Need some MATH advice (no I'm not asking how to solve a problem).

[Hoeboy]

Ok this one math class is killing me. I go sit in class everyday and everything he says goes over my head. At first I thought I was the only one but even the people who I thought were smart apparently have some difficulty understanding the logic behind what he is teaching. The math class I'm talking about is this (taken directly from the university catalog):

Introduction to Mathematical Analysis I
Rigorous study of calculus and its foundations. Structure of the real number system. Sequences and series of numbers. Limits, continuity, and differentiability of functions of one real variable.


I've taken all the pre-req to the class and some of the stuff he talks about are still confusing. He writes his own book and that is what he uses. It was a rushed job so the grammars are off and I guess some of the symbols are wrong as well. But I guess what really bugs me is I cannot grasp an understanding of the importance or basic logic of why we prove the things we prove. Can anyone who has taken this class or something similar (based on the description I gave of the course) point me towards the textbook they used? I think I need to refer to a second source outside of his book if I really want to understand this stuff. And it would be really helpful if the book has pictures and a good explanation of the purposes of the proofs.

 

[Chaotic42]

The best Calculus book ever:

How to Ace Calculus: A streetwise guide

I was intergrating 30 minutes after I learned what a limit was.

 

[LordJezo]

This is the book that got me through calc..

It's a great book. Very easy to understand!

 

[Chaotic42]

Originally posted by: LordJezo
This is the book that got me through calc..

It's a great book. Very easy to understand!

I also have that book!

 

[Hoeboy]

I'm not sure if that book would be useful. I finished all three years of calculus awhile ago. This math is more about the theories underlying calculus and other junk.

 

[agnitrate]

This is the one my school uses : book

This book rules compared to the one I had in high school. It's rather expensive though so you probably want to check out other peoples' suggestions first. Good luck! Math is very rewarding when you finally 'get it'. Unfortunately, that often takes hours of slaving over problems to finally achieve. Lord knows I have

-silver

 

[XZeroII]

Originally posted by: Chaotic42
The best Calculus book ever:

How to Ace Calculus: A streetwise guide

I was intergrating 30 minutes after I learned what a limit was.

I'm taking Calculus now, and our professor believes that you can't just jump right into stuff, you have to understand why you are doing what you are doing and why. Before we learned what a derivative was, we learned the formulas and reasoning behind what a derivative is. It will hopefully help later in the course.

 

[agnitrate]

What do you mean the theories underlying it?

Everything in a calculus book should be spelled out. I'm not sure what you mean by 'underlying' unless you mean the actual proofs of why something works.

Maybe you can give an example?

-silver

 

[Hoeboy]

Guys, I already passed Calculus. This math class is all proofs and theories. It's an upper division class (Calculus is a lower division class).

 

[wyvrn]

I'm in Calc II now and it's fairly challenging. Theory plus word problems, you gotta love word problems

I'm glad I don't have to go beyond Calc II, it's not my thing. Do you have to take this class?

 

[Hoeboy]

Originally posted by: agnitrate
What do you mean the theories underlying it?

Everything in a calculus book should be spelled out. I'm not sure what you mean by 'underlying' unless you mean the actual proofs of why something works.

Maybe you can give an example?

-silver

Okay let me see... Not being able to understand the class thus far, I'm not sure if I'm able to come up with a good example. But so far we've "supposedly" learned about proving the existence of rational #'s, irrational #'s, real numbers, etc. in between two numbers that are rational, irrational, and real. We learned about bounded sets of numbers, neighbors, and we're building up to the proof of why the limits in calculus works. In fact we rarely compute ANYTHING nor do we really use any numbers. We only use sets of numbers and we have to write in funky math notations.

 

[Hoeboy]

Originally posted by: wyvrn
I'm in Calc II now and it's fairly challenging. Theory plus word problems, you gotta love word problems

I'm glad I don't have to go beyond Calc II, it's not my thing. Do you have to take this class?

Im a math major so yes. I heard this class is what holds a lot of math major back And I have to take two years of this!!! Calculus 1, 2, 3 is a breeze compared to this junk!

 

[gopunk]

have you tried office hours?

 

[agnitrate]

Originally posted by: Hoeboy

Originally posted by: agnitrate
What do you mean the theories underlying it?

Everything in a calculus book should be spelled out. I'm not sure what you mean by 'underlying' unless you mean the actual proofs of why something works.

Maybe you can give an example?

