Discrete mathematics lecture notes pdf Yuh-Dauh Lyuu Dept. I If we must select 3 math and 4 CS faculty for a committee, Lecture Notes in Math 212 Discrete Mathematics Sergey Finashin METU, Depart. It is differentiated from continuous mathematics, such that the numbers are starkly different from each other. It is a 3 credit course taught for 3 hours each week. Proofs Lecture 1: Introduction to discrete mathematics Nitin Saxena? IIT Kanpur 1 Administrivia This is an introductory course to the mathematics needed in CSE. – More Discrete Mathematics, 2007, David A. • We use the notation a R b to denote (a,b) R and a R b to denote (a,b) R. A function from A to B, denoted f : A B, is an assignment of exactly one element of B to each element of A. Sample Notes on Discrete Mathematics Miguel A. Contents Prev Up Next. Pelik ´an – K. 2 Syllabus for Discrete Mathematics II Lecturer: Professor Glynn Winskel (gw104@cl. Mathematics; NOC:Discrete Mathematics (Video) Syllabus; Co-ordinated by : IIT Madras; Available from : 2016-01-12. PDF Cultivate a sense of familiarity and ease in working with mathematical notation and common concepts in discrete mathematics. I A is calleddomainof f, and B is calledcodomainof f. The recommended text is K. Logical Notation Propositional Connectives and Quanti ers Logical notation uses symbols of two kinds: propositional connectives, such as ^(\and"); _(\or"); :(\not"); and quanti ers 8(\for all"); 9(\there exists"): Discrete Mathematics and its Applications, Kenneth H. Discrete mathematics deals with objects that come in discrete bundles, e. Duong) Elementary Mathematics, 148 pp. Contents. Gábor Horváth, Szabolcs Tengely. These notes for a graduate course in set theory are on their way to be-coming a book. 600 F2019 Lecture 1: Permutations and combinations Download File . Plummer: Matching theory´ (Elsevier, Amsterdam This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. (with X. , 3. 1-1. C L Liu, D P Nohapatra, “Elements of Discrete Mathematics - A Computer Oriented Discrete Mathematics Lecture Notes, Yale University, Spring 1999 L. Anna University , Chennai Department of B. Logic 6 1. TMH. g. Lerma. – Discrete Mathematics Notes, 2008, David A. 5 Sets and Boolean algebra 2. vertex, edge Lecture Notes on Discrete Mathematics Introduction to Discrete Mathematics Definition: Discrete Mathematics is the branch of mathematics dealing with countable, distinct, and separate objects. 2 Statements (propositions), connectives and truth tables 2. Rosen, Fifth Edition. 4 Using Gates to Represent Formulas 98 2. If you find the course difficult then you are advised to buy this book, read the corresponding sections straight after the lectures, and do extra exercises from it. 4. 1 M. Interconnections, generalizations- and specialization-relations between sev- Oct 15, 2024 · Introduction to Discrete Mathematics Handwritten Lecture Notes PDF Discrete Mathematics is an important subject in the fields of mathematics and computer science. Hauskrecht CS 441 Discrete Mathematics for CS Lecture 7 Milos Hauskrecht milos@cs. Applications: Computer science, cryptography, algorithm design, network theory, etc. Contents Introduction 5 Chapter 1. The complete lecture notes Number Theory I (PDF - 2. Lecture notes . Lecture Notes. E-Computer Science and Engg Fifth Semester Discrete Mathematics Handwritten Lecture Notes - Free Version (Regulation 2008) Attachment : DM Notes Part 1. 7 MB) can be used as the online textbook for this course. discrete mathematics handwritten notes pdf are very useful for discrete mathematics students in enhancing their preparation and improving their chances of success in discrete mathematics exam. De nitions and Proofs by Cases De ning a Function by Cases Functions in algebra are usually de ned by formulas, for instance: f(x) = x2 + x+ 1: Sometimes a function is de ned by several formulas corresponding to di erent values of This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. Jun 8, 2022 · Contents Tableofcontentsii Listoffiguresxvii Listoftablesxix Listofalgorithmsxx Prefacexxi Resourcesxxii 1 Introduction1 1. B. Lov´asz – J. Ross and C. Grading. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting Syllabus:- SPPU-SE-Comp-2019-PAT-Syllabus Prerequisite for DM:- Analysis of DM:- Theory Section:- Notes: DM-Unit-1-Notes DM-Unit-2-Notes DM-Unit-3-Notes DM-Unit-4-Notes DM-Unit-5-Notes DM-Unit-6-Notes PPT: unit-1-Part-1 unit-1-Part-2 unit-1-Part-3 unit-2-relation-function unit-3-permutation_combination unit-4-graph-theory unit-5-tree Theory Question Bank:- Assignment Section:- DM_Assignment-1 Homework should be submitted in the beginning of the lecture on the deadline. 