Function in discrete mathematics ppt Introduction Sets, relations, and functions are foundational concepts in discrete mathematics and computer science. Domain, Cdomain Image, Preimage Injection, Surjection, Bijection Inverse Function Function CSE 20: Discrete Mathematics for Computer ScienceProf. It defines a relation as a set of ordered pairs, and discusses the domain and range of relations - the set of first and second elements of the ordered pairs. It then discusses different number systems such as decimal, binary, octal, and hexadecimal. Download presentation by click this link. An ordered pair connects an element from one set to an element of another set. It’s only a one-semester course, so there are a lot of topics that it doesn’t cover or doesn’t cover in much depth. Sandhya Umrao. Prime Sep 1, 2025 · Discrete Mathematics is a branch of mathematics that is concerned with "discrete" mathematical structures instead of "continuous" ones. Rosen SEVENTH EDITION. Understanding these concepts is essential for modeling and solving problems in computer science. Mar 17, 2019 · Discrete Mathematics: Recursion. Relations are rules that connect input and output numbers. Dive into sets, logic, proof techniques, counting principles, and more. It begins by defining a function as a mapping or assignment of elements from one set (the domain) to elements of another set (the codomain). Prove that the Onto? Discrete or Continuous? Domain? Range? Function? One to one? Onto? Discrete or Continuous? Domain? Range? Function? One to one? Onto? Discrete or Continuous? Domain? Range? Function? One to one? Onto? Discrete or Continuous? The number of employees a company had in each year from 2004 to 2009 were 25, 28, 34, 31, 27, and 29. Unit This blog contains Engineering Notes, Computer Engineering Notes,Lecture Slides, Civil Engineering Lecture Notes, Mechanical Engineering Lectures PPT, Injective function Definition: A function f is said to be one-to-one, or injective, if and only if f(x) = f(y) implies x = y for all x, y in the domain of f. Additionally, it emphasizes the simplification involved in ignoring constants and unimportant details when Some slides are companion slides for Discrete Mathematical Structures: Theory and Applications by D. It defines key concepts such as propositions, truth values, logical connectives like negation, conjunction, disjunction, implication, biconditional, and quantifiers. We will often be working with functions with finite domains, so this kind of picture is often more useful than a traditional graph of a function. It defines basic concepts such as propositional variables, logical operators, truth tables, logical equivalence, predicates, quantifiers, and translating between logical expressions and Oct 31, 2019 · Discrete Mathematics and Its Applications Kenneth H. To explore these concepts in detail, we begin with the following core topics. It provides examples of recursively defined sequences, functions, and sets. The domain is the set of inputs, the codomain is the set of all possible outputs, and the range is the set of actual outputs This document provides an introduction to logic and set theory. This document provides an overview of the topics covered in a discrete structures course, including logic, sets, relations, functions, sequences, recurrence relations, combinatorics, probability, and graphs. 2. Additionally, it includes examples and exercises to illustrate these concepts. Discrete 1) The document summarizes key concepts from a discrete mathematics course including sets, operations on sets, functions, sequences, and sums. What is a relation. A function is then drawn as a curve (set of points) with only one y for each x. Alternative: A function is one-to-one if and only if f(x) f(y), whenever x y. It begins with learning outcomes and prerequisites, then introduces relations through examples like family relations. Section Summary. It begins by defining key logic concepts such as propositions, truth values, and logical operators. pdf), Text File (. - Download as a PPTX, PDF or view online for free Jul 23, 2025 · Functions are an important part of discrete mathematics. Recursion is related to mathematical induction. But the hope is that this will give you a foundation of skills that you can build on as you need to, and particularly to give you a bit of mathematical maturity—the basic understanding of The document provides information about relations and functions: - It defines key terms like relation, domain, range, ordered pair, and function. The course covers topics including set theory, relations, functions, combinatorics, recurrence relations, generating functions, and proof techniques. Malik and M. Discrete mathematical structures include objects with distinct values, like graphs, integers, logic-based statements, etc. A function is said to be an injection if it is one-to-one. Recursively Defined Functions Recursively Defined Sets and Structures Structural Induction Recursive Algorithms Factorial Exponentiation GCD Binary Search Merge Sort Proving Correctness of Recursive Algorithms. Why Care about Discrete Math? Digital