# General Math FAQ

#### Questions About Placement

Never. The Math Department does not have a placement exam.

We think it works better to make an initial placement based on your background, test scores and interests. Then, *crucially*, we use the drop/add period to adjust as we get more information during the first two weeks of the semester. Placement involves many complex issues that cannot be measured on a multiple-choice test during orientation. This two-step approach is more flexible, and we feel, more reliable, but it does require students to take an active role and make realistic decisions.

*Everything*we know about this is written down in exhaustive detail here on this web site. Check out the information on the undergraduate home page and the placement home page.- Representatives from the Math Department will be available at the Academic Expo during Orientation and at Freshman Registration to help you figure this out. However, it will save time and help you get a better answer if you check out the online information first.
- Student recommendations can also be very useful, so you should talk to other students with similar background and goals who have been a Princeton for a year or two.
*However*, some of the placement rules have changed starting in Fall 2012 and many courses have been renumbered and redesigned recently. The information here on the web site has been updated for AY 2015-2016. - Your academic advisor or Director of Studies should also be able to help you think about this.

Start by checking out the information on the undergraduate home page and the math placement page. Everything we know about placement is there including

- an overview of the courses that freshmen and sophomores usually take,
- placement guidelines based on various test scores and high school background,
- contact information in case you need to consult with a representative of the department after you have thoroughly reviewed all the online information,
- links to detailed course descriptions.

First, stay calm. Lots of people are in this situation and the system allows you to try out more than one option before you make a final decision. As a general rule we recommend that you sign up for the harder or more advanced of the courses you are considering and be prepared to use the two-week drop/add period wisely. Most freshman math courses give a quiz early on to help you make an informed choice.

If possible, attend the first few lectures of both courses you are considering to get a better feeling for what will be expected. You don't need to worry about space in the course. The Math Department will make room for you in a course if that is the course you need. You may have trouble getting into a very popular section of a course, but you won't be closed out of the course (or a time) altogether. If you are trying to switch into a course during drop/add and the course is full, just let us know.

The more common dilemmas are discussed in more detail on the individual course web pages but here are some general remarks about some of them:

**If the placement guidelines say you should take MAT104 but you feel ready for MAT201:**Attending the first few lectures may have reinforced this feeling since it all seems quite familiar early on.

• You'll know more after the first quiz. Most students find that the expectations here are much more rigorous than any encountered in the past in high school, even if you took some classes at another university. Don't skip the recommended Princeton math course*unless you can actually do most of the problems on an old final exam*. If you can't meet this standard, then you are taking a very big risk if you sign up for the next course in the sequence. Sample exams are available from most course web pages.**The placement guidelines say you should take MAT103 but you feel ready for MAT104**:

• see previous item**Your placement recommendation says that you can take MAT201 or MAT203**:

• Here you must choose between two courses that cover the same topic with different levels of mathematical abstraction. In this case attending the first few lectures, doing the homework and taking the first quiz should give you the needed information. For most students the answer will become clear by the end of drop/add. 201 is a very serious course, and for most purposes it provides the background you need in multivariable calculus. Choosing between 201 and 203 is largely a question of taste, so feel free to try 203 for a week or two and then it will be easy to switch down to 201 if you want. If you are undecided as the drop/add deadline approaches, talk to your instructor or consult majors/advisors in your future department or you can talk to the associate undergraduate representative or the placement officer.**You need to choose between MAT104 or 175:**

• MAT175 is a "terminal" course; in other words, it is meant to be the last math class you take at Princeton. It is not sufficiently rigorous to prepare you for more advanced math courses. It*minimally*satisfies the math requirement for some programs. Choosing 175 closes off some options, and this is an argument for attempting the more rigorous alternative. You may need to consult your academic adviser about this decision.**Drop/add is almost over and you still can't decide!**

• By the end of drop/add you really need to make a commitment one way or another. These courses move very quickly and you don't want to waste valuable time and energy trying to predict the future. Talk to your instructor, your director of studies or academic adviser or the associate departmental representative.

