Calculus Placement FAQ

List of FAQ Topics

• The Brown Calculus Placement Examination
• Sorting Out Brown's Calculus Courses
• For Students Who Have Studied Calculus Outside of the USA
• Opportunities To Make Sure That You Are In The Correct Math Class
• Placement Beyond the Calculus Sequence
• NonCalculus Math Courses Appropriate For First Year Students

How is the information on the math placement questionnaire used to place me in a math class?


If you have not taken an AP exam, your placement can be regarded as tentative. In any case, you'll have plenty of chances to switch courses if it turns out you're not in the right course. This can be done during Orientation (see the Calculus Placement Exam below) or even during the first week or two of classes (see the question on switching classes).

1. What if I haven't studied any calculus in high school?
   If you have had little or no calculus but your secondary school preparation is firm, take Math 9 (or Math 7). Don't take a placement test. If your math preparation is weak, consider Math 5-6 and, if you have questions, consult with Prof. Jeffrey Hoffstein at the time and place of the Calculus Placement Exam..

2. May I take Math 9 or 7 or 5-6 even if I took a full year of calculus in high school?
   If you have had two semesters of calculus, with reasonable grades, take Math 10 (or Math 17 or Math 19). You should not take Math 9 or 7 or 5-6.

3. I don't have my AP score yet. How do I decide on what course I should take?
   Ultimately this is a choice you will make with your advisor during Orientation. In the meantime, use your course grade, your own assessment of how well you learned the material in your calculus class, and the table given below to choose the course that you think is most appropriate.

4. Will I be able to change my math course after the beginning of classes?
   Yes, once again after discussion with your advisor. (See the Opportunities section below for further details.)

5. I studied some calculus, but I didn't take an advanced placement exam. What should I do?
   Use the table listed below to make a preliminary selection of the most appropriate course. But don't worry too much, since there will be plenty of opportunity to make sure you end up in the correct class. In particular, you might consider taking the Math Placement Exam during Orientation. This nonbinding exam will help you decide which is the right course for you.

1. What is the Brown Calculus Placement Exam?
   The Calculus Placement test is a self-graded, multiple-choice exam. The exam is completely optional. Your score will not be known to anyone but yourself. In particular, it will not be recorded or used for any official purpose. We shall offer course recommendations based on your exam score. Clearly, those recommendations will be more reliable if you have done some reviewing before taking the exam.

2. Should I take the Calculus Placement Exam?
   All entering students are welcome to take the placement exam, but it will especially helpful if you fall into one of the following categories.
   • If you have had one semester of calculus, take the Calculus Placement Test to help decide between a first-semester course like Math 9 or 7 or 5-6 and a second-semester course like Math 10 or 17 or 19.
   • If you have had two semesters of calculus, have not taken an AP test and wish to be placed in a course more advanced than Math 10, take the Calculus Placement Test.
   • If you have taken the AP test and wish placement more advanced than the one recommended on the basis of your AP score, take the Calculus Placement Test.

3. When is the Calculus Placement Exam given?
   The Calculus Placement Exam will be given on Monday during the Orientation Program (Monday August 30, 2010 from 1:00-3:00 PM in Salomon 001), the day before you meet with your advisor.

4. When will I get my grade on the placement exam?
   Results and recommendations will be available at the time of the test.

5. Do I have to take the calculus placement exam?
   No, the calculus placement exam is optional. Its purpose is to help you choose the right math course.

6. If I take the placement exam, are its results binding?
   No, the results and course placement are purely advisory. We don't even keep a record of the results.

1. Brown seems to have a vast array of calculus courses. Could you give me a brief overview of what is offered?
   The Brown Math Department offers a number of overlapping calculus courses so that people with different backgrounds will be able to find a course at the right level.

   Math 5-6	-	1st semester calculus spread over two semesters
   Math 7	-	1st semester calculus with social science applications
   Math 9	-	1st semester calculus
   Math 10	-	2nd semester calculus
   Math 17	-	2nd semester calculus for students with Advanced Placement background
   Math 19	-	2nd semester calculus plus extra engineering topics for students with Advanced Placement background
   Math 18	-	3rd semester (multivariable) calculus
   Math 20	-	3rd semester (multivariable) calculus plus extra engineering topics background
   Math 35	-	3rd semester (multivariable) calculus, honors
   Math 52	-	linear algebra
   Math 54	-	linear algebra, honors

   Many students will have taken calculus in high school, so they will be able to place out of one or more of our courses.
   Math 17 is for students who have done well in a year of AB Advanced Placement calculus or the equivalent.
   Math 19 is the version of Math 17 recommended for engineering students.
   Math 18 is the standard placement for students who have done well in a year of BC Advanced Placement Calculus or the equivalent.
   Math 20 is the version of Math 18 recommended for engineering students.
   Look below for an expanded description of the content of each course.

