Course Alert!

Hello Everyone!

You may noticed I haven’t posted here for 3 years. I won’t keep writing here. But…

I am shifting my focus from writings blog posts towards creating video lectures.

I created some video lectures about mathematics. Here is the link on udemy:

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!

Principal Component Analysis 4 Dummies: Eigenvectors, Eigenvalues and Dimension Reduction

George Dallas

Having been in the social sciences for a couple of weeks it seems like a large amount of quantitative analysis relies on Principal Component Analysis (PCA). This is usually referred to in tandem with eigenvalues, eigenvectors and lots of numbers. So what’s going on? Is this just mathematical jargon to get the non-maths scholars to stop asking questions? Maybe, but it’s also a useful tool to use when you have to look at data. This post will give a very broad overview of PCA, describing eigenvectors and eigenvalues (which you need to know about to understand it) and showing how you can reduce the dimensions of data using PCA. As I said it’s a neat tool to use in information theory, and even though the maths is a bit complicated, you only need to get a broad idea of what’s going on to be able to use it effectively.

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