• In rare cases, students do switch courses after drop/add if that really becomes necessary. This can involve quite a bit of paperwork because you will need permission from the math department, from your new course instructor and from your dean or director of studies. Once you have all the paperwork lined up, you will need to go to the registrar's office in person to seal the deal. Such changes cannot be made through SCORE. Additional fees may also apply but these are a relatively minor consideration.)

In most cases the answer is yes, especially if you need the course to do more advanced course work in your department. Chances are good that the course you took in high school is not equivalent in rigor to the corresponding Princeton course. Check out the department's web page for the course carefully.

Take the sample final available on the course web page. Can you do *any* of the problems? For many students, the answer will be no. Review your old notes and try again. Can you do at least 60% of the exam?

If you still think you should skip the course, bring your graded exams from your high school course to the placement officer. You will need his/her permission and you may be required to take an exam to demonstrate your knowledge before making it official that you can skip the course.

#### Questions about Changing Courses/Sections

Start by talking to your instructor, but he/she may be as new to Princeton as you are in some cases. You can also check with the placement officer or with the associate undergraduate representative, the person who oversees all the lower division math courses.

Drop/Add is a two week period at the beginning of each semester during which students can add, drop or swap classes without paying an extra fee. Because it can be quite difficult to determine which math course is the right one based on standardized test scores or high school grades, the math department uses this time to help students try out a math class to find the one that best suits them rather than relying on a placement exam.

Once classes begin, you can adjust your classes through TigerHub provided space is available. Some courses may close entirely, or particular times of a course may close. It is a high priority for the math department that all the students who need a math course should be accommodated, but space is limited. We cannot guarantee that a student will be able to choose a particular section at his/her most-preferred time, but we will do our best to make sure that students are not closed out of a needed course entirely.

If a scheduling conflict cannot be resolved through TigerHub, then students should contact LeeAnn Coleman or stop by her office in 315 Fine Hall. If you send e-mail, your message should include

- your
*Princeton*netid; - Which course you want to add, with a brief explanation of why you need the course;
**all**the times when the course is offered when you have an opening in your schedule;- You may include information about preferred instructors, and we'll take it into account if we can.

If you need to consult with someone about your choice of math course, then send e-mail to the associate departmental representative.

You can talk to your instructor or to Jennifer Johnson, the person in the math department who oversees the lower division courses. But first check out the FAQ below on the general structure of Princeton math courses. The expectations for exams are likely quite different from what you are used to from high school, and it is easy to misunderstand what your first math test really means. If it turns out that you are in the wrong course, our system is very flexible, but it gets a bit more complicated to make adjustments once drop/add is over. Please come talk to someone soon! Help is available.

#### Questions on What to Expect in a Freshman Math Class at Princeton

Generally speaking our courses are more fast-paced and rigorous. Because they are full of students who are ambitious and hard-working, the standard for doing well is naturally elevated. Most of the courses 100 through 202 are similar in spirit to high school courses, but by comparison they are extremely fast-paced and rely more on independent work outside of class. In order to distinguish among this group of talented and highly-motivated students, the exams tend to be very challenging. Even compared to similar courses at other universities these courses tend to move quickly. For example, the material covered in the largest freshman course (MAT201) is frequently taught over two semesters at many other well-respected universities. Moreover, your instructor will generally expect a much deeper mastery of the material than you have experienced before. It can be a bit of an adjustment, but it will prepare you well for more advanced work in other departments.

These classes meet three times per week, for 50 minutes. During that time the instructor will give an *overview of the key points* of the day's topic, with as many examples as time allows. You will do much of your learning *outside of class*, working on your own, or perhaps with a study group *to master the remaining details*. We expect that most students will need to work 3 or 4 hours outside of class for every hour in class in order to do well. Although your instructor will often quickly review material from previous courses (e.g. completing the square or a basic trigonometric identity like the addition formula for sine), there will likely be gaps in your background knowledge. It will be assumed that you will recognize these gaps and work to fill them in, taking advantage of the many sources of help available to you.

