Holy Cross Mathematics and Computer Science
Holy Cross Mathematics and Computer Science
This course is the continuation of MATH 135 (Calculus 1) from the fall. If you are joining the class from a different section of MATH 135, you will have covered essentially the same topics as we did in this section, so there should not be any surprises. If you took a course or courses roughly equivalent to MATH 135 in high school or at another college, you may find things that are unfamiliar. If so, you may need to do some extra review work to catch up, but I will be happy to advise you on this and to answer any questions you might have.
Note: If you earned a grade of C or below in MATH 135, you should be aware that there are many topics we will study this semester that draw heavily on material from MATH 135 that you may not have learned completely the first time around. To succeed in this course, you may need to review and/or relearn some things from that first semester. While this is certainly possible, I cannot say that it will be easy. You may find that this course moves more quickly than MATH 135 did.
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 now 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). We will begin this semester by studying their big result -- the Fundamental Theorem of Calculus and then learn a number of applications of this theorem. The topics to be covered this semester are:
The objectives of this course are:
The text book for the course is Calculus: Single Variable (Early Transcendentals), Third Edition, by Jon Rogawski and Colin Adams, Freeman/MacMillan Education (the same text as last semester). We will cover (most of) Chapters 5 - 10 this semester.
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 136 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 mathematics teachers 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, 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. You do not need to be a "math genius" 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, Tuesday, Wednesday, and Friday this semester. If attending class wasn't important, all college courses would be taught as MOOCs or by correspondence, and your tuition would be much lower!
Use the textbook and class notes actively. Don't just use them to look for worked problems similar to ones on the problem sets. Plan to look over the section to be covered each day before coming to class. That will make the lecture or other class activity more understandable. After the class, if things were not clear, you will find alternate explanations of concepts that may help you past a "block" in your understanding. 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. If necessary, make a list of questions to ask in office hours or at the next class. Another thing to bear in mind while reading your text is that the result of an example is often secondary to the process used in obtaining the result -- that process is the real point, and that's what you should take away from studying the example.
Take notes and use them. This may seem obvious, but in my experience too many students seem to copy down everything on the board diligently, and then never look at their notes again. Used intelligently, your notes can be a valuable resource as you work on problem sets and prepare for exams. Indeed, one technique that many students find helpful is to recopy the class notes, filling in details that might have been clear the first time, putting in extra examples, explanations or ideas that really helped them understand the material, and so forth.
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. The best way to use your time is to do a few problems, a little reading from the book, and reviewing of class notes every day.
Perhaps 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 mathematical subject of calculus. This includes understanding key examples and techniques, plus knowing the statements of the major results (theorems) and the main ideas 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 (including on examinations) I will ask you 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 final exam for this course will be given at the established time for MTWF 8:00am classes: 3:00pm on Thursday, May 7.