Well, read it now, and read also Royden's Real Analysis and ``Baby Rudin''

(aka ``Principles of Mathematical Analysis''). Don't stop reading until you

have understood the basics. Then, when your course begins, work to master

what you have already read at least twice. When someone asks a question in

class, write it down,and later, work out the answer on your own, if you did

not know the answer when it was asked. Don't expect the professor to

explain everything. That way, if he or she does explain everything, you

will be pleasantly surprised. Don't expect the professor to exaplain

anything. That way, ... Well, you know the rest. The more you do for

yourself, and the less you rely on the professor to do or explain problems

and their solutions to you, the better off you will be, because in class,

``the person learning is the person doing the work'' (Harry Wong, among

others). As you study the subject, try to find connections to other

subjects, such as applications to PDEs, applications in R.A. of set theory,

algebra and linear and multilinear algebra. As you read, make a notebook in

which you practice making up problems of your own, before the book or the

professor asks you to do them. If someone else needs help understanding a

topic, help them. (But if they need help on a solo assignment, of course,

refuse.) If the professor asks a question of the class, it may not be

rhetorical. Try to judge this, but you are better off to answer it, rather

than leaving the professor to form opinions about you from thin air. If you

did so wonderfully as you say you did in advanced calculus, you should learn

quickly what answers are right and which ones are wrong, and so you should

be able to soon begin really demonstrating that you are ``on top of

things''. Do not wait until the night before a test to study for it. Keep

good notes, and type them up, if possible. Try indexing them. (Software

should be available to handle this problem.) Make this a routine habit.

With the availability of modern writing, typing and type-setting software,

this should be almost a piece of cake. When your professor assigns some

problems to do, take a sheet of paper for each problem, and write the

problems at the top of the sheets. Carry those in a notebook, and for each

problem, write very plainly all your solution, perfectly, starting on the

appropriate page on which you already have stated the problem and continue,

if necessary, on a fresh second sheet of paper. Number each page carefully.

Review your solution as many times as necessary to make sure you have

eliminated any errors or unclear sentences or computations. Design the

notation so that it is self-consistent, complete and efficient, as a

communication vehicle for your ideas about the correct solution of the

problem.

Matt

-----Original Message-----

From: maintainer_wiz [mailto:

maintainer_wiz@...]

Sent: Tuesday, July 09, 2002 5:09 PM

To:

probability@yahoogroups.com
Subject: [probability] Re: real analysis I (how scary is it?)

Bartle's "intro to measure theory and lebesgue integration".

-- In probability@y..., "Insall" <montez@r...> wrote:

> What text are you using?

>

> Matt Insall

> -----Original Message-----

> From: maintainer_wiz [mailto:maintainer_wiz@y...]

> Sent: Tuesday, July 09, 2002 3:54 PM

> To: probability@y...

> Subject: [probability] real analysis I (how scary is it?)

>

>

> Can anyone provide me with pointers or opinions on what to expect

and

> how to survive real analysis I? I've done very well in my

undegrad

> advanced calc classes, so should I necessarily take this as an

> indication that I should be able to follow the course? Just

> wondering here. R.A.I. will be my first graduate level course.

>

> Thanks,

> MW

>

>

> Your use of Yahoo! Groups is subject to the Yahoo! Terms of

Service.

>

>

>

> [Non-text portions of this message have been removed]

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