Note to Math 120 students

## A Note to Math 120 Students from the Department of Mathematics

Welcome to Math 120. This is a course in precalculus.

### What makes this course interesting?

The use of precalculus and its consequences cuts across many disciplines, ranging from biology to business to engineering to the social sciences. We hope that seeing how precalculus can be used to solve real world problems will be interesting.

### What makes this course difficult?

The hardest thing about precalculus is algebra.

You all know from previous math classes how one course will build upon the next, and precalculus is no exception. Math 120 will introduce a basic toolkit of examples and then focus on multi-step problems and applications. Some of these problems are lengthy and algebra mistakes can lead to hours of frustration. We will not be reviewing algebra, since that is a prerequisite for this course. However, there are a number of algebra/skill problems scattered throughout the book to help you review.

Very few of you will go on to major in mathematics or computer science, but most of you will eventually see how precalculus is applied in your chosen field of study. For this reason, we aim for ability to solve application problems using precalculus. We will work through a large number of "word problems" ("story problems") or "multi-step problems". This is one key place Math 120 will differ from a typical high school course. It is also important to note that the ability to apply precalculus 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 common misconceptions

Misconception #1: Theory is irrelevant and the lectures should be aimed just at showing you how to do the problems.

The issue here 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, the student must attain some 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 real purpose of the classes and homework is to guide you in achieving the aspiration of the course: command of the material. If you have command of the material, you should do well on the exams.

Misconception #3: It is the teacher's job to cover the material.

As covering the material is the role of the textbook, and the textbook is to be read by the student, the instructor should be doing something else, something that helps the student grasp the material. The instructor's role is to guide the students in their learning: to reinforce the essential conceptual points of the subject, and to show their relation to the solving of problems.

Misconception #4: Since you are supposed to be learning from the book, there's no need to go to the lectures.

The lectures, the reading, and the homework 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 orient the student in learning the material.

Misconception #5: Since I did well in math, even precalculus, in a good high school, I'll have no trouble with math at UW.

There is a different standard at the college level. Students will have to put in more effort in order to get a good grade than in high school (or equivalently, to learn the material sufficiently well by college standards).

### 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 precalculus by simply watching the instructor and TA perform. For this reason, the homework is THE heart of the course and more than anything else, study time is the key to success in Math 120.

### How much time will I need to spend on this course to succeed?

This course is intended for students who will need calculus in their subsequent courses and in their careers. It is intended to be a much more challenging and in-depth course than most high school calculus courses. You should allocate a lot of time for homework and studying for exams. The University policy in the case of a 5-credit course is 10 hours per week. The ten hour requirement is an average for all students who have fully mastered the prerequisite materials. Some students may need more than 10 hours outside class if, for example they need to review the prerequisite material or if they learn at a slower pace than others.

It is much better to spread your studying as evenly as possible across the week; cramming 15 hours of homework into the day before an assignment is due does not work. You will find this course moves at a much faster pace than a high school course and you should be careful not to fall behind. Pacing yourself, using a time schedule throughout the week, is a good way to insure success; this applies to any course at the UW, not just math. (Textbook Author Note: Over the last 10 years of teaching this course, the single biggest problem encountered by students in this course is poor management of study time.)

### What resources are available to help me succeed?

Math 120 is a challenging, university-level course and the math department would like to see every one of you pass through with 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 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 TA's make themselves very accessible to help their students and you should not be afraid to ask for advice or help.

• All students in Math 120 are encouraged to use the Math Study Center (MSC), located in B-14 of the Communications building. This facility is devoted to helping students in their Precalculus and Calculus courses. MSC is open many hours each week; you can find the current hours on the MSC website. 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.

Some students use the MSC as a place to meet a small group of fellow students and work through problems together. Explaining solutions to one another is often the best way to learn. Talk math with people as often as you can!

• A large amount of material is available on line (including old quizzes, midterms and finals) at
Best of luck this quarter!