-silver

Okay let me see... Not being able to understand the class thus far, I'm not sure if I'm able to come up with a good example. But so far we've "supposedly" learned about proving the existence of rational #'s, irrational #'s, real numbers, etc. in between two numbers that are rational, irrational, and real. We learned about bounded sets of numbers, neighbors, and we're building up to the proof of why the limits in calculus works. In fact we rarely compute ANYTHING nor do we really use any numbers. We only use sets of numbers and we have to write in funky math notations.

Sounds more like a number theory/discrete math course. That's what I'd be searching for on the web. Unfortunately, I haven't taken a class in either of those topics so I can't really be of any help to you. Hopefully somebody else can though. Bump!

-silver

 

[Hoeboy]

Originally posted by: gopunk
have you tried office hours?

Don't really have much time to go see him. He is only on campus Tuesdays and THursdays. I have a class right before his and I work as well. Even if I manage to squeeze into his office hours, I probably won't be the only one there. This guy is tough. He takes 2.5% of your grade away everytime you miss homework. I'm thinking of dropping the class and asking him if I can still attend. That way I'll have no pressure in terms of grade and can relax a bit to try to absorb some stuff and take it again next semester.

 

[wyvrn]

Well good luck. I couldn't torture myself like this.

Originally posted by: Hoeboy

Originally posted by: wyvrn
I'm in Calc II now and it's fairly challenging. Theory plus word problems, you gotta love word problems

I'm glad I don't have to go beyond Calc II, it's not my thing. Do you have to take this class?

Im a math major so yes. I heard this class is what holds a lot of math major back And I have to take two years of this!!! Calculus 1, 2, 3 is a breeze compared to this junk!

 

[brtspears2]

I just buy the solutions guide and work out the odd problems from there.

 

[Insomnium]

Rigorous study of calculus and its foundations. Structure of the real number system. Sequences and series of numbers. Limits, continuity, and differentiability of functions of one real variable.

All that seems just like Calc1 and II, except on the low down and dirty/theoretical level. Someone told me about a Calculus book that presents a lot of theory - with a lighthouse on the cover or something? - and supposedly does a TON of proofs that are actually understandable. I wish I knew what the book was but you can look into it or I can ask. It won't have proofs of real number system type stuff though, but everything else will be in there.

 

[Hoeboy]

bump for more s uggestions

 

[Reel]

I am taking a class that seems similar in nature:

The course focuses on both the theory and practice of using the computer to solve mathematical problems, with a particular focus on understanding and eliminating sources of error. Topics include: solving linear and non-linear systems of equations, numerical integration and differentiation, numerical solution of differential equations, and interpolation.

I do not know just how similar they are. It is also a follow-up to the calc series from the math dept but it tends to be for CS majors and other such computer dorks. We don't use sets much but we spend more time on numerical approximations and methods such as Lagrange polynomials and Euler's method. The textbook we use which is mediocre at best is Numerical Analysis by Burden + Faires.

 

[ThreeLeggedGnome]

Originally posted by: Chaotic42
The best Calculus book ever:

How to Ace Calculus: A streetwise guide

I was intergrating 30 minutes after I learned what a limit was.

now thats a derivative joke!

 

[Mday]

Originally posted by: Hoeboy

Introduction to Mathematical Analysis I
Rigorous study of calculus and its foundations. Structure of the real number system. Sequences and series of numbers. Limits, continuity, and differentiability of functions of one real variable.

is this class real analysis?

if it is, well, there is nothing there really is to explain, you start from the beginning, with the delta epsilon and stuff.

ask the professor to slow down. or ask for a more dumb'd down version of the subject.

 

[Mday]

the purpose of proofs is to make sure you arent spewing out garbage.

 

[rob3rt]

Hoeboy,

I graduated this past May and majored in math. I have to say that Analysis was the worst math class I took. To this day, I still don't know squat about all that nonsense I supposedly learned in there. I understand exactly how you feel.

My advice to you is to get this class over with. Hopefully you don't have to count it towards your Major GPA, or pray you get a B at least. Visit the professor as often as you can. I'm sure he knows that Analysis sucks so he'll understand. Get together with some of your classmates to work on problems. I can assure you that they are probably in the same boat as you are. I would definitely get this class over with, it is really a pain.

I found one of Lang's books to be pretty good. They also have a solutions manual so you can workout some of the problems.

Here's the book and the solutions manual. I think they have a deal if you order both for $99.

Anyways, good luck! You'll need it!

 

[Hoeboy]

that looks like a real good book rob3rt. the fact that it has a solutions manual is an added plus since this guy gives us homework yet neither goes over it or provides a solution!