2. I took the Advanced Placement Exam. Which calculus course should I take?
   Depending on your score on the AP exam and on which exam you took (AB or BC), we recommend the following calculus courses.

   AB Calculus Exam Score Credit Placement 1 none Math 9 (or 7 or 5) 2 none Math 9 (or 7 or 5) 3 none Math 9 (or 7) 4 Math 9 Math 17 (or 19) 5 Math 9 Math 17 (or 19)*						BC Calculus Exam Score Credit Placement 1 none Math 10 (or 9 or 7) 2 none Math 10 (or 9 or 7) 3 Math 9 Math 17 (or 19) 4 Math 9-10 Math 18 (or 20 or 35) 5 Math 9-10 Math 18 (or 20 or 35)
   * Students who receive a 5 on the AB exam and are willing to do some studying on their own to learn the additional BC material (infinite series and Taylor series, polar coordinates and parametric equations, and first and second order ordinary differential equations) may also consider taking one of the third semester calculus courses (Math 18, 20, or 35). Consult with your advisor during Orientation.

   See below descriptions of Math 10, 17 and 19, and of Math 18, 20, and 35.
3. I didn't take the Advanced Placement Exam. Which calculus course should I take?
   If you studied calculus in a program such as an A-level British-type system or in an International Baccalaureate program, see the section below for advice on courses and credits. If you simply studied some calculus in high school, but didn't take a standardized calculus exam, the following table will help you choose the appropriate course. It is also probably a good idea to take the Math Placement Exam during freshman week. But don't worry too much about it now, there will be time when you arrive on campus to make sure you're in a right course.

   High School Math Background	Placement
   No calculus, weak grades in algebra and trigonometry	Math 5
   No calculus, good grades (A's and B's) in algebra and trigonometry	Math 9 (or 7)
   One semester calculus, good grades (A or high B)	Math 10
   Two semesters calculus, weak grades	Math 10
   Two semesters calculus, good grades, did not study infinite series and Taylor series, polar coordinates and parametric equations, and first and second order ordinary differential equations	Math 17 (or 19)
   Two semesters calculus, good grades, covered infinite series and Taylor polynomials	Math 18 (or 20)
   Two semesters calculus, good grades, covered infinite series and Taylor series, polar coordinates and parametric equations, and first and second order ordinary differential equations, strong interest in Math	Math 35

4. I can't decide between courses. What should I do?
   If you are having trouble deciding between two possibilities, it is strongly advised that you choose the higher-level class. It is relatively easy to drop down to the lower one within the first week or two of the course, but much more difficult to move up if you find you've already seen the material.

5. What are Brown's Second Semester Calculus Courses (Math 10, Math 17 and Math 19)?
   

   Math 10	Math 10 is the second semester of the introductory calculus sequence. It covers techniques of integration and applications of integration, sequences and series including Taylor series and power series, parametric curves, polar coordinates and first (and some second) order differential equations.
   Math 17	Math 17 is for students who have the equivalent of a one-year AB calculus AP course. It treats in more detail the topics of Math 10, assuming that students already have studied integration and its applications.
   Math 19	Math 19 is a version of Math 17 especially suited for students of engineering and physics. It has an additional weekly problem session devoted to applied problems.

6. What are Brown's Third Semester Calculus Courses (Math 18, Math 20, and Math 35)?
   There are three distinct third-semester calculus courses at Brown: Math 18, 20 and 35. All three courses cover functions of two and three variables, partial derivatives, maxima and minima, gradients, space curves, multiple integrals, calculation of volumes and surface areas, cylindrical and spherical coordinates, and an introduction to vector analysis, specifically line integrals and Green's Theorem, and, to some extent, surface integrals and Stokes' Theorem and the Divergence Theorem.

   Math 18	Math 18 is the standard multivariable calculus course. It's appropriate for anyone who is going on to study math or any of the sciences, as well as for people in the humanities or social sciences who are interested in continuing their mathematical education. Students taking Math 18 normally have taken either Math 10 or Math 17, or have received an honor grade (3 or higher) on the Advanced Placement BC calculus exam.
   Math 20	Math 20 is a version of Math 18 specially adapted for concentrators in Engineering or Physics with an additional weekly problem session devoted to applications. It has the same prerequisites as Math 18.
   Math 35	Math 35 is the honors version of third-semester calculus. It covers the same material as Math 18, but at a more theoretical level and in more depth. It's recommended for students with high motivation and interest in mathematics who have shown high achievement (i) through their work in Math 10, 17 or 19; or (ii) through a score of 4 or 5 on the Advanced Placement BC calculus exam; or (iii) through their work in a course equivalent to Brown's second semester calculus courses.

