The Art of Logic, Proof and Modern Heuristic in Mathematics
- 2.5 hours on-demand video
- 1 article
- 7 downloadable resources
- Full lifetime access
- Access on mobile and TV
- Certificate of Completion
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- Fundamental Principles of Logic
- Propositional Logic
- Conditional Statements
- Logical Connectives
- Biconditional Statements
- Predicate Logic
- Direct Proof
- Proof by Contraposition
- Proof by Contradiction
- Proof of Uniqueness
- Proof by Cases
- Proof by Induction
- How to Solve Problems
- Modern Heuristic
- Heuristic Reasoning
- How to Prove Theorems
- At least high school mathematics
- Willingness to learn
- Embracing failure
This is a perfect course for the ones who want to excel at rigorous math and who want to be a discoverer or inventor with a heuristic mindset!
Heuristic is the study of discovery and invention. Heuristic mindset is the basis of all discovery and invention in the history of human beings.
In this course we will see the general outline of MODERN HEURISTIC. The course has 3 main parts:
In this part we will see the basic and advanced concepts in logic that lay the foundation of building rigorous mathematical arguments.
Here, we will cover general proof techniques in mathematics. Proofs techniques include:
proof by contraposition
proof by contradiction
proof by cases
existence and uniqueness proof
proof with sets
proof by mathematical induction
This part includes the general steps and advices in approaching problems. We will use the steps and advices mentioned in this section combined with logic and proof techniques to learn how to solve complex problems and how to prove mathematical statements.
The course will be updated several times a month with new problems and sections according to the demand of the students. Especially Modern Heuristic section will be updated every week with new concepts and problems.
I hope you enjoy the course!
- Computer Science Students
- Mathematics Student
- Software Engineers
- Computer Scientists
- Software Developers
- Math Enthusiasts
- Data Scientists
- System Analysts
- Business Analysts
- Anyone who wants to be a discoverer
- Anyone who wants to be an inventor
We will see:
the main logical operator which is negation (a.k.a. not) operation
the main logical connectives which are and, or, xor, conditional and biconditinoal connectives
the order of precedence of operations and connectives
We will see:
What each of tautology, contradiction and contingency means
What logical equivalence means
How to determine whether two compound propositions are equivalent to each other
De Morgan Laws
In this quiz, we will see how we can express uniquness by quantifiers.
Suppose we have a propositional function P(x) with a certain domain A.
We want to show that P(x) is true only for one element in its domain.
In other words we want to show that there exists a unique element in the domain that makes P(x) true.