# MAT103 Calculus I

**Schedule: **MW at 8:30 AM, at 10 AM, at 11 AM or at 1:30PM, Fall and Spring. Optional review sessions are not scheduled through the registrar and will be set up only at the beginning of the semester.

**Brief Course Description: **An introduction to the mathematics of change and a gateway to further work in the natural sciences, engineering, economics and finance as well as the social sciences. Develops the technical concepts of limits and continuity, derivatives and integrals in the single variable setting. Important applications of these include optimization, the geometry of curves, approximation and error analysis, counting and estimating roots, average behavior and estimating change, computing area of planar regions. Includes the rudiments of differential equations and modeling through curve sketching and initial value problems. Emphasizes the development of critical reasoning and communication skills in a quantitative setting.

**Prerequisites: **MAT100 or equivalent, solid pre-calculus background from high school, recent math SAT score of 670 or higher, ACT math score of 28 or higher.

**Who takes this course?** Most students in this course are first-year students, many of whom are still undecided about a major. If you consider economics or any of the natural sciences this course is a must. Many students interested in medicine or public policy also take this course.

**Placement Information: **MAT103 is* roughly* equivalent to AB calculus or the mandatory calculus portion of Math HL in the IB program. We *estimate* that any one of the following is *minimally* equivalent to this course, comparable to a grade of C: 5 on the AB exam or 6 on the IB Math HL exam or a B on the British A-levels exam or 4 on the BC exam. A year of high school calculus with good grades may be comparable, but it is difficult to say for sure, since programs can vary quite a bit.

Jumping ahead of your recommended placement is not always impossible, but be aware that the pace and the work load of university courses won’t be like high school. Learning two semesters worth of math in a single semester will be excessively stressful and should not be undertaken lightly. Your work load will be demanding even if you are in the right course.

Talk to your advisers and listen to what they say with an open mind. Advice from other students is useful, but advisers have a broader perspective about the Princeton academic experience.

**FAQ: **

Make sure you leave room in your schedule to take 100, and remember that 100 is offered only in the fall semester at two times. If you do sign up for 103, you will take a placement quiz early in the semester. Take this placement recommendation seriously and be ready to make adjustments if necessary. The sooner you commit to the right course, the better.__You want to take MAT103 but it is probably a stretch. Your advisers are telling you to take MAT100 but that does not feel right to you.__

It is just not true that 175 is easier than 103, and it is very difficult to do well in 175 without a solid knowledge of the material in 103.__You want to be an economics major and your math placement says MAT103, but you have heard that MAT175 is actually much easier than MAT103.__

Your best path to completing the BSE program is to start in the course that is the best fit for your current knowledge. Taking courses that you can successfully complete is the most efficient plan in the long run. Many successful BSE students start in 103.__You want to be an engineer and you are worried that you will be behind unless you start in 104 or 201.__

The longer you delay, the more you will forget what you know from high school. If you need to take calculus, sooner is better.*You are very excited about being at Princeton and you don’t want to take math in your first semester even though you know you will probably need it later.*

The math department does not use calculators in its introductory classes. If you normally rely on your calculator to translate a function or equation into a graph, to solve equations, or to find values of trigonometric functions at the standard angles, then you should be conservative in your choice of calculus class.__What kind of calculator do you need for calculus at Princeton?__

Calculators can be useful, but these courses want to teach students how to think independently in a quantitative setting and calculators can function as substitute for thinking at the beginning. Students need to learn the basic vocabulary and grammar of mathematics so that they can recognize patterns and common features by working through simple well-chosen examples. For instance, a program like 'Google translate' can be helpful to a person with basic knowledge of a language to decipher a complicated sentence or even to write a correct one, but without a good foundation to refine and direct its application, the results of blindly applying this useful technological tool can be wildly off the mark.__Are you serious about no calculators? Why?__

Try the sample problems to test your 103 knowledge. If you can solve most of those problems, go ahead and sign up for 104 but take the placement quiz results seriously. Seek help early! Whatever course you start in will have a placement quiz early on to help you make this decision. Talk with your academic adviser or the math advisers at registration.__Based on the course description for MAT103 you think you are probably ready for MAT104 but you don’t have test scores to back that up.__