Math Xa
Introduction to Functions and Calculus
Fall 2001
Course Orientation Information
Introduction
Math X aims to provide you with a deep understanding of
topics from precalculus and calculus as
well as a strong sense of what mathematics is useful for
and how you can apply mathematics in
your work and studies. We want you to leave the course
with a solid set of mathematical skills and
a high degree of mathematical confidence so that you are
well-equipped for future studies, whether
in mathematics, biology, chemistry, economics, or other
disciplines. In order to do this we will use
multiple approaches to problem solving and we will stress
understanding the ideas behind the math
formulas and techniques that we learn.
The sequence Math Xa/Xb covers all of the material in
Mathematics 1a. In terms of prerequisites
for other courses at Harvard, Math Xa/Xb is considered
equivalent to Math 1a. During the spring
semester, in Math Xb, will also cover some of the material
from Math 1b as well: geometric series
(of particular interest to those pursuing economics and
finance) and differential equations (with
biological, medical and economic applications).
In Math X we will integrate calculus and precalculus
material. The course begins with a thorough
exploration of how to describe, interpret and represent
quantitative information, with particular
emphasis on the important concepts of relationship and
function. We'll start discussing the
fundamental ideas of calculus, including change, rates,
limits and derivatives. We will end the
semester with a short unit on using rates of change to
define functions that will serve as a bridge to
the spring course, Math Xb.
We will have an entire year to reinforce the most important
ideas and skills of calculus and its
prerequisites by working with them in numerous contexts.
The span of one year gives us enough
time to work on eliminating any mathematical weak spots you
might feel you have and to help you
to become familiar with and draw on your strengths.
Remember to enjoy yourself this semester - often students
take math because they feel that they
have to take it. In this course we will introduce a large
number of examples and problems that
people actually care about. For example, whether or not
large-scale global wars (for dwindling
resources like food and space) are likely to break out
during our lifetimes. Many of the examples
will be drawn from the biological sciences and economics,
so you will have a chance to examine
some of the other subjects that you are interested in from
the point of view of mathematics and
modeling.
Format of the Course
Math X is taught in small classes in order to provide an
environment where students are active
participation and dialogue is promoted. Small class sizes
allow us to tailor the classes to your needs
and to offer you more individual attention. Normally, the
size of each section is limited to 15
students.
There will be twice-weekly math lab sessions. These labs
are designed to focus both on problem
solving and on conceptual understanding. If you think of
mathematics as a science, you can think
of the labs as science labs where you work on problem solving.
There will be twice-weekly math lab sessions. These labs
are designed to focus both on problem
solving and on conceptual understanding. If you think of
mathematics as a science, you can think
of the labs as science labs where you work on problem solving.
The labs that you will be working on this semester are:
- Modeling data using linear and exponential functions.
- Newton's Law of Cooling and the the Galapagos Iguana.
- Describing and Analyzing Biomedical Data.
- Compound Interest and the Growth of Investments.
- The Evolution of Prices in a Simple Economy.
- Thomas Malthus, Population Growth and Necessary Evil.
- The Number "e," Exponential Functions and Derivatives.
- Resource Wars: The Future of Global Conflict.
Course head
| Name |
Dale Winter |
| Office |
Room 506, Science Center |
| Phone |
(617) 495-9063 |
| e-Mail |
amanita@math.harvard.edu |
I am here to help ensure that the class runs smoothly for you.
My main responsibility is to
coordinate all of the sections of the class, so that they all
run uniformly. To this end, you should
feel free to contact me at any point during this semester if
any issues arise, such as a family
emergency, which might cause you difficulty in keeping up
with the class. In general, you should
contact your section leader first, to let them know what is going on.
This semester my office hours are:
- Monday: 1:30-2:30pm, 506 Science Center.
- Wednesday: 2:30-3:30pm, 506 Science Center.
- Thursday: 8:00-10:00pm, Loker Commons.
- Friday: 2:30-3:30pm, 506 Science Center.
Any student (from any section) in Math Xa is welcome at any of those
times.
Teaching Fellows
Course Text
Calculus: An Integrated Approach to Functions and Their
Rates of Change. (Preliminary Edition.) by Robin Gottlieb.
Available from the Coop.
Calculators
Any graphing calculator will be an tremendous
asset in this course. I strongly recommend that you
use a calculator and bring your calculator to class
and lab each day. You will be allowed to use
your calculators on all tests and examinations except
for the gateway tests.
Math Question Center
During the semester, the Math Department operates and staffs a
drop-in center where you can go for help with your math courses.
This Math Question Center is staffed by the course assistants from
courses Xa through 21b, as well as some of the graduate students and
faculty from the Math department.
The Math Question Center is normally open between 8pm and 10pm, Sunday
through Thursday. (It is closed on Friday and Saturday night.) At
present the Math Question Center is located in Loker Commons. It will
open in the next few weeks. For the latest news on the Math Question
Center,click
here.
