Holy Cross Mathematics and Computer Science
Holy Cross Mathematics and Computer Science
MATH 135 (Calculus 1) is a beginning calculus course and does not assume any prior exposure to this area of mathematics.
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 Premedical Concentration. There is another beginning calculus course called MATH 133 (Calculus with Fundamentals 1) that has more class time -- 150 minutes per week. It is designed for students who enter college with a somewhat weaker mathematics background or who might need the additional class time to master the course material. If you are taking this course for general interest, out of habit, or to fulfill a Common Area Requirement, you are welcome, but you might also want to consider the MATH 110 (Topics in Mathematics) courses that we offer regularly.
If you took the BC Calculus AP Exam and scored a 4 or 5, you should start in MATH 241 and you will forfeit two AP credits by taking this course.
If you have taken a year of calculus in high school and scored a 4 or 5 on the AB Calculus AP Exam, you should start in MATH 136 (Calculus 2) and you will forfeit one AP credit by taking this course. In any case, if your high school calculus course was a solid one and you did well, then this course will be almost entirely review for you. Consider starting in MATH 136 if this is your situation; students who have taken calculus before, even those who did not take the Calculus AP examination, often find that MATH 136 is a better starting point. Successful completion of MATH 136 alone also satisfies the mathematics requirement for the Biology and Economics majors.
This course continues to MATH 136 (Calculus 2) in the spring semester, but this particular section will not continue (i.e. you will take the course at a different time, with a different instructor, if you go on).
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, with any other mathematics faculty member, or with your faculty adviser.
Calculus is the mathematics of change. First developed in the 17th century, it has been a major part of mathematics since that time. Calculus 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, I will go out on a limb and say that calculus is also one of the crowning achievements of the human intellect. If you approach it in a receptive and adventurous manner, you are in for an exciting journey of exploration as you learn it!
Two men, Isaac Newton and Gottfried Leibniz, are often 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 start of the spring continuation of this course, MATH 136, will be devoted to their big result -- the Fundamental Theorem of Calculus.
The topics to be covered this semester are:
See the course schedule below for a more detailed week-by-week breakdown of the semester. An even more detailed day-by-day schedule is maintained on the course homepage.
The objectives of this course are:
The text book for the course is Calculus (Single Variable, Early Transcendentals version), 3th edition by Jon Rogawski and Colin Adams, Freeman/Macmillan (available in the H.C. bookstore, and elsewhere). We will cover Chapters 1 - 4 this semester. The follow-up Calculus 2 (MATH 136) course uses the same textbook. So hold on to it if you think you will continue (even if it is not next semester).
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 a poor way to encourage this sort of active learning, and a poor use of limited class time. On the other hand, having students work through questions individually or in a group setting during class with oversight and supervision from an experienced teacher 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 a relatively short video presentation 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 (with the opportunity to ask questions and get immediate feedback from me). Besides using class time more productively, this approach also has the benefit 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.
The presentations have been prepared specially for MATH 135 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 have done things previously. 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!
Your active participation will be important for the success of what we do. Unless specifically directed otherwise, please turn off all cell phones, pagers, I-pads, computers and other similar electronic devices for the duration of each class meeting -- your full attention will be required.
A good "work ethic" is key. Contrary to what you might have heard or might believe, mathematics professors definitely want you to learn and do well in their courses! But you will also need to do your part by working hard. You do not need to be a "math genius" (whatever that means) to master this material and do well. But you will need to put in a consistent effort and keep up with the course.
Come to class. Unless you are deathly ill, have a genuine family emergency, etc. plan on showing up here at 8:00 am every Monday, Wednesday, and Friday this semester. If attending class wasn't important, all college courses would be by correspondence, and your tuition would be much lower!
Take notes as you watch the videos. Hold onto the worksheets and your solutions to problems from class. Use them! Used intelligently, your notes on the video presentations, the in-class worksheets, and the textbook will be your most valuable resources as you work on problem sets and prepare for exams.
