### Description of Course Goals and Curriculum

This is an introductory Calculus course whose goal is to give you a more comprehensive understanding of fundamental calculus concepts. These concepts include integrals, derivatives, the fundamental theorem of calculus, limits, etc. If you have taken AP calculus (especially BC), then you are likely to have seen many of these topics before, but this course does move rather quickly and goes a bit more in depth. In fact, the professors expect that you have at least seen some calculus before. Their goal is to refine the skills that you might already have; so, the class tends to move quickly through the material covered. There are 3 fifty-minute lectures per week, which take place in a small classroom set-up (roughly 20 people per class). In class, you will mostly be taught through the professor’s explanation of these problems and any questions that you and your peers ask during class. The teaching style is very much “learn-by-doing.” What we mean by this is that the professors like to do a bit of conceptual review and A LOT of practice problems. They often stress that doing practice problems is the best way to understand the basics, as they expect you to be able to extrapolate, invent, and understand more challenging problems on exams.

The course ranges from 2 to 3 forty-five-minute quizzes, depending on the semester that you’re taking it. There is a midterm and a final exam which are worth roughly the same amount of your final grade and then weekly problem sets count for the remainder of your final grade. The design of the course allows you to focus on a few important topics for the quizzes before testing your overall knowledge on the midterm and final exams. It is very much cumulatively structured and it is important to keep this in mind for the entirety of the course because if you’re very confused about a certain concept, it pays off in the long-run to try to disperse your confusion as soon as possible instead of moving on and being confused about a later concept. In other words, ASK QUESTIONS IN CLASS. The professors are very approachable your classmates will thank you (because, chances are, they’re confused too)!

### Learning From Classroom Instruction

The syllabus says that things will be fast-paced, take this very seriously because this is definitely the case. If you pay attention to what’s going on as the professor moves from one board to the next, then following their thought process is not too difficult. However, this means that if your attention is elsewhere for too long you might get lost. Every board in the room is usually filled up, so just in terms of visual learning, it’s important to follow the instructor closely so as to not lose where you are. Solutions are written on the board, but sometimes not every step is written in order to save time or because the professor assumes that you already know this step. For instance, there were many situations where students asked about a particular jump from one step to another for a problem and the professor quickly wrote out the missing steps. Suddenly, the entire class was once again following the problem. These kind of subtleties are important to keep track of as you are trying to understand example problems.

If you are truly lost or even if you were following and just did not understand one small step, don’t be afraid to raise your hand and ask! Again, the professors will be happy to answer your questions, so don’t be too intimidated. You might even get another example problem out of your question.

As mentioned before there is an emphasis on “learning-by-doing,” however being able to follow the practice problems in class means that you need to have most of the basic knowledge for that topic under your belt. For instance, if there is a topic related to trigonometric functions being discussed in class, there is an assumption that you are familiar with the unit circle and trigonometric identities. The instructor has a lot of material to cover and as a result does not dwell on teaching the very basics assuming that you have looked over them on your own. The course covers about three chapters from the Thomas’ Calculus, Early Transcendentals, Single Variable with Second-Order Differential Equations, 12th edition textbook and the even skimming over the important section of the text for that week (BEFORE you come to lecture) makes following the lecture a lot easier.

### Learning For and From Assignments

There are three main resources that are provided by the instructor to help you prepare for exams. This includes problem sets, practice problems, and old exams. Other resources include office hours and weekly review sessions, as well as McGraw study halls. GO TO WEEKLY REVIEW SESSIONS!!! It gives you a chance to go over your PSETs with peers, ask conceptual questions, get help on problems that you were unsure how to do, etc. Problem sets take longer than you may anticipate because although the questions cover relatively basic concepts, there’s usually quite a few of them. Problem sets are typically good for gaining basic knowledge of the topic, however, do should not rely purely on these problem sets to prepare you for the quizzes or exams. This practice only includes the simplest problems that you will be required to do. Actual exam questions will take multiple topics that were taught and intertwine them. The problem sets do not help with practicing problems that have multiple interwoven topics.