3 Valid and invalid arguments 2. They originated as handwritten notes in a course at the University of Toronto given by Prof. COMPSCI 230: Discrete Mathematics for Computer Science April 8, 2019 Lecture 22 Lecturer: Debmalya Panigrahi Scribe: Kevin Sun 1 Overview In this lecture, we begin studying the fundamentals of counting discrete objects. Wright, Discrete Mathematics (Fifth Discrete Mathematics Lecture Notes, Yale University, Spring 1999 L. Used with permission. A function (or “map”, or “operator”) is a rule that associates to every element of a set one element in another set. Rosen. These lecture notes are based on the content we will cover in Mathematical Finance in Michaelmas term, 2024 - 25. For example + is a binary operation de ned on the integers Z. A graph Gis an ordered pair (V;E), where V is a nite set and graph, G E V 2 is a set of pairs of elements in V. Hauskrecht Functions • Definition: Let A and B be two sets. where we enjoy the continuity of functions and the set of real numbers. LOGIC: Logic is the study of the principles and methods that distinguish between a valid and an invalid argument. The document outlines the course objectives and units for the MA3354 Discrete Mathematics course. Textbook: Discrete Mathematics and its Applications by Kenneth H. Plummer: Matching theory (Elsevier, Amsterdam, 1979) 1 Apr 18, 2016 · The document discusses discrete mathematics and provides examples of problems that can be solved using discrete mathematics. Hauskrecht Binary relation Definition: Let A and B be two sets. 1 Formulas 92 2. – Number Theory for Mathematical Contests, 2007, David A. 3. where they were given in class). pitt. There are many downloadable free Discrete Mathematics books, available in our collection of books. tech i year – i sem (r22) (2022-2023) department of computer science & engineering malla reddy college of engineering & technology (autonomous institution – ugc, govt. Propositions 6 1. • On the other hand, several things could be done concurrently: Lecture Notes in Discrete Mathematics. Lecture 1: Absolute Values and Discrete Valuations (PDF) Lecture 2: Localization and Dedekind Domains (PDF) Outline 1 De nitions 2 Theorems 3 Representations of Graphs: Data Structures 4 Traversal: Eulerian and Hamiltonian Graphs 5 Graph Optimization 6 Planarity and Colorings MAT230 (Discrete Math) Graph Theory Fall 2019 2 / 72 Lecture Notes for College Discrete Mathematics. This note covers the following topics: fundamentals of mathematical logic , fundamentals of mathematical proofs , fundamentals of set theory , relations and functions , introduction to the Analysis of Algorithms, Fundamentals of Counting and Probability Theory and Elements of Graph Theory. 7 Review Notice the connective, 'and', that is used to join them. 2 Permutations and Combinations The course, Discrete Structures, is a 3- credit unit course for students studying towards acquiring the Bachelor of Science in Computer Science. com at mention your Name, College, Subject, and your GPay, or Phone pay, or Paytm Chapters 2–5 of this book are very close to the material in the notes, both in order and notation. Discrete Discrete Mathematics Lecture Notes Prof. Besides reading the book, students are strongly encouraged to do all the This section provides a complete set of lecture notes for the course and an outline of Discrete Mathematics. Discrete Mathematics. I Number theory is the branch of mathematics that deals with integers and their properties I Number theory has a number of applications in computer science, esp. Quantifiers 10 1. 4M: Module Name Download Description Download Size; Contents: References: pdf of MTH202: Set theory and discrete mathematics LECTURE NOTES The instructor of this course owns the copyright of all the course materials. txt) or read online for free. A written record of the lec-tures will be available on the web, usually a day after the lecture. D. 3 2 / 21 Lecture 3: Quantifiers, start on Inference and Proofs (pdf, pptx) -- Note: pdf is the handout given in class. Lecture 1 (Monday, September 26) I Mathematical Induction We let P(n) for n 1 to be some statement. 