Grading, Homework, Tests and Exams
Grade Breakdown
Your semester grade is based on a weighted average of all of the
scores that you accumulate throughout the semester. The table given
below shows the weight that will be given to each of the parts of the
course.
| Component |
Percentage |
| Labs |
15% |
| Homework and Gateway Tests |
20% |
| Mid-terms1 |
35% |
| Final Exam |
30% |
| Total |
100% |
1 Your higher-scoring mid-term will be worth 20%, and the
other mid-term will be worth 15%.
If your grade on the final exam is higher than the grade from your
composite score, then your final grade for the course will be the same
as your grade on the final exam.
The Curve
In this class we will have a simple was to convert numerical scores
into letter grades. This method is:
| Range of numerical values |
Corresponding Letter |
| 90-100 |
A |
| 80-89 |
B |
| 65-79 |
C |
| 50-64 |
D |
| 0-49 |
E |
When the course head calculates your final grade at the end of the
course, he will calculate a score on a 0-100 point scale using the
scores that you have obtained during the course, and using the grade
breakdown given above. Your course grade will then be obtained using
this table. In the event of a fractional score, the course head will
always round up to the nearest integer. The course head may modify
these letter grades with a "+" or a "-" if both he and your section
leader believe that your performance in the course warrants this.
There is only one set of circumstances under which the course head
will deviate from the policy outlined above. This will be to ensure
that at least 20% of the people in the class get grades of "A" or "A-"
and at least 30% of people in the class get grades of "B+," "B" or
"B-."
Homework
Each week you will be assigned three fairly short homework
assignments. Generally speaking, homework is due at the next section
meeting. For example, the homework assigned on Monday is due at the
beginning of class on Wednesday, etc.
You can find the assignments and solutions by clicking here.
Solutions to the homework assignments will be posted on the course web
site very soon after the homework is collected. For this reason,
no late homework can be accepted except in the case of
unavoidable personal emergencies (such as hospitalization) or an
absence from class that is officially sanctioned by Harvard
University.
At the end of the semester, your fourlowest homework
assignments will be dropped.
Each homework assignment will consist of five questions. Over the
course of the semester, the composition of these questions will
average out to be something like:
- 65%: Mathematical operations, solving equations, amking
calculations. Fairly straight-forward uses of course content and
concepts that do not involve complicated applications or
modeling.
- 25%: Mathematical modeling of phenomena, starting with a
fairly precise and explicit description of the phenomena that can be
readily translated into mathematical symbols, graphs, etc. (Problems
like this will typically also involve calculations, solving equations,
etc.)
- 10%: Investigations into more complicated phenomena.
(This will likely also involve both modeling and mathematical
operations.)
Exams
The course-wide exams will be given on:
- Thursday, October 18. 7:00pm-9:00pm. (Science Center D.)
- Thursday, November 29. 7:00pm-9:00pm. (Science Center D.)
- Friday, January 18, 2002. (This is subject to change.
Time and place to be announced.)
If you find that you have an unavoidable conflict with either
of the first two exams times, please contact
the course head at the first opportunity. If you have a truly
unavoidable conflict with the final exam time,
then you must petition the registrar. Neither the course head
nor any of the teaching fellows can
change the time or day of the final exam, and are expressly
forbidden from making special
arrangements for individual students to take the final exam on
alternate days or at alternate times.
Gateway Tests
During the course, you will be required to take and pass four
mastery-oriented tests called gateway tests. These tests will be
straight-forward tests of fundamental skills. You may take the
gateway tests as many times as you need to. Before each test, you
will be provided with
an extensive collection of practice problems (complete with answers)
that will
seem eerily similar to the problems that appear on the
actual gateway tests. In our experience, students who make an earnest
effort to work out all of the practice problems usually have little
trouble passing the gateway tests.
To take a look at a sample gateway test, click here.
(This is an example of a "Calculating Derivatives" gateway test.)
The subjects of the gateway tests and the times that they will be
given during class are:
- Gateway 1 (Fundamental operations of algebra): Thursday September
27.
- Gateway 2 (Concepts of Derivatives): Thursday November 8.
- Gateway 3 (Solving Equations): Thursday November 15.
- Gateway 4 (Calculating Derivatives): Thursday December 6.
You can re-take the gateway tests during any Section Leader's office
hour or during any of the optional lab sessions. These optional labs
will be held on:
- Tuesday November 20.
- Tuesday December 11.
- Thursday December 13.
When you pass a gateway, it counts the same as one perfect score for a
homework assignment.
For every gateway test that you have not passed by 5pm on
Friday December 14, your final grade for the whole course will be
reduced by one letter. For example, if you don't pass any of the
gateways by 5pm on Friday December 14, then your "A" would turn
into an "E."
Day-by-Day Guide to Xa Fall 2001
To view this, click here.
Sectioning for Harvard Math Courses
To section:
Use any Harvard computer to telnet to 'hilbert.math.harvard.edu'.
When prompted to 'login', type 'section'. At the password prompt,
press 'enter'.
Follow the online instructions from there. Alternatively, from any
web browser go to the Math
department home page and click on the sectioning link in the upper
right hand corner. If there is a problem with your sectioning
assignment, contact Susan Milano in office 308 in the Science Center
(milano@math.harvard.edu).
Return to MathXa Course Page