Struggling with Math Problems in Apostol's Book - What Should I Do?

[uman]

Hi all. What do you do when you are reading a math book and there are multiple problems you can't solve in a chapter?

For example, I am trying to learn from Apostol's book "Mathematical Analysis". In the problems at the end of the first chapter there are two that I haven't been able to figure out how to solve. It seems like the solution should be so simple but I'm just not seeing it. (There are two more I haven't attempted yet, but I think I can solve them.) Does this mean I'm not ready for the book and should get an easier one? Or is not being able to solve a couple problems in a chapter normal?

In case anyone's wondering, here's one of the problems I haven't been able to figure out:

Let $$w$$ be a given complex number. If $$w\not=\pm 1$$, show that there exist two values of $$z=x + iy$$ satisfying the conditions $$cos(z)=w$$ and $$-\pi<x\leq\pi$$.

The identity $$cos(z) = cos(-z)$$ says that if there is one such $$z$$, there have to be two... Other than that I'm at a loss.

 

[e(ho0n3]

Hi all. What do you do when you are reading a math book and there are multiple problems you can't solve in a chapter?

I keep a set of notes per book with a section with problems that I can't solve.

Does this mean I'm not ready for the book and should get an easier one? Or is not being able to solve a couple problems in a chapter normal?

If you're able to solve all the problems in the book without trouble, I would say the book was too easy.

Let $$w$$ be a given complex number. If $$w\not=\pm 1$$, show that there exist two values of $$z=x + iy$$ satisfying the conditions $$cos(z)=w$$ and $$-\pi<x\leq\pi$$.

The identity $$cos(z) = cos(-z)$$ says that if there is one such $$z$$, there have to be two... Other than that I'm at a loss.

Try to solve a more specific problem, say w = 0, w = i, or w = 1 + i. This should provide you with some insight.

 

[Defennder]

For example, I am trying to learn from Apostol's book "Mathematical Analysis". In the problems at the end of the first chapter there are two that I haven't been able to figure out how to solve. It seems like the solution should be so simple but I'm just not seeing it. (There are two more I haven't attempted yet, but I think I can solve them.) Does this mean I'm not ready for the book and should get an easier one? Or is not being able to solve a couple problems in a chapter normal?

Personally I don't know of anyone who is able to solve every single problem in a given textbook. Usually the authors would throw in a few difficult ones for every chapter's exercises. But that doesn't mean you shouldn't attempt to solve them.

 

[uman]

Thanks for the encouragement. The first chapter was starting to get boring (as "first chapters" tend to do) so I decided to move on and come back to try to solve those problems again later.

One of the ones I didn't attempt was proving the Cauchy-Schwarz inequality for complex numbers (the book gives a hint that looks like it makes this reasonably easy although I haven't tried) which according to the book is an extremely important result in analysis... so I may have to come back to that sooner rather than later, lol.

 

[NeoDevin]

You can also try posting the questions and your attempt at solutions in the homework help section of this forum.