A description of course policies for 67-467/667 Spring 2006.
Instructor: Dr. Jayanthi Ganapathy
Office: Swart 216.
Telephone: 424 7355 (my office). 424 1333 (the math dept. office). 235 2435 (home).
E-mail: ganapath<at>uwosh.edu (office); ganapath<at>northnet.net (home).
Office hours: MWF 11:30 AM – 1:00 PM. Appointments are available at other times, if absolutely necessary.
Text (required): A Friendly Introduction to Real Analysis Single and Multivariable, second edition by Witold A. J. Kosmala. (Publishers: Pearson/Prentice Hall)
Topics covered
Chapters 1- 7. If time permits, chapter 8. Chapter 1 only a quick review.
Supplements
(required): Notes to accompany…. by Dr. Jayanthi Ganapathy (the Tan Book).
Reference books available at the Mathematics Section of the POLk library:
- An accompaniment to Higher Mathematics by George Exner.
- Proof, Logic and Conjecture by Robert S. Wolf.
- Mathematical Thinking: Problem Solving and Proofs by John P. D’Angelo and Douglas B. West.
- Introduction to Real Analysis, second edition, by Robert G. Bartle and Donald R. Sherbert.
The Polk Library’s mathematics collection includes numerous books on Advanced Calculus and introductory and elementary Real Analysis. Be sure to take a look at some of them.
Objectives
- Deeper understanding of the theory behind the major Calculus concepts: limits of functions and continuity, sequences and series, differentiation and integration.
- Leaning a few new concepts, and in some cases the theory behind some of them. For example, convergence and divergence of sequences, Cauchy sequences and subsequences.
- Problem solving: Learning to identify what is given (assumptions or hypotheses) and what needs to be proved (conclusions). Learning to think of possible ways the conclusions can be proved using the hypotheses, either by employing definitions or pre-established results related to the conclusions in the problem, and roughly ‘mapping out' a strategy that will lead one from the hypotheses to the conclusions.
- Absorbing certain frequently used proof techniques and recognizing situations where such techniques could be successfully employed to prove results; understanding the standard types of proof techniques, such as, mathematical induction, direct proof, proof by contradiction, and recognizing when to use which.
- Understanding how to prove equivalent statements, and necessary and sufficient conditions (if and only if statements).
- Learning the basics of proof writing: progress from disconnected ideas that crudely constitute the proof of a given statement that one initially develops by working on a given problem, and then by trial and error and a series of writing and rewriting exercises arrive at a smooth, easy to follow, connected, mathematically accurate proof. This may involve initially working ‘backwards' some times and then rearranging and reorganizing. A finished proof should not start assuming the conclusion and then proceed to ‘verify' the hypotheses.
- Learning to communicate abstract mathematical ideas and thoughts through mathematical logic and reasoning.
Tests, homework and grades
During the semester, there will be three tests, and several homework assignments, on mostly problems selected from the attached assignment sheet. The test scores together will contribute 150 points, and together the scores on the homework assignments will contribute 100 points to the course point total at the end of the semester. The letter-grade scheme, based on your percentage total (PT) at the end of the semester is as below:
A 225 (90 %) PT 250 (100 %)
AB 212.5 (85 %) PT < 225 (90 %)
B 200 (80 %) PT < 212.5 (85 %)
BC 187.5 (75 %) PT < 200 (80 %)
C 175 (70 % ) PT < 187.5 (75 %)
CD 162.5 (65 %) PT < 175 (70%)
D 150 (60 %) PT < 162.5 (65 %)
F 0 ( 0 % ) PT < 150 (60 %)
No test or homework grade will be dropped.
I do not grade on a curve (Translation: no artificial inflation/deflation of individual grades based on the whole class performance).
Class attendance
Class attendance will be used in the following way: You must not miss more than three one and one half hour class periods for the entire Spring semester 2006. For every class period over three that you miss, your grade for the course at the end of the semester will be reduced by one letter grade (for example, B will become BC for the fourth absence).
Only staying the whole period is counted as one full class attendance. If you have a good reason to be late once in a while or to leave class early, you must discuss your reasons with me ahead of time whenever possible, or before leaving the class. I generally take attendance in the beginning of the period. If you happen to not be here until after I have taken attendance on any given day, it is your responsibility to stop at my desk before leaving class to make sure I have recorded your presence that day. According to the student handbook, attendance is required unless the individual instructor announces a policy that contradicts that. Thus the policy that I have stated above regarding the impact of and expectations related to attendance is perfectly within my rights as an instructor. Please make sure you understand this policy clearly, and stay in my class only if you are able to abide by it.
