MATH 301: Real Analysis I

Mathematics Department, Bryn Mawr College, Fall 2011

Professor: Victor Donnay	Lecture: MW 11:30 – 1 pm TTh 8:15 – 9:45 am Rm. 336
Office: Park Science Building #330
Phone: 526-5352, E-mail: vdonnay@brynmawr.edu	Office Hours: tba

Course TA: Frank Romascavage, Rm. 436 Park,

Email: fromascava@brynmawr.edu, Phone: ext 526-7482

Pre-requisites: The pre-requisite for the course is Math 201 (Multi-variable calculus). Math 203 (Linear Algebra) and Math 206 (Transitions) are strongly recommended. We will be studying material that you (might) have seen in Calculus (Math 101, 102 and 201). In those courses, the focus was on how to do various types of problems. In Real Analysis, the focus is on understanding the underlying ideas of calculus using formal mathematical reasoning.

Texts: Real Analysis, by Frank Morgan. We will cover chapters 1- 16.

Course Web Site: accessible from Prof. Donnay's homepage,

Materials for the course will be found primarily on the web site; some materials will be posted on the course Blackboard site.

TA: There will be regular TA sessions for the course. My expectation is that you will attend the TA sessions regularly. The problems I assign are challenging and I do not expect students to be able to complete all the homework unless they attend the TA sessions.

Learning Goals of the Course: In this course, you will:

Learn to communicate your mathematical reasoning in writing and verbally, both via informal arguments and via more formal proofs.

Develop your ability to work as an independent and self-sufficient learner:

What to do when you do not know what to do

How to take what you have learned in one situation and apply it to a new and different situation (transfer of knowledge)

Get comfortable with not knowing the answer immediately

Learn material we have not covered in class by reading the book and applying this newly learned information to solve problems.

Decide for yourself whether you understand material and learn how to ask yourself questions to check your understanding.

Become part of a community of learners who support, encourage and learn from one another.

Learn the key concepts of calculus including:

- limit of a sequence,

- open and closed sets,

- continuity of a function,

- conditions which insure the existence of a maximum (or minimum) of a function,

- derivative and integral of a function.

You will demonstrate your mastery of this material by:

- knowing the definitions of these key concepts and the statements of the main theorems associated with them,

- giving examples which illustrate these definitions and theorems,

- giving rigorous mathematical proofs employing these concepts.

Exams:

There will be two mid-term exams and a final exam. These exams are all self-scheduled. The tentative schedule for the Mid-term exams is:

Mid-term 1 in the 5^th or 6^th week (Sept 26-30^th or Oct. 3-7^th).

Mid-term 2 in the 10^th or 11^th week (Nov. 7-11^th or 14-18^th).

Homework:

Homework will be assigned each week. Part of the homework will be due the following Monday (Tuesday) (the basics) and part will be due the following Wednesday (Thursday) (more advanced). You are allowed two late homework assignments without penalty. Late homework must be turned in no later than the next class. After your two late homework assignments, any late homework will be assessed a penalty. You are not allowed to look at any posted solutions until you have handed in your homework.

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.

The best way to learn mathematics is by doing. At this level of more theoretical mathematics, problems can take a lot of thought and experimentation to complete. Part of the goal of the course is to help you develop strategies to attack these hard problems (draw pictures, make simpler mini-problems, read the text very carefully, discuss with your classmates).

Much learning happens by trying, doing as much and as well as you can, then getting feedback and trying again. So each week you will be asked to revise one HW problem from the previous assignment (if there is a problem you have not mastered) and resubmit.

Quizzes: There will be a short quiz each week. It will be due on Mondays (Tuesdays) at 5pm and will cover the basic material that we have covered in the previous week. The quizzes will be assessed Mastery (M), Developing (D), Not Yet (NY). If you do not demonstrate mastery on the first try, you can redo. The goal is for you to learn the material. Persistent is a key trait for success in all endeavors; if you are willing to keep working at it, I am pleased to support and encourage your efforts.

Math Culture Requirement: Students will attend two math talks over the course of the semester and write a one-page reaction paper for each talk. There are many aspects to mathematics; attending these talks will give you opportunity to learn about these opportunities. The first talk must be done by Friday Nov 4^th. The paper must be handed in within one week of the talk.

Options Include:

a. Weekly Math Colloquium, Monday at 4pm, that alternates between Bryn Mawr and Haverford.

b. The Distressing Math Collective, Thur 7pm, Park 328.

Classroom:

During class, there will be a mixture of lecturing by the professor and time spent by the students working out problems, discussing their results in groups and having whole class discussions. Research has shown that this type of active participation leads to improved learning.

We will occasionally use Mathematica during class time, but no previous Mathematica experience is assumed.

The group work does not go well when members of the group are absent. Therefore it is important that you attend to class. Please be respectful of your fellow students. If you decide to take this course, you must commit to attending class regularly.

Final grades will be determined using the following percentages:

Homework, Quizzes, Class participation	20%
Midterm 1	22.5%
Midterm 2	22.5%
Final Exam	35%
Total	100%