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Math 1a - Introduction to Calculus
Fall 2004
Course Information

Course Info
Schedule (MWF)
Schedule (TuTh)
HW Solutions
Math Dept.


Welcome to Math 1a! In this course, we will study the foundations of calculus, the study of functions and their rates of change. Along the way, we hope you will learn to appreciate the ubiquity of mathematics in our daily lives; to read, write, and critique mathematical arguments; and to analyze new problems with mathematical modeling.


The derivative measures the instantaneous rate of change of a function. The definite integral measures the accumulation of a function over an interval. These two ideas form the basic for nearly all mathematical formulas in science. The rules by which we can compute the derivative (respectively, the integral) of any function are called a calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way.

Course Details

Course Head

Matthew Leingang
Preceptor in Mathematics
Science Center 323
Office hours: 2:00-4:00pm Tuesdays and Wednesdays

Section Leaders

Several faculty and graduate student teaching fellows trained by the department and experienced in teaching calculus. Section leaders lead the section meetings, and assign homework. All homework, assignments, quizzes, and exams are identical across sections.

Course Assistants

Each section is assigned a course assistant, typically an undergraduate. The course assistant conducts a weekly problem session to supplement the section meeting and answer questions, and grades homework.

Note there is a difference between the calculus courses and many sectioned courses in other departments. Our primary instruction happens in sections, while our discussion "sections" are called "problem sessions" and led by course assistants.

Reading Assignments

We will generally require that you read the material in the textbook before we discuss it in class, as opposed to reading it after the class. Before class you will go online to your section's web site and answer a few questions. Most of these will be multiple-choice, but there will always be one free-response question in which you can talk about what specifically troubles you from the reading. Your section leader will read all your response and prepare class accordingly.

In order to reward your effort in doing pre-class reading assignments the assignments will be graded for effort and that grade figured into your course grade. Free-response questions will be graded mostly on effort.

Section Meetings

Sections meet three hours per week: Mondays, Wednesdays, and Fridays for one hour or Tuesdays and Thursdays for 90 minutes. Each section has a weekly 90-minute problem session. During your section your instructor will continue the teaching of the material that was introduced in the text. Be prepared to ask and answer questions as the goal of a small-section class is to learn through discussion.

You must use the math department's computer program to select a section before Wednesday, September 22, at 1:00pm. This is a different process than sectioning for other FAS courses. A document about sectioning is attached to this syllabus. You can also find more information here.


Homework will be assigned each class meeting and due the next class meeting. It will be returned, graded, at the following class meeting. Solutions will be made available on the course web site. Late homework will not be accepted. The equivalent of one week's homework assignments will be dropped in the final grade calculation. That is, if you are in a MWF section, the lowest three homework scores will be dropped, and if you are in a TuTh section, the lowest two.

Homework problems are themselves an extension of the course material. This is not like high school in which there are a limited number of "types" of problems in mathematics and your teacher is responsible for showing you how to do each type. Some problems will require you to apply the concepts of the class and the textbook to solve problems not explicitly covered in class.

By all means you may work in groups on the homework assignments. However, each student must turn in his or her own write-up of the solutions, with an acknowledgment of collaborators. This is in line with good habits of scholarship in general.

For help with homework, talk to your section leader or course assistant or visit the Math Question Center.

Quizzes and Exams

The department recommends into Math 1a those with an 18 or higher on the first part (precalculus) of the Harvard Math Placement Test. Our research has shown that 1a students who do not heed the precalculus prerequisites often do poorly. In order to make sure students have the necessary background (and have dusted it off well enough to use it), there will be two precalculus quizzes on consecutive Fridays, October 1 and 8, from 3-4pm in Science Center Hall C. The one on which you score highest will count as 5% of your final grade. The quizzes will cover the basics of algebra, trigonometry, logarithms, and graphing.

An optional precalculus primer has been made available in case you would like a book to study from. There are also precalculus books in the textbook reference section of Cabot Library. The Math Warm-Up Series is also designed to help remember some of the most important topics of precalculus.

There are two midterm exams, one on Wednesday, October 27, and one on Wednesday, December 8. Both occur from 7-9pm in Science Center Hall C. The final exam is tentatively scheduled for Thursday, January 20, 2005. No calculators will be allowed on the exams.

Exams are to test your mastery of the course topics. Exam problems may be like homework problems but may also synthesize various parts of the course.


Your course grade will be determined as the following weighted average:

Precalculus Quiz 5%
Pre-Class Reading Assignments 5%
Homework 10%
Midterm I 20%
Midterm II 25%
Final 35%
Total 100%


Calculus: Concepts and Contexts, 2nd edition, by James Stewart. Brooks/Cole, ISBN 0-534-37862-5. There is a companion web site to the text, and you may find the Review of Algebra [PDF 140KB] linked there useful.

Schaum's Outlines: Precalculus, by Fred Safier, ISBN 0-07-057261-5. This is recommended only if you want something to study from for the precalculus quizzes.

Page maintained by Derek Bruff (bruff@fas.harvard.edu).
Last updated on September 24, 2004.