Class participation
The level of your class participation is likely to play a significant role in my decisions related to ‘borderline’ cases, when determining the letter grades at the end of the semester.
What I expect from you and what I will offer
A strong background in Introduction to Abstract Mathematics (67-222, with a grade of C or better, is a pre-requisite for this course) will be assumed. In particular, you must be able to read and feel comfortable filling in missing details as is often required for readers of abstract material, specifically proofs in mathematics. You must be able to use logic and reasoning to sort out information, make observations, draw conclusions, and finally write a smooth flowing connected proof. You must have familiarity with writing proofs to a certain extent. Having completed one or more courses such as 67-342/542 and 67-346/546 in which proof writing is generally emphasized is certainly a plus but not a requirement. Please review the 67-222 material, particularly the material that covered the concepts that are reviewed in our text in chapter 1 (for example, material on sets and functions including notations).
The Tan book I have referred to on the opening page is a supplemental collection of notes I have written and have copies made available (only) at the University Books And More. It contains detailed solutions to problems most of which are selected from the book. The Tan book also contains thought-provoking questions, and missing details in some of the solutions, which you are expected to fill in yourself. The last few pages of the Tan book have solution hints to many exercises listed in the ‘assigned problems’ document posted on d2l. The text itself has hints/answers to many exercises. The hints and/or answers included in the Tan book are for mostly only those assigned problems for which the text does not offer help. Make it a habit to read the textbook before and after any given topic is covered in class, and read the Tan book as well. You must do the assigned problems as soon as I have started to do examples in class from any section in the textbook. Keeping up with homework will be helpful not only in understanding the concepts more clearly but also with assignments that you will be asked to turn in at relatively short notice. This is an important activity to help you acquire the skill needed for the successful completion of the course. Typically in class, I will cover the needed theory to illustrate new concepts, and go over some of the solutions found in the Tan book. You will be expected to read the rest of the solutions in the Tan book out-of-class. For those solutions that I do not go over in class, you are expected to initiate questions and discussions if you do not understand any part of what you read, or if you have any comments related to them that you wish to bring up in class. It is also likely (I hope!) that you will be asked to do problems in class either on your own or preferably in groups. By engaging in the type of learning activities described above, it is expected that you will gain the knowledge and understanding that is needed to succeed in this course. You then apply the knowledge you have thus gained to solve the problems on the tests.
When it comes to style of teaching, you might find that the percentage of class time I spend on lecturing is more (or may be less, for some of you) than what you are used to previously. However I do expect a considerable level of student involvement through asking and answering questions, and possibly through in-class group work. If you are some one who might have difficulty staying focused and listening, I am afraid my class is not a good fit for you. Please be aware of that, and be willing to make the necessary adjustments before it is too late.
What you should know about tests
The tests are highly likely to be scheduled out-of-class at the Testing Center. This is because I seriously doubt you would want to have in-class exams that will allow you only one hour and a half to work on problems. Please talk to me if this is likely to present a problem especially due to your schedule and the Testing Center hours that never extend beyond 6 PM. Though it may happen at times, I do not believe in testing whether you can re- solve the very same problems you might have seen before in class or homework with very little change. If you have such expectations I am afraid my class is not a good fit for you. Generally on the tests, you must not expect problems that only require you to simply mimic and regurgitate solutions you saw on the homework or in class. I expect you to understand the concept and then apply what you have learned to solve problems.
Anticipated pace of topic coverage and out-of-class help
There are 25 sections to cover after a quick review of important ideas from chapter 1 that we might need at various times in the next six chapters. This means I will have to move at a pace that may be too fast for some (and possibly too slow for yet others!). You need to learn to deal with this situation, and not find it a source of irritation. I hope to cover about one chapter per week setting aside time for occasional review and time for additional discussion of difficult material. Mathematics is not a subject one can learn by listening to a teacher for three or four hours a week. Most of your learning takes place out of class, and it is my hope that you don’t underestimate the importance of getting out of class help. I am in a much better position to give you the kind of ‘customized’ instruction to you individually in my office than in the classroom during regular class period. Unfortunately this is not the way I want it given the time pressure you are under but this is the reality and we all have to do our share to make it work to our advantage. Thus it is important you come in for help when you have questions. Please make it a habit to read the textbook and the Tan book before and after any given topic is covered in class. It is very important to keep up with the material, and not fall behind. Come in to see me in my office during the scheduled office hours, if you have trouble understanding anything. I would also be willing to give out of class review sessions at your request whenever you feel you would like to have one, provided there is a fair number of students who want it.
