Daffodil International University SE 123 Discrete Mathematics Fall 2024 Lecture 01 PDF

Daffodil International University (DIU) Department of Software Engineering (SWE) SE 123 – Discrete Mathematics Fall 2024 Department of Software Engineering – Discrete Mathematics  Lecture 01 Course Introduction Discussion on OBE of...

Daffodil International University (DIU) Department of Software Engineering (SWE) SE 123 – Discrete Mathematics Fall 2024 Department of Software Engineering – Discrete Mathematics  Lecture 01 Course Introduction Discussion on OBE of Discrete Mathematics Department of Software Engineering – Discrete Mathematics 2 Course Instructor v Mohammad Azam Khan, PhD v Assistant Professor, Dept. of SWE, DIU. v Email: [email protected] v Webpage: https://azamkhan.owlstown.net v Address: Room # 907, Knowledge Tower, DIU. v Contact: +82-010-7598-4459 (WhatsApp) Department of Software Engineering – Discrete Mathematics 3 Course Overview v Course Title: Discrete Mathematics v Semester: 2nd v Section: F, G, H, and J. v Schedule: Please follow the class routine (Fall 2024) v Class: Offline and/or Online. Department of Software Engineering – Discrete Mathematics 4 Course Resources v Book: Discrete Mathematics and Its Applications by Kenneth H. Rosen, Seventh Edition. v Supplementary readings: Ø Epp, S., Discrete Mathematics with Applications, 3rd edition, PWS Publishing Company Ø Bauer, D., Lecture Notes in Discrete Math, Stevens Tech edition v Availability of course materials and slides: Ø DIU Blended Learning Center Ø Google Classroom Ø Course webpage v Software/Tools used: Ø Google Colab Ø Python Department of Software Engineering – Discrete Mathematics 5 Goal of the Course v Focus on discrete mathematical structures and objects. v Key aspects and topics of discrete mathematics: Ø Formalize various mathematical concepts such as sets, functions, relations, and graphs. Ø Develop problem-solving skills arise in computer science, combinatorics, cryptography, and other fields. Ø Analyze algorithms for efficiency and correctness through techniques like recurrence relations, asymptotic analysis, and graph theory. Ø Model and analyze real-world problems, such as network flows, scheduling problems, and logical reasoning. Ø Foundation for computer science and related fields, covering computing, data structures, algorithms, and so on. Department of Software Engineering – Discrete Mathematics 6 Course Learning Outcomes (CLOs) with Mappings Program Learning Learning Domains CLOs CLO Description BNQF Skill Outcomes (PLOs) (C, P, A) Interpret the concept and scope of CLO1 application of propositional and PLO2 C2 Fundamental Domain predicate logic. Apply the set theory and probability in CLO2 different application related to software PLO1 C3 Fundamental Domain logic development. Analyze the mathematical problems in CLO3 discrete domains to understand PLO2 C4 Fundamental Domain problem Statements and plan solutions. Evaluate logical solutions using graph theory and binary trees with CLO4 PLO4 C5 Fundamental Domain programming concepts based on real- life examples. Department of Software Engineering – Discrete Mathematics 7 Course Outline (Brief) vPropositional and predicate logic v Set theory and probability v Mathematical problems in discrete domains v Graph theory and binary trees Department of Software Engineering – Discrete Mathematics 8 Course Outline (Detailed) Week Lesson Topics 1 Lesson 1 Discussion on OBE of Discrete Mathematics Lesson 2 Proposition and its condition, negative proposition. 2 Lesson 1 Compound proposition, logical operators Lesson 2 Logic and Proofs, Logical equivalences. 3 Lesson 1 Different logics: AND, OR, Exclusive OR, Conditional, Bi-conditional logic, etc. Identifying characteristics of those logics and practicing Truth tables in class Lesson 2 Understand logical equivalence and solve using the truth table Class Test -1 4 Lesson 1 Use logical equivalence to solve problems Lesson 2 Learn predicate and nested quantifier syntax, apply them to different scenarios, and practice in class 5 Lesson 1 The basic concept of probability Lesson 2 Sample space derivation for any situation Department of Software Engineering – Discrete Mathematics 9 Course Outline (Detailed) Week Lesson Topics 6 Lesson 1 Problem-solving related set theory Lesson 2 Sets and Subsets 7 Lesson 1 Comparison among number sets Lesson 2 Venn diagrams Class Test -2 8 Lesson 1 Set Operations Lesson 2 Practicing problems related to set theory 9 Lesson 1 Revision before midterm Lesson 2 Understand basic Functions Midterm exam (Tentative) 10 Lesson 1 Different types of functions Lesson 2 Application of Functions Department of Software Engineering – Discrete Mathematics 10 Course Outline (Detailed) Week Lesson Topics 11 Lesson 1 Understand Sequences and Sums and compare them with programming basics Lesson 2 Comparative analysis between function and relation, Number Theory: The division algorithm, divisibility and the Euclidean algorithm, prime numbers, congruence, application of congruence 12 Lesson 1 Introduction to relation Lesson 2 Application of functions and relations with real-world examples, Induction and Recursion: Mathematical Induction, Recursive Definitions and Structural induction, program correctness. 13 Lesson 1 Introduction to Graph Theory Class Test -3 Lesson 2 Graph Terminology 14 Lesson 1 Graph construction Lesson 2 Different types of graphs Assignment (Ideation) Department of Software Engineering – Discrete Mathematics 11 Course Outline (Detailed) Week Lesson Topics 15 Lesson 1 Application of graph theory Lesson 2 Graph theory- related problem solving, transitivity, reflexivity, equivalence classes, congruence, closure of relations and functions 16 Lesson 1 Introduction to binary tree Lesson 2 Different types of binary trees 17 Lesson 1 Application of binary trees Lesson 2 Different Algorithms of Graph Theory 18 Lesson 1 Application of Graph Theory, Euler and Hamilton Paths. Final exam (Tentative) Lesson 2 Industry Session Assignment (Submission) Presentation Department of Software Engineering – Discrete Mathematics 12 Marks Distribution Description Marks Class attendance 7 Assignment 5 Presentation (Mandatory) 8 3 Quizzes 15 Midterm exam 25 Final exam 40 Total 100 Department of Software Engineering – Discrete Mathematics 13 Thank You! Q&A Department of Software Engineering – Discrete Mathematics 14