3 Truth and Logical Truth 102 Download MA8351 Discrete Mathematics Lecture Notes, Books, Syllabus, Part-A 2 marks with answers and MA8351 Discrete Mathematics Important Part-B 16 marks Questions, PDF Book, Question Bank with answers Key. Hauskrecht CS 441 Discrete Mathematics for CS Lecture 9 Milos Hauskrecht milos@cs. 42 inches from a wall. Kenneth H. Rosen, "Discrete Mathematics and its Applications”, TMH, Fifth Edition. Vesztergombi: Kombinatorika (Tank onyvkiad o, Budapest, 1972); Chapter 14 is based on a section in L. 4. It is a very good tool for improving reasoning and problem-solving capabilities. 1 What is Mathematical Finance? Mathematical Finance is the study of the mathematics used to model and analyse financial markets The full lecture notes (PDF - 1. 2. , 1 or 2 babies. However, the lectures go into more detail at several points, especially proofs. 1 What is a group? De nition 1. Lecture notes 100% (1) Discrete Mathematics Lecture Outline 1 Propositions 2 Logical Equivalences 3 Normal Forms Richard Mayr (University of Edinburgh, UK) Discrete Mathematics. Macauley (Clemson) Lecture 1. 1: If Gis a nonempty set, a binary operation on G is a function : G G!G. 3 Syllabus Show class website. Proofs 13 1. R. 412 kB 18. 1 Download MA3354 Discrete Mathematics (DM) Books Lecture Notes Syllabus Part-A 2 marks with answers MA3354 Discrete Mathematics Important Part-B 16 marks Questions, PDF Books, Question Bank with answers Key, MA3354 Discrete Mathematics Syllabus & Anna University MA3354 Discrete Mathematics Question Papers Collection. The existence, enumeration, analysis and optimization of discrete struc-tures. Here \discrete" (as opposed to continuous) typically also means nite, although we will consider some in nite structures as well. Chapter 1. DISCRETE MATHEMATICS. 2 Exercises 99 2. (web edition, 2000). A. Front Matter 1 MTH211: Discrete Mathematics (Fall 2020) Course Objectives: Discrete Mathematics is branch of Mathematics which deals with discrete structures like logic. 3. • Discrete mathematics and computer science. (web edition, 2008). The text covers the mathematical concepts that students will encounter in many disciplines such as computer science, engineering, Business, and the sciences. edu 5329 Sennott Square Functions II M. Lov asz and K. Using mathematical induction, our goal is then to prove that 8n, P(n) is true. Math needed to be a good programmer. 3: Permutations and combinations Discrete Mathematical Structures 3 / 6 Independent events Consider a quiz with four true/false and three multiple choice questions, (a){(e). 1 Kick off with CAS 2. 6 Digital logic 2. This set of notes has been compiled over a period of more than 30 years. See full list on web. Many different systems of axioms have been proposed. Lov´asz and K. ac. This document provides an introduction to fundamental concepts in mathematical logic, including propositions, compound propositions formed using connectives, and truth tables. Hauskrecht Basic discrete structures • Discrete math = – study of the discrete structures used to represent discrete objects LECTURE NOTES PROGRAMME – BCA SEMESTER- IV DISCRETE MATHEMATICS (BCA-401 ) UNIT I . This course covers elementary discrete mathematics for computer science and engineering. Discrete mathematics • Discrete mathematics – study of mathematical structures and objects that are fundamentally discrete rather than continuous. In contrast, continuous mathematics deals with objects that vary continuously, e. I wrote a good part of these notes in allF 2006; I revise them every time I teach the course. The topics covered are useful in the theory, systems and application areas of computer science. This course is introduction to discrete structures which are not the part of main stream courses. These free discrete mathematics bca 2nd sem notes pdf will help students tremendously in their preparation for discrete mathematics exam. Explain what “Discrete Math” is all about: math is a web of connections, not a linear chain of topics. Discrete Mathematics for Computer Science. Santos. 3 means the 3-rd item of the 1-st section of Chapter 2. EXAMPLES : • If S1 = {a,b,c} and S2 = {1,2} then the associations Lecture Notes: Discrete Mathematics for Computer Science Vladimir Lifschitz University of Texas at Austin Part 1. The web also contains other information, such as homework assignments, solutions, useful links, etc. 1. The text covers the mathematical concepts that students will encounter in many disciplines such as computer science, en-gineering, Business, and the sciences. Types of Mathematics. – Concepts from discrete mathematics are useful for Studying Discrete Mathematics at Savitribai Phule Pune University? On Studocu you will find 142 lecture notes, practice