In addition to introducing the main ideas and techniques in class, the instructors from all the sections work together with the course head to set the course content and pace, to provide a good list of problems for you to think about, and then to help you answer the questions that come up as you work problems on your own. The team of instructors will use their expertise to prepare interesting exams for you, exams that give you a good chance to show what you have learned and to deepen your understanding a bit more while you work through problems on the test. You will be expected to think and adapt during the exams, not just remember how to do problems that you have seen before in the homework or precept. This can be quite an adjustment, but in the long run we think this will make these courses much more useful to you.

You do not need a calculator for your math class. We do not use/require them.

Generally they require a steady time commitment throughout the semester. Last minute cramming may have worked well in high school, but it tends to be very ineffective in university math courses.

We expect that the weekly problem sets will take at least 3 hours to complete, but this can vary quite a lot depending on your background and goals. To get the most out of the time you spend in class, most students need to read ahead in the textbook before class and spend time reviewing the notes and examples after class. To do well on exams in courses like MAT100 up through MAT202, you need to work a lot of extra problems from old exams. We expect that these courses will probably require around 10 hours per week on average.

More advanced classes like MAT203/204 or MAT214-MAT218 can be more time-consuming, but the assumption is that these courses are for people with a very strong interest and aptitude, who want to develop a real expertise. Generally, the more abstract and proof-based the course, the more time it will take to complete the problem sets and master all the new ideas.

Just remember, there are many sources of help, so if you do get in over your head, don't despair! Talk to your instructor or your director of studies as soon as possible!

Homework is typically worth about 10% of the course grade in introductory courses like MAT100 up through MAT202 and homework averages tend to be about 90% or higher in those courses. For MAT100 through MAT202, near perfect homework functions more like a class participation component. The problems on quizzes, midterms, and final exams will often be more difficult then the routine homework problems. Some instructors will assign additional, more challenging, homework problems that are not from the textbook, but usually not. More often, the instructor or course head will provide access to old exams or quizzes from previous semesters so that you can practice (on your own, outside of class) with more difficult problems in preparation for your exams. In MAT203 and MAT204 the problem sets count a bit more and are less routine. In MAT214 and higher, the problem sets are very challenging and make up a major component of the course grade.

Once you have mastered the basics in the homework assignments in courses like MAT100 up through MAT202, you should begin to work through problems from old exams from previous semesters and think deeply about these questions. This will be your main tool for doing well in these courses. It takes time to digest the material and to develop the necessary expertise, so last minute cramming for exams is generally ineffective. Use the old exams to help you figure out what your questions are. Go over them with your study group, ask your instructor about them in office hours, or work on them in a session with your peer tutor.

Historically, about 25% of the students in 103, 104, 201, 202 receive a grade of A or A-. About 45% of the students receive a grade of B+, B or B-. The average score is typically in the low B range. Most of the remaining 30% of students get a grade of C+, C or C-. These are not quotas, and there is generally some variation in different courses and different semesters. Old exams are typically posted on the Blackboard web site for a course and should give a clear idea of the expectations for the course.

Because we think it is more useful to ask more interesting questions, midterm and final exam averages tend to be around 65% in these courses, but averages of 50% occasionally happen.

If you know what to expect, then it will be easier for you to stay calm and work steadily on a hard exam where you don't know how to do all the problems. These exams develop and test your ability to work under pressure, but this is also a skill that you can learn! On rare occasions an exam might turn out to be unexpectedly hard, and then a score of 60% can even turn out to be an A or A- in the end; the ability to shrug off your doubts and have faith in the work you have done to prepare can make an enormous difference in the outcome on such an exam.

