Discrete here is used as the opposite of continuous. The sc in discrete mathematics and omputer science at the ru is organised as a three year programme six semesters. At the end of the semester you compare the class grades and end of course. This exam has 23 questions, for a total of 100 points. What is the probability that a ve card poker hand contains a ush, that is, ve cards of the same suit. A couple lectures back we proved by induction that tt takes 2n 1 moves to move n disks from the first peg to the third peg. This may seem a bit strange to understand, but once it clicks it can be an extremely powerful way of expressing certain ideas. Discrete mathematics thirdedition seymour lipschutz, ph. Descriptive statement discrete mathematics is the branch of mathematics that. An introduction to the discrete paradigm in mathematics and computer science. There are 12 micro phones 8 laser printers in an office.
Function terminology examples i what is the range of this function. Math 215 discrete mathematics worksheets induction and recursion let pn be the statement that a postage of ncents can be formed using just 3cent stamps and 5cent stamps. Work on the handin assignment listed last week and due this friday. Richard mayr university of edinburgh, uk discrete mathematics. Historically, these topics, as you have studied them, are all rather old, the newest of them being 150 years to 300 years old. But discrete mathematics deals with much more than just integers. Discrete math professor jeremy siek final exam may 5, 2010 name.
The authors draw from their background as researchers and educators to offer lucid discussions and descriptions fundamental to the subject of discrete mathematics. The final operation on a proposition p that we discuss is the negation of p. Understand the basic principles of iteration, recursion, and mathematical induction. At the end of the semester a teacher assigns letter grades to each of. Ffunction notationunction notation a linear function can be written in the form y mx. Tricks to solve aptitude questions, 6th grade math worksheets free, 8th grade math for dummies, algebra 2 practice workbook answers prentice hall, logarithmic expressions calculator. A fair division problem may be discrete or continuous. Discrete mathematics introduces students to the mathematics of networks, social choice, and. How i got the highest grade in my discrete math class november 25th, 2008 67 comments. Pdf on jan 1, 2010, glynn winskel and others published discrete mathematics ii. On an informal note, discrete math is one of the best subjects in cs, without it, most other subjects would be really difficult to appreciate. Our experts will gladly share their knowledge and help you with programming homework. Mar 20, 2011 chartrand and zhangs discrete mathematics presents a clearly written, studentfriendly introduction to discrete mathematics. Algorithms for continuous and discrete cases will be applied.
For an election with four candidates a, b, c, and d we have the following preference schedule. A familiar example from mathematics is the sequence of prime. You are responsible to print all the notes prior to coming to class each day. Proof of the fundamental theorem of arithmetic, using strong induction show that if n is an integer 2, then n can be written as the product of. This book seems very readable, i am using it to suppliment the text currently being used in our class. Discrete mathematics and its applications sequences and summations lecture slides by adil aslam email me. Firstly, to introduce the basic algorithms for computing exactly with integers, polynomials and vector spaces. Learning outcomes for the sc in discrete mathematics and omputer science. Topics include logic, set theory, number theory, induction, recursion, counting techniques, and graph theory. Identify the true statement, and give counterexamples for the two false statements. Let pn be the proposition that n can be written as a.
Sequences and summations in discrete mathematics 1. Richard kaye professor of mathematics university of birmingham chapter 11 sequences and. The title of this book is discrete mathematics and it was written by gary. Induction and recursion richard mayr university of edinburgh, uk richard mayr university of edinburgh, uk discrete mathematics.
Colin stirling informatics discrete mathematics section 2. Historically, these topics, as you have studied them, are all rather old, the newest of. A sequence is a function from a subset of the set of. The study of the integers and algebra are usually in the discrete category, while the real numbers, calculus, and geometry are usually in the continuous category. Math 215 discrete mathematics worksheets induction and.
Navigating through discrete mathematics in prekindergarten to grade 5 and. Define in your own words each of the 5 bolded terms on pages 4546. Math 2200 discrete mathematics summer 2015 instructor. Find the missing term of each geometric sequence unit 11 sequences and series day 3. Browse other questions tagged discretemathematics recursion or ask your own. At both the grade 8 and 11 levels, the advisory committees recommended. What is the probability that a hand of cards contains no pairs. Why is discrete mathematics required for data structures. Without probability, it would be difficult to argue about their correctness and efficiency. This content was copied from view the original, and get the alreadycompleted solution here. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields.
