MA415-50, Fall 2011

Real Analysis

Course ObjectivesBeginning with an examination of the real numbers, this course examines in depth the concepts and theorems behind calculus.  This includes sequences, limits, continuity, differentiation and integration.  This is a writing intensive course, and involves at least 15 pages of writing that can be revised if needed.

Class Schedule:  Tuesday, Thursday 6 – 7:15 p.m., Howard Hall 211

Instructor:  B. Gold

Office Location:  HH 247

Office Telephone:  (732) 571-4451

E-mail Address:  bgold@monmouth.edu

Office Hours:  Monday 2:30 – 3:30, Tuesday 4:30 – 5:30, Wednesday 1-2, Thursday 3:30 – 4:30, or by appointment or chance.

Required Texts:  Kenneth Ross, Elementary Analysis:  the Theory of Calculus

Course Requirements:  Pre-class reading questions (on e-campus due by 3 p.m. of the day we first work on that section), homework assignments, written presentations (submitted to the e-campus dropbox, using Word’s Equation Editor), in-class group work, definitions quizzes, weekly true-false questions (TFQ on schedule), three in-class examinations, cumulative final examination.  SINCE THIS IS A WRITING INTENSIVE COURSE, YOU CANNOT PASS THIS COURSE UNLESS ALL FIVE WRITTEN PRESENTATIONS HAVE RECEIVED A SATISFACTORY GRADE.

Methods of Evaluation and Grading Policy:  The grade comes 3% from pre-class e-campus reading questions, 2% from in-class activities, 10% from homework, 30% from written presentations, 4% from definitions quizzes, 6% from TFQs, 10% from each in-class exam, and 15% from the final exam.  However, if you fail to submit any of the written presentations, you will get an incomplete in the course, which will change to an F if still not submitted by the end of the following semester.

On a scale of 0 to 100, grades of:

     A and A- will be assigned to scores of 90 and above

     B+, B and B- will be assigned to scores between 80 and 90

     C+, C and C- will be assigned to scores between 65 and 80

     D+, D and D- will be assigned to scores between 50 and 65

     F will be assigned to scores below 50.

Attendance Requirement:  This course is the culmination of your theoretical work in mathematics at Monmouth.  As a result, you will be really stretched to your maximum capabilities learning the concepts, important examples, and methods of proof.  Class participation is essential for learning this material.  Therefore, attendance is required except for medical or other normally excused reasons.

Last date to Withdraw with automatic assignment of “W” grade:  November 8, 2011.

 Statement on Academic Honesty:  You may work in groups of no more than 3 on figuring out homework, but even then you must write up your homework in your own words.  Groups may not discuss the homework at all with other groups - come see me or e-mail me if you need a hint.  No “whole class” homework!  For the reading questions, true-false questions, and the five written presentations, you must work entirely on your own.  If I get two papers that are similar, I will give both students a 0 for that presentation, and for the second such incident, will report it to the University Disciplinary Committee.

Examination Rules:  No student is permitted to have at his or her desk any books or papers that are not given out or expressly permitted by the instructor.  Possession of such material will be regarded as evidence of intent to use the information dishonestly.  No communication between students during the examination is permitted.  If there are questions, or if there is a need for additional material, the instructor should be asked.  In accordance with the academic honesty policy of Monmouth University each exam will contain the following pledge:

“I, ____________________________, certify that I have read the above rules for examinations, and that I have abided by them. By signing, I affirm that I have neither given nor received aid during this examination, and I understand that violation of this affirmation may result in suspension or expulsion from Monmouth University.”

Statement on Special Accommodations:  Students with disabilities who need special accommodations for this class are encouraged to meet with me or the appropriate disability service provider on campus as soon as possible.  In order to receive accommodations, students must be registered with the appropriate disability service provider on campus as set forth in the student handbook and must follow the University procedure for self-disclosure, which is stated in the University Guide to Services and Accommodations for Students with Disabilities.  Students will not be afforded any special accommodations for academic work completed prior to the disclosure of the disability, nor will they be afforded any special accommodations prior to the completion of the documentation process with the appropriate disability office.

Tentative Schedule (may be changed during the course of the semester):

Date

Section

Homework assignment (due the following class)

9/6

§1 - §3

2.2, 2.3, 3.2, 3.4, 3.6; and e-campus reading “quiz” on §4

9/8

§4

4.1 - 4.4 parts bdhijklnprsv; TFQ

 

 

 

9/13

§4

4.6, 4.10, and written presentation 1 (to e-campus dropbox)

9/15

§5, §7

5.2, 5.3, 7.1, 7.2, 7.3bdfhjnt, 7.4; TFQ

 

 

 

9/20

§8

8.2abc, and show lim(-1)n(n+1)/n does not exist.

9/22

§8

8.10 and written presentation 2; TFQ

 

 

 

9/27

§9

9.1bc, 9.2

9/29

§9

9.8, 9.10bc, 9.16a (due 10/6); TFQ

 

 

 

10/4

Exam 1

(through §8)

10/6

§10

10.10 and e-campus problems; written presentation 3

 

 

 

10/11

§10

10.6a and prove that sn = n/(2n+1)  is a Cauchy sequence

10/13

§11

11.2, 11.4; TFQ

 

 

 

10/18

§11

Problems assigned on e-campus

10/20

§17

17.4, 17.6, 17.10a, and problem on e-campus; TFQ

 

 

 

10/25

§17

Written presentation 4

10/27

§18

18.2, 18.6; TFQ

 

 

 

11/1

§20

20.2, 20.6, 20.11b, 20.12 (due 11/8)

11/3

Exam 2

(through §17); TFQ

 

 

 

11/8

§28

28.2ad, 28.4, 28.8

11/10

§28 and §29

29.1bdf, 29.2, 29.6; TFQ

 

 

 

11/15

§29

Written presentation 5

11/17

§32

e-campus problems; TFQ

 

 

 

11/22

 §32

 32.2, and for f (x) = x3 on the interval [0,b] (follow example 1)

11/24

Thanksgiving

break (Friday classes meet on this Wednesday; so we don’t)

 

 

 

11/29

§19, §33

19.1bd, 19.2ab

12/1

§33

33.8a and e-campus problems; TFQ

 

 

 

12/6

Exam 3

(through §32)

12/8

§34

34.2b, 34.4 (this is ONE function, not three; sketch it first!); TFQ

 

 

 

12/13

§34

 

 Notes to Students:  You are expected to read the section for the day prior to class, and, when it’s the first day on that section, reply to reading questions in the “Quizzes” section of e-campus.  Homework from that section is due at the following class, unless I specify that some may be postponed one period.  Rewrites are due the class after they're returned to you.  I’ve assigned very few problems which have answers at the back of the text; however, usually looking at one just before or just after the one assigned, and how the book did it, will often help.

Weekly true-false questions will be posted on e-campus.  This is part of the writing-intensive part of the course.  For each, you’re to decide whether it is true or false, and then show this, either with a proof (if it’s true) or a counter-example (if it’s false).  The purpose of these questions is to summarize important properties we’ve been studying.  Occasionally it will take a somewhat different form, in which case specific directions will be provided.