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