7. What are Brown's Linear Algebra courses?
   Linear Algebra and Calculus form the foundations of the mathematics used in applications, as well as of most higher-level mathematics. Linear Algebra as taught in Math 52 covers vector and matrix algebra with applications. The honors version of Linear Algebra is Math 54. It bears the same relation to Math 52 as Math 35 does to Math 18 or 20. Math 54 is offered in both semesters. It may be taken before Math 35 (which is only offered in the first semester).

8. What are the prerequisites for studying more advanced (100 level) mathematics courses?
   Three semesters of calculus and a semester of linear algebra are the ordinary prerequisites for any 100-level mathematics course (except for Math 126, which does not require linear algebra).

9. May I take a class that is more advanced than recommended?
   Yes, it is fine to begin in a more advanced course. There will be opportunities during the first couple of weeks of the semester to drop back, if you feel the course is too difficult. The most common situations are students who are unsure between the following pairs of courses:
   

   Math 9	or	Math 10
   Math 10	or	Math 17
   Math 17	or	Math 18.

10. May I take a class that is less advanced than recommended?
    Generally, the answer is yes, provided that you haven't already received college credit at Brown for the course. In other words, if you receive credit for Math 9 or for both Math 9 and Math 10 because of your score on the advanced placement math exam, then you cannot take those courses again for credit.
    However, we strongly discourage students from taking courses at Brown that largely duplicate material that they have already studied in high school. The reason is simple. You have a short four years at the university to experience a variety of disciplines and to study some of them in depth. Yes, by essentially retaking a course, you might get an "easy A" without having to do a huge amount of work. But the only person you'll be fooling, and also the person you'll be cheating, is yourself. So if you're recommended for a course, we suggest that you at least start at that level. If, after you attend a class or two and take a look at the syllabus, you decide that you belong in a lower level, it's easy to switch classes. But always keep in mind that if you're not being challenged in your courses at Brown, then you're not taking full advantage of what Brown has to offer you.

11. I'm planning to be an engineering major. Which calculus courses should I take?
    You should consider taking Math 19 and Math 20, or, if you have placed out of second semester calculus, start with Math 20. After that, you should consult with your advisor in the engineering department for advice on which courses offered by the Math and Applied Math Departments would be most useful for your major.

12. Are there noncalculus courses that are appropriate for freshman?
    Yes. See the section on other math courses.

1. I took an British A-levels (or an equivalent course). Which calculus course should I take?
   I studied calculus in an International Baccalaureate program. Which calculus course should I take?
   British A-levels and the International Baccalaureate generally cover at least as much material as the Advanced Placement BC course in the United States. Assuming that you did well in you course, you most likely belong in third semester calculus (Math 18, 20, or 35). If your preparation is weak, you might consider second semester calculus (Math 10, 17, or 19). (If you're not sure, the Math Placement Exam given during freshman week can help you decide.) If you spent a semester beyond basic calculus studying multivariable calculus and/or linear algebra, you may be able to place out of one or both of these courses.
   On your placement card, you should simply indicate that you took the A-levels or an IB program and give your final grade in the course. Then sign up for the course you feel is most appropriate. If you're unsure, just choose a class and don't worry about it. There will be many opportunities during freshman week or the first couple of weeks of classes to change your mind.

2. I studied calculus British A-levels, International Baccalaureate, or a similar program. How do I get credit for my course?
   First, it is important to understand the difference between placement and credit. The Mathematics Department is generally happy to grant you placement into any course that you feel you are capable to taking. We may offer you advice that you are not yet ready to take a course, but ultimately you make the decision and live with the consequences.
   Credit for the mathematics that you studied at anyplace other than at Brown is granted by the University through the office of the Dean of the College. This is done automatically for students who have taken one of the Advanced Placement Exams, but is handled on an individual basis for other students. Information about this procedure is described on the web site of the Dean of the College.
   Some concentrations (majors) at Brown require that you have studied a certain amount of mathematics. You can demonstrate this by either taking the appropriate courses at Brown, by receiving university credit as discussed here, or by talking to the concentration advisor in the appropriate department. It is often possible to fulfill the requirement by passing a course at a higher level. (For example, if a certain concentration requires Math 9 and 10, and if you take Math 18, they will probably be satisfied that you also know the material in Math 9 and 10.)

