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 who plan on pursuing the Pre-Health Professions program. Calculus 1 comes in ``two flavors'' -- multiple sections of MATH 135 and this course -- MATH 133.
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 (5 x 50-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. But only one section is planned at this time, and that will meet at 8am again.
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.
If you have any questions about which calculus class is right for you, or if you think another mathematics course might be a better choice for you, please feel free to consult with me, with our Chair, Prof. Steven Levandosky, or with any other mathematics faculty member.
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:
See the course schedule below for a more detailed week-by-week breakdown of the semester. There are also even more detailed day-by-day schedules available on the course homepage and in the Moodle site for this course.
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. In addition to the physical book, you will need access to the WebAssign online homework system. The HC bookstore will be selling a "bundle" consisting of the book pages together with a WebAssign access code, but you have the option of purchasing these from other sources if you prefer.
It is expected that Holy Cross students will have textbooks and other required class materials in order to achieve academic success. If you are unable to purchase course materials, please go to the Financial Aid office where a staff member will be happy to provide you with information and assistance.
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:
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, Wednesday, 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. 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 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 5 hours in a typical week for work outside of class (work on the problem sets, the weekly review session with our ``TA'' Tori Zamarra, etc.). The best way to use your time is to do a few problems, view the course videos and read in 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 for the course will be based on
I will be keeping your course average in numerical form throughout the semester, and only converting to a letter for the final course grade. The course grade will be assigned according to the following conversion table (also see Note below):
For all exams and quizzes, the topics to be covered will be given out well in advance of the date. I will also provide a list of practice problems and solutions for the exams.
If you ever have a question about the grading policy or your standing in the course, don't hesitate to ask me.
All education is a cooperative enterprise between teachers and
students. This cooperation works well only when there is trust and
mutual respect between everyone involved.
One of our main aims as a department is to help students become
knowledgeable and sophisticated learners, able to think and work
both independently and in concert with their peers. Representing another
person's work as your own in any form (plagiarism or ``cheating''),
and providing or receiving unauthorized assistance on assignments (collusion)
are lapses of academic integrity because they subvert the learning process
and show a fundamental lack of respect for the educational enterprise.
You will encounter a variety of types of assignments and examination
formats in mathematics and computer science courses. For instance,
many problem sets in mathematics classes and laboratory assignments
in computer science courses are individual assignments.
While some faculty members
may allow or even encourage discussion among
students during work on problem sets, it is the expectation that the
solutions submitted by each student will be that student's own work,
written up in that student's own words. When consultation with other
students or sources other than the textbook occurs, students should
identify their co-workers, and/or cite their sources as they would for
other writing assignments. Some courses also make use of collaborative
assignments; part of the evaluation in that case may be a rating of each
individual's contribution to the group effort.
Some advanced classes may use take-home
examinations, in which case the ground rules will usually allow no
collaboration or consultation.
In many computer science classes, programming projects are
strictly individual assignments; the ground rules
do not allow any collaboration or consultation here either.
It is the responsibility of faculty in the department to
lay out the guidelines to be followed for specific assignments in
their classes as clearly and fully as possible, and to
offer clarification and advice concerning those guidelines
as needed as students work on those assignments.
The Department of Mathematics and Computer Science upholds the
College's policy on academic honesty.
We advise all students taking mathematics or computer science courses
to read the statement in the current College catalog carefully and
to familiarize themselves with the procedures which may be
applied when infractions are determined to have occurred.
A student's main responsibility is to follow the guidelines laid down by the instructor of the course. If there is some point about the expectations for an assignment that is not clear, the student is responsible for seeking clarification. If such clarification is not immediately available, students should err on the side of caution and follow the strictest possible interpretation of the guidelines they have been given. It is also a student's responsibility to protect his/her own work to prevent unauthorized use of exam papers, problem solutions, computer accounts and files, scratch paper, and any other materials used in carrying out an assignment. We expect students to have the integrity to say ``no'' to requests for assistance from other students when offering that assistance would violate the guidelines for an assignment.
In this course, all quizzes and examinations will be closed-book. No sharing of information with other students or consultation of online sources in any form will be permitted during exams. On group discussion and possible similar assignments, close collaboration with the other members of your group is expected. On the individual problem sets, discussion of the questions with other students in the class, with Tori Zamarra or the tutors in the Calculus Workshop, and with me during office hours is allowed, even encouraged. However, your final problem solutions on the part B assignments should be prepared individually and the wording and organization of your final problem solutions should be entirely your own work. Moreover, if you do take advantage of any of the above options for discussion of problems with others, you will be required to state that fact in a "footnote" accompanying the problem solution. Failure to follow this rule will be treated as a violation of the College's academic integrity policy (this is a link available in online version).
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.
Week | Dates | Class Topics | Reading (Rogawski and Adams) |
---|---|---|---|
1 | 8/30,31, 9/1 | The real number system | 1.1 |
2 | 9/4,5,6,7,8 | Functions -- linear, quadratic, combinations | 1.1-1.3 |
Quiz 1 Friday | |||
3 | 9/11,12,13,14,15 | Piecewise, trig, exponential functions | 1.3-1.6 |
Quiz 2 Friday | |||
4 | 9/18,19,20,21,22 | Logarithms, finish Chapter 1 | 1.6-1.7,2.1 |
Exam 1 Friday (Chapter 1) | |||
5 | 9/25,26,27,28,29 | Limits and continuity | 2.2-2.5 |
Quiz 3 Friday | |||
6 | 10/2,3,4,5,6 | More on limits | 2.5-2.7 |
Quiz 4 Friday | |||
10/9,10,11,12,13 | No class -- Fall break | 3.1 | |
7 | 10/16,17,18,19,20 | Begin derivatives | 3.1-3.2 |
Exam 2 Friday (Chapter 2) | |||
8 | 10/23,24,25,26,27 | Product and quotient rules, rates of change | 3.2-3.4 |
Quiz 5 Friday | |||
9 | 10/30,31, 11/1,2,3 | Chain rule | 3.5-3.7 |
Quiz 6 Friday | |||
10 | 11/6,7,8,9,10 | Implicit differentiation, log and exp derivatives | 3.8-3.9 |
Exam 3 Friday (3.1-3.8) | |||
11 | 11/13,14,15,16,17 | Related rates, extreme values | 3.10,4.1-4.2 |
Quiz 7 Friday | |||
12 | 11/20,21 | MVT, shape of a graph | 4.3-4.4 |
No Class Wednesday, Thursday and Friday -- Thanksgiving break | |||
No Quiz this week | |||
13 | 11/27,28,29,30, 12/1 | Applied optimization | 4.6-4.7 |
Quiz 8 this Friday | |||
14 | 12/4,5,6,7,8 | L'Hopital's rule, Newton's method | |
Exam 4 Thursday (3.9-3.10,4.1-4.7) |
The cumulative final exam for this course will be given at the established time for MWF 8:00am classes during the regular final examination period. Watch for an announcement from the Registrar.