MATH 301: Real Analysis II

Mathematics Department, Bryn Mawr College, Fall 2009


Professor: Victor Donnay

Lecture: Mon, Wed, Fri  9-10 or 11- 12  Rm. 336

Office: Park Science Building #330


Phone: 526-5352, E-mail: vdonnay

Office Hours:




TA Sessions: Tuesday 4 – 5pm, Wednesday 7:30 – 9 pm, Thursday  3 – 4:30pm all in Rm. 336 with Chris Micklewright, We have reserved Rm. 336 starting a half-hour before the TA session and continuing for a half-hour after the TA session so you can keep working on your hw there with your classmates.



Course "Play-by-Play". 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 Micklewright’s mailbox in the math lounge.

You may hand in a final quiz redo by 5pm Thursday too; put that under Prof. Donnay’s 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 take-home 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:

Bi-Co Noyce Teacher Scholarship Kick-Off Event: Tuesday Dec 1 at 7 – 8:30  

“Math and Science Education: Social Justice, Triumphs and Challenges”

Room H109 of Haverford’s 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 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 Monday’s 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 week’s Wed and Friday hw so you can review your hw more quickly. The hw will be returned by Monday’s class.

The exam is self-scheduled. I will have it available on Monday. You may take it any time before Friday’s 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 week’s 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.