1. During Orientation, how can I make sure that I'm signed up for the best math class for me?
   First, if you didn't take an AP exam, or if you don't think that your score on the AP exam is a good indication of your calculus knowledge, take the Brown Calculus Placement Exam. Your grade on this exam will allow us to provide you with a nonbinding recommendation of the best math course. Second, if you have any questions, come to the Brown Math Department Open House during Orientation. There will faculty members available to talk to you and to answer your questions. (Plus some tasty snacks!)

2. May I switch to a different math class after classes start?
   Yes, definitely. During the first week or two of classes, you can switch to a different math class by simply filling out a add/drop form and getting your new instructor to sign the form. And up to mid-semester, you can still add courses in the same way, though there is a small fee. However, there are a couple of caveats:
   • There are typically several sections offered of each calculus course. Students are not allowed to switch arbitrarily between sections of the same course. In particular, the sections taught by teaching fellows and junior faculty often have enrollment limits.

   • If you switch into a course, the professor will expect you to make up the work that you've missed. So if you're shopping courses during the first week or two of classes, be sure to keep up with the work in all of them.

   • It is much easier to switch down if you find a course is too hard than it is to switch up if you find a course is boring. So for example, if you're not sure whether to take Math 10 or 17, or Math 17 or 18, it's probably best to start with the higher level. [Of course, if you're taking two lab science courses and an English course that has 1000 pages of reading a week, it's fine to opt for the easier math course!]

3. Do Brown students shop classes at the start of the semester?
   Brown has no formal "shopping period," but most Brown students do shop during the first week or two of classes. If you're not sure which math course is the right one for you, we encourage you to attend two courses for a week or two and then decide. You'll need to sign up for one, and be sure to keep up with the work in both until you decide, but if you decide to switch, the process is quite easy. [Every calculus class will have at least one section, taught by a full professor, with no enrollment limit. But other sections may have enrollment limits.]

1. I have already taken multivariable calculus. What course should I take next?
   If you took a full semester college-level multivariable calculus course, then you may begin with linear algebra. (See the list of topics for Brown's multivariable calculus course to be sure that you covered all of the topics.)

2. I have already taken a linear algebra course. What course should I take next?
   If you took a full semester college-level linear algebra course, then you do not need to take Math 52 (or 54). If you also took a multivariable calculus course, then you may be prepared to begin with our 100-level math courses. Good 100-level math courses with which to begin include Math 101 (analysis), Math 106 (differential geometry) Math 126 (complex analysis), Math 153 (algebra), and Math 161 (probability). Note that Brown's 100-level math courses are proof-oriented, so if your multivariable calculus and linear algebra courses did not include substantial work with proving theorems, you might want to consider taking either Math 35 or Math 54.

1. I'd like to continue studying math at college, but I'd prefer not to take calculus sequence. What other options do I have?
   There are a number of courses offered by the Mathematics Department that will introduce you to various beautiful areas of mathematics that are not in the calculus sequence. These include (not all are offered every year):

   • Math 2 - What is Mathematics?
     A broad overview of the subject, intended primarily for liberal arts students. What do mathematicians do, and why do they do it? We will examine the art of proving theorems, from both the philosophical and aesthetic points of view, using examples such as non-Euclidean geometries, prime numbers, abstract groups, and uncountable sets. Emphasis will be placed on appreciating the beauty and variety of mathematical ideas. The course will include a survey of important results and unsolved problems that motivate mathematical research.

   • Math 8 (sometimes given as Math 1 in the First-Year Seminar Program) - The Mathematical Way of Thinking
     Topics in geometry of four and higher dimensions, relationships to different parts of mathematics as well as interrelations with physical and biological sciences, literature, cognitive science, philosophy, and art.

   • Math 42 - Introduction to Number Theory
     An overview of one of the most beautiful areas of mathematics. An ideal course for any student who wants a taste of mathematics outside of, or in addition to, the calculus sequence. Topics include: prime numbers, congruences, quadratic reciprocity, sums of squares, Diophantine equations, and as time permits, such topics as cryptography and continued fractions.

2. May I use noncalculus math courses, such as Math 1, 2, 8 or 42, as part of my concentration?
   That depends on the concentration. They may not be used as part of a standard Mathematics concentration. It's probably not worth worrying about things like this during your first year. But if you want to know, then make an appointment to talk to the concentration advisor in your department.