Not every branch of mathematics is equally easy to understand. From the standpoint of teaching, some of the branches are easy to teach. Which particular branch of mathematics is tougher than most others to understand as well as to teach?
Good question.
Rather no single answer. Someone comes easily to linear algebra. Someone comes easily to mathematical analysis. All envy the person and the one who helps teach these branches of mathematics. For example, I did not like the theory of probability and statistics. As a result, has been forced to do just that.
Good question.
Rather no single answer. Someone comes easily to linear algebra. Someone comes easily to mathematical analysis. All envy the person and the one who helps teach these branches of mathematics. For example, I did not like the theory of probability and statistics. As a result, has been forced to do just that.
Vyacheslav,
If one is accustomed to set theory and the beauty of general topology, then I suspect that person will find probability and statistics difficult to teach. In parts of my undergrad course on computer vision, I teach (review) calculus and some probability theory. And I find calculus much easier to teach. At the graduate level, I teach the topology of digital images and proximity space theory. That is pure pleasure for me and, seemingly, for my grad students. That has been my experience.
@Hemanta, how about Partial Differential Equations? Maybe Difference Equations!? Here is an interesting issue that James would like it! INFINITY!!!
http://www.publishersweekly.com/978-0-465-02240-3
I agree with you James. That beauty and pleasure to help explore difficult areas of mathematics.
Dear Prof. Jacic,
The book by Ian Stewart (one of my favourite authors) and comments about Stewart's wide-ranging interests in mathematica, are wonderful. Many thanks for giving the link to this review.
Dear Prof. Lyashenko,
It is definitely the discovery of the beauty of topics in topology (revealing it for my students) and the pleasure in exploring these beauties (and pearls) that energises me in my teaching. And maintaining a vision of the beauties of the topics in mathematics (often apparently difficult for students to tackle but more approachable for students) does appear to help my students, once they catch hold of my enthusiasm for the ins and outs of the treasures of topology and its myriad applications.
Dear Professor Jacic,
When I was a student, I felt, Differential Geometry is a tough thing to understand. Later, I have seen that Rollo Davidson's explanations regarding Stochastic Geometry are actually tough to understand.
As for teaching, I have found that teaching Measure Theory and Special Functions is quite difficult because the students find these two fields quite tough to follow.
It depends on the specific person and its ability or not to do abstract generalizations that some branches need to be done. If somebody can understand the meaning of a linear space, then he/she will be good in linear algebra and other linear based branches. If somebody can understand the limiting procedure, then he/she can be an expert in calculus. So, the question cannot be answered generally.
Dear Demetris,
In your eyes, which particular branch is tough to understand?
You are right; a general answer may not actually be possible. How about a specific answer from you?
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