IT221: Discrete Math

Welcome to the Course

Introductions

Your Instructor

• Email: robert_b@payap.ac.th
  
• Office: PC314 (Office hrs by appointment)

Different branches of Mathematics

What is Discrete Math

Discrete mathematics is the study of discrete mathematical structures (like 0,1,2…) rather than “continuous” ones (such as 0.1,0.101, 0.1001).

Why study this course?

• Discrete Math is key to effective and efficient programming

• Discrete approaches simplify a problem by reducing the possibilities for solutions

• Many important shortcuts and algorithm improvements come from applications of this discipline

• Many failures of computing and business come from the lack of understanding of Discrete Math.

Course Resources

-Textbook Resources

-Software Resources

- Slides and Handouts

• Enrollment Url: https://canvas.instructure.com/enroll/RGTRTX
• Login URL: https://canvas.instructure.com

Callouts

Some examples of the topics we will study

Permutations

The most popular mathematician in the world is throwing a party for all of his friends. As a way to kick things off, they decide that everyone should shake hands.

• Assuming all 10 people at the party each shake hands with every other person (but not themselves, obviously) exactly once, how many handshakes take place?

Combinatorics

At the warm-up event for Oscar’s All Star Hot Dog Eating Contest, Al ate one hot dog. Bob then showed him up by eating three hot dogs. Not to be outdone, Carl ate five. This continued with each contestant eating two more hot dogs than the previous contestant.

• How many hot dogs did Zeno (the 26th and final contestant) eat?
• How many hotdogs were eaten all together?

Logical deductions

After excavating for weeks, you finally arrive at the burial chamber. The room is empty except for two large chests. On each is carved a message:

• Chest 1: If this chest is empty, then the other chest’s message is true.
• Chest 2: This chest is filled with treasure or the other chest contains deadly scorpions.

You know exactly one of these messages is true. Which one is it?

Graphics

Back in the days of yore, five small towns decided they wantedto build roads directly connecting each pair of towns. While the towns had plenty of money to build roads as long and as winding as they wished, it was very important that the roads not intersect with each other (as stop signs had not yet been invented). Also, tunnels and bridges were not allowed.

• Is it possible for each of these towns to build a road to each of the four other towns without creating any intersections?

Course Outline

• Unit 0: Introduction and Preliminaries
• Unit 1: Sets: Definitions, Functions, Counting
• Unit 2: Combinations, Permutations and Sequences
• Unit 3: Predicate Logic
• Unit 4: Trees
• Unit 5: Graphs Theory
• Unit 6: Presentations and Review

Course structure

• Lecture Slides
• Classroom challenges
• Exercises
• Chapter Review
  • Practice Test
  • Key Terms
  • Key Equations
  • Key Concepts
  • Review Exercises
• Module Quiz

Assessment

• Exercises: 10%
• Module Quizzes: 30%
• Mid term: 30%
• Final exam: 30%

Some Errorous Examples

Mistake 1: Armour Plating of Airplanes

Mistake 2: Shark attacks and ice cream consumption

Mistake 3: Measles vs Marriage

Mistake 4: Illusion