Department of Mathematics and Statistics

Summer 2007 mailing to the class of '11

Welcome to Swarthmore! We suspect you are planning to take some math or statistics here; most Swarthmore students do. There are 3 different groups of courses from which a first-year student typically chooses. The best known and most popular, but not necessarily the best for you, is the calculus sequence. The second group is statistics (Stat 1, 11, 31). The third might be called "the rest of math;" courses on basic ideas (Math 3) or on areas not covered in the calculus sequence (Math 29). If you are planning a major that requires or recommends the traditional calculus topics (majors such as Physics, Chemistry, Engineering, Economics, and of course Mathematics) you will probably want to start or continue with the standard calculus sequence (Math 15, 25, 27, 34), although you may well wish to branch out after a semester. If you have limited space in your program for mathematics, but would like an overview of how calculus is used in various fields, such as economics and biology, we have an abbreviated calculus sequence that might appeal to you (Math 15, Math 23). For the rest of you, consider a math/stat course from outside the calculus sequence this Fall - one goal of the first two years at college is to expand your horizons.

Back to top of page

Courses

Below are descriptions of the courses first-year students usually take. Please see the catalog for fuller descriptions of the courses below and of more advanced courses. Be sure to consult the 2007-08 catalog, not an earlier one; the math/stat curriculum and numbering has changed. A placement testination is required for entrance to each math course below; see "Placement Procedures" later.

Stat 1. Statistical Thinking. For students who want an intuitive appreciation for the role played by statistics in the collection and analysis of data and do not anticipate that they will ever need to actually do statistical analysis in their work. If you think that there is any chance you may major in a field that uses statistics (such as biology, psychology, and economics), we recommend you take Stat 11 instead. No credit will be granted for Stat 1 to students who have taken or received credit for any other Stat course.

Stat 11. Statistical Methods. (also cross-listed as SOAN 10E) For students who want a practical introduction to the use of statistical methods with the aid of software. Stat 11 satisfies the recommendations of many Swarthmore departments for their majors. Note: some departments prefer that their majors take this course later in their program, once the relevance of statistics is more clear. You place out of Stat 11, and get one credit towards graduation from Swarthmore, by getting a 4 or 5 on the Statistics AP testination of the College Board.

Stat 31. Data Analysis and Visualization. (Spring only) This course studies the methods for exploring and modeling relationships in data and introduces modern techniques of statistical graphics. Prerequisites: Stat 11 or a score of 4 or 5 on the AP Statistics test. Writing course

Mathematics

Math 3. Introduction to Mathematical Thinking. (Spring only) This course explores, at an elementary level, what mathematics is, what kinds of questions mathematicians ask, how those questions are answered, and how mathematics teaches skills useful in all walks of life. Class work will include lectures, discussions, and hands-on exploration. Evaluation will be based on problem sets, writing assignments, tests, and a final project. There may be some opportunities along the way to mix in traditional pre-calculus material. This course cannot be counted towards a mathematics major. Not intended for students who place out of Math 15. Writing course

Math 15. Elementary Single Variable Calculus (Calculus I). The first semester of calculus, with an emphasis on an intuitive understanding of the concepts, methods, and applications. Students who have never had calculus tend to do better in this course than those who take it a second time, so if you have had calculus, try to place out of this course.

Math 23. Brief Survey of Calculus II and III. A survey of key topics in single and several variable calculus. This continuation of Math 15, which covers a portion of the topics from Math 25 and Math 33, is for students who do not plan to take any more calculus. There will be an emphasis on applications in the biological and social sciences.

Math 25. Calculus II. A continuation of Math 15 for students who wish to major in mathematics, chemistry, physics, or engineering, or who want a more thorough treatment of the topics in single variable calculus. This course covers the fundamental theorem, integration, geometric series, Taylor polynomials and series, and an introduction to differential equations. Students majoring in mathematics, chemistry, physics, or engineering are required to have placement or credit for either Math 25 or Math 26.

Math 25S. Calculus II First-year Seminar. (Fall only) Covers the same material as Math 25. This section is intended for students who are eager to do science and math and feel that their knowledge and skills can best be bolstered by a seminar format[SM1]. This seminar features an intensive, interactive environment with lots of hands-on activities, such as group work, computer work, and frequent student presentations. See discussion of first-year seminars at the end of this section.

Math 26. Advanced Calculus II.(Fall only) For students who place out of the first half of Math 25, this course goes into more depth on sequences, series, and differential equations than does Math 25. Students majoring in mathematics, chemistry, physics, or engineering are required to have placement or credit for either Math 25 or Math 26.