materials, tutorial work, practical The following information is the bibtex citation for these notes if you want to cite them as a reference: @Book{381notes, author = {Sara Billey, James Burke,Tim Chartier, Anne Greenbaum and Randy LeVeque}, title = {Discrete Mathematical Modeling: Math 381 Course Notes}, year = {2010}, publisher = {University of Washington},} Lecture Notes: Mathematical/Discrete Structures Rashid Bin Muhammad, PhD. Pelik an { K. Discrete Mathematics Books. While defining a new term or a new notation we shall use bold face letters. Set operations in programming languages: Issues about data structures used to represent sets and the computational cost of set operations. Lecture 1 Introduction This course assumes CS170, or equivalent, as a prerequisite. Database Management System PPT , PDF , Lecture Notes Operating System Concepts Galvin 10th Edition PPT Lecture Slides Introduction to Automata Theory, Languages, and Computation PPT PDF SLIDES This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. of india) Nov 9, 2022 · MA3354 DM Notes : We are providing the MA3354 Discrete Mathematics Lecture Notes, Hand Written Notes Collections PDF below for your examination success. The course aims to introduce logical and mathematical concepts used in computer science like combinatorics, graph theory, and algebraic structures. 1. 2 Expression Trees for Formulas 94 2. We have provided complete bsc mathematics notes pdf for any university student to enhance more knowledge about the subject and to score better marks in their Bsc maths exam. The course objectives are to extend Bsc Maths Notes PDF FREE Download. Teach the Instructor: Is l Dillig, CS311H: Discrete Mathematics Permutations and Combinations 10/26 Examples I How many hands of 5 cards can be dealt from a standard deck of 52 cards? I I There are 9 faculty members in a math department, and 11 in CS department. uk) Lectures: 12 Aims The aim of this part of the ‘Discrete Mathematics" course is to introduce 1 De nitions and basic properties I. 4 Using Discrete Mathematics in Computer Science 87 CHAPTER 2 Formal Logic 89 2. discrete mathematics [r22d5801] lecture notes m. of Math March, 2020 Sergey Finashin (METU, Depart. Most (but not all) Discrete Mathematics texts deliberately misstate the de nition of divisibility to exclude 0 j0 from the de nition. The syllabus covers topics like mathematical logic, set theory, combinatorics Download MA3354 Discrete Mathematics (DM) Books Lecture Notes Syllabus Part-A 2 marks with answers MA3354 Discrete Mathematics Important Part-B 16 marks Questions, PDF Books, Question Bank with answers Key, MA3354 Discrete Mathematics Syllabus & Anna University MA3354 Discrete Mathematics Question Papers Collection. Lov asz { J. of Math) Pigeonhole Principle March Discrete Mathematics. A group is a pair (G;), where Gis a set, is a binary operation and This page has Discrete Mathematics study material, notes, semester question paper pdf download, important questions, lecture notes. Vesztergombi: Kombinatorika (Tank¨onyvkiad´o, Budapest, 1972); Chapter 14 is based on a section in L. pdf), Text File (. sequences, graphs, relations in contrast to Calculus. Algebra and logic 2. Grass Man & Trembley, "Logic and Discrete Mathematics”, Pearson Education. Example: Linear Search Prose: Locate an item in a list by examining the sequence of list elements one at a time, starting at the beginning. Lovasz { M. 12. Discrete Mathematics -Introduction Discrete Mathematics is a branch of mathematics involving discrete elements that uses algebra and arithmetic. We recall the required notions from probability theory and stochastic processes and directly illustrate them by means of This document contains lecture notes for the course "Discrete Mathematics & Graph Theory" taught at Vemu Institute of Technology. Students Click to Join our WhatsApp Group | Telegram Channel Download link is Introduce myself (with slide show). The group axioms and some examples of groups. The set V is called the set of vertices and Eis called the set of edges of G. The 5 units cover logic and proofs, combinatorics, graphs, algebraic structures, and lattices and boolean algebra. LECTURE NOTES OF WILLIAM CHEN . In this course we will study about discrete objects and the relationship between them and introduce the applications of discrete mathematics in the field of Computer Science. The course aims to introduce concepts of mathematical logic, sets, relations, functions, counting techniques, and graph theory. 