MATH 301: Real Analysis II
Mathematics
Department, Bryn Mawr College, Fall 2009
Professor:
Victor Donnay 
Lecture:
Mon, Wed, Fri 910 or 11
12 Rm. 336 
Office:
Park Science Building #330 

Phone:
5265352, Email: vdonnay 
Office
Hours: 
TA Sessions: Tuesday 4 – 5pm, Wednesday
7:30 – 9 pm, Thursday 3
– 4:30pm all in Rm. 336 with Chris Micklewright, cmicklewri@brynmawr.edu. We have
reserved Rm. 336 starting a halfhour before the TA session and continuing for
a halfhour after the TA session so you can keep working on your hw there with
your classmates.
Course "PlaybyPlay". Outline of
what is covered during each class and HW assignments.
Last Assignments: You have until 5pm on Thursday to turn in the last
homework. You should put it in Chris MicklewrightÕs mailbox in the math
lounge.
You may hand in a final quiz redo by 5pm
Thursday too; put that under Prof. DonnayÕs door. Any final enrichment essays
are due by then too.
The HW answer keys will all be available on
Blackboard by Thur at 5pm.
Also there will be an answer key from Midterm
2 on Blackboard.
Final Exam Period:
During Exam Period, Professor Donnay
will hold office hours as follows:
Friday Dec 11: 1 – 3:00 pm
Monday Dec 14: 11 am – 12:30 pm
Wed Dec 16: 10 11:30am
Chris will hold his regularly
scheduled TA sessions but the rooms will vary:
Tuesday, December 15, 4:00
PM  5:00 PM PK 349 M
Wednesday, December 16, 7:00
PM  9:00 PM PK 336 M
Thursday, December 17, 3:00
PM  4:30 PM PK 349 M
Class Review Session: Saturday Dec 12 from 10 am – 12pm. Room
349.
We will first brainstorm together to
create the list of topics. Then we will go over specific questions and
problems.
Student run Review Session: Monday Dec. 14 at
1pm in Rm. 349. Come and work with your classmates to prepare for the exam.
I encourage you to use the Review Template Sheet in
preparing for the exam.
Basic Information for Final Exam:
The final exam is a takehome exam. It
will be handed out in class on Wednesday. You may do the exam whenever you
choose during the exam period. It is a three hour exam and it is closed book 
except you will be able to write notes on one side of a 3 inch x 5 inch index
card. No other outside materials such as books or notes are allowed. You may have a calculator for the exam.
You may take the exam in any location you choose; of course it should be a
place where you will not be disturbed while taking the exam.
When you are done, immediately return
the exam to Professor Donnay's office. If he is not in, put the exam under his
door. Sign the sheet outside his door to indicate that you have returned the
exam.
Topics for the Exam: Most of the exam will be
on material since the last exam. That includes:
Compactness Ch. 9
Existence of Maximum and Minimum Ch. 10
Connected and Disconnected Sets and the Intermediate Value
Theorem Ch. 12.
Part of the exam will be cumulative so
there will also be some questions from material that we covered earlier in the
semester.
On Final Exam, there will be a question
on proof by induction. I will also ask you to outline the proof of one of the
following two important theorems: The Max – Min Theorem or the
Intermediate Value Theorem. In giving the proof, you should quote other results
(theorems and propositions that we have proved in class). For example, as part
of the IV Theorem proof, we use the f([a,b]) is connected
which is true because f(connected set)
is connected. You do not have to prove that f(connected) is connected; you can
just state this as a result that we have proven. But you should state clearly
what results you are using.
Midterm 2 Test:
Advice
for reviewing for the midterm in terms of Key Concepts and a template for
reviewing for the test. List of key concepts and
then a more detailed list of topics. List
of proofs that you will be responsible for on the exam. Instructions
for the exam (if you did not yet sign this instruction sheet, do so and
return to Prof Donnay on Wed).
Feedback on Exam 2 and instructions for test
redo.
Math Enrichment Component:
BiCo Noyce Teacher
Scholarship KickOff Event: Tuesday Dec 1 at 7 – 8:30
ÒMath and Science Education:
Social Justice, Triumphs and ChallengesÓ
Room H109 of HaverfordÕs
Koshland Integrated National Sciences Center. The program will feature a panel
of Bryn Mawr and Haverford alumni who majored in STEM disciplines and went on
to careers in science education. If you would like to have dinner in the
Haverford dinning hall with the speakers from 5:30 – 6:30pm, please email
Kim Lipetz at klipetz@brynmawr.edu. You
can use the dinner as one of your enrichment events.
