Math Xa           Introduction to Functions and Calculus         Fall 2002
   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 might actually care about: Many of the examples will be drawn from the biological sciences, medicine, social 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.

You will work on a total of eight labs during the semester (see table below). Other lab sessions will be devoted to review for the midterm exams, and opportunities to take or make up gateway tests. The day by day schedule of topics and events indicates when labs are held, and which labs are optional.

Lab Title Date started Date completed Due date
1 How the brain counts: Linear and exponential regression. Tuesday October 1 Thursday October 3 Tuesday October 8
2 Newton's Law of Cooling and Ebbinghaus' Law of Forgetting Tuesday October 8 Thursday October 10 Tuesday October 15
3 Describing and analyzing biomedical data. Tuesday October 15 Thursday October 17 Tuesday October 22
4 The long term impact of human activity on marine ecosystems. Tuesday October 22 Thursday October 29 Tuesday November 5
5 World population growth and sustainable development. Tuesday November 5 Thursday November 7 Tuesday November 12
6 Distance, velocity and acceleration. Tuesday November 12 Thursday November 14 Tuesday November 19
7 Can anybody ever win the War on Drugs? Tuesday November 19 Thursday November 21 Tuesday November 26
8 How long will the Earth's natural resources last? Tuesday December 10 Thursday December 12 Tuesday December 17

Course head

Name Dale Winter
Office Room 430, Science Center
Phone (617) 495-5735
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: Any student (from any section) in Math Xa is welcome at any of those times.


Teaching Fellows

Teaching Fellow e-Mail Address
Dale Winter amanita@math.harvard.edu


Course Text

There is no required text book for Math Xa or Math Xb.

In the past, students who attended class and lab on a regular basis found that they could get most of what they needed for the course without extensive use of a textbook.

If you feel that you need or would like to do additional reading in the course, most college text books with "Precalculus" or "Calculus" in the title will include material relevant to Math Xa. Below is a list including many of the books that have been used recently in undergraduate mathematics courses at Harvard. Many of these books are available through the Harvard library system if you would like to use them on a casual basis. (To check the library's holdings, click here.)

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.

If you are contemplating the purchase of a new calculator, the model that Math Xa and Xb students have found the easiest to use in the course is the TI-83 Plus. If you do not own a graphing calculator, then buying one will be a much better investment than spending $100+ on a textbook that you will hardly ever use.

If you already own a high-end graphing calculator that is roughly equivalent to a TI-83 Plus (or better), you are welcome to use it in the course. The one strong suggestion is that you bring the Owners Manual for your calculator to college with you.

You will be allowed to use your calculators on all tests and examinations (including the final exam) 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.

In the past, Math X students have found that the Question Center is a very useful resource, and that a lot of the time that they spent there was both fun (difficult to believe, I know) and very productive. The Math Question Center is usually very well staffed with Math Xa course assistants and faculty on Sunday, Tuesday and Thursday nights.

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-." In all of the time that we have used this system, such a modification has never been necessary.

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 homework assignments and solutions for Math Xa from Fall 2001 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.

By the end of the semester, you will have completed approximately 25 homework assignments in the course. To mitigate the effects of severe distractions (e.g. Ec 10 midterms and Expos papers) on your math homework, your three lowest 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:

Exams

The course-wide exams will be given on: 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 Topic Date first given Link to review problems
1 Fundamental Rules of Algebra Thursday October 3 Click here
2 Concepts of Derivatives Thursday November 14 Click here
3 Calculating derivatives Thursday December 12 Click here


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:
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 Wednesday December 18, 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 Wednesday December 18, then your "A" would turn into an "D." That said, you should note that every student who has actually learned the material of the course has eventually passed every single gateway test (usually with plenty of time to spare). The keys to passing the gateways tests are mastery of the fundamental concepts and calculations of the course, and the ability to keep trying until you succeed.

Day-by-Day Guide to Xa Fall 2002

To view this, click here.

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