computers are based on discrete “atoms” (bits). Thus, relations are generalizations of functions. The process of using generating functions to solve recurrence relations involves rewriting the relation Nov 1, 2025 · Introduction This is a course on discrete mathematics as used in Computer Science. Ex-p ∨ ￢ p is always true, it is a tautology. The document provides an overview of discrete mathematics and its applications. For example, a function in continuous mathematics can be plotted in a smooth curve without breaks. It defines a function as mapping elements from one set to unique elements in another set. Unit 2 discusses mathematical induction, counting techniques, and number theory topics. Examples are given to illustrate domain and range. The document provides an overview of sets in discrete mathematics, detailing their definitions, properties, and notations. While downloading, if for some reason you are not able to download a presentation, the Apr 5, 2019 · Functions • A function f from a set X to a set Y is a relation from X to Y such that x X is related to one and only one y Y • X is called the domain & Y is called the range. 1 Propositional Logic. Therefore, both a computer’s structure (circuits) and operations (execution of algorithms) can be described by discrete math. Give a rule for finding the function's value at n+1 in terms of the function's value at integers i n. Set operations in programming languages: Issues about data structures used to represent sets and the computational cost of set operations. Fields like combinatorics, graph theory, and computation theory are This document defines functions and related terminology such as domain, codomain, range, one-to-one functions, onto functions, and bijections. - It discusses how to determine if a relation is a function using the vertical line test or by checking if each domain value is mapped to only one range value A relation is a set of ordered pairs that shows a relationship between elements of two sets. Introduction to Logic. Generating functions can be used to represent sequences as power series and solve recurrence relations. Topics Covered Logic and Set Theory Functions and Sequences Algorithms & the Big-O! This document outlines the course content for a Discrete Structures course taught by Dr. It explains concepts such as asymptotic notation, examples of growth rates, and comparisons between algorithm efficiencies using various functions. A function assigns a single element from the codomain to each element in the domain. S. Recursive algorithms solve problems by reducing them to smaller instances of the same problem. This document discusses functions in discrete mathematical structures. It defines a function as a relation where each input is paired with exactly one output. Transcript and Presenter's Notes Title: Discrete Mathematics Functions 1 Discrete MathematicsFunctions 2 Definition of a function Mar 16, 2019 · An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Lov ́asz and K. ppt), PDF File (. The function can be represented as f: A ⇢ B. Do Subscribe and share to others. It defines discrete mathematics as the study of mathematical structures that have distinct, separated values rather than varying continuously. A proposition is a declarative sentence (that is, a sentence that declares a fact) that is either true or false, but not both. A set is said to contain its elements. • In computer science, we want to understand how quickly an algorithm can solve a problem as The document discusses recursive definitions, which define an object in terms of itself. Methods are provided for converting between these different bases, including dividing or grouping bits and multiplying by the place value. Chapter 1 covers propositional logic, propositional equivalences, predicates and quantifiers, and nested quantifiers. While recursive definitions and algorithms are elegant, iterative equivalents are This document introduces some basic concepts in number theory, including primes, least common multiples, greatest common divisors, and modular arithmetic. 1 Defining sets Definition. It is characterized by the fact that between any two numbers, there are almost always an infinite set of numbers. Jan 1, 2025 · Explore the concepts of functions in discrete mathematics, including one-to-one, onto, and correspondence functions, with illustrative arrow diagrams and examples. Definition of a Function. . It defines what a function is as a mapping from a domain set to a codomain set, and introduces related concepts like domain, codomain, range, and the notation for functions. ppt - Free download as Powerpoint Presentation (. The course is all about Discrete Mathematics Full Course using THREE BASIC BOOK. The document also discusses tautologies and contradictions. 2) It covers topics like basic set theory, operations on sets like union and intersection, subsets, power sets, Cartesian products, and cardinality. The document also defines related terms like domain, codomain, image, and pre Outline Introduction Sets Logic & Boolean Algebra Proof Techniques Counting Principles Combinatorics Relations,Functions Graphs/Trees Boolean Functions, Circuits Introduction to Discrete Mathematics What Is Discrete Mathematics? An example: The Stable Marriage Problem The Stable Marriage Problem In the future we will: Prove that the assignment is stable (reading tonight). 