Use the videos and textbook actively. Watch the video on the material to be covered each day before coming to class. That will often be necessary to make the class activity understandable. After the class, if things did not become clear, you might want to rewatch a video. In the textbook, you will also find alternate explanations of concepts that may help you past a block in your understanding. But be aware Watching the class videos is not like watching a TV show or a movie. And reading a math book is not like reading a novel. You will need to watch and/or read attentively, with pencil and paper in hand, pausing to work through examples in detail and taking notes. If necessary, make a list of questions to ask in office hours or at the next class.
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. You should expect to budget at least 6 hours in a typical week for work outside of class, and perhaps more than that during the weeks of exams. The best way to use your time is to keep up with the videos, do a few problems, a little reading from the book, and reviewing of class worksheets 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, or attending the Calculus Workshop in the evenings Sunday-Thursday.
Finally, be aware this course is not only about learning how to solve a set collection of particular types of problems. It is about learning and mastering the whole mathematical subject of calculus. This includes understanding key examples and techniques, plus knowing the statements of the major results (theorems) and the main ideas behind showing why they are true. The answers worked out in specific examples are often secondary to the ideas being illustrated or the process used in obtaining the results -- those ideas or the process are the real point, and that's what you should take away from studying the examples. In addition, from time to time I will ask questions that are not quite the same as anything you have seen before, but that draw on those ideas and processes you have seen. Being able to apply what you know in new situations like that is probably the best demonstration that you have really learned the material for this course.
Grading for the course will be based on:
Important Notes:
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):
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 examinations will be closed-book. No sharing of information with other students in any form will be permitted during exams. On group discussion and computer lab write-ups, 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 the tutors in the Calculus Workshop, and with me during office hours is allowed, even encouraged. However, your final problem solutions 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.
The following is an approximate and evolving schedule. Some rearrangement, expansion, or contraction of topics may become necessary. I will announce any changes in class and on the more detailed day-by-day schedule maintained on the course homepage.
| Week | Dates | Class Topics | Sections in Rogawski/Adams |
|---|---|---|---|
| 1 | 8/31, 9/2 | Course introduction, linear and quadratic functions | 1.1, 1.2 |
| Precalculus diagnostic quiz Friday, 9/2 | |||
| 2 | 9/5, 7, 9 | Basic classes of functions, trigonometric functions, inverse functions | 1.3-1.5 |
| 3 | 9/12 ,14, 16 | Exponential and logarithm functions, begin limits | 1.6, 2.1 |
| 4 | 9/19, 21, 23 | Tangents and velocities, limits | 2.2, 2.3 |
| Exam I -- Friday, 9/23 | Chapter 1, 2.1 | ||
| 5 | 9/26, 28, 30 | Limit laws, continuity, evaluating limits by algebra | 2.3, 2.4, 2.5 |
| 6 | 10/3, 5, 7 | Trigonometric limits, limits at infinity, properties of continuous functions | 2.6-2.8 |
| 10/10, 12, 14 | No class -- October break | ||
| 7 | 10/17, 19, 21 | Derivatives, product and quotient rules | 3.1-3.3 |
| 8 | 10/24, 26, 28 | Trig derivatives, higher derivatives | 3.4, 3.6 |
| Exam II -- Friday, 10/28 | Chapter 2, 3.1-3.3 | ||
| 9 | 10/31, 11/2, 11/4 | Chain rule, implicit differentiation, exponential and logarithmic derivatives | 3.7, 3.8, 3.9 |
| 10 | 11/7, 9, 11 | Related rates, extreme values | 3.10, 4.2 |
| 11 | 11/14, 16, 18 | MVT, the shape of a graph, L'Hopital's Rule | 4.3-4.5 |
| 12 | 11/21 | Curve sketching and asymptotes | 4.6 |
| No Class Wednesday, 11/23 and Friday, 11/25 -- | |||
| Thanksgiving break | |||
| 13 | 11/28, 30, 12/2 | Optimization | 4.7 |
| Exam III -- Friday, 12/2 | 3.4-3.10, 4.2-4.5 | ||
| 14 | 12/5, 7, 9 | More on optimization, Newton's Method, Course wrap-up | 4.7, 4.8 |
The final exam for this course will be given at the scheduled time for MWF 8am classes.