What is Analysis? Answers to Questions for Comp Sci Students

[thushanthan]

Hi

I am going to finish my calculus sequences with this semester [1,2&3 (Vector Cal)].

Currently I am enrolled in Computer Science program in my university. I am interested to

study about Analysis. I need some clarifications about Analysis. Please guide me...

My questions are:

1. What is Analysis ? Is Mathematical Analysis and Analysis are same?

2. Do people use it real life ?

3. What topics in Mathematics I should study to become an Analyst[?] ? Should I change

my major to Math or Is it possible to do it with Comp Sci?

PS: I have completed my Linear Algebra course. Differential Equations - I didn't take it yet!

Thank you. Excuse my English.

 

[Robert1986]

Remember all the times in Calc when your book said something like "The proof of this theorem is beyond the scope of this book."? Well, Analysis is the course in which those theorems are proven. However, to prove them, you have to start from a pretty basic level and build your way up. This branch of math (as I understand it) originated as a way to put calculus on a solid theoretical foundation. I suggest you read through an analysis text and decide if you like it.

The question about how much its used is hard to answer. On the one hand the answer is "yes" because it forms the theoretical basis for calculus and, on occasion, some people use calculus in real life.

On the other hand, it is never ever "used" (except by other mathematicians using known results to prove new results, or similar things) because it can't really, directly, be used. It is a branch of pure mathematics that more resemble a high art form than a strict science.

Though, I think this is what many people like about math. It requires a tremendous amount of creativity to be able to do. It is like mathematicians make this universe in their heads, and then play there all day. On the other hand, the subject can be incredibly useful and practical to know. For example, I'm a math major but I also work at this small manufacturing company. There have been several occasions at which I have been able to use my math skills to solve a problem. Now, I am not majoring in math to have the ability to solve problems at a small manufacturing company (for the same reason that one does not major in art to be able to paint bathrooms), but this is a very positive side of knowing math.

 

[thushanthan]

Thank you Robert1986!

I think Analysis is too abstract unlike my Calculus courses. So if I can, I will try to take

some abstract math courses before going to Analysis.

 

[SophusLies]

It doesn't answer your questions but, for me, analysis was the first course that I felt changed my thinking. I was forced to express my ideas in a precise way. It also got me good at "real" integration (not just some tricks), the series/convergent stuff.

 

[Dembadon]

Thank you Robert1986!

I think Analysis is too abstract unlike my Calculus courses. So if I can, I will try to take

some abstract math courses before going to Analysis.

See if your institution offers a course that introduces students to different proof methods and techniques. This will help ease you into the type of thinking that is required for the more theoretical mathematics courses. There are many different names for these types of courses, so if you have an advisor, I would make an appointment and see if you can find out if such a course is offered to you.