CS 103 Discrete Structures Lecture 01 Introduction to the Course Chapter 1 section 1.1 by Dr. Mosaad Hassan

Course Policies Textbook Attendance Grade Breakup Discrete Mathematics and Its Applications, 7th global ed. by K. Rosen Attendance 75% in is mandatory You are not allowed to miss lectures for the exams of other courses Grade Breakup Homework: 10% Two Midterm Exams: 25% each (6-7 wk, 12-13 wk) Comprehensive Final Exam: 40% Chapter 1 section 1.1 by Dr. Mosaad Hassan

Midterm Exams 75 minute duration Will cover all lectures delivered before the exam date Will consist of MCQ’s, fill-in-the-blanks, questions with short answers, writing of proofs, and drawing of diagrams If you miss any of these exams for any reason, you will have to appear for a makeup exam on the Thursday of the last week of teaching. This exam will cover all lectures delivered in the semester. It will consist of writing proofs, drawing of diagrams and answering questions having 0.5-1 page answers. Chapter 1 section 1.1 by Dr. Mosaad Hassan

Course Policies Course Website Office Hours Homework Assignments Course plan, slides Office Hours Posted on the office door If you want to met outside the office ours, send an email to confirm availability Homework Assignments Submission through email only Late submission will result in zero marks Plagiarism Chapter 1 section 1.1 by Dr. Mosaad Hassan

How to do well in this course? BEFORE EVERY LECTURE Read the relevant portion of the textbook DURING EVERY LECTURE Ask questions if anything is not clear AFTER EVERY LECTURE Review the lecture slides. IF anything is not clear THEN (discuss it with your fellow students) AND (ask me about it at the beginning of the next lecture OR visit me in my office during office hours OR email me about it) Solve all exercises assigned after each section IF unable to solve, THEN ask me for help Chapter 1 section 1.1 by Dr. Mosaad Hassan

What are Discrete Structures? Structures that are naturally discrete and not continuous Integer are discrete. They have distinct values. They are non-continuous. Real numbers are not discrete but continuous. They can vary smoothly and continuously. Discrete: Cars, books, students in a class Continuous: Gasoline in a car, width of a book, weight of a student

What is Discrete Mathematics? Discrete mathematics is mathematics that deals with discrete structures. In it we learn the concepts associated with discrete objects, their properties, and relationships.  We can view it as the mathematics that is necessary for decision making in non-continuous situations

Five Themes of Discrete Mathematics Mathematical Reasoning Combinatorial Analysis Discrete Structures Algorithmic Thinking Applications and Modeling

Five Themes of Discrete Mathematics Mathematical Reasoning Understanding mathematical reasoning in order to: Read, comprehend, and construct mathematical arguments. Construct proofs by using mathematical induction which is a valid proof technique. Combinatorial Analysis Discrete Structures Algorithmic Thinking Applications and Modeling

Five Themes of Discrete Mathematics Mathematical Reasoning Combinatorial Analysis An important problem-solving skill is the ability to count or enumerate objects. How one can perform combinatorial analysis to solve counting problems and analyze algorithms, not on applying formulae. Discrete Structures Algorithmic Thinking Applications and Modeling

Five Themes of Discrete Mathematics Mathematical Reasoning Combinatorial Analysis Discrete Structures How to work with discrete structures used to represent discrete objects and relationships between these objects. These discrete structures include sets, permutations, relations, graphs, trees, and finite-state machines. Algorithmic Thinking Applications and Modeling

Five Themes of Discrete Mathematics Mathematical Reasoning Combinatorial Analysis Discrete Structures Algorithmic Thinking Some problems are solved by designing an algorithm. Afterwards a program can be written to implement the algorithm All activities that include algorithm specification, verification, and analysis (of memory and time required to perform it) Applications and Modeling

Five Themes of Discrete Mathematics Mathematical Reasoning Combinatorial Analysis Discrete Structures Algorithmic Thinking Applications and Modeling Discrete mathematics has applications in a large number of areas. Examples: computer science, data networking, chemistry, business, and the Internet. Modeling with discrete mathematics is an important problem-solving skill.

Course Contents Logic and proofs Sets, Functions, and Relations Mathematical induction Counting Discrete probability Relations Graph theory Trees Boolean algebra Chapter 1 section 1.1 by Dr. Mosaad Hassan