College of the Holy Cross
Calculus Course Description

For information on my teaching philosophy, please click here. Attendance is really important to me. Please make the effort to come to class. If you contact me ahead of time and the absence is excused, then I will make every effort to provide you with the information that you missed. Otherwise, it is your responsibility to get notes from one of your peers and to make sure that you understand the material that you missed.

For Math 131 students: If you plan to take a full year of calculus, the registration system will place you automatically into my continuing course in the spring semester. You can always switch to another section for the spring semester. Please note that taking one semester of calculus does not commit you to taking the second semester!

Is This Course Right for You?

The Department offers a variety of Calculus courses, each directed to students with certain plans and goals. For more information about the Calculus sequences at Holy Cross, particularly for information about how AP credit is handled at the College, please go to this website Introductory Courses and AP Credit. Try to start out in the course that fits your background and needs...but if you realize after a week or so that you probably should switch to a different course, just talk to me about it and we'll move you. This is your education, let's get you placed into the appropriate course so you can optimize your learning!

Note that the College's Common Area Requirements permit you to choose between taking two science courses or, alternatively, taking one science along with one math. Several courses count as Mathematical Science Common Area Requirement courses. In addition to any Calculus course, a topics in math course (MATH 110) or any Computer Science course also satisfies the Common Area Requirement for Mathematical Sciences. These alternative courses are definitely worthy of your consideration!

Please read through this section to determine if you are enrolled in the right course. If, after reading this, you are still uncertain as to whether or not this is the best course for you this semester, please speak to me privately. Please note that only Math 136 presupposes any exposure to Calculus in high school, even though a number of students have already had some Calculus.

If you are considering majoring in Biology, Chemistry, Mathematics or Physics, then you should take the MATH 131-132 sequence. You should begin in either MATH 131 (Calculus for Physical and Life Sciences I, which is the first of the two semester sequence), MATH 133 (Intensive Calculus for Physical and Life Sciences, which is equivalent to MATH 131 but this one meets five days a week & has a weekly review session to provide additional support) or MATH 136 (Advanced Placement Calculus, which is the equivalent of MATH 131 & MATH 132 concentrated into one semester...don't be intimidated by the title of this course, it's really for any student who has already had a year of Calculus before coming to Holy Cross). If you are considering applying to medical school, but you are not intending to be a science major, then you are still encouraged to begin in MATH131, MATH 133 or MATH 136 (as appropriate). If you are intending to take further mathematics courses beyond Calculus, then you should begin in MATH 131, MATH 133 or MATH 136.

What is the difference between MATH 131 and MATH 136? The former is part of a two-semester sequence, MATH 131-MATH 132. It covers a year's worth of calculus in two semesters. The fall semester is differentiation and the spring semester is integration. MATH 136 covers this same material in only one semester. MATH 136 goes through differentiation and integration, spending more time on integration. It's for students who have already studied calculus in high school and don't want to start from scratch --- these students still want to re-do differentiation at the college level, but they have already seen it before. MATH 133 (Intensive Calculus for Science I) is the same as MATH 131 -- it covers differentiation, but it meets five times a week in order to allow more time for students to transition to college-level mathematics and also to allow for more precalculus review. So, in brief, if you've had zero calculus you should take MATH 131 or MATH 133. If you've had some calculus, you should take MATH 131 or MATH 136. The nice thing about MATH 136 is that you finish the calculus sequence a semester earlier, but the class does proceed at a faster pace. You may start in Math 136 and then move down to Math 131 if you realize the pace is too fast.

Another calculus sequence offered at Holy Cross, MATH 125 and MATH 126 (Calculus for the Social Sciences I and II) is designed for Economics majors or minors and Economics/Accounting majors. These are considered to be terminal courses, which means that a student who chooses this calculus sequence is not expected to take any additional math courses at the College. Many other non-science majors who wish to continue their study of mathematics or who want to satisfy one portion of the Natural Science/Mathematics common area requirement take one of these courses, although the department recommends that students consider a topics course (MATH 110) instead. Please note that there is a substantial amount of overlap between MATH 126 and MATH 132 (Calculus for Physical and Life Sciences II). MATH 132, however, contains additional topics that will be needed for later mathematics courses.