1. It also discusses types of functions like one-to-one, onto, and bijective Generating functions represent an infinite sequence as a single mathematical object that can be manipulated algebraically. Mar 31, 2019 · Discrete Mathematics . This document provides an introduction to functions and their properties. This article is all about functions, their types, and other details of functions. Further elaboration or clarification would be necessary for a more coherent summary. They are free and completely customizable. The pigeonhole principle is also introduced as stating that if more items are put into fewer Function. Tautology?Tautology? A compound proposition that is always true, no matter what the truth values of the propositional variables that occur in it, is called a tautology. L Al- zaid Math1101. An example of a string length function maps strings to their lengths. It includes examples, definitions, and demonstrates how to represent relations using matrices, as well as the composition of For functions over numbers, we can represent an ordered pair (x, y) as a point on a plane. This is the contrapositive of the definition. The document discusses functions and their properties. Logical connectives combine propositions and quantifiers specify whether statements apply to all or some cases There are two important rounding functions, the ceiling function and the floor function. It then explains how logical operators can combine propositions using truth tables. Common examples of generating functions are presented for various sequences like the constant sequence {1,1,}, the sequence of powers of 2, and binomial coefficients. Recall: A function takes EACH element from a set and maps it to a UNIQUE element in another set f: X Y x X, y such that f(x) = y Let A and B be sets. Functions can be represented numerically in tables, visually with graphs, algebraically with explicit formulas, or verbally. The document consists mainly of symbols and shapes, lacking textual information. txt) or view presentation slides online. It then gives examples of specifying functions explicitly and with formulas. Functions are the rules that assign one input to one output. Shachar Lovett Today’s Topics: Functions Properties of functions For functions over numbers, we can represent an ordered pair (x,y) as a point on a plane. In discrete math often we need to round a real number to a discrete integer. A function assigns exactly one element of a set to each element of the other set. Some examples given are problems involving a This document discusses functions and their properties. Relation generalizes the notion of functions. It introduces quantification and propositional functions. Propositions are statements that can be either true or false. The domain of a relation is the set of first elements of each ordered pair, while the range is the set of second elements. Covers definitions, types, inverse functions, and composition. Unit 4 covers algebraic structures like groups, rings and fields. Vesztergombi Course Requirements Minors: 30% ÐÏ à¡± á> þÿ Ñ þÿÿÿþÿÿÿ¹ º » ¼ ½ ¾ ¿ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï Ð This document defines relations and functions. It does not provide detailed content or context to summarize meaningfully. The syllabus covers sets, relations, functions, algebraic Recursively Defined Functions To define a function on the set of nonnegative integers 1. A function is a special type of relation where each input has exactly one output. Relations can be represented visually using arrow diagrams or directed graphs to show the connections Then {(0, a), (0, b), (1, a), (2, b)} is a relation from A to B That is 0Ra but not 1Rb * Functions as relations Recall that a function f from a set A to a set B assigns exactly one element of B to each element of A The graph of f is the set of ordered pairs (a, b) such that b=f(a) Because the graph of f is a subset of A x B, it is a relation Hi, welcome to the course of Discrete Mathematics / Discrete Structure OR Discrete Mathematics for Computer Science. Nov 3, 2014 · Discrete Mathematics: Growth of Functions Section Summary • Big-O Notation • Big-O Estimates for Important Functions • Big-Omega: • Big-Theta Notation: The Growth of Functions • In both computer science and in mathematics, there are many times when we care about how fast a function grows. The This means that the function \ (f\) sends 1 to 2, 2 to 1 and 3 to 3: just follow the arrows. Unit 3 is on propositional logic, logical equivalence and proof techniques. The course objectives are to enhance logical thinking and problem solving abilities. 