Discrete structures lecture notes stanford university. No matter what the individual parts are, the result is a true statement. Richard mayr university of edinburgh, uk discrete mathematics. The rules of mathematical logic specify methods of reasoning mathematical statements. However, there are other topics that belong under the discrete umbrella, including computer science, abstract. Rosen, eighth edition, mcgraw hill, isbn 9780072880083, isbn10 0072880082. Discrete math is needed to see mathematical structures in the object you work with. Topicsincludepropositionallogic, discrete mathematics, and linear algebra.
Discrete mathematics for computer science some notes jean gallier abstract. Induction is covered at the end of the chapter on sequences. Next come chapters on logic, counting, and probability. This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. Mathematical logic for computer science is a mathematics textbook, just as a. Universal quantification mathematical statements sometimes assert that a property is true. Gilt provides insider access to todays top brands for women, men, kids, and home as well as local experiences, amazing getaways, and gourmet finds at up to 70% off mathematical logic discrete mathematics by. The relation on the set of integers is reflexive and transitive. Introduction to formal methods for reasoning and to mathematical tech niquesbasictocomputerscience. Mathematical logic, set theory, the real numbers, induction and recursion, summation notation, asymptotic notation, number theory, relations, graphs, counting, linear algebra, finite fields. Discrete mathematics logic tutorial exercises solutions 1.
Discrete mathematics pdf notes dm lecture notes pdf. Logic alphabet, a suggested set of logical symbols mathematical operators and symbols in unicode polish notation list of mathematical symbols notes 1. This course covers elementary discrete mathematics for computer science and engineering. These are notes on discrete mathematics for computer scientists. The usual tool in mathematics to do so is the notion of a set. Some of the reasons to study logic are the following. This is a course on discrete mathematics as used in computer science. Undergraduate notes in mathematics arkansas tech university department of mathematics. Topics include formal logic notation, proof methods. Greek philosopher, aristotle, was the pioneer of logical reasoning. Mathematical logic for computer science is a mathematics. The ability to reason using the principles of logic is key to seek the truth which is our goal in mathematics.
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. The study of logic helps in increasing ones ability of. Discrete mathematics discrete mathematics study of mathematical structures and objects that are fundamentally discrete rather than continuous. Wuct121 logic tutorial exercises solutions 2 section 1. Discrete mathematics for computer science some notes. A mathematical rule of inference is a method for deriving a new statement that may depend on inferential rules of a mathematical system as well as on logic. Hence, there has to be proper reasoning in every mathematical proof.
This is a course note on discrete mathematics as used in computer science. Logic question1 i if x 3, then x mathematical logic evolving around the notions of logical validity,provability,andcomputationwascreatedinthe. Problems on discrete mathematics1 ltex at january 11, 2007. We will develop some of the symbolic techniques required for computer logic. Simply put, a proof is a method of establishing truth. However, i wanted to discuss logic and proofs together, and found that doing both. Cheat sheetstudy sheet for a discrete math class that covers sequences, recursive formulas, summation, logic, sets, power sets, functions, combinatorics, arrays and matrices. The technique of using the concept of a set to answer questions is hardly new. This course does not have a web ct or vista account. Discrete mathematics and its applications, kenneth h. So, need applied discrete maths logic, set theory, graph theory, combinatorics, abstract algebra. A course in discrete structures cornell university. Discrete structures lecture notes vladlen koltun1 winter 2008. It emphasizes mathematical definitions and proofs as well as applicable methods.
Discrete mathematics introduction to propositional logic. Formally encode how the truth of various propositions influences the truth of other propositions. Although this character is available in latex, the mediawiki tex system doesnt support this character. The text covers the mathematical concepts that students will encounter in many disciplines such as computer. You should all get the hang of it by the end of the quarter. Use symbolic connectives to represent the proposition juan is a math major but not a.
At the hardware level the design of logic circuits to implement in. The discrete mathematics notes pdf dm notes pdf book starts with the topics covering logic and proof, strong induction,pigeon hole principle, isolated vertex, directed graph, alebric structers. We now present three simple examples to illustrate this. This book is designed for a one semester course in discrete mathematics for sophomore or. This page intentionally left blank university of belgrade. Examples of objectswith discrete values are integers, graphs, or statements in logic. Logical reasoning provides the theoretical base for many areas of mathematics and consequently computer science. Learn introduction to discrete mathematics for computer science from university of california san diego, national research university higher school of economics. In contrast to real numbers that have the property of varying smoothly, the objects studied in discrete mathematics such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values. In predicate logic, predicates are used alongside quantifiers to express the extent to which a predicate is true over a range of elements. Discrete math cheat sheetstudy sheetstudy guide in pdf.
Combinatorics, graph theory, the idea of function, recurrence relations, permutations, and set theory are all part of discrete math. Discrete mathematics courant institute of mathematical. Propositional logic is a mathematical system for reasoning about propositions and how they relate to. He was solely responsible in ensuring that sets had a home in mathematics. However, the rigorous treatment of sets happened only in the 19th century due to the german math ematician georg cantor. Well build more complex compound propositions out of those of atomic propositions. It deals with continuous functions, differential and integral calculus.
Discrete mathematics uses a range of techniques, some of which is seldom found in its continuous counterpart. Number theory athe math behind the rsa crypto system. Sequences and series are among the most important applications of. This course will roughly cover the following topics and speci c applications in computer science. Mathematical logic introduction mathematics is an exact science.
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. Like beauty, truth sometimes depends on the eye of the beholder, and it should not be surprising that what. Discrete math concerns counting, probability, sophisticated forms of addition, and limit processes over discrete sets. This is a book about discrete mathematics which also discusses mathematical rea soning and logic. Discrete mathematics demystified bgu math homepage. Logic is particularly important because it is the mathematical basis of software.
Propositional logic is a mathematical system for reasoning about propositions and how they relate to one another. Slides of the diagrams and tables in the book in both pdf and latex can be down. The participants of the party form a set, whose elements are alice, bob, carl, diane, eve, frank and george let us denote this set by p. Introduction to discrete mathematics for computer science. Discrete mathematics propositional logic tutorialspoint. Discrete mathematical structures by tremblay and manohar pdf. Any collection of things, called elements, is a set. The disjunction of propositions p and q is denoted by p q and has this truth table. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic. All information will be made available only on this web page. How important is discrete math compared to calculus in. Mathematical logic discrete mathematics by tremblay manohar pdf.
Wuct121 discrete mathematics logic tutorial exercises. The deck of cards is a set, whose elements are the cards. A tautology in math and logic is a compound statement premise and conclusion that always produces truth. Predicate logic richard mayr university of edinburgh, uk richard mayr university of edinburgh, uk discrete mathematics. The emphasis here will be on logic as a working tool. Fundamentals of mathematical logic logic is commonly known as the science of reasoning.
Lecture notes in discrete mathematics arkansas tech faculty web. Before we explore and study logic, let us start by spending some time motivating this topic. This text explains how to use mathematical models and methods to analyze problems that arise in computer science. From a night class at fordham university, nyc, fall, 2008. Here you can download the free lecture notes of discrete mathematics pdf notes dm notes pdf materials with multiple file links to download. Using quantifiers to create such propositions is called quantification. The notion of a proof plays a central role in this work. Free discrete mathematics books download ebooks online.
795 320 885 216 548 60 225 630 86 92 1390 870 603 900 604 1054 1426 1224 778 337 156 408 233 439 28 866 10 265 1242 1323 1386 731 1135 1111 855 545 1253 1025 1353