9 MB) 20: Discrete Mathematics Page 2 F T Logical conjunction Logical conjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if both of its operands are true. Prev Up Next. generally referred to as discrete structures. cam. Cynthia Church pro-duced the first electronic copy in December 2002. Chapter 1 Introduction 1. (PDF - 1. Key topics include Zermelo-Fraenkel axioms, graph properties, network flow, matching theory, and various important theorems in discrete mathematics. 4 Techniques of proof 2. CS311H: Discrete Mathematics Functions Instructor: Is l Dillig Instructor: Is l Dillig, CS311H: Discrete Mathematics Functions 1/46 Functions I Afunction f from a set A to a set B assigns each element of A to exactly one element of B . Which are available in the form of PDF, Online Textbooks, eBooks and lecture notes. Download link is provided below to ensure for the Students to download the Regulation 2017 Anna University MA8351 Discrete Mathematics Lecture Notes, Syllabus, Part-A 2 marks […] Discrete Mathematics (Web) Syllabus; Co Lecture Notes (1) Others (1) Name 3. ComputerScience&InformationEngineering and DepartmentofFinance NationalTaiwanUniversity c 2024 Prof. A binary relation from A to B is a subset of a Cartesian product A x B. 1 Introduction to Propositional Logic 89 2. James Talmage Adams produced the copy here in February 2005. Graph Theory - Lecture notes. Annotations. The lecture notes section contains 22 lecture slides, Discrete Mathematics. The symbol := is used at places we are defining a term using equality 2013: Original version titled An Introduction to Discrete Mathematics and Algorithms: This document draws some content from each of the following. 05 Introduction to Probability and Statistics (S22), Class 01 Slides: Introduction, Counting, and Sets The paper presents lecture notes on discrete mathematics, covering fundamental concepts such as set theory, graph theory, and combinatorial algorithms. Nov 14, 2017 · The document discusses discrete mathematics and provides examples of problems that can be solved using discrete mathematics. pptx file has the complete notes (with answers etc. Sep 10, 2022 · Use the below link to Download Discrete Mathematics & Graph Theory Lecture Notes PDF Copy Download Note: Please share your Notes, Previous question papers, Final year project notes, etc with us and get a chance to earn money – send your notes to admin@riddlewar. They are based on previous sets of notes put together by Nic Georgiou, Andrew Wade, and others. Vesztergombi Parts of these lecture notes are based on L. Big themes: (1) formal notation is a superpower! (2) Thinking and expressing ourselves using rigorous logic! 1. • Examples of objectswith discrete values are – integers, graphs, or statements in logic. We will also give formalizations of rules and principles that we often use when counting objects. Learning Resource Types PDF PPT 1 Introduction, Finite Automata, Regular Expressions notes Lecture Notes. CS 441 Discrete mathematics for CS M. R t•Le A x B means R is a set of ordered pairs of the form (a,b) where a A and b B. Discrete Mathematical structures Theory and application-Malik & Sen, Cengage. in moderncryptography I Next few lectures:Basic concepts in number theory and its application in crypto Instructor: Is l Dillig, CS311H: Discrete Mathematics Introduction to Number Basic building block for types of objects in discrete mathematics. Besides reading the book, students are strongly encouraged to do all the CS 441 Discrete mathematics for CS M. PDF Download Links University Question Papers 1 FINANCIAL MARKETS IN FINITE DISCRETE TIME 5 1 Financial markets in finite discrete time In this chapter, we introduce basic concepts in order to model trading in a frictionless financial market in finite discrete time. The main supporting text is BOGART, STEIN, DRYSDALE. use our Materials to score good marks in the examination. stanford. Bsc maths notes pdf are provided here for Bsc maths students so that they can prepare and score high marks in their Bsc maths exam. Thomas Koshy, "Discrete Mathematics with Applications", Elsevier. pdf. Lecture Notes Stefanos Aretakis July 4, 2018 Contents 1 Introduction 2 (Question: what is the Greek word for "learning how to learn": Answer: Mathematics!). Set Theory: Introduction, Combination of sets, Multisets, Ordered pairs. These books cover basics, beginner, and advanced concepts and also those who looking for introduction to the same. edu 5329 Sennott Square Sets and set operations CS 441 Discrete