Math 27. Linear Algebra.Linear equations and functions (the simplest type), but in any number of dimensions. Considered part of the calculus sequence since it is very useful for multivariable calculus. Math 27 covers both the theory behind linear algebra and the computations necessary to solve applied problems. Students interested in a treatment of this material that more heavily emphasizes concepts, theory, and learning to do proofs, should consider taking one of Math 28 or Math 28S instead. Note that a student with 1.5 AP credits may enroll in Math 27 without taking Math 26, but this is not recommended for anyone who needs Math 26 to complete the calculus requirements for their major.

Math 28. Honors Linear Algebra/Math 28S, Honors Linear Algebra First-year Seminar. A more theoretical treatment of the material in Math 27. The problems in Section 4 of our placement test are intended, in part, to show you the flavor of this course (and of Math 35). Math 28S is for advanced students who are ready for the style of junior-senior seminars. See discussion of first-year seminars at the end of this section.

Math 29. Discrete Mathematics. An introduction to noncontinuous mathematics, including graph theory and combinatorics. Finding the shortest route through a road network is an testple of discrete math; at each intersection there is a small number of choices, but overall the number of choices is astronomical, so brute force won’t work. Math 29 is especially useful for computer science and many social sciences. Offered every semester. Note: The spring version of Math 29 tends to place a greater emphasis on the connections between computer science and discrete math. Writing course

Math 33. Basic Several Variable Calculus. This course considers differentiation and integration of functions of several variables, with an emphasis on two and three dimensions. Note: the Department strongly recommends that students take Math 34, which provides a richer understanding of the material covered in Math 33. Because Math 34 has a prerequisite of linear algebra (Math 27, or some flavor of Math 28), Math 33 is offered for those students whose programs have limited space for mathematics. Students may not take both Math 33 and Math 34 for credit.

Math 34. Several Variable Calculus. Same topics as Math 33, covered in more depth, using concepts from linear algebra. Students may not take both Math 33 and Math 34 for credit.

Math 35. Honors Several Variable Calculus. (Spring only) This version of several variable calculus will be more theoretical, abstract, and rigorous than the treatment in Math 34.

Back to top of page

Should you buy a graphics calculator?

No course in our Department requires a graphics or symbolic calculator. Our courses typically use computers for such calculations. But calculators are welcome and often useful, other departments may make heavier use of them, and many Swarthmore math students use them. The most common brand is Texas Instruments, and some faculty are familiar with the TI series.

Back to top of page

First-year Seminars

The Math/Stat Department is offering two first-year seminars, one at the second semester calculus level (Math 25S) and one at the honors linear algebra level (Math 28S).

What is a math seminar? First, like all seminars, it's smaller. The first-year seminars are limited to 12 students, whereas regular class sections may be 30 or more. And as with all Swarthmore first-year seminars, part of the goal is to form an informal advising group through which you learn the ways of Swarthmore. But the biggest difference between a math course and a math seminar is in the style of learning. You learn cooperatively by discussing math with your peers, through getting up to the board and explaining your insights and solving problems. Lectures by the professor are limited. Seminars typically meet in a seminar room, around a table with blackboard all around.

To accomplish this style of learning one needs more class time. So math seminars tend to meet twice the normal number of hours. The amount of material covered is the same, so it's still a 1-credit course, but many students feel they learn it better in a seminar, have more fun, and become friends with their seminar-mates.

But don't take our word for it. Here are some comments from two students who took the linear algebra seminar:

Here are some comments from a student who took our calculus seminar:

To indicate an interest in registering for our first-year seminars, please read the next section on pre-registration and lotteries.

Back to top of page

Pre-registration and Lotteries, Fall 2007

At Swarthmore, registration for courses has 2 steps: first you preregister by computer, then certain courses are lotteried or adjusted. Registration for first-year students for their first semester will follow these two steps just as all other registration periods do. We hold a pre-registration for essentially all the fall courses first-year math students take:

Stat 1, 11
Math 15, 23, 25, 25S, 26, 27, 28, 28S, and 29.

A lottery means that a course has an enrollment limit, and if more students register, some will be excluded. For testple, first-year seminars are restricted to twelve students. In the fall, the classes that may be lotteried are Stat 1, Stat 11, Math 25S and Math 28S. Stat 1 and 11 are offered every semester, so students will not have to wait long to get into them.

Math/Stat does something few other departments do. For most courses, if a section gets too big, instead of lotterying, we move students to less crowded sections that fit in their schedules, and sometimes we change how many sections we offer and/or when we offer them. In order to do this we need to collect information that other departments do not collect.

The procedure is as follows.

1) On Friday afternoon, August 31, after you have consulted with your advisor, you will participate in the College's regular online pre-registration. If you are thinking of taking a math or stat course, you must list it during this preregistration process. If you fail to list it during this electronic preregistration, we cannot guarantee you a slot.

2) If you preregister for a math course that we did not recommend for you (or if we have not made a recommendation because you did not take a placement test or do well enough on an AP or IB), the preregistration program will not accept your choice.

