Learn what most have forgotten about derivatives, functions, maxima and minima
What you'll learn
- The concepts: Functions, functions of a single and multiple variables, slope, gradient and tangent to a curve, minima, maxima and optima. When dealing with data science or machine learning we often speak of optima. Here the concepts of derivative and optima are discussed with a view to understanding what all this terminology means.
- The course is based on the meaning (conceptual meaning) of functions, derivatives and finding minima and maxima. Details are not the focus.
- This course is conceptual and simply points at what things that are currently solved computationally mean.
- You must already understand some algebra
Many people might take an interest in AI, data science and machine learning, just to mention some of the most current fields of interest.
Most of these fields are highly dependent on calculus and, more generally, concepts like minima, maxima and derivative
You might be a mathematician, but if you are not a mathematician and only barely remember the terms “derivative” and “slope”, and if you also want to understand the fundamental meaning of these terms, this course is for you.
What is optimising?
Optimizing: “The action of making the best or most effective use of a situation or resource. - online definition”
Artificial Intelligence and optimization: In the AI field optimizing relates, broadly speaking, to finding the “optimum” possibility for a given task.
I recommend to read, for example this article: Management AI: Deep Learning And Optimization by David A. Teich to understand the relevance of optimisation. Here you will learn from the foundations of curves, functions and variables to the meaning of derivative and the relationship between function, derivative and optimum points such as minima and maxima.
We also discuss how the actual calculations are carried out computationally by computers and by using programming languages. With all, it is important to understand the concepts that are being used by these languages and here we give a basic conceptual description that should help you move on to the next level or gain confidence in what you are already doing.
Who this course is for:
- Beginner scientist, computer scientist or other with an interest to understand what calculus, derivative and stationary points, minima and maxima means.
- Beginner scientist, computer scientist or other that has forgotten what it is meant by derivative and stationary points.
- Beginner scientist, computer scientist or other that is starting to use algorithms but needs to get back to the fundamental concepts of calculus (mostly derivation and finding critical points such as maxima and minima).
