Annotations. New York: College Board; Computer Science Teachers Association. (2005). The New Educational Imperative: Improving High School Computer Science...

Ngày tải lên: 12/02/2014, 19:20

... telephone)?  Which informations we may consider for the future (e.g. email, birthday, bankaccount, webpage, ip, image, holographic picture, etc )?  By means of which information should we sort ... course Historical development of databases Databases Introduction Michael Emmerich Leiden Institute for Advanced Computer Science, Leiden University January 17, 2012 Michael T. M. Emmerich Databases Preliminaries Introductory ... stone-plates, books, libraries, microfiche, etc.  not to be ingnored, many concepts/principles developed then - look at town library’s organization!  often hierarchical sorting of information (efficient...

Ngày tải lên: 16/03/2014, 16:20