Table of Contents

1. Is This The Right Course For You?
2. Course Description
3. Textbook
4. What Will Work For This Course And Class Meetings Be Like?
5. Advice On How To Succeed In This Class
6. Grading Policy
7. Course Schedule
8. Final Examination

Is This The Right Course For You?

Calculus 1 is the recommended starting mathematics course at Holy Cross for students who have not taken calculus in high school, and who plan on majoring in Mathematics, Chemistry, Physics, Biology, Economics or Economics/Accounting, or pursuing the Pre-Health Professions program. This course is essentially an intensive section of MATH 135 (Calculus 1) featuring extra class time, some review of precalculus topics, and a greater level of support for students whose math backgrounds from high school might be less strong. If you are taking a mathematics course mostly out of habit, to fulfill a Common Area Requirement, or for general interest, then you are certainly welcome in this course. But you might also want to consider the MATH 110 (Topics in Mathematics) courses that are offered regularly. Those courses have a different agenda than this one -- they are designed to introduce you to intriguing and perhaps unexpected aspects of the subject and they are not geared toward the requirements of more advanced courses that make use of ideas from calculus.

Both MATH 133 and MATH 135 are first college-level calculus courses. Neither assumes that you have any calculus background. If you have taken calculus before and done reasonably well, you will find everything we do here to be review of material you already know and you may prefer to start with MATH 136 (Calculus 2).

We will use the same textbook and cover the same material (most of the first four chapters of the text) as the multiple sections of MATH 135. The most obvious difference between MATH 133 and MATH 135 is that Calculus with Fundamentals meets for 250 minutes each week (our section: 2 x 50-minute periods + 2 x 75-minute periods) rather than 150 minutes (3 x 50). MATH 133 is designed especially for students whose high school background in mathematics might not be as strong and/or who feel that they could benefit from the extra class time. The extra time allows us to to review precalculus topics as necessary, to spend more time on the more difficult topics, to use a range of different approaches for classwork appropriate for students with different learning styles.

One thing to be aware of when you think about courses for next semester -- MATH 133 continues to Calculus with Fundamentals 2 (MATH 134) in the spring semester. But only one section is planned at this time, and that will meet MTWRF at 10am.

If you have any questions about which calculus class is right for you, please feel free to consult with me, with our Chair, Prof. Steven Levandosky, or with any other mathematics faculty member.

Course Description

Calculus is the branch of mathematics that focuses on ways of understanding and quantifying change in processes in the real world. First developed in the 17th century, it has been at the center of mathematics and science ever since. It is important because it is the basis for a major portion of the science and technology that shape the contemporary world. Many of the techniques used to study motion of objects in physics, kinetics of chemical reactions, growth or decline of populations of organisms in biology, growth of national economies, and many other phenomena in the real world involve calculus. Although it might sound like an exaggeration to say it, calculus is also one of the crowning achievements of the human intellect. You are in for an exciting journey of exploration as you learn it!

Two men, Isaac Newton and Gottfried Leibniz, are given most of the credit for developing the calculus. Their contribution was primarily explaining the relation between finding the rate of change of a function (the derivative) and computing the "total accumulation" of a function over an interval (the definite integral).

The topics to be covered this semester are:

• Unit I: The "library of functions" -- the basic polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions, their properties and applications
• Unit II: The conceptual meaning of the derivative of a function: rates of change, tangents, and applications
• Unit III: "Shortcuts" for computing derivatives
• Unit IV: Applications of derivatives to the study of functions, related rates, optimization problems, and so forth

See the course schedule below for a more detailed week-by-week breakdown of the semester.

Textbook

The text book for the course is Calculus, 3rd edition (Early Transcendentals version) by Jon Rogawski and Colin Adams, W.H. Freeman (Macmillan Higher Ed). I think you will find reading and studying this book to be challenging, but ultimately rewarding.

What Will Work For This Course And Class Meetings Be Like?

In order for students to get as much as possible out of a course, regular active participation and engagement with the ideas are necessary. Mathematics educators are coming to the realization that a straight lecture approach in class is both a poor way to encourage this sort of active learning, and a poor use of limited class time. On the other hand, mathematics teachers are learning that having students work through questions individually or in a group setting during class is a good way to help them develop a deeper understanding of the mathematics involved.

So, we will be using a modified flipped classroom approach in this course. This means in particular that instead of listening passively to a lecture on new material each day and taking notes in class, then doing problems based on that material outside of class, you will be expected to view one or two short video presentations on the new material before coming to class almost every day, and then you will be doing activities in class based on the material from the video presentations. Besides using class time more productively, another benefit of this approach is that, unlike an in-class lecture, a video can be paused and/or viewed repeatedly as many times as you like if something doesn't click the first time.

These presentations have been prepared specially for this class by me (Prof. Little) and I will adjust them and or make more/different ones as the semester proceeds if necessary. So be assured that this is being done specifically for you, for your benefit, and with your needs in mind. You will need to set aside time in your schedule to view the assigned videos on a regular basis, and you will be unprepared for class if you do not. I will set aside some time each day for you to ask questions about the material from the videos if things were not clear or if you want to see more examples. But most days, most of your time in class will be devoted to active work on the material--practice problems or smaller-scale projects in groups where you will need to apply what you have learned.