Nature of course material
This is a course in which abstract material is the norm, though there are several instances in which you will be doing some computational work as you did in Calculus. Proofs are not an exception as they have probably been in most of the courses you have taken so far. Proofs will be done pretty much everyday. Very few applications if any will be covered. This is a branch of pure mathematics. Though it has applications, the primary focus will be on teaching the underlying mathematical principles and importantly gaining strength in mathematical reasoning and communication of abstract mathematical thoughts. I strongly urge you to understand that, and learn to live with it.
Essentially we will be covering the principles related to sequences, limits and convergence/divergence of sequences, subsequences, limits of functions, continuity and uniform continuity of functions, differentiation and integration, and infinite series including tests for convergence/divergence. If time permits, we will study sequences and series of functions including pointwise and uniform convergence of such sequences and series.
More on out-of-class help
Though the math department office (Swart 115) usually maintains a list of private tutors for various courses offered by the mathematics department, I have my doubts about whether there would be anyone to tutor for this course. In any case, if you would like to hire a tutor or would like to be a tutor who would like to add your name to the list, then you might find it worthwhile to pay a visit to the math department office.
The University counseling center offers assistance and advice on various course-related issues such as test anxiety, math anxiety, time management, preparing for tests in general, and many other issues. The center is located in Dempsey 201 (phone: 2061). Please do not hesitate to visit the center and familiarize yourself with the various free services the center offers.
If you would like to be added to a list of students who wish to find out-of-class study partners, and are also interested in knowing how to contact other such students in this class, please see me soon. I will have you add your name, schedule and contact information to a list (the out-of-class study partner list) a copy of which will then be made available to every student included in the list.
Classroom behaviour
Proper student behavior is expected in my classroom. This means that unnecessary and disruptive non-course related talking, laughing, sleeping and doing anything other than reading and discussing the course material when the class is in progress will not be tolerated. If you are in the habit of falling asleep in class, please expect to be called on! If you think you might fall asleep in class due to having had a particularly restless night before class, or due to some medical reason, you must talk to me before the period or before leaving class. I do not have much patience for students sleeping in class. I will not hesitate to take whatever action is necessary to control discipline problems of any sort.
There is likely to be a wide range of abilities in the class. Those of you who are very good at grasping mathematics quickly might find the class too slow or not adequately challenging for you. I suggest that you get involved by helping others in the class or by answering questions in class, if you plan to stay on in my class. If this material is too elementary for you and you feel you are wasting your time, unless you can find a way to meet this requirement without taking this class, I suggest you stay involved as I have suggested above or ask me for challenging projects. Tuning me out or doing such disrespectful things as playing with your calculator or cell phone or reading when you should be listening or when you should be doing the work I ask you to do are unacceptable. Sleeping or doing work other than what is being done in class or any such disrespectful behavior is unacceptable as well.
As harsh as all this sounds, I do encourage a relaxed, friendly and unintimidating class room environment that will allow students to freely participate in the instructional process. Your attitude and demeanor towards your fellow students and me will to a large extent determine the kind of atmosphere we have in the class.
Miscellaneous
Please bear in mind that the teacher is only partly responsible for how you do in the course. The larger portion of the responsibility for your success or failure lies in how well you handle individual problems and how willing you are to seek help, and work at your problems. I would like to see every one of you do well and learn well, and I am willing to do my very best to help you learn. The rest is up to you.
There will be no make-up tests. If you have to miss a test or homework submission deadline due to extra-ordinary circumstances, please inform me ahead of me if at all possible (make use of the extensive contact information found on page 1) so alternate arrangements could be made if absolutely necessary.
I am likely to be using e-mail and the Desire to Learn (d2l) site that has already been set-up for my Advanced Calculus class to communicate with you. In addition to syllabus and homework I have also posted on d2l a document that describes the objectives of the course. Please make it a habit to check your e-mail, and the d2l site (www.uwosh.edu/d2l). If you need help navigating through the d2l site, please stop by my office.
The policies stated in this document are subject to change. But I will try my best to stick with the policies as stated here.
I wish you a successful and enjoyable semester. Please feel free to come and talk to me if I can be of any help. But please do not wait until it is too late for me to help you.