Most Difficult Math Subject

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Jason76

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I think trigonometry is the most difficult due to the amount of identities to know, and also trig equations. It's more difficult than even Calculus or Diff. Equations. What math subject is the most challenging to you?

But actually, trig outside of identities and trig equations, is very easy.
 
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Jason76 said:
I think trigonometry is the most difficult due to the amount of identities to know, and also trig equations. It's more difficult than even Calculus or Diff. Equations. What math subject is the most challenging to you?

But actually, trig outside of identities and trig equations, is very easy.
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If you know the derivations - you don't have to remember much of the identities.

I remember only the following (aside from definitions of sin, cos, tan, sec, etc. and their values at 30°, 45°, 60° & 90°):

cos(A+B) = cosA * cosB - sinA * sinB

sin(A+B) = sinA * cosB + cosA * sinB (It will take too long to derive these)

Pythagorean theorem → sin2Θ + cos2Θ = 1 & sec2Θ = tan2Θ + 1
 
I think trig is easiest. AP Calc is most definitely the hardest.
 
I found abstract algebra to be the hardest for two reasons.

First, it involves operations and objects that do not necessarily match the operations and objects that are familiar to us from arithmetic, algebra, and calculus.

Second, it deals with commonalities among seemingly quite disparate systems so your sense of analogy gets all messed up.

Of course, I am not a mathematician so it probably is quite easy for those with a talent in that direction.
 
JeffM said:
I found abstract algebra to be the hardest for two reasons.

First, it involves operations and objects that do not necessarily match the operations and objects that are familiar to us from arithmetic, algebra, and calculus.

Second, it deals with commonalities among seemingly quite disparate systems so your sense of analogy gets all messed up.

Of course, I am not a mathematician so it probably is quite easy for those with a talent in that direction.
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I would have to agree with you. But after becoming familiar with number systems to increase your "toolbox of analogies" an introductory abstract algebra textbook might not be too bad. Seeing objects in their greatest generality (groupoids - a set with an operation) and slowly increasing the complexity is my favorite approach to learning the subject.

For example:

groupoid (add right/left inverses) => quasigroup (add identity) => loop (add associativity) => group.

And of course it can branch out in many other ways, for example adding associativity first gives what's called a semigroup, an identity element thrown into a semigroup will give what's called a monoid. adding left inverses (or right inverses) to a monoid gives a group.

It is far and large my favorite subject, but I'm starting to think my brain is not built for it :cool:
 
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daon2 said:
An introductory abstract algebra textbook might not be too bad.

I found the topic fascinating, but very hard work because I had to discard so many mental assumptions. Its difficulty lies within, in abandoning your intuition. Once your intuition has been sufficiently expanded, it probably looks easy. (Though my recollection, dim after almost five decades, still shudders at the word "kernel.")

And of course it can branch out in many other ways, for example adding associativity first gives what's called a semigroup.

My dim recollection is that we spent a fair amount of time on semigroups, which my teacher said had enough structure to be interesting but not so much as to be confining.

It is far and large my favorite subject, but I'm starting to think my brain is not built for it :cool: I enjoyed the course (despite the work), but it convinced me that I was no mathematician. I could only follow where others had blazed a path.
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I completely agree with statements about abstract algebra.

Like quantum mechanics - I had to put my intuitions in some inside pocket.
 
Jason76 said:
I think trigonometry is the most difficult due to the amount of identities to know, and also trig equations. It's more difficult than even Calculus or Diff. Equations. What math subject is the most challenging to you?
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I have read all of the replies.
I would ask all of you if you have looked into ​ algebraic topology or ​ category theory ?
 
Linear Algebra for me, but I think that was a direct correlation to the horrible teacher I had in college.

Oh, and if anyone decides to become an actuary like me, you will be introduced into a world of math that you have never seen.
 
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Well, it is all depending on the teacher. For me I find Discrete Math to be quite challenging because it has nothing to do with solving equations, but it requires logical knowledge and good approach to prove the problems ;-)
 
Trig identities are actually incredibly easy after memorization. Also trig intergals and derivatives are way easier after memorizing.
 
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