This approach might be unfamiliar to many of you and it might take some getting used to. But I am convinced that it is an improvement over the ways we used to do things and I'm also convinced that you can be relied on to take this seriously and keep up to date on viewing the video presentations before class. For those of you who are first year students, you will find that college courses in general ask you to take more individual responsibility for your learning than high school courses. But you are ready for that extra responsibility!

Most weeks, we will be following a schedule something like this:

• Monday, Tuesday and Friday will be devoted to question time, possible additional examples related to the topic for the day, and individual or group work. Again, for most of these days, there will be a short video presentation on the material that you should view before coming to class, since the day's activity will draw on that material. These will be available from the course Moodle page.
• Thursdays (after the first week) will be devoted to quizzes and in-class exams. There will be four exams and 8 quizzes in all. Quizzes will last 30 minutes, after which we will continue on to a new topic for the rest of the period. You will have the whole 75-minute period for exams (if you need that much time).

Advice On How To Succeed In This Class

A good "work ethic" is key. You do not need to be a "math genius" to master this material and do well. But you will need to be an active student, put in a consistent effort and keep up with the course. This means, in particular:

Come to class. Unless you are deathly ill, have a serious family emergency, etc. plan on showing up here at 8:00 am every Monday, Tuesday, Thursday, and Friday this semester. If attending class wasn't important, all college courses would be by correspondence, and your tuition would be much cheaper!

Really use the textbook, videos, and other course materials. One of the reasons for using the video presentations is that they allow you to pause and/or repeat segments if something doesn't "click" the first time (unlike a traditional lecture). The textbook is another valuable source of alternative explanations, if you use it the right way. Don't just leaf through sections to look for worked problems similar to those on the problem sets. Reading a math book is not like reading a novel, though. You will need to read very carefully, with pencil and paper in hand, working through examples in detail and taking notes. Make a list of questions to ask in office hours or at the next class. Bear in mind while reading your text is that the answer to a example problem is almost always much less important than the process used to obtain the answer. For this reason, authors sometimes intentionally leave certain routine steps out with the expectation that you will supply them in order to understand what is going on completely.

Take notes and use them. You will probably want to take notes as you view the course videos since that is a primary way you will see new ideas introduced and problems worked ``in real time.'' Used intelligently, your notes can be a valuable resource as you work on problem sets and prepare for exams.

Set up a regular study schedule and work at a steady pace. It's not easy to play catch-up in a mathematics course, since every day builds on the previous one. Even though MATH 133 meets 250 minutes/week, you should still expect to budget at least 6 hours in a typical week for work outside of class (work on the problem sets, the weekly review session with our ``TA'' Lauren Clair, etc.). The best way to use your time is to do a few problems, viewing the course videos and reading the book every day.

Most importantly, if you are having difficulty learning something, get help as soon as possible. You can do this by asking questions during class (any time something isn't clear) seeing me during office hours, by attending the weekly review session for our section held by Lauren Clair, or attending the Calculus Workshop--7-9pm Sunday-Thursday.

Grading Policy

Grading for the course will be based on

1. Four in-class tests, together worth 40% of the course grade. (Since everyone can have a bad day now and again, I will weight the lowest exam grade significantly less in computing the exam average -- "12,12,12,4" to be specific.)
2. A two-hour final exam, worth 20% of the course grade. This will be given at the regular time for MWF 8:00am classes, I believe. The day and time will be announced by the Registrar after the start of the semester.
3. Weekly quizzes, worth 15% of the course grade. (There will be eight of these quizzes in all but I will use only the 5 highest scores.)
4. Written reports from small group discussions -- one report from each group. Information regarding the expected format will be given out with the first assignment of this kind. Together, worth 10% of the course grade.
5. Weekly problem sets, worth 15% of your course grade. Each of these will consist of two sections -- one on the online LaunchPad system, the second a shorter written assignment to be handed in on paper. Most weeks, a problem set will be posted on Thursday, covering the material in the Thursday, Friday and the next week's Monday and Tuesday meetings. You should work on the problems starting on the weekend and in the early part of the week. No credit will be given for late homework, except in the case of an excused absence, or with my permission.
6. Occasional extra credit assignments may be offered. (For instance: attend a science-related event on campus and write a short response essay.) These will be announced in class and on the course home page as they arise.

For all exams and quizzes, the topics to be covered and a list of practice problems will be given out well in advance of the date.

If you ever have a question about the grading policy or your standing in the course, don't hesitate to ask me.

Course Schedule

The following is an approximate week-by-week schedule. There is also a more detailed day-by-day schedule maintained on the course homepage. Some rearrangement, expansion, or contraction of topics may become necessary. I will announce any changes in class and here.

Final Examination

The final exam for this course will be given at the regular time for MWF 8:00am classes. Watch for announcement from the Registrar.