3) If you preregister for a course that has multiple sections, you will be directed at some point to a second online form just for that course. You will be asked questions about your availability for other sections of the same course.

By Saturday morning, September 1, at 9am we will post the enrollments outside our department office. They will also be available by computer. You must check this information because we may have lotteried you out of a course or moved you to another section, perhaps a newly created section.

4) If you are satisfied with your math enrollment (and all your other preregistrations), you are done with registration. If you are not satisfied, come to the in-person registration at 11am on Saturday. Also, seek out Prof Johnson between 9 and 11am.

Back to top of page

Credit for Work Prior to Swarthmore

Neither the AP exams nor the IB exam correspond completely with our courses. Nonetheless, credit is awarded according to the following policy:

1 credit (for Stat 11, and placement into Stat 31) for

1 credit (for Math 15, and placement into Math 23 or Math 25) for

1.5 credits (for Math 15 and half of Math 25, and placement into Math 26) for

2 credits (for Math 15 and Math 25, and placement into Math 27) for

Caution: If you take any course at Swarthmore for which you have received credit by AP or IB score, you will lose that credit.

The College Board sends your AP scores to Swarthmore directly, but it is always a good idea to bring your official AP or IB transcript with you in case we don't have your scores. These scores are the only automatic way to get credit for your prior work. If you take our own placement test, you may be placed out of a certain course without being awarded credit for it, but this lack of credit should not cause you any problems. Most departments or other institutions that require college mathematics quite happily accept advanced placement itself or, failing that, credit for any coursework subsequent to advanced placement (as opposed to requiring credit for a specific introductory course). For instance, engineering programs and medical schools usually accept credit for more advanced math courses. If you are concerned about this issue, check with the appropriate program or department advisor when you get here.

What if you have taken mathematics courses at another college or university prior to Swarthmore? It does not matter whether your previous mathematics work was done at a secondary school or at a college or university: we will not give you automatic credit for this work. First-year students who have taken calculus at a university need to take either our own calculus test (for placement), or an AP or IB exam (for credit). If you want the credit for an outside purpose, say medical school, then your credit from the other institution may already suffice. Be sure to get a transcript.

If you really want credit for a course you took before Swarthmore, here are your options. To get credit for Math 15 or Math 25, students may take the regularly scheduled final exam for that course during the fall of their first year; if they receive a straight C or better, they will be granted credit (without a grade). Students who intend to do this should notify the First-year Math Placement Advisor, Aimee Johnson, during Orientation Week. To receive credit for a higher-level course, students should refer to the College policy outlined in the Bulletin (under "Attendance at Classes"). Note: Credit obtained in the ways outlined above is subject to the rule that you cannot take more than 10 credits in one academic year without paying extra tuition.

Back to top of page

Placement Procedures

Students enter Swarthmore with widely varying preparation and aptitude in mathematics. Placement is a Departmental recommendation that tries to ensure you enroll in a course that is right for you. To help make that recommendation, the Department requires that you take one of the placement testinations we give, or earn credit via one of the following two standardized testinations: AP Calculus (not Statistics) or a Higher Level IB Mathematics.

The Department's placement tests, described in the next subsection, are used for placement purposes only, not for credit. Placement results do not appear on your transcript.

First-year students must take either a Swarthmore test or do well enough on one of the 2 standardized tests mentioned above in order to take a mathematics course. Students who have not will not be allowed to enroll in a mathematics course at Registration.

What if you have not taken any calculus or took a little but do not feel you learned very much? It may be that you have no need or desire to take calculus while at Swarthmore. We offer two levels of introductory statistics (Stat 1 and Stat 11) as well as a course in mathematical thinking (Math 3) which may be more appropriate Math/Stat courses for you, and which do not require a placement score. If you do plan to take calculus, you will begin with Math 15 and must first pass our Calculus Readiness Test when you arrive in the Fall. There is a version of that test included in the summer mailing packet, and you can check your answers at our readiness_answers web page. If you plan to take Math 15 in your first semester and have trouble with this test, you should email Professor Aimee Johnson at aimee@swarthmore.edu to discuss what you can do to become better prepared for calculus before you arrive at Swarthmore. Note that if you plan to major in Engineering, you must pass or place out of Math 15 in your first semester to have a chance of finishing the major in four years.

