Which is the toughest of the following topics in Maths: i) Calculus ii) Trigonometry iii) Combinatorics iv) Algebra?

Personally, I think Trig (at least when it is used as part of advanced Calc.) The reason is that it is really abstract. My experience is that people who study physics handle it better because they have an application for it and it is not just a bunch of disconnected abstract concepts.

Combinatorics is the toughest. It is tough because you have to work on discrete sets. Analytical tools of algebra and analysis are not directly applicable here. You have to find ways to apply them on combinatorial problems. Diophantine equations, theory of partitions etc are really difficult topics because a problem looking very simple but may have very complicated proofs. For example consider Pillai Equation 􏰑􏰏

ax^m+by^m=k, where a,b,m,n,k are all integers greater than 1 and mn>=6. It is believed that it has only finitely many solutions. Looks very simple. But no proof is known so far.

Calculus is the more difficult of the four, since it requires the use of trigonometry and algebra. Combinatorics is really just counting problems but it does require the use of algebra.

Trigonometry

It really depends on your bent.

Any of them can be tough. The best definition that I know of "a difficult subject" is : one that the learner has

not met before.

Work on any subject: learn the definitions; learn how to apply them; and practise, over and over --the same problems and new ones. Practise until it becomes second nature.

Maths.

it depends for me combinatorics

foo

There is no "s" on the end of "math."