Welcome to Math 32L with Clark Bray


Instructor

Clark Bray, 022 Physics Building, 660-2822, cbray@math.duke.edu
Office hours: Wednesdays, 1:00-3:00pm

Links

Math 32L Course Homepage  -- This page contains much of the information for the 31L course, including the course syllabus (I recommend printing the syllabus and posting it in a convenient place) and textbook information. 

Math Information for First-Year Students -- This page has many useful links; make sure to familiarize yourself with it.

Blackboard -- There are TWO Blackboard sites containing information relevant to students in this class.  One is for all students enrolled in 32L, containing study materials and information about the course.  The other is only for students enrolled in my classes; this will only be used for recording and reporting grades.  Your grades will be (securely) posted there so that you can know your grades as quickly as possible, and so that you can verify that they have been recorded correctly.

Sample Lab Report -- Here is an example of what I would like to see on the lab reports.  Note the level of rigor, the readability, and the use of both equations and verbal explanations. 

Solutions to Lab Quiz, Integrating to Infinity

Solutions to Lab Quiz, Normal Data Sets

Exam 1 Solutions

Exam 2 Solutions

Exam 3 Solutions

Notes on Present and Future Values, and Continuous Money Streams -- These are notes that I wrote several years ago in a class similar to this one.  It is important to note however that that class was not part of a "block" course, and so I was free to introduce some nonstandard notations that you will not see on the final exam for this current course.  I do recommend that all students read this material since I feel it is a clear exposition of the ideas you need to understand for this course -- but make sure to be aware of the difference in notation before taking the final exam in this course.

Values of Sine and Cosine at Standard Angles -- All students are strongly advised to know the values of the six trig functions at the standard angles (all multiples of pi/4 and pi/6); this short commentary and the linked diagram will help you both remember these values, and understand the fundamental relationship between trigonometry and the unit circle.

The Remainder Theorem and the Factor Theorem -- These are fundamental facts about polynomial algebra, and they are simply stated and easy to prove; but for some reason they are not covered in most high school curricula any more.  I strongly encourage students to look at this brief description and ensure an understanding of these theorems and their proofs.  (But don't worry about the example on the second page.)

The Most Common Errors In Undergraduate Mathematics -- This is a collection of common errors that befall many students; you may find that reading this will help you avoid errors on exams in the future.

Additional Practice Problems for Differential Equations -- These were supplemental problems in my Math 31L class last semester.  I encourage students to give these a look to make sure that you can understand how to solve them.  (Make sure you comfortably understand problems 1-3 before you move on to the challenge problem!)

Labs

In this course you will attend weekly labs.  These labs serve to help you learn the material in a more interactive way.  You will work in groups of three or four (determined by me), doing a series of exercises and problems as a team.  I will be there with a lab assistant to introduce the lab, and help you along if you have trouble. 

For some labs, students will be required to do a lab report; for others, there will be a lab quiz. 

Lab reports must be prepared as a group by all of the members of the lab team within one week of the performance of the lab.  I will give you instructions indicating what I expect the reports to include.  These reports will be graded.

Lab quizzes will be taken in lab the following week, to make sure that all students have enough time to study the material.

Students should make note of the fact that in addition to being graded themselves, the material from the labs will make up approximately one fourth of the final exam for this course.


Lab Report Instructions

Here you will find the lab report instructions for those labs with reports, in the cases where I do not give such instructions during the lab period:

Pollution Lab Report Form

Present Value / Future Value Lab Report Form

Homework

Homework problems are assigned for every lecture, and students should ideally complete each assignment on the day of the lecture.

Make sure you staple your homeworks!  We cannot give credit to students for work that was lost as a result of not being stapled.  Also, make sure to put at the top of the front page your name, the section number(s) for those problems, and the course information (Math 32L, Clark Bray)

In order to give flexibility to students, the assignments for the previous three lectures will be picked up in class every Friday at the beginning of class, and will be graded and returned as soon as possible. 

No late homework will be accepted. 

In calculating homework grades, the lowest of your homework scores will be dropped.  The purpose of this policy is to handle exceptional circumstances such as a serious illness.  Please do not request to have late homework accepted.  Also, it is inadvisable to skip a homework unless absolutely necessary, since only one homework will be dropped.

Working together in groups on homeworks is strongly encouraged!   You will find that the people you are working with either (1) understand something you don't, in which case they can explain it to you; (2) understand something that you do understand, but from a different point of view -- these additional perspectives can prove to be very useful; or (3), don't understand something that you do understand -- in which case you have the opportunity to explain it to them...  I think you will find that in the process of explaining something, very often you will achieve a better understanding yourself.

Of course, it goes without saying that even though you may work in groups, the homeworks you turn in must be your own work.   You may share ideas, perspectives, approaches to problems, but copying is not allowed.  Furthermore, keep in mind that the homeworks are primarily a learning tool, and count for a fairly low percentage of your grade.  Do not deprive yourself of this invaluable learning opportunity!