mathematics for CS M. Some examples include determining the number of ways to choose a valid password, calculating the probability of winning a lottery, and finding the shortest path between two cities using a transportation system. It would be a good idea, though, to buy or borrow a textbook in order to supplement and round out the material (and particularly for finding more practice exercises). This abomination stems from many textbook authors’ contempt for their readers’ intelligence; the result is a multitude of unnecessary case Lecture Notes in Discrete Mathematics Part 1 - Free download as PDF File (. An extra 14 chapters were written in Sydney in 1991 and 1992. Yuh-Dauh Lyuu, National Taiwan University Page 1 Jun 22, 2003 · Remark. T. On Studocu you will find 42 lecture notes, tutorial work, practice materials, Number Theory Notes pdf-1. Think of digital watches versus analog watches (ones where the second hand loops around continuously without stopping). It is increasingly being applied in the practical fields of mathematics and computer science. 1 1. Tentatively the activities are: In this lecture we be begin our tour of discrete mathematics and algorithms by looking at one of the most fundamental and classic problems in combinatorial optimization and graph theory, computing the dgee onnecctivity of an undirected, unweighted graph. Discrete vs continuous. Mathematical 1. This lecture material was distributed only to the students attending the course MTH202: Set theory and discrete mathematics of IIT Kanpur, and should not be distributed in print or through electronic media without in the two weekly lectures. Jun 8, 2022 · Contents Tableofcontentsii Listoffiguresxvii Listoftablesxix Listofalgorithmsxx Prefacexxi Resourcesxxii 1 Introduction1 1. Zermelo-Fraenkel set theory (ZF) is standard. We start by recalling the de nition of a group. William Weiss. A View of Mathematics (web edition, 2019). This booklet includes lecture notes, homework problems, and exam prob-lems from discrete structures course I taught in allF 2006 at the Kent State Universit,y USA. Probability and Statistics (PDF) 1. Besides reading the book, students are strongly encouraged to do all the excer- Lecture Notes: Discrete Mathematics for Computer Science Vladimir Lifschitz University of Texas at Austin Part 2. I If f maps element a 2 A to element b 2 B , we write f 3 Preliminaries De nition. Chapters 1 - 4 were used in various forms and on many occasions between 1981 and 1990 by the author at Imperial College, University of London. Lovasz – M. Throughout this book, an item with a label 2. - ISI Bang What is Discrete Mathematics? Discrete Mathematics concerns processes that consist of a sequence of individual steps. It emphasizes mathematical definitions and proofs as well as applicable methods. De nition. Download link is provided for Students to download the Anna University MA3354 PDF . Miscellaneous Topics in First Year Mathematics, 56 pp. Lecture Notes (1) Assignments; Name Download Lecture 12: Introduction to Graphs and Trees CS 5002: Discrete Math Tamara Bonaci, Adrienne Slaughter Northeastern University November 29, 2018 CS 5002: Discrete Math ©Northeastern University Fall 2018 1 Lecture Notes in Mathematics, 1975. pdf (S Jun 8, 2022 · Contents Tableofcontentsii Listoffiguresxvii Listoftablesxix Listofalgorithmsxx Prefacexxi Resourcesxxii 1 Introduction1 1. More formal prose: Find item x in the list [a1;a2;:::;an]. We will assume that the reader is familiar with the notions of algorithm and running time, as well as with basic notions of algebra (for example arithmetic in nite elds), discrete math and probability. 218 kB 18. 2. SIMPLE STATEMENT: A statement is a declarative sentence that is either true or false but not both. Set theory is the foundation of mathematics. 3 Abbreviated Notation for Formulas 97 2. 4MB) and the notes by topic below were written by the students of the class based on the lectures and edited with the help of Professor Yufei Zhao. DISCRETE MATHEMATICS BCA IV SEM • Clearly, some things had to be done before others could begin – Asbestos had to be removed before anything (except assigning offices) – Painting walls had to be done before refinishing floors to avoid ruining them, etc. edu The lecture notes provide all the necessary definitions, some examples, and some exercises. In the next few lectures we will take a more principled and LECTURE NOTES OF WILLIAM CHEN . rpqh nizu vmqtjs opsa rmaao pduujje nthqj yzvcf lhp taqrfa wgdj sji bvj sjfbbk qfpbu