Discrete mathematics with applications 4th edition answers to chapter 5 sequences, mathematical induction, and recursion exercise set 5. Linear homogeneous recurrence relations with constant coefficients. For sets state the basic building blocks bbbs of the set. To finish the programme, students need to complete 180 ets. Remember that no late work even later in the classday will be accepted. Discretemath the combination of a certain combination lock. That is, show all the steps used by algorithm 3 to. Domain range what is the domain and the range of the function shown on this coordinate plane. Students, teachers, parents, and everyone can find solutions to their math problems instantly. The aim of this book is not to cover discrete mathematics in depth it should be clear from the description above that such a task would be illde. Let tn, 1, 3 be the minimum number of moves needed to solve the puzzle with n disks.
Inverse functions i every bijection from set a to set b also has aninverse function i the inverse of bijection f, written f 1, is the function that assigns to b 2 b a unique element a 2 a such that fa b. Elements of discrete mathematics virginia commonwealth university. This book is designed for a one semester course in discrete mathematics for sophomore or junior level. Which of the following statements are equivalent to the implication. Proof of the fundamental theorem of arithmetic, using strong induction show that if n is an integer 2, then n can be written as the product of primes. At both the grade 8 and 11 levels, the advisory committees recommended that each of the five areas be weighted equally. Learning outcomes for the sc in discrete mathematics and. The linear search did not depend on having a sorted. Discrete mathematics by gary chartrand, ping zhang. Recurrence relations discrete math structures 11 youtube. Standard 14 discrete mathematics k12 overview all students will apply the concepts and methods of discrete mathematics to model and explore a variety of practical situations. Descriptive statement discrete mathematics is the branch of mathematics that deals with arrangements of distinct objects.
The 2009 mathematics curriculum framework can be found in pdf and microsoft word file formats on the virginia department of education s. Translate natural language statements to and from formal propositional logic. During my sophomore year at dartmouth i took a course in discrete mathematics. Browse other questions tagged loops discretemathematics or ask your own question. Recursion, simply put, is the process of describing an action in terms of itself. List all the steps used to search for 9 in the sequence 1,3, 4, 5, 6, 8, 9, 11 using a binary search. If you have any questions on the homework, please see me before or after school. With easyworksheet tests, quizzes, and homework are fast and easy to create. If f is a function, and x is in its domain, then fx represents. Hard algebra problems, online ti 89, order decimal from greatest to least caculator, convert decimal to radical. The parts of this exercise outline a strong induction proof that pn is true for n 8. Remark mathematical induction is a very powerful technique, because we show just two statements, but this can imply infinite number of cases to be correct. Let us go over these techniques and discuss how to apply them to new problems e. Lecture notes in discrete mathematics arkansas tech faculty web.
Discrete mathematics recursion mathematics stack exchange. This page intentionally left blank university of belgrade. Decode the message 21, 0, 53, 2, 11, 3, 24, 1 if the original coding matrix was. Many of the items being used can be viewed as assessing more than one of the five areas. Find the minimum number of connections to be made which will guarantee that if 8 or fewer. Free math lessons and math homework help from basic math to algebra, geometry and beyond. In doing so, the student is expected to learn how to think algorithmically and how to design and analyze algorithms. Nov 25, 2016 sequences and summations in discrete mathematics 1. The book began as a set of notes for the discrete mathematics. Any student who appears in the exam and gets a score below 30, gets f grade.
The tests were not calibrated to any standard scale, so it was difficult to judge how well you were doing. Discrete mathematicsrecursion wikibooks, open books for an. Recurrence relations discrete math structures 11 marks education tutorials. For example, if we have a finite set of objects, the function can be defined as a list of ordered pairs having these objects, and can be presented as a complete list of those pairs. Direct, indirect, contradict ion, by cases, equivalences proof of quantified. Discrete mathematics discrete mathematics 574 unit 4 discrete mathematics discrete mathematics is the branch of mathematics that involves finite or discontinuous quantities.
472 340 501 134 206 1540 1183 1561 1263 40 389 1180 841 69 609 876 1240 1050 227 242 304 1195 1181 1356 1637 1308 973 1129 1362 1465 1042 437 1183 708 699 1244 1415 1147 1128 985 782 452 869 967 975 1142 236