This is a site about Mathematics and its teaching. I intend to share a number of ideas that, in my opinion, may help introduce mathematical concepts in a more intuitive and appealing way, favoring a holistic point of view on the subject.

I believe that some of the reasons why many students find Mathematics difficult are:

a) A presentation of the subject as a collection of methods to solve different problems, with an emphasis on the procedural aspects as opposed to a more high-level or bird’s-eye exposition;

b) A lack of historical perspective and motivation;

c) A pervasive Bourbakist style, consisting of a perfectly systematic, rigorous and soulless list of definitions and theorems;

d) A lack of relevant examples;

e) A lack of connection to other subjects like Physics, Engineering and Computer Science;

f) Favoring algebraic arguments over geometric ones;

g) Little or no discussion of the fundamentals and the philosophical underpinnings of the subject.

I am planning to publish new posts regularly, aiming at alleviating the above mentioned pitfalls. No particular theory is presented systematically, and the discussed topics will be rather elementary. Although my initial motivation was the teaching of Calculus and the first few posts deal with that subject, I will publish posts on other topics, including Analysis, Differential Equations, Geometry, Machine Learning and possibly other areas of Math.

I have been active on MathStackExchange for a number of years:

https://math.stackexchange.com/users/633848/greyes

and I have a GitHub account for personal use and to collaborate with my students:

https://github.com/greyes69