Welcome to Math 102 with Clark Bray
Spring 2007-08


Instructor:  Clark Bray, 035 Physics Building, 660-2822, cbray@math.duke.edu
Office hours: Thursday 1-4pm, or by appointment

Teaching Assistants:  
George Lam -- 274F Physics Building, 660-2867, glam@math.duke.edu
Office Hours:  Monday 4-5pm; Tuesday 3-4pm

Textbook:  Mathematics for Economists, Simon and Blume; Notes on Integrals for Math 102, Bray (available for download on Blackboard)

Links and Downloads

Syllabus -- This document shows all of the sections that will be covered in this course, in chronological order.  As we proceed through the semester, I will add homework exercises before or soon after we complete each lecture.

Schedule of Lectures -- This schedule has the dates of all of the exams, and a rough schedule indicating which lecture (from the syllabus) will be given on each class day.  Students are urged to read the appropriate sections of the book BEFORE the lecture, so that they will have a general idea of what problems will be addressed and what approaches will be taken so that they can make better use of class time.  Note that very often, there will be material in the book that we will not have time to present in class, so it is also important to read the appropriate section of the book AFTER the lecture as well.

Note, the schedule of lectures is just an approximation; we may find ourselves ahead of or behind schedule, depending on some unknowns.  Your regular attendance in class will ensure that you will be aware of such changes.

Additional Homework Problems -- Here you will find the problems that are labelled with "AHP" on the syllabus.

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

Blackboard -- This will mostly be used for recording and reporting exam grades in this class.  Your exam 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.  Make sure to log in after each assignment is returned to make sure that the grade was recorded correctly; if it was not, contact me as soon as possible so that the correction can be made. 

Homework scores will NOT be recorded on Blackboard, since there is no way to allow the grader access to post homework scores while still keeping your exam scores confidential.  The grader will maintain the homework gradesheet separately.

(Note -- ignore the "Total Score" reported on Blackboard in this course!  Blackboard is not set up to compute totals the way I prefer to do it, so its computations of totals are completely irrelevant in this course.)

You will find on Blackboard the document "Notes on Integrals for Math 102", which is one of the references for the course.  

You will also find there a document of scans of all of my personal lecture notes from the Fall 2007-08 course.  You may use these as a tool for helping you take notes if you prefer.  For example, you might bring these to class with you, and then add your own notes on the same page in a different color pen.  

But these personal notes come with the following comments and disclaimers:
- They might not include everything we will do in class this semester.
- They are very terse, and are more like an outline than a text reference.  They are NOT to be considered a substitute for class attendance.
- They might contain errors; if you find one, please let me know.
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.

Some comments about Single Variable Integrals -- This is a document that I wrote in the Fall of 2004 after teaching the Math 103 section about integrals of parametric functions.  When we get to the integrals portion of this course, the first part of this could be useful to you.

My other Course Websites -- Students can find here all of the websites for every course I have ever taught. 

Java Applets -- This is a site that was created by a colleague at Stanford; several of the tools there could be useful to you for visualizing multivariable functions. 

Exam Solutions

2007-2008 Spring:
Exam 1
Exam 1 Solutions
Exam 2
Exam 2 Solutions
Exam 3
Exam 3 Solutions

2007-2008 Fall:
Exam 1
Exam 1 Solutions
Exam 2
Exam 2 Solutions
Exam 3
Exam 3 Solutions

2006-07 Spring:
Exam 1
Exam 2
Exam 3
Exam 1 Solutions
Exam 2 Solutions (Note, there are computational errors in the solution to problem 1a)
Exam 3 Solutions (Note, there is an arithmetic error on number 5; the answer should be 11, not 7.)

Homework

Homework problems are assigned for every lecture, and students should ideally complete each assignment on the day of the lecture.  The assigned problems for each lesson will be listed on the syllabus.

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, and the section number(s) for those problems.

In order to give flexibility to students, the assignments for the previous three lectures will be picked up in section every Tuesday, and will be graded and returned as soon as possible. 

No late homework will be accepted without the Short Term Illness Notification.

In calculating homework grades, the lowest of your homework scores will be dropped.  The purpose of this policy is to handle exceptional circumstances.  Please do not request to have late homework accepted without filling out the Short Term Illness Notification.  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:

Homework average:   50 possible points (the lowest homework score is dropped)
Tests:                           300 possible points (3 exams x 100 points each)
Final Exam:                 200 possible points
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Total:                            550 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. 

I will periodically distribute a list of all student total scores in the class (with names removed), so that students can see exactly how their own total scores compare to the rest of the class. 