Alternatives: If you have not
succeeded in attending two talks during the semester, you can do short papers
about famous math people who are connected to our Real Analysis course (Ex.
Cantor, Cauchy, Weierstrass, Bolzano, Heine, Borel, etc).
Math Move – to be
announced.
Reserve Books: I have put a
number of analysis books on reserve for our course in Collier Science Library. My
top recommendations from the ones there are:
Elementary Analysis: The Theory of Calculus by Kenneth A.
Ross.
Fundamental Ideas of Analysis
by Michael Reed
Methods of Real Analysis by
Richard Goldberg
Introduction to Real Analysis
by Bartle and Sherbert.
I have also put copies of the
textbook from the Transitions course on reserve: Reading, Writing and Proving
by Daepp and Gorkin.
It can be useful to see how
other authors discuss the same material. Sometimes they will explain it
differently and in a way that makes more sense or that goes into more detail
than our textbook.
There is a copy of Calculus
by Steward, edition 6E, on reserve.
Midterm 1 Preparation: Use
our weekly review lists as a guide to what material we have covered. For
Monday, go over those lists and put a star next to the topics you think are
most likely to be on the test – knowing that I could ask questions on any
topic that we have covered.
By 9pm on Sunday night, please email me if there is a specific topic you
would like me to review. We will do review in class on Monday. For MondayÕs
class, make up a problem that is similar to what you think might be on the exam
and include an answer key for the problem. A good strategy is to pick a type of
problem you have been having trouble with. I will go over your answer and give
you feedback on it.
Also, rather than office
hours on Monday afternoon, I will hold a review session on Monday evening from
7:30 – 9:30 pm. I will post answer keys for this past weekÕs Wed and
Friday hw so you can review your hw more quickly. The hw will be returned by
MondayÕs class.
The exam is selfscheduled. I
will have it available on Monday. You may take it any time before FridayÕs
class. You will have 3 hours and will need to take the test in the science
library.
Schedule Summary: Mondays – quiz corrections due.
Hand in old quiz together with corrections (explain your previous mistake and
explain what the correct answer is). New quiz is due at 4pm.
Wednesdays
– hw due.
Fridays
– hw due and one hw correction from previous weekÕs hw is due.
After HW corrections are
handed in, I will post a HW Answer Key in Blackboard under Course Documents.
Do you not use the Answer Key
if you are still working on hw corrections.
Copies of the old quizzes and
quiz review sheets are attached below.
Weekly Quiz: The quiz will be
available on the shelf outside my office (Rm. 330), starting at 5 pm Friday.
When you are ready to take the quiz, pick up a copy and go directly to Collier
Science Library and do the quiz. You will have 20 minutes. You may use a
calculator. You may not use any books or notes. When you are done with the
quiz, immediately return the quiz to my office: you can slide the quiz under y
door. When you return the quiz, check off your name on the class list. The
quizzes will typically have a mixture of true/false questions and short answers
related to the topics listed on the weekly review sheet.
The quiz must be completed
and returned to my office by 4pm on Monday.
Quiz Redo Policy: If you have
made any mistakes on the quiz, you will have the opportunity to correct the
mistakes, hand in your corrections and improve your score on the quiz.
Procedure: For each problem
you got wrong, write an explanation of what you did wrong and what is the
correct way to do the problem. Hand in these corrections, stapled to your
original test paper, by the start of class on the following Monday. If your
write up correctly answers the question, you will be credited with a correct
answer and your quiz score will be adjusted.
Quiz Materials: the weekly quiz review
sheets and copies of the quizzes.
Homework Grading Policy:
The homework makes up 15% of
your grade. 10% of this total will be awarded for effort. Each homework problem
is scored either 3 (= demonstrates mastery of the material), 2 ( = developing;
shows some mastery but not yet complete), 1 ( = made an effort but not yet able
to do the problem), 0 ( = not attempted).
You will receive full credit
for effort on each problem for which your score is 3, 2 or 1. You will not
receive credit for effort on problems that are scored a 0. The percentage of
homework problems that receive effort credit will be translated into a score
out of 10 at the end of the semester.
5% of your homework grade
will be awarded for demonstrating mastery of the material and will be determined
by your scores on the homework.
Late Homework: Twice during the semester you may hand
in homework late without any penalty.
You have up to one week after the homework is due to hand it in. After
you have used up your quota of late homeworks, additional late homeworks will
be assessed a penalty: 25% deduction if one class late, 50% deduction if two
classes late, 75% deduction if 3 classes (one week) late; not accepted after
one week.