Discrete Mathematics
Learn Essential Mathematics for Programming
What you'll learn
- Understand discrete mathematics and mathematical logic
- Understand what propositions are
- Perform operations on propositions
- Understand one-way and two-way conditional statements
- Read truth tables
- Understand logical equivalence
- Tell apart statements that are always true from those that are never true
- Apply the laws of logical equivalence
About this course
This course teaches discrete mathematics, the math you need to master programming and computer science, with a focus on mathematical logic. It starts with an introduction to discrete mathematics and logic. Then you learn what propositions are and how to operate on them, followed by the one-way conditional and the two-way conditional. Next you move on to truth tables and how to read them, the idea of logical equivalence, statements that are always true or never true, and the laws of logical equivalence. It ends with worked examples and the idea of the propositional function. The course suits students of programming, computer science and communications, and anyone who wants to sharpen logical thinking. You do not need advanced math, because the lessons begin at the start and build up with examples. All you need is the wish to understand the basis of logical thinking. By the end you will be able to understand mathematical logic, use truth tables, and apply the laws of logical equivalence to solve problems and think like a programmer.
Expected outcomes
- Master the fundamental concepts of mathematical logic and their practical applications.
- Ability to use truth tables to analyze programming propositions.
- Understand and apply logical laws in code development.
- Enhance analytical and logical thinking skills for solving technical problems.
Learner reviews
Course content
1Discrete Mathematics (Mathematical Logic)
12 lectures
- Course IntroductionIntroduces the discrete mathematics course: how it differs from continuous math, its link to the binary logic of computers, its importance in computer science and engineering, and the main topics from mathematical logic to truth tables and equivalence.5:24
- Introduction to Discrete MathematicsShows why we study discrete mathematics: to develop logical thinking and solve programming problems, and introduces proofs through a flawed proof that seems logical and concludes two equals one, revealing its error in the division step.12:05
- Mathematical LogicIntroduces mathematical logic with the hotel riddle that plays on how we think, then defines a proposition and its truth value true or false, and uses examples to separate what is a proposition from what is not.11:32
- Concept of AssumptionsClarifies the concept of propositions: they must be declarative statements that can be evaluated as true or false, not commands, questions or statements with unspecified unknowns, and shows combining propositions and the negation symbol with an example.15:04
- Operations on AssumptionsExplains logical operations on propositions: negation (not) as a unary operator, the and operation and its truth table, inclusive or and its table, and exclusive XOR which rejects two identical values.13:14
- Unidirectional Conditional OperationExplains the logical implication (if-then) and how it differs from if-then in programming, with its truth table: it is false only when a true premise leads to a false conclusion, plus wordings for it and examples.17:07
- Bidirectional Conditional OperationExplains the converse, inverse and contrapositive of a conditional statement, then the bi-conditional (if and only if), its truth table and the different ways of expressing it.12:22
- Truth Tables RecognitionExplains how to build a truth table for compound propositions: choosing the number of rows and columns, filling in true and false values, and evaluating the logical operations step by step in order of precedence.12:13
- Concept of Logical EquivalenceExplains logical equivalence between two compound propositions and how to prove it with truth tables, with examples on the converse, inverse and contrapositive, and the difference between ordinary or and XOR.16:11
- Logical Statements Always True/FalseDefines tautology, contradiction and contingency, how to tell them apart with a truth table, how negation turns one into the other, and proving equivalence by showing p if and only if q is a tautology.12:33
- Laws of Logical EquivalenceCovers the logical equivalence laws such as De Morgan's law and the domination, identity and associative laws, and applies them to prove two expressions equivalent without a truth table.15:12
- Practical Examples + Concept of Default VariableApplies the equivalence laws to prove that certain statements are tautologies or equivalent instead of using truth tables, then defines a propositional function and how it becomes a proposition once its variables are fixed.15:41
Instructor
Dr. Eng. Mohamed Al-Khodour
This course is part of the diploma