When you go through problems, it could help to map out each step and why you’re doing it. Choosing certain challenging problems to do this for will help you remember the mental process you have when solving these types of problems and prevent mental-blocks during the exam. Take examples that you remember being difficult from class or PSETs to do this for. It’s helpful to think “If I was given this, how would I solve it?”; do this and bring questions to your professor, and they might give you an example to illustrate and explain through. This is especially helpful when you’re trying to anticipate the kinds of questions that might show up on quizzes and exams.

Try to study with other people!!! It helps to go through the practice problems they give for exams by yourself, mark the problems that you were unsure of/didn’t know how to do and then reconvene with friends/peers. This helps especially because your friends might understand things you dont, vice versa; you can teach each other, which helps to solidify your knowledge. It might even help to look for more practice together and talk through how to do them. Keep in mind also that no one should overpower the other in terms of explaining because that defeats the purpose of learning from each other. One of the biggest issues with exam questions is finding those one or two tricks/remembering that one theorem that helps you solve the problem. The more connections you make and the deeper you understand the material you learned, the easier it will be to retrieve it on the exam.

There’s typically a section of the review sheets provided that are filled with harder or “challenge” questions which reflect more of what will be on the quizzes and exams. It’s best to go through the practice problems first and then test yourself with the harder problems to see how well you actually know the material, as opposed to how well you know how to go through the steps of solving a certain type of problem. We say this because it’s pretty easy to get in the habit of just memorizing how to solve problems and not why it makes sense to solve it in the way that you did.

### External Resources

A resource you could use at your own discretion is WolframAlpha. This engine helps calculate basic integrals and more complex mathematical equations, however it does not give a step by step explanation so it is by no means a substitute for going to review sessions or office hours. Do the problems on your own and then use the engine just to check whether or not your answer is right, if the instructor has not provided answers for that particular problem. If your answer is wrong and you can’t pinpoint where you made a mistake, it might be helpful to go to McGraw tutoring or your professors office hours.

Khan Academy is another great resource! This was actually really helpful when there was a particular concept that we were just not understanding and we were unable to understand the professor/book’s explanations of how to do certain problems. Sometimes just seeking new ways of explanation can really help you to understand yourself. It might even help to do some of the problems Khan suggests on your own and then watch how he solves them to make sure than you understand.

McGraw study hall and the MAT 103 review sessions are very helpful but in order for them to actually be productive for you, there is a certain amount of preparation that you must do on your own beforehand. At the very least, if you are confused about many things, it helps to know what aspects of each topic you are confused about. Keep track as you studying; maybe, make a list of some of the topics and problems that confuse you most and bring this list to the tutors to guide your study sessions.### What Students Should Know About This Course For Purposes Of Course Selection

This is one of the few classes we would recommend for people who do not have a huge math background, or may believe that math is not their strong-point, and are going to pursue degrees that require any type of computational ability. MAT 103 is typically already a prerequisite for many departments (ECON, MOL, CHM, etc.), but it always helps to ask your academic advisor if the department you are thinking about might require computational skills as you move into doing research for a Junior paper and thesis.

This class is one that can help with future courses at Princeton if you put a good amount of work into it and get all that you can out of it. Courses such as ECO 202 will assume that you have a good hold on MAT 103 concepts and you will most definitely need these concepts in order to be successful in the course.

If you need to take MAT 175 or MAT 104, then MAT 103 is also very helpful for reestablishing mathematical concepts that you may have forgotten. Some concepts even pop up on courses like CHM 201/CHM 202 which may say that you do not need calculus but end up using calculus concepts to explain some important equations anyway. Although you may initially feel that the class is isolated in and of itself, in the long-run, it is one of those classes here at Princeton that prepares you well for your future courses. Consider whether or not you will potentially be required to know any sort of calculus for a future class (even though these classes may not specifically mention it) in order to weigh if MAT 103 is a class that will be beneficial to you.