For more information about the Calculus sequences at Holy Cross, particularly for information about how AP credit is handled at the College, please go to the link above.

The Topics Covered in Calculus

The best way to find out about Calculus itself is to read the preface in your text book. Calculus is undisputed as one of the greatest achievements of the human intellect. It was developed over 300 years ago independently by Leibnitz and Newton. The goal of this course is to convey principal methods of Calculus and their utility for today's applied scientist.

When I describe Calculus to others, I typically say it is the mathematics of rates of change. Prior to Calculus, you studied functions. Functions are fundamental to mathematics -- how well you do in this class, for example, is a function of how much you study and of how well we work together as teacher and student. Calculus starts with the study of functions. It will examine them by surveying their behavior -- particularly their rates of change. For example, how does your Calculus performance change as the amount of time you spend studying changes?

In Math 136, the entire text book is covered (Chapters 1 - 8) in the fall. In the full-year course, the first semester covers differentiation (Chapters 1 - 4) and the second semester will cover integration (Chapters 5 - 8).

Your Instructor's Approach to Teaching

Most of the class meetings will be presented in an interactive lecture format. There will be opportunitites to ask questions and to participate in the discussion. Please be willing to speak up if something is not clear or if you spot an error during my presentation. My lectures are not designed to be passive events for the students -- I will ask questions and you will work problems during the class meeting. Don't be surprised if you are called upon by name! As new material is presented, I will use various techniques to measure the extent of your understanding. For example, I may ask everyone to work on a problem and then call on a volunteer to put the solution on the board. Be prepared to pick up your pencil and think during the class period. For information on my teaching philosophy, click here. I will incorporate as many classroom activities as possible, given the time constraints of the course. I have a high expectation that you will work extra problems on your own, outside of class. The homework you turn in should represent only a fraction of the problems that you do each week. I look forward to seeing many of my students during office hours to go over both homework questions and other problems.

I am an applied mathematician. Applied mathematics explores the interdependence of mathematics and the sciences. In addition to being in the Department of Mathematics and Computer Science, I am also a member of the Environmental Studies faculty. In attempting to solve problems, applied mathematicians, engineers and scientists use a variety of approaches and techniques. While mathematics permits us to clarify and understand the physical aspects of a problem, so can physical insights assist us in finding the appropriate mathematical line of approach. You will find that my approach as an applied mathematician will influence this course -- my examples will be based in the real world as much as possible. For more information on my research, click here.

Advice on How to Succeed in this Class

As a student at Holy Cross, you are bright and have done well in mathematics courses. It has been my experience that most people studying mathematics hit a "wall" at some point -- a time when simply attending class is no longer sufficient to learn the material. You probably know people who hit the wall during high school -- and they either stopped taking math courses or else took some time to learn how to study. Those who stopped taking math might claim that they can't "do it", but I propose that many of them could succeed in mathematics if they learned how to study. Perhaps you won't hit the wall at all -- each person is different. Many students who arrive at college having found mathematics relatively easy and straightforward in the past might find themselves caught off guard if the material stops coming to them naturally.

If this happens to you, please don't panic! It simply means that you've reached the point where you need to learn how to study mathematics. You don't have to be a "genius" to do well in Calculus, but you might need to teach yourself a few tricks about how to study mathematics. For example, a math text book can't be read in a linear way as you might read a novel. You need to stop and start and stop and start in order to absorb and work the material. Indeed, I am of the opinion that you can master this material if you put in a consistent effort and keep up with the course material. Come to class, read the textbook, take notes and set up a regular study schedule. Plan to spend a minimum of 8 hours per week for work outside of class. Please come see me during office hours (or set up an appointment via email) if you'd like to discuss "how to study" strategies. I'd be happy to take a look at your class notes and to assist you appropriately. The Calculus Workshop is held in Swords every Sunday through Thursday eveningfrom 7:00pm to 9:00pm -- this is an opportunity to study and work problems with other students and to get free assistance from successful math majors.