About Math 135, section F2, summer 2006

Course description History (why calculus?) This section Student work and grading

Course description

The majority of students in this course are planning to major in biology, pharmacy, or business, all of which require at least one semester of calculus. Other students from such majors as psychology who think they may need "more" mathematics also take Math 135. Calculus is a wonderful intellectual achievement - there are even some students who take the course to see how beautiful the subject is! Here's the official course description:

01:640:135-136. CALCULUS I, II (4,4)

For liberal arts majors. Prerequisite for 135: 01:640:112 or 115 or appropriate performance on the placement test in mathematics. Prerequisite for 136: CALC1. Credit restrictions: CR1, CR2.

Math 135: Analytic geometry, differential calculus, applications, and introduction to integral calculus. Math 136: Transcendental functions, techniques of integration, polar coordinates, and series.

This course is a more descriptive version of calculus 1 suitable for students who need the language and some knowledge of the methods of calculus, but it is generally not intended for students who will be taking further courses in the calculus sequence and who will be intensively applying calculus methods in their majors. Such majors include biochemistry, biophysics, chemistry, computer science, geology, mathematics, meteorology, physics, or any variety of engineering. Students who believe they may study those majors should take the Math 151 version of calculus.

History (why calculus?)

Calculus originated as a way of describing certain methods used in understanding and solving problems originating in geometry and physics. The language of the subject shows this ancestry. Calculus has been very successful. Calculus also "happens" to be suitable to describe and study many problems in biology and economics. Any problems which involve rates of change (how soluble is substance A in substance B as the concentration of substance C varies?) or accumulation of changes (what is the present value under certain interest rate assumptions of a stream of mortgage payments to be made monthly over the next 20 years?) is a problem which likely can be described using calculus. Frequently this description will suggest certain ways of solving the problems using the methods of calculus. That's why the subject is required in so many majors.

To me, Math 135 has two parts. One is showing clearly the definitions and methods of "Calc 1". Another part, just as important, is establishing the context for the course: why it is interesting and relevant to the students who take it. I don't think my personal doctor frequently takes derivatives or computes integrals (although a friend of mine who is an M.D. does abstract math as a hobby!). But that doctor must be able to read and understand complicated graphical and numerical information. I believe that learning calculus increases the chance of success for such activity, and can be useful in many situations, both in further course work and "on the job". Showing students that context is part of my goal in this course. Also, if I explain the subject well, maybe you'll think at least part of it is pretty!

This section

I've taught Math 135 a number of times. Some records of my teaching Math 135 can be found using links from my home page including material from the most recent "instantiation".

I wrote the following a week ago (June 19) in a message to students who were enrolled in this section and whose e-mail addresses I could get:

... I am planning something a bit unusual. The standard syllabus for the course is available at
The textbook mentioned there is generally used in Math 135. The price for this text when new is about $120 and the used price is about $80 to $90 (prices in the Rutgers bookstore). The overwhelming majority of students in Math 135 do not continue on in calculus. Many students resell their texts. The price of basic calculus textbooks is very high given that much of the text will not be used by students and also considering that the material is rarely applicable to the students in Math 135. After consulting with various colleagues, I've decided to ask students to buy a much cheaper book. I won't require students to buy the standard text. I looked at various calculus "review books", such as the one in Schaum's outline series. I decided to ask students to buy a text in Barron's College Review Series: "Calculus" by Elliot C. Gootman. The book is available at the Rutgers store in New Brunswick. Its list price is $16.99.

This text will supply straightforward instructional support for the computational aspects of the course. Students in Math 135 should be interested in some of the more descriptive and non-classical uses of calculus: its applications to, for example, business and biology. It will be my job to supply this "context" for the calculus course. I will create web-based notes which students will be able to use. Examples of the kind of material I'll offer can be seen using the web page created when I most recently taught Math 135:
Please click on the links for the course diary.

Students who have already purchased or own the standard textbook will not be disadvantaged. I will generally follow the list of topics in the syllabus, and my quizzes, exams, and homework will be at the appropriate level for the course.

I hope you share my desire to do "something" effective about the price of textbooks, and that you will help me decide if what I am planning is a practical approach. I certainly want the course to be successful for the students involved and I am prepared to devote time and energy for this to happen. I also remark that I don't intend to create another calculus book (such a divine inspiration hasn't come to me!) but to create useful web material intended specifically for the students in Math 135 at Rutgers.

One consequence of this selection of "support" by course text is that the support for students will be much "leaner" than usual. Here I mean "less fat" and less redundancy (a smaller safety net): you will have less to read and many fewer instructional resources. This means you should Summer school classes go very fast, and students who take them should be well-motivated (!) and be able to give the classes the attention they deserve. I believe these observations are even more important for this section. Please let me repeat my sincere ambition written in the message quoted:
I certainly want the course to be successful for the students involved and I am prepared to devote time and energy for this to happen.

Student work and grading

I will give homework assignments and I may occasionally give work to be done in class which will be collected. I will grade this work in order to help students, and students who hand in this work will get credit for their attempts. This will be about 10 to 20% of the course grade. The balance of the grade will be earned through exams.

There will be two in-class exams which will each count for 100 points, and a final exam which will count for 200 points. In addition, I will give an early exam (on Monday, July 3rd) which will count for 50 points. The reason for an early exam is to notify students about their progress in the course as soon as possible. I remark that usually calculators will not be allowed on exams, but graphing calculators can be very useful in this course.

Maintained by greenfie@math.rutgers.edu and last modified 6/25/2006.