The Art of Logic, Proof and Modern Heuristic in Mathematics
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46 students enrolled

The Art of Logic, Proof and Modern Heuristic in Mathematics

Learn the Fundamentals of Rigorous Math with Modern Heuristic Reasoning
5.0 (1 rating)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
46 students enrolled
Created by Mert Atlı
Last updated 5/2020
English
English [Auto]
Current price: $13.99 Original price: $19.99 Discount: 30% off
5 hours left at this price!
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This course includes
  • 2.5 hours on-demand video
  • 1 article
  • 7 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Assignments
  • Certificate of Completion
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What you'll learn
  • Fundamental Principles of Logic
  • Propositions
  • Quantifiers
  • Propositional Logic
  • Conditional Statements
  • Logical Connectives
  • Biconditional Statements
  • Predicate Logic
  • Argument
  • Proof
  • Direct Proof
  • Proof by Contraposition
  • Proof by Contradiction
  • Proof of Uniqueness
  • Proof by Cases
  • Proof by Induction
  • How to Solve Problems
  • Modern Heuristic
  • Analogy
  • Heuristic Reasoning
  • How to Prove Theorems
Requirements
  • At least high school mathematics
  • Willingness to learn
  • Perseverance
  • Embracing failure
  • Curiosity
Description

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:

  1. Logic:

    In this part we will see the basic and advanced concepts in logic that lay the foundation of building rigorous mathematical arguments.


  2. Proofs:

    Here, we will cover general proof techniques in mathematics. Proofs techniques include:

    1. direct proof

    2. proof by contraposition

    3. proof by contradiction

    4. proof by cases

    5. existence and uniqueness proof

    6. proof with sets

    7. proof by mathematical induction

    8. combinatorial proofs


  3. Modern Heuristic:

    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!

Who this course is for:
  • Computer Science Students
  • Mathematics Student
  • Software Engineers
  • Computer Scientists
  • Programmers
  • Software Developers
  • Math Enthusiasts
  • Data Scientists
  • System Analysts
  • Business Analysts
  • Engineers
  • Anyone who wants to be a discoverer
  • Anyone who wants to be an inventor
Course content
Expand all 29 lectures 02:41:05
+ Welcome Video
1 lecture 03:01

Welcome video :) Lets explore the overall structure and content of the course!

Preview 03:01
+ Introduction to Logic
1 lecture 03:32

We will start with some core definitions such as proposition, propositional variable and compound proposition.

Preview 03:32

Test what you have learned in the previous lecture.

Quiz: Introduction to Logic
3 questions
+ Propositional Logic
3 lectures 11:36

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

Preview 06:49

Test what you have learned in the previous lecture.

Quiz: Propositional Logic
7 questions

We will learn how to calculate number of possible rows in a truth table.

Truth Tables
02:39

We will see how to construct a truth table.

Truth Table Construction
02:08

Test what you have learned in the previous lectures.

Truth Tables
3 questions
Lets apply what we have learned so far.
Assignment 1
9 questions
+ Logical Equivalences
2 lectures 07:37

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

Preview 03:43

Lets test your understanding of logical equivalences.

Logical Equivalences
5 questions

We will cover an example and several special logical equivalences.

Logical Equivalences in Actions
03:54

Test what you have learned in the previous lecture.

Quiz: Logical Equivalences
4 questions
Welcome to the challenge of logical equivalences!
Assignment 2
5 questions
+ Milestone 1
1 lecture 01:24

Review what we have covered so far! If you are going too fast, you may need to slow down! Learning math is a slow process.

Preview 01:24

Recap the concepts we have seen so far.

Milestone Quiz
6 questions
+ Predicates and Quantifiers
1 lecture 06:52

We will see predicates and quantifiers. We will cover existential and universal quantifiers.

Predicates and Quantifiers
06:52

Test what you have learned in the previous lecture.

Quiz: Predicates and Quantifiers
6 questions
+ Nested Quantifiers
2 lectures 10:40

We will see how nested quantifiers are stated and how they must be read.

Nested Quantifiers
08:15

We will see that negating nested quantifiers are so easy!

Negating Nested Quantifiers
02:25

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.

Uniqueness Expression
3 questions
+ Milestone 2
1 lecture 01:14

We have covered great deal of logic so far.

Preview 01:14
+ Logical Inferences
3 lectures 20:52

We will see what an argument is. We will cover logical inference methods like modus ponens, modus tollens, hypothetical syllogism and disjunctive syllogism.

Logical Inference
08:50

Lets test your understanding of logical inferences.

Rules of Inference
4 questions

The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method has been exploited in many automatic theorem provers.

Resolution Principle
07:18

We explore an easier proof of resolution principle.

Resolution Principle
4 questions

We will see how to make inference with quantifiers. We will see the instantiation and generalization of existential and universal quantifiers.

Inference for Quantified Statements
04:44

Lets test your understanding of inferences overall.

Inference Overall
3 questions
+ Milestone 3
1 lecture 00:43

Congrats! You have seen great deal of concepts in logic!

Preview 00:43