Calculators

We will not be using calculators in any aspect of this course.  You may use a calculator on a homework problem if you feel that it will help you understand the concepts, but you may not make any reference to the use of a calculator on the homework you turn in, except in the case of a problem that requires substantial and nontrivial arithmetic.

Calculators will NOT be allowed on the final exam or on the in-class exams.  I also generally discourage their use on the homeworks, since students may develop a dependence that will hurt them on the exams.

You are encouraged though to take advantage of the online resources linked to from this page, including the Java Applets (there are many tools there that can help you visualize and develop a geometric intuition for some of the ideas in this course).


Getting help

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

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. 

Exams and Quizzes -- Students are not allowed to have any outside help during exams or quizzes. 


Attendance

Attendance at all lectures and sections 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 much more difficult to you.

Absences from exams 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 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 exam.

Students should note that use of the Short-term Illness Notification form is subject to the Duke Community Standard, discussed and linked above.  In particular, it is expected every student will take reasonable responsibility for his/her own health at least to the extent that such health is needed to be able to participate in classes.  Here are some examples:

-- If on the day of an exam in this course you have a debilitating headache caused by a virus, then it would be appropriate to use the short term illness form.  However, if you have a debilitating headache caused by a hangover, it would not be appropriate to use the short term illness form.

-- If on the day of an exam in this course you have a severe cold caught two days earlier while camping outside for basketball tickets, then it would be appropriate to use the short term illness form.  However, if you have had the cold for two weeks and are still camping outside for basketball tickets, it would not be appropriate to use the short term illness form.



Additional Comments

As was discussed in the section on Grading and Exams, the goals of this course are higher than those of high school math courses, and even higher than most single variable calculus courses.  Specifically, students in this course will be expected not only to be able to perform computations, but also to be able to demonstrate comprehension of the ideas behind those computations.

We expect students to demonstrate this comprehension by showing the process used to perform the computation, with sufficient commentary to allow the reader to conclude the thought process the student was using in working that problem.  

The correct numerical answer does not guarantee that the student will get full or even majority credit for the problem.  Rather, students will be graded on the validity of the method of computation, the extent to which the computation and commentary demonstrate the student understands the underlying ideas, and the clarity of those explanations.

It is very likely that this system of evaluation is very different from the ones the students might have become accustomed to in high school.  
To a great extent, this is a writing class.

This might sounds like an outrageous statement, but the fundamental point here is that this course, just like a history course or a political science course, is about the comprehension and communication of ideas.  Obviously the types of ideas in question are different, but like many or even most other courses on a college campus, this course requires students to understand concepts, and then to communicate that understanding through writing.  In this course the writing comes in the form of the answers that the student gives to homework and exam problems, rather than essays.  

Students should take very seriously the idea that the solutions they write for the homework and the exam problems should reflect this perspective.  All too often students think of the writing they do on an exam to be simply a personal convenience for them -- that is, a tool to keep them from having to work the problem entirely in their heads.  This is NOT the right attitude, and it will not lead to the desired credit on the exam.

Instead, think of your writing on homework and exam problems as being documentation of your thought process.  You are communicating to another person, namely the grader, and your goal is to communicate that you understand the tools needed to solve the given problem and that you know how to implement those tools.  Of course in communicating that to the grader, you will also write down the necessary algebra to allow you to arrive at the final answer.
Write neatly!  

The all-too-common attitude in high school mathematics courses is that the answer is the only thing that matters; if the grader can read the answer, then the clarity of the rest of the work is not relevant.

As per the above comments, this is not the case in this course.  Everything that is written on the exam is going to be read and considered for the contribution it makes to demonstrating comprehension of the ideas.  So it must all be legible.

The same standards of neatness and legibility appropriate to, say, a history class should be applied in this mathematics class.  Because of the types of notation used we do not expect that the student will type the solutions to homework problems; but, we expect that the solutions will be written neatly and legibly, the papers should not be crumpled or stained, and there should not be large areas of the paper scratched out.  (If you are not sure how to work a problem and if you are going to put its solution on the same page as that of another problem, you should do your scratch work on another piece of paper, and then write out the solution neatly on the paper you will turn in.)

Furthermore, note that the flow of ideas over the page should be reasonable.  Ideally, it should be "top down", or perhaps two or three column if the student prefers.  Either way, the grader should be able to look at the page and effortlessly identify the location of the beginning of the argument, and easily follow each successive step until arriving at the conclusion.

Note, explanations that bounce around the page in a seemingly random pattern will be more difficult for the grader to follow, which invariably leaves the grader finding less clarity.  This can lead to the awarding of fewer points.