What is Real Analysis and How Does it Compare to Calculus?

[khemix]

what is real analysis? is it only the proofs of calculus or something else?

also what are the prerequisites? i have calculus I-II and linear algebra. the course is called intro to analysis and is a year long. the description says it will cover all of rudins principles of math. analysis with additional material. enrolment is restriced to people who have taken calculus I-II with theory, which i didnt. i talked to the professor and he said a lot of people had trouble doing it with only the calculus i took. so should i make preperations or take the course?

thank you for ur time

 

[lurflurf]

Rudin assumes very little previous calculus. The problem is many people are thrown when they transition from computational to a theoretical approach. If you are at theory there should be no problem. Otherwise review your previous calculus from a theoretical perspective. In particular given a known result you should be able to prove it (or at least understant a proof of it), understand the conditions on it that are often glossed over and understand why theresultt fails without the condition.
Examples
1) a differentiable function is continuous
2) chain rule
3)fundamental theorem of calculus

 

[HallsofIvy]

In my opinion, the real question is WHY you took "the calulus you took" rather than the "calculus with theory". If you had a choice between the two and chose the "non-theory" calculus, it may be that you would simply not have any interest, or
talent" in Analysis. Analysis is basically the theory behind calculus.

 

[sutupidmath]

you took "the calulus you took" rather than the "calculus with theory". .

I wish i had a choice like this at my univ. so i wouldn't have to do all the theory on my own. But it was extremely helpful and worth, and let's not forget joy that i derived out of it too!..lol..

 

[khemix]

In my opinion, the real question is WHY you took "the calulus you took" rather than the "calculus with theory". If you had a choice between the two and chose the "non-theory" calculus, it may be that you would simply not have any interest, or
talent" in Analysis. Analysis is basically the theory behind calculus.

i enrolled in it initially (it was called calculus with theoy) but found it overwhelming at first. we used spivaks book and i found it too time consuming. so i dropped down to honors calculus for sciences as i didnt want to kill my gpa. I am in life science (pharmacy to be exact) so i didn't need it anyway. my school said calculus with theory was only needed by mathematicians, not scientists. when i took linear algebra i started really liking the proofs and theorems, and wanted to continue with more math as i already did my organic chemistry requirements in first year. but i don't have the pre-reqs to do the analysis course. my professor said he had a few students that had a very difficult time doing the analysis course without the theory calc because they were unable to do the questions.

so my question is what exactly is needed to do a real analysis course? I've looked at amazon reviews of rudins book and it says all i need is basic calc.

Rudin assumes very little previous calculus. The problem is many people are thrown when they transition from computational to a theoretical approach. If you are at theory there should be no problem. Otherwise review your previous calculus from a theoretical perspective. In particular given a known result you should be able to prove it (or at least understant a proof of it), understand the conditions on it that are often glossed over and understand why theresultt fails without the condition.
Examples
1) a differentiable function is continuous
2) chain rule
3)fundamental theorem of calculus

so do you think its better to relearn calculus using the advanced book? the 3 examples you list are in rudins book, so won't i learn them there?

i am really confused because some posters said analysis is the theory of calculus. but then why would you need a theory course in calculus to understand the theory of calculus? wouldn't that be repeating what you already learned? what it comes down to is i have no idea what real analysis is and what is necessary to learn it.

 

[maze]

Analysis will be much more time consuming and difficult than a calc course based on Spivak. It is not the same thing as what you would learn in a calc theory class (though there are connections), and you will definitely not need analysis in a field like pharmacy. Heck, many (most?) physicists have never even taken analysis.

That said, I really like analysis from a purely mathematical standpoint, and when I took my first course on analysis, it raised the way I thought about math to a higher level. If 1) you are comfortable with making rigorous proofs, 2) you genuinely like math for the fun of it, and 3) you have enough time for it, then I highly recommend it. Otherwise, not so much.

 

[lurflurf]

so my question is what exactly is needed to do a real analysis course? I've looked at amazon reviews of rudins book and it says all i need is basic calc.



so do you think its better to relearn calculus using the advanced book? the 3 examples you list are in rudins book, so won't i learn them there?

i am really confused because some posters said analysis is the theory of calculus. but then why would you need a theory course in calculus to understand the theory of calculus? wouldn't that be repeating what you already learned? what it comes down to is i have no idea what real analysis is and what is necessary to learn it.

Really even basic calculus is needed for Rudins book. It is a matter of how good one is at proofs, how much effort one applies, and how well one can understand things. Do you want to do things the easy way or the hard way. Consider the commonly offered calculus courses.
-precalc
-for social/life science (any watered down intro calculus book)
-for enginearing/physical science (any intro calculus book)
-with theory (spivak level)
-analysis (baby rudin level)
-analysis (papa Rudin level)

Usually Papa Rudin level books assume previous calculus. Any level up to and including baby Rudin previous material helps by making it possible to absorb material faster, better, and easier. That said many people have trouble getting used to Rudin, especially since it is often not written in the most clear and undestandable manner. If you cannot undestand at the proofs of the results you know you are likely to have a hard time. So I recommend that you read through however many proofs you have time for should smoth thee transition. Also pratice inventing proofs. At least analysis proof are easier than synthesis problems in that you only need to rember 3 or 4 methods, but 250 or so reations must e remembed to solve synthesis problems.

 

[khemix]

Really even basic calculus is needed for Rudins book. It is a matter of how good one is at proofs, how much effort one applies, and how well one can understand things. Do you want to do things the easy way or the hard way. Consider the commonly offered calculus courses.
-precalc
-for social/life science (any watered down intro calculus book)
-for enginearing/physical science (any intro calculus book)
-with theory (spivak level)
-analysis (baby rudin level)
-analysis (papa Rudin level)

Usually Papa Rudin level books assume previous calculus. Any level up to and including baby Rudin previous material helps by making it possible to absorb material faster, better, and easier. That said many people have trouble getting used to Rudin, especially since it is often not written in the most clear and undestandable manner. If you cannot undestand at the proofs of the results you know you are likely to have a hard time. So I recommend that you read through however many proofs you have time for should smoth thee transition. Also pratice inventing proofs. At least analysis proof are easier than synthesis problems in that you only need to rember 3 or 4 methods, but 250 or so reations must e remembed to solve synthesis problems.

what is baby and papa rudin? did his dad write a book too?

so is it only the exposure and experience i need for analysis? an anology i can offer is physical chemistry I. its a useless course, in that it is just a rapid summary of thermodynamics and quantum theory where no results are proven. in second year, we are re-learning all of this and deriving all the results (i am doing this now). technically, none of the first year knowledge is assumed and i am doing fine even though i forgot most of the first yr stuff.

 

[lurflurf]

what is baby and papa rudin? did his dad write a book too?

so is it only the exposure and experience i need for analysis? an anology i can offer is physical chemistry I. its a useless course, in that it is just a rapid summary of thermodynamics and quantum theory where no results are proven. in second year, we are re-learning all of this and deriving all the results (i am doing this now). technically, none of the first year knowledge is assumed and i am doing fine even though i forgot most of the first yr stuff.

baby and papa are knicknames for two Rudin books.
Principles of Mathematical Analysis=baby Rudin
Real and Complex Analysis=papa Rudin

Yes the exposue and experience is what is needed not any particular result. Though if one did use Rudin as a first book besides misery this person would need to do some extra computational practice.