Math 452 – Real Analysis I
Fall 2009; Dr. Friedman
Math 452 is one of the most challenging courses offered in undergraduate mathematics. The challenge is well worth it as
the content you will be learning is interesting, far-reaching and extremely applicable to other fields (in and outside of
mathematics).
In order to succeed in this course, it is strongly recommended that you plan your schedule so that adequate time is
available for you to invest in this course. The amount of time required will, of course, vary from week to week and from
student to student. However, it is almost certain that you will spend more time preparing for this course than for other
mathematics courses [except, perhaps, Abstract Algebra].
Some minimum requirements for success
1. It is expected that you have skimmed the section to be discussed prior to the class lecture to familiarize yourself with
terms that will be used and so that you know what material to review from previous chapters that will help you to
better understand the lecture. Even with this preparation, do not expect that you will be able to understand and
absorb the details of the lecture while it happens. Learning mathematics at this level only begins in the classroom.
The large majority of the understanding happens while struggling with problems and re-reading the text and notes.
2. It is expected that you will carefully re-read the chapter after it is discussed in class so that you may better absorb the
lecture, see more examples, and begin to sort through and organize the details. Note that reading a mathematics text
book is not an easy task and must be done with pencil in hand! Expect that you will need to actively “read” a
chapter (or some subset of it) several times before you begin to understand it.
3. Each week, you should complete and understand the homework assignment. [see guidelines below for more detail].
4. Come to class prepared with questions from the previous lecture and/or from homework. While we may not be able
to get to all questions during class, we can attempt to identify critical places where the class is struggling. When you
seek help outside of class, you must come prepared, having already worked through the problem(s) on your own.
You should have specific questions and bring along with you the work that you have attempted.
Homework Guidelines
For each chapter, there will be two types of problems defined as follows.
I. Assignment: These problems will be formally written-up and submitted and must meet the guidelines established in
the following bullet points.

Problem sets will be submitted either weekly or biweekly and will typically be due on Thursday by 3pm.

Your assignment must be stapled, must be legible [to me!], must not have jagged edges, and must have problems
worked in order [or carefully noted where the out of order problem is located]. Also, the statement of each problem
must be written. Homework that is not legible must be typed [legibility is strongly recommended]. Assignments
that fail to meet these guidelines will be returned ungraded.

Grading: I will grade roughly at least half of the problems that you submit, depending on the assignment and
whether most of the graded problems are proofs. Problems will be worth up to 10 points depending on the amount
and type of explanation required. Problems requiring proof will be graded for both content and writing style.

Working together on homework problems in a higher level mathematics course tends to generate some questions
with regard to what constitutes legitimate, scholarly collaboration versus cheating [though this is undoubtedly not
your intention]. Since I will not make any distinction in penalty for cheating that is intentional versus that which is
unintentional, it is important that you carefully consider and abide by the following items [these do not apply to
supplemental problems]. If you have any uncertainties regarding what constitutes cheating in this class, it is your
responsibility to ask me for clarification.
1. Short answer problems, true/false and computational problems of any kind should all be completed
independently including your brief explanations. There should be no collaboration on these problems with
classmates or anyone else, although you are welcome to ask me for help.
2. Working together to identify strategies needed to solve the proofs in the homework is not only acceptable, but
very desirable. However, joint work should occur after each person has had a chance to work on the problem
individually and should consist of working on strategy only, not organization of ideas and/or how to write up the
solution. It may be appropriate to avoid writing things down altogether (just discuss). If you don’t understand
the discussion well enough to be able to reproduce it on your own, then your use of the information would
constitute an abuse.
3. It is not acceptable for you to tell a classmate how to do a problem. Note that this is not the same as having a
discussion about strategy and figuring things out together. Obviously, you may not copy another student’s
homework nor permit yours to be available for someone else to copy.
4. If you consult anyone outside of class for help on a submitted problem (a faculty member besides me, a student
who is not currently taking the course, etc), you must cite the person(s) at the beginning of the write-up for that
problem.
Some helpful hints…
If you are stuck on a problem, always begin by trying to reduce a general statement to one regarding a specific case and
try to solve for the specific case. This technique often helps to reveal the general solution. Be sure to review pertinent
definitions, theorems and examples in text and notes. Also note that you may use statements of previous exercises [in
current and previous chapters] without proof, even if they were not assigned. Of course, any such use must be cited or I
will be looking for the proof.
You may find it helpful to keep a list of theorems, exercise results and examples for major concepts.
There are “solutions” to the odd numbered problems in the back of the text. These are never complete. I strongly
recommend that you do not use these hints until you have seriously worked on the problem yourself. You will gain very
little or no understanding of the problem from having the critical idea given to you.
Imagine that every problem [even computations] in the exercises is followed by “explain” or “why” or “prove”, etc. For
computations, you may simply cite a theorem that you are applying or you may have to show why your computation is
correct. Theoretical questions nearly always require a proof. I can think of only a very few problems that truly require no
explanation. If you think you’ve found one of these, please ask me in class so the information gets announced to
everyone. Problems that are not sufficiently justified will earn a reduction in score and could possibly earn no credit,
depending on the specific problem.
II. Supplemental: The challenging subject area that this course presents requires that students work a large number of
problems of varying difficulty in order to gain the required level of competency. Thus, while you are asked to formally
write up some problems for a grade, there are others that in my professional judgment are critical for you to consider
either to gain a more complete understanding of the subject or to help in solving an assigned problem. I have identified
these as supplemental problems.
You need not submit the supplemental problems, nor even spend the time to write them up carefully. However, spend
enough time so that you understand the ideas contained in them. Perhaps you may use them as a partial review for a quiz
or test.