What if you have taken courses beyond calculus? Students who have taken college courses beyond first-year calculus may receive additional placement. American students are most likely to have taken one or more of Linear Algebra, Multivariate Calculus, Discrete Mathematics, and Differential Equations. Foreign students are likely to have taken courses that cover a mixture of some of these topics. If you are thinking of a major or minor in mathematics, the right course for you is probably Honors Linear Algebra (Math 28 or Math 28S) - even if you have had linear algebra before, Honors Linear Algebra is likely to be quite different - but sometimes a higher placement is recommended, sometimes a lower one. In any event, you may still need to take at least parts of the Calculus test discussed earlier or additional linear algebra and multivariate tests we have put on the Web; see the discussion of your case in the upcoming subsection,"Should you Take a Swarthmore Math Placement test?" It is best to take these tests over the summer. Then, upon arrival at Swarthmore, you should consult the Math/Stat First-Year Placement Advisor, Professor Johnson. Bring to her as much material from your postcalculus courses as possible: your tests, homework sets, your texts (or at least know their titles and authors - the color is not enough!)

Must you follow our placement recommendation? Try it. If it turns out to be either too hard or too easy, you can switch. Swarthmore students have two weeks in which they can add and drop courses without penalty, after consulting their advisors.

Back to top of page

Department Placement Tests

The Department administers two placement tests:

A Calculus Placement Test for students whose preparation might place them out of one or more semesters of calculus. The last section is used for placement into honors sections. This test is included in the summer mailing; you may take it at your convenience over the summer (untimed, more than one sitting allowed, but closed book) and mail it back. Please refer to the section "Should You Take a Swarthmore Math Placement test?" to see whether you should take it. A timed offering of the test will be given at Swarthmore during Orientation Week in August as well, but it is very much to your advantage to take it over the summer if you can. If you take our test and mail it in over the summer, our recommendation will be waiting for you at the start of Orientation Week. If you take our test on campus during Orientation, under rushed conditions, the results may not portray you well, as it will be a long time since you may have thought about calculus, and your skills may likely be rusty.

A Calculus Readiness Test for students who have not had calculus or are unsure if they are ready to begin calculus or other first-year college math courses. It is closed book and untimed, but you should do it in one sitting. The Readiness Test is required for all students who do not take our Calculus PlacementTest (or do not have placement by an AP or IB score) and who think they may take some math at any time in their Swarthmore careers. Even students who do take the Calculus Placement Test may be required to take the Readiness Test as well. There is a version of the Readiness Test included in the summer mailing packet, and you can check your answers on our readiness_answers web page. You should take it this summer if you have not had calculus, or if you start on the Calculus Placement Test and find that you can’t do very much of it. Taking the Readiness test now will give you and us early warning if it looks like mathematics at Swarthmore will be hard for you. See the further instructions on the cover of the Readiness test.

The time and place for the Orientation Week version of these tests will be listed on the schedule that you receive when you arrive on campus in the Fall. Usually it is the day after the main first-year arrival date.

Back to top of page

Should You Take a Swarthmore Math Placement Test?

If you are positive that you will never take any math during your Swarthmore years, you do not have to take our test. (Note that you do not need to take our test in order to take statistics courses.) The purpose of making you take a test is to help us make a recommendation to you for the Swarthmore course that is most consistent with your mathematical preparation. In most cases you don't have to take our test if you have received credit by way of an AP or Higher Level IB test. However, if you are concerned that this automatic placement is incorrect, we urge you to take our test. Our test is not assigned a letter grade, and it will never become part of your record in any math courses that you take.

If you do choose to rely solely on your AP or IB, then be sure to bring a copy of your certificate to Swarthmore and check our placements results at the start of Orientation to see if we received your score. Sometimes these scores do not get to us directly; without one, and without results on our own placement test, you will not be let into any math course.

So find yourself in the following categories. If you fit several categories, the one which gives you the most placement applies. Note that, although the calculus placement test determines which course in the calculus sequence you place into, you are encouraged to consider starting with a course outside the calculus sequence!

You have not studied calculus.

You have studied calculus but have not taken an AP or IB Higher Level math test.

You took the IB Higher Level Math test and

You took the AP Calculus AB test and

You want to take one of our Honors courses (28/28S, Honors Linear Algebra; 35, Honors Multivariate Calculus).

You haven't received your IB or AP score yet.

You can't take our placement test until very late in the summer.

You took the British A-Levels or some other national test instead of an AP or IB math test.

You want to start at Swarthmore in something outside the calculus sequence, say, statistics or discrete math.

You have taken courses beyond calculus and want to place out of them (e.g., linear algebra, multivariable calculus, differential equations, discrete math).

http://www.swarthmore.edu/NatSci/math_stat/placement/advanced_work.html

None of the above.

Preparing for our Placement Tests

We encourage you to review for a few hours, especially if it has been some time since you studied calculus. The Calculus Placement test covers much of the material in Swarthmore's first-year calculus sequence: Math 15 and Math 25. See the catalog for a description of the relevant topics. The final section asks some honors (proof) questions for those who wish to place into more theoretical versions of the second-year courses. The Readiness Test covers high school algebra (Part I), graphs and functions (Part II), and trigonometry (Part III).

Back to top of page

Back to Placement Info page