3) Examples are provided to illustrate concepts like Venn diagrams, disjoint sets, complements, and set Discrete mathematics is the study of mathematical structures that are countable or are discrete in nature. Oct 7, 2014 · Discrete Mathematics: Functions. Set Theory Basic building block for types of objects in discrete mathematics. Sen The document discusses the key topics in discrete mathematics that will be covered across 5 units. Graphs of Functions A Couple of Key Functions In discrete math, we frequently use the following functions over real numbers: x (“floor of x”) is the largest integer x. Domain? Range Lecture slides on functions in discrete mathematics for computing. In this course, we will deal with various types of This document provides an overview of mathematical logic. The whole playlist here you can download the code including the PPT Slides that was used in the video session. A graph of the function in example 3 above would look like What is discrete mathematics? logic, sets, functions, relations, etc Logic: artificial intelligence (AI), database, circuit design Counting: probability, analysis of algorithm Graph theory: computer network, data structures Number theory: cryptography, coding theory Topic 1: Logic and Proofs Logic: propositional logic, first order logic Proof Home | UCSB Computer Science The document covers chapter 2 of a discrete mathematics course, focusing on relations including definitions of product sets, inverse relations, and various types such as reflexive, symmetric, antisymmetric, transitive, equivalence, and partial ordering relations. Discrete MathematicsDiscrete Mathematics What are propositional equivalences? 2. - Download as a PPT, PDF or view online for free Discrete Mathematics Functions Ordered tuples and Cartesian Product Function and Representations Types of Functions 1. Unit 1 covers sets, relations, functions and their properties. • f = { (a, 3), (b, 3), (c, 5), (d, 1)} Discrete Mathematics: Functions Function description • Functions are described as: • Set of ordered pairs, example f as given before • Using a The document describes Chapter 1 of a textbook on discrete mathematics and its applications. Some key points made include: - Discrete mathematics deals with objects that can only assume distinct, separated values. The objects in a set are called the elements, or members, of the set. Discrete mathematics 1. A set is an unordered collection of distinct objects. While downloading, if for some reason you are not able to download a presentation, the Note the difference between a relation and a function: in a relation, each a ∈ A can map to multiple elements in B. It provides examples of graphical representations of functions and discusses concepts like whether a function is one-to-one or onto based on its graph. It covers concepts such as subsets, power sets, set operations (union, intersection, complement), and the concept of the empty set. We say x is mapped into y. In this lecture, we will explore these concepts in detail From working with statistics, we know that data can be numerical (quantitative) or descriptive (qualitative). The document discusses types of relations like reflexive, symmetric, and transitive relations. 3. The arrow diagram used to define the function above can be very helpful in visualizing functions. Nov 26, 2012 · Discrete Mathematics Relations. The document discusses Big-O notation, which measures the scalability of algorithms rather than their speed as data volume increases. Why Are You Studying this Course. - It explains how to represent relations using ordered pairs, tables, graphs, and mappings. Generating functions provide an elegant technique for counting problems by This document discusses relations in discrete mathematics. K. Operations like differentiation, integration, and multiplication on generating functions can be used to count objects even when the underlying sequence is defined symbolically or combinatorially. The document discusses properties of functions like injectivity Sep 4, 2014 · An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. When data is numerical, it can also be discrete or continuous. Specify the value of the function at 0 2. Publisher: McGraw Hill Reference Texts (links available at the course-page): Course notes from “mathematics for computer science” Discrete Mathematics, Lecture Notes, by L. Finally, it provides examples Math Presentation templates Create enjoyable presentations with these entertaining Google Slides themes and PowerPoint templates featuring designs revolving around numbers and Math. Let's take a look at a comparison of these concepts: Types of mathematics Mathematics can be broadly classified into two categories: Continuous Mathematics ─ It is based upon continuous number line or the real numbers. A relation is a set of ordered pairs. This course will develop your mathematical maturity Discrete mathematics provides the mathematical foundations for many computer science courses Data Structures Algorithm Analysis and Design the i-th term in the sequence (indexing from 0) is the coefficient of xi in the generating function. It begins by defining discrete mathematics as the study of mathematical structures that are discrete rather than continuous. They form the building blocks for various advanced topics such as logic, combinatorics, graph theory, and algorithms.