A Note to Math 125 Students from the Department of Mathematics
What makes this course interesting?
This course covers integral calculus. In a typical problem, you need to compute something by slicing it up into very small pieces and then fitting the slices back together. For example, to find the volume of a sausage, you slice the sausage up into thin pieces, find the area of each slice and then use calculus to put these areas together to get the volume. These ideas have many applications in physics, engineering, biology and economics. Another example is computing the total stress on a steel girder used in the construction of a skyscraper.
What makes this course difficult?
The hardest thing about calculus is precalculus. The hardest thing about precalculus is algebra.
You know from previous mathematics courses that each course builds on the ones that precede it, and Math 125 is no exception. You need a strong command of the material from Math 124. This means that the basic computation you will do in Math 125 is the reverse of differentiation. Some of the techniques for doing this are tricky.
Very few of you will go on to major in mathematics or computer science, but most of you will eventually see how calculus is applied in your chosen field of study. For this reason, we aim to develop your ability to solve applied problems using calculus. Some of the homework problems are quite lengthy and building your mathematical problem-solving stamina is one of the aims of this course. If you have taken the Math 120 or Math 124 at UW, you know what this all means. If you have not, it means that you will encounter many word problems, also called story problems, and other multistep problems. This is one important way in which Math 125 differs from a typical high school course. In addition, it is important to note that the ability to apply calculus requires more than computational skill; it requires conceptual understanding. As you work through the homework, you will find two general types of problems: calculation/skill problems and multi-step/word problems. A good rule of thumb is to work enough of the skill problems to become proficient, then spend the bulk of your time working on the longer multi-step problems.
Five important things to understand about Math 125
Misconception #1: Theory is irrelevant and the lectures should be aimed just at showing you how to do the problems.
The problem with this view is that we want you to be able to do ALL problems – not just particular kinds of problems – to which the methods of the course apply. For that level of command, you must develop conceptual understanding and develop judgment. Thus, a certain amount of theory is very relevant, indeed essential. A student who has been trained only to do certain kinds of problems has acquired very limited expertise.
Misconception #2: The purpose of the classes and assignments is to prepare the student for the exams.
The purpose of classes, homework, worksheets, and other course activities is to guide you in achieving the central goal of the course: command of the material. If you have a strong command of the material, you should do well on the exams.
Misconception #3: It is the teacher's job to cover the material.
The textbook presents the course material, but the instructor has a different role. The instructor's role is to guide the students in their learning: to reinforce the essential conceptual points of the subject, and to show how they are used to solve problems.
Misconception #4: Since you are supposed to be learning from the book, there is no need to attend lectures.
The lectures, the reading, the homework, and the worksheets should combine to produce true comprehension of the material. For most students, reading a math text won't be easy. The lectures should serve to help you organize and understand your study of the material.
Misconception #5: Because I did well in mathematics, including calculus, in a good high school, I'll have no trouble with math at UW.
There is a different standard at the college level. Students generally need to devote more time and effort to college mathematics than they did in high school.
How do I succeed?
Most people learn mathematics by doing mathematics. That is, you learn it by active participation; it is very unusual for someone to learn calculus by simply watching the instructor and TA solve problems. For this reason, homework is at the heart of the course and more than anything else, study time is the key to success in Math 125. We recommend at least 10 hours of study per week, outside of class. Also, during the first week, the number of study hours will probably be even higher as you adjust to the viewpoint of the course and brush up on precalculus/algebra skills. In effect, this means that Math 125 will be a commitment of at least 15 hours per week; roughly equivalent to a part-time job! This time commitment is in line with the University Handbook guidelines. In addition, it is much better to spread your studying as evenly as possible across the week; cramming 10 hours of homework into the day before an assignment is due does not work. Pacing yourself, following a regular study schedule throughout the week, is a good way to help ensure success; this applies to any course at the UW, not just math.
What is the course format?
On Monday, Wednesday and Friday, you will meet with the instructor for the course in a 50-minute-long class. On either Tuesday or Thursday (usually Thursday, but it may change depending on the particular quarter schedule), you will have an 80-minute section of 30 students. During this section, you will work in small groups on worksheets designed to lead you through particular ideas related to this course. The TA for the course will circulate among the individual groups to ensure everyone is progressing. Finally, on the remaining Tuesday or Thursday, you will meet for 50 minutes; this section is typically devoted to question and answer and a short quiz. All midterms are taken in your 80-minute section; these exams are written as 50-minute exams, but the extra time cuts down on time pressure.
What resources are available to help me succeed?
Calculus is a challenging course and the math department would like to see every student have a positive experience. To help, a number of resources are available.
- Your instructor and TA will be accessible to help you during office hours, which will be announced early in the first week of the term. If you are new to the university, you might have the false impression that professors are aloof and hard to approach. Our faculty and TAs make themselves available to help students and you should not be afraid to ask for advice or help.
- The Department of Mathematics operates a Math Study Center (MSC), located in B-14 of Communications. This facility is devoted to helping students in our introductory mathematics courses only. The center has extensive hours of operation that will be announced the first week of class. The MSC is staffed by advanced undergraduate and graduate students who can help you with difficulties as you work through the course. In addition, many faculty hold office hours there as well. One useful piece of advice: The MSC is often overcrowded the day before homework is due; this is another good reason to spread out your study time over the week.
- Some students use the MSC as a place to meet a small group of fellow students in the course and work through problems together. Explaining solutions to one another is often the best way to learn.
- A large amount of material is available online (including old quizzes, midterms, final exams, and worksheets) at
- Some students additionally hire a tutor for private help; see a list of tutors.
We hope you find Math 125 both challenging and rewarding, and we wish you every success in the course.