In MAT203/204 a somewhat more generous grading scheme is used, along with more challenging problems. Students determined to get a stronger mathematical foundation for future course work in other fields (like physics) can take these more demanding (compared to MAT201/202) calculus and linear algebra courses without risking GPA damage.

In MAT214 through MAT218, the extremely challenging courses for math majors, students are asked to learn a whole new way of thinking about mathematics. In these courses we again use a more generous grading scheme to encourage those students who want to learn how to think like a mathematician to invest the time and energy required without undue risk. In these courses undergraduate math majors run tutoring sessions that are especially helpful in making the transition to thinking like a mathematician.

Obviously it feels very different to take an exam with an average of 65% (which usually corresponds to some kind of B) after years of taking high school exams where a score of 65% generally meant failure. In most high schools, students expect to recognize the problems on exams and simply remember how to solve them. We put significant effort into asking exam questions that are based on the practice problems, but where you must adapt and *figure out* how to solve using the ideas and techniques you have already been working with in the practice problems. These exams are meant to be an intense learning experience in and of themselves, but you really have to adjust your expectations to take this into account.

These harder exams can be a bit painful at first, but we firmly believe that they give you a much better opportunity to learn the course material well enough to apply it effectively in your future course work in many different fields where mathematical analysis is a useful tool. One of the big challenges in your first Princeton math class will be to redefine what it means to learn mathematics, what it means to fail and what it means to succeed.

Often students falsely believe that everyone else in the class understands more. Be brave and ask questions in class and in office hours! Keep working problems. It takes time to develop these skills. We hope you will learn to enjoy being asked to do a math problem that you don't already know the answer to and that you will get better at finding your way to a solution. But OK, even if you don't see that happening, try to learn to keep working steadily, ask questions, and above all, believe in the curve!

Typically this indicates that a student has continued working throughout the course, turning in mostly complete homework assignments, seriously preparing for exams and achieving a basic understanding of most topics, but with possibly substantial gaps in conceptual and technical mastery. A grade of C indicates that the student should expect to experience some difficulty in completing any later courses that rely on the current course as a prerequisite.

Note that a score of 5 on the AB exam reflects C-level knowledge of MAT103. Similarly a score of 5 on the BC exam reflects C-level knowledge of MAT104. These exams do not test for the level of mastery that the corresponding Princeton course aims for. If a freshman student had to work hard to get a 5 on the AP exam, and/or the student had to work hard to get a math SAT score above 750, and/or the student did not take any math in the senior year of high school, then a more conservative choice of math class would be wise.

#### Questions about Getting Help

The McGraw Center at Princeton offers a variety of resources including individual tutoring and tutor-facilitated study groups for most of the freshman math courses. (Check their website for a list of supported courses.) This is a great resource which we highly recommend.

It can be very helpful to use a study group to talk about questions that came up during class or as you were going over your notes. The McGraw Study Halls are a good place to meet people from the same course if you are trying to put together a study group. Some courses have undergraduate course assistants that run review or problem sessions. These can also be a great way to connect up with others in the class and form a study group.

Or take your questions to your instructor's office hours. You don't need an appointment for this and if your instructor's office hours don't work well for you, it is usually easy to set up an alternate time. You can go to any instructor's office hours and these are usually posted on the course web page on Blackboard. Keep in mind that a visit to office hours will go better if your instructor can see that you are working to learn the material, generating questions as you go. This will make it much easier for him/her to give you real help.

For some students individual peer tutoring is a better option, and this is available through the residence colleges or the McGraw center. Talk to your director of studies as soon as you think this might be needed as it can take a few days to get this set up. Sometimes you will need to try more than one tutor before you find a good match. As with office hours, you will get more from your tutor if you take a more active role. Your tutor will need your active cooperation in order to find the best ways to help you.

Talk to your instructor about help options for your specific course or consult the associate undergraduate representative about your situation and options.