Grading and Exams

Final grades for the class will be determined by the total number of points earned in the class.  These points are given based on performance on the items below, with the following maximum possible scores:

Eight Labs (report or quiz):        240 possible points (8 labs x 30 points each)
Homework average:   60 possible points
Tests:                           300 possible points (3 exams x 100 points each)
Final Exam:                 200 possible points
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Total:                            800 possible points


The student should be prepared for the fact that the grading system for these exams is NOT the same as the one most students became accustomed to in high school. There are two main properties in particular of the high school system that will not be used in this class :

1) In most high school grading systems, there are fixed, arbitrary numbers that determine the cutoffs between different letter grades -- these cutoffs were invariant, and independent of the exam. The problem with this that it forces the instructor to create exams that are always the same difficulty; in other words, the instructor must make sure that all exams will yield the same mean score. Furthermore, it requires that the distribution of scores also be roughly constant. Achieving both of these goals is not only difficult, but impossible to perform perfectly.

This system ties the instructor's hands severely, and is totally unnecessary! Of course it is important that final letter grades for a class follow a prescribed plan, so that those letter grades have some meaning outside of the context of that class. Ensuring that is actually easier if the instructor chooses the cutoff numbers after having seen the distribution of student scores. The cutoffs can then be chosen while incorporating important considerations such as the difficulty of the exam, or any other points about the exam that may be relevant.

2) The class average on exams in most high schools was usually expected to be somewhere in the mid-eighties. While this is reasonable considering the nature of high school, it is not always appropriate for a college setting.

In this class, certainly, there are expectations for the student that are much more demanding than those of most high schools. We expect that the student will achieve much more than the mere ability to reproduce what he or she has seen in class. In particular, we expect that the student will achieve an understanding of the ideas that are at the foundation of the methods -- and thereby gain the ability to apply those ideas to situations that he or she has not already been exposed to.

Since the expectations of this class are more difficult than those of high school, it stands to reason that the exams, designed to test the students mastery of these more lofty goals, must involve more difficult questions; and therefore, the exams must be more difficult. Clearly this will result in class averages that are lower than what one would expect if the exams were more like those of high school. It will also tend to result in score distributions that are more broad, since the students responses can be expected to be more varied.

The student should be fully aware of these points before taking an exam in this class.

It is very dangerous to associate letter grades with performances on individual exams, because it is very difficult to predict how the distributions for those exams will interact when the total score distribution is formed. Therefore, the class will usually be informed only of the class median and mean for a given exam -- letter grades will not be assigned. Rough cutoffs may be given to assist the student in understanding his or her performance, but I emphasize that these rough cutoffs have no relevance in determining final averages. The best idea one can get about his or her performance is to compare his or her score to the mean and the median scores.




Gateway Tests

These tests will not be used in computing grades for the course.  However, all students must pass the Gateway exam before receiving a grade for the course.  The exam will be given during one of the lab sessions; students that do not pass will be given an opportunity to take the exam again.


Calculators

We will be using the TI-83 in the lab portion of this course.  Make sure to read about the department policy on calculators.  Calculators will be allowed on exams, but it should be noted that certain models are banned from use!  Specifically, any calculator capable of symbolic manipulations is not allowed (for example, the TI-89).

Getting help

There are several resources that students should be aware of; make sure to read the Sources of Help for First-Year Students.

You are highly encouraged to make good use of the Math 32L Help Room.  It is located on East Campus, and is staffed for an extensive set of hours every week.  You can also come to my office hours, or just swing by sometime to see if I'm available.  If you need to make a special appointment to see me, send me an email.

I'd also like to emphasize that classmates can be an excellent resource as well.  I refer you above to my comments on this in the homework section.

Be sure to realize that you are encouraged to use these resources for more than just help on the homework...  Ask questions about general ideas you are having trouble with, specific parts of the lectures that you did not understand...  Of course you should also seek help with homework if you find yourself stuck on a problem for an extended period of time.



Honor Code

The Honor Code is taken very seriously on Duke campus, and you are all reminded to make certain you are familiar with it. 

In this course some collaboration is allowed and encouraged, but of course your work must all be your own.  Here are some specific comments about the graded items in this class:

Homeworks -- You are encouraged to work in groups to exchange ideas and help each other understand how to approach problems, but the student's work must be his or her own.  Copying and dictating are not allowed. 

Labs -- All students in a group must participate in the execution of the lab, and also in the writing of the lab report if that is required.  The lab report is NOT intended to be divided into sections that each student writes individually!  All students in the group must be present during the writing, and must contribute to all parts of the report.  If one of the students in the group does not contribute, the other students are required to omit his or her name from the report.  In such a case, late lab reports will not be allowed for that student.

Exams and Quizzes -- Students are not allowed to have any outside help during exams or quizzes.  Calculators meeting department criteria (see the discussion above on calculators) will be allowed on all exams.


Attendance

Attendance at all lectures and labs is required . If you miss a lecture, it is your responsibility to catch up on the topics that you missed. You should keep in mind that in this course, the material builds on itself; if you miss some of the material, subsequent lectures will seem more difficult to you.

Absences from exams and quizzes will be excused only for reasons such as serious illness or appropriate official university activities.  In either case, a written notification from the dean is required.  In the case of illness, this must be done with the Short-term Illness Notification form.  In the case that an absence from an exam or quiz is excused, the grade will be determined based on your performance on the final exam for the course, and relative to the performance of the rest of the class on that item.

In the case of an excused absence from lab, students will be required to complete the lab and write the report individually.