You may have to get outside your comfort zone and speak up more in class to get the help you need. Most instructors welcome your questions, and although you may imagine that everyone else in the class is understanding more than you are, this is rarely the case. Asking questions makes the class more lively and interesting and leads to very useful class discussion. It helps the instructor do a better job and encourages others in the class to join in and you will then benefit from their questions as well. It may sometimes happen that the instructor will ask you to discuss it after class or in office hours on the rare occasions when he/she judges that this question is not of general interest. So be brave, and ask!

It is also possible that you are in the wrong math class. Again, asking questions will help your instructor know if you have the background you need for the course. In that case, it won't be difficult to find a class that is a better fit for you, but the sooner we figure this out, the better!

Go to office hours. You don't need an appointment for this. (If you can't make your instructor's office hours, then e-mail him/her to make an appointment at a better time.) You can go to any instructor's office hours and they should all be posted on the course web page in Blackboard. This may be a good way to find an instructor whose style works better for you, or just a way to hear the same idea explained by a different person. Be prepared with specific questions when you go to office hours. Even if they are vague. You want the instructor to see that you have thought about the questions already yourself and the explanations you get will make more sense to you if you have already invested some time and effort into trying to understand on your own.

You can try going to a different instructor's section if there is room. Sometimes you have to find a teacher whose style is a better match for you. If there is room in the section the math department will generally allow you to switch. After drop/add this requires some paperwork and a smallish fee (at least compared to what you have already invested). It is better to make the switch official since your grade for the course will be assigned by the instructor you belong to officially, and it won't count in your favor if it looks like you just stopped coming to class.

Contact the associate departmental representative or the undergraduate administrator if you need to discuss making a change in your math class.

- For questions about lower division math courses (i.e. 101 through 204), contact the associate departmental representative or the placement officer.
- For questions about being a math major, or the introductory courses for math majors (214 through 218), contact the departmental representative.
- For placement questions, especially in upper division courses, or for questions about skipping a 200-level course, contact the math placement officer.
- For record-keeping and administrative questions or for questions about drop/add procedures, contact LeeAnn Coleman in Fine 315. If you are not sure who to contact, Mrs. Coleman can help you find the appropriate person to ask.

#### Miscellaneous

It depends on what you want from the course. A good understanding of the material generally comes more easily with class attendence and if you don't go to class regularly, the instructor probably won't have much sympathy when you bomb the midterm or final exam. (So you won't want to end up a borderline case when the final curve is decided.) Neither will the instructor feel much inclined to answer your questions in office hours. But if you are very confident and won't need to bank any good will with your instructor, your grade will be computed based on your performance on the exams just like anyone else. You will probably have to work harder than other students in the class to get the same result and you will of course be responsible for any announcements made in class. We try to post all these on the course web site on Blackboard, but you'll need to be vigilant about checking there and your instructor will likely feel that announcing information in class repeatedly is sufficient.

Hate is a little strong, but most instructors find this to be rude. We mostly try to maintain a grown-up attitude and shrug it off, but it is difficult to ignore sleeping students, especially the ones that snore. Some instructors will wake you up, which can be embarrassing. Yes, we understand that you are sleep-deprived, but if you really can't stay awake in class it is probably better not to go. Just sleep in. Asking questions in class can help you stay awake, so try that. Most instructors really want their students to ask questions.

Well, hate is a bit strong, but most instructors (and other students in the class) consider it rude and distracting when students come to class and read e-mail or check in on Facebook. It is usually pretty obvious and it will cost you some good will with most instructors. You may think that your instructor will appreciate the fact that you showed up, but this is not the case. There is really no point in coming if you can't pay attention and it only makes it harder for other people to get something useful out of the very limited time you have in class with the instructor.

If you think the class is not useful, then you can do something to change that by keeping up with the readings and assignments, paying attention in class and asking lots of questions. Most instructors will find such efforts to be an extremely valuable contribution to the class, thereby earning you a lot of good will and making the class more effective. So if you go to class, try to get as much out of this time as possible by making every effort to follow the discussion and by asking questions when appropriate.