"Work hard, go to the lecture, do homework, ask questions, use instructor's office hours, work in group, go to the tutoring center, practice the sample exams ... " are probably the keys of success in most of undergraduate courses. Well, these kinds of advices are too theoretical and general. I wonder how to give more specific advices to students who will be taking my classes. I think they should be from the view of students. So, I asked some former students how they were successful in my class. The short anwer was "working hard". But they were very generous to share more detailed advice/study methods to prospective students that I copy below under their permissions. There is no such best method of studying, you have to figure out what works best for you, but the below advice are super helpful and practical in my opinion.
I deeply appreciate Jillian Bernotaitis, Nicole Baker, J. C., N. Costa, D. P., Amanda M., and Alexis R. for their generosity to share with us their experiences and advice.
Me: How to achieve an A in MTH 2554? What is your advice to prospective students to be successful in this course?
Jillian: In order to be successful in MTH 2554, it is very important that you come to class. MTH 2554 is a difficult class that includes many abstract ideas that are hard to wrap your head around, especially if you are just reading from the book. Going to class and having the professor explain the concepts using multiple examples, as well as draw them out, allows you to have a better understanding. The book can be helpful if you need some more clarification or simply want to review, but going to class gives you a better idea of the concepts from the start.
It is also important to do the homework. Actually implementing what you have learned in class and doing some problems on your own allows you to better understand the content as well as see where you are struggling. Doing the homework helps you narrow the specific areas you are having trouble with, which allows you to ask more relevant questions and resolve your confusion much sooner. You get homework almost everyday, which can be a little overwhelming. Nevertheless, making it a priority to do the homework will help you greatly. If you have a busy week, you should try to do at least a few of the homework problems before the next class that way you still have the concepts fresh in your head. At minimum, you should do the homework problems before taking the exam. When studying for the exams, I would review some of the homework, especially problems that I struggled with initially.
Doing the practice exams were also extremely helpful. They not only provide extra practice problems, but they also give you an idea of how the exam will be formatted and how the questions for each concept will be worded. It may seem simple, but going to class and doing the practice problems assigned makes a huge difference. Many of the sections and concepts of this class are very visual, so it is important that you do multiple practice problems and get familiar with visualizing the problems. I personally benefited greatly from drawing the problems out. Even if you are not a good drawer, the action of drawing the parts of the problem allows you to break down the problem and better understand it. The more problems you do the easier it gets to picture the problem, so make the effort to do the practice problems.
Me: Which sections are most difficult? How can you study them?
Jillian: Each section of the class had its own unique difficulties, but the sections that I found to be the most difficult were sections in chapter 15 that were towards the end of the class. The sections were mainly about double and triple integrals and using them to find the surface area and volume of a given solid. I found it tricky especially when it came to visualizing the solid. However, after doing multiple practice problems, you begin to find patterns and methods of approaching these types of problems that make them easier to understand. Each problem is unique in its own way, so before you try to solve the problem, you must know what the solid is and its boundaries.
It is very helpful if you draw it out. Even if you are having trouble knowing where to begin, sketching out your thought process and ideas of what the solid looks like will help you figure out the problem. Sometimes drawing the 2D domain is helpful if you can not visualize the 3D solid or if the 3D solid is simply too complicated to draw. Either way, having a visual that you can actually see on paper allows you to easily break down what you know about the solid and what boundaries you need to use to solve the problem. Drawing the solid out right away also allows you to easily see if the solid is circular, which means you can use polar coordinates to make the problem much easier.
These types of problems can be long and sometimes complicated, but if you practice doing these types of problems, you get used to going through the process. It becomes a habit and makes the problems seem less daunting. These problems can also be very time consuming, so being more familiar with the process to solve these problems can really save you a lot of time on exams. The most important thing to remember is to draw the solid out first and break down the aspects of the solid in order to find the information needed for the double or triple integrals.
I also found some of the sections in chapter 16 to be a bit tricky with line integrals. Nonetheless, the approach was relatively the same. Do as many practice problems as you can, so you can see the different ways the concept can be applied. If possible, draw out the problem, and break down the problem into individual steps. Just take the problem one step at a time.
Me: How to achieve an A in MTH 2554? What is your advice to prospective students to be successful in this course?
Nicole: Aside from showing up and paying attention in class, taking notes, doing homework, and those regular activities that everyone is aware of, the way to get an A in Professor Tran's class is to use the sample exams! Take the exam as soon as you can, and don't look at your notes. Circle the questions that you know you forgot how to do. Then, go back to that section of the textbook and your notes and do multiple examples until you re-familiarize yourself with the topic. Then, a couple of days before the exam, take the sample exam AGAIN. Make sure you understand those problems, because they will prepare you very well for the real exam. Once in a while, there are things that you will be tested on that are not in the sample exams. To go the extra mile, you can look over the main ideas/formulas/examples for each section of the chapter before the test.
Also, try your best to understand how and why formulas and methods work rather than simply trying to memorize them. Find ways to think about if your answer makes sense or not. The explanation of the formulas will usually be given in class, but it is sometimes difficult to think about. Don't be afraid to challenge your mind to go deep and figure it out! You can do it. The textbook will usually show where formulas come from as well. Use your resources.
Me: Which sections are most difficult? How can you study them?
Nicole: Section 14.2 was quite difficult. I think the most helpful thing is to keep working until you fully understand a problem. Halfway understanding because you saw the answer is not the same as understanding and being able to work through it on your own. For this particular chapter I looked up some more video examples on the internet until I saw several different examples. Once you get a feel for the types of questions that will be asked, it is not too difficult, but it is not something that comes super naturally to most people, so I would definitely take extra time on this topic.
The other difficult section for me was 14.7, mostly because it was tedious. It is important in this section to keep track of what you are doing and why. Finding the absolute minimum and maximum involves many steps, but if you think about what you are doing it is not too bad, there is just a lot of room for error. Take the time to go through a few examples all the way by yourself so you can get the rhythm of it.
Me: How to achieve an A in MTH 2554? What is your advice to prospective students to be successful in this course?
J.C.: What I did in order to achieve an A in MTH 2254 was by doing the homework everyday. It will seem boring and unnecessary but it really does help a lot in the long run.
Another thing to do is to go to the SI sessions. They may seem slow and boring especially if it's right after lesson but it helps by making sure you use your brain to see if you really did understand what was being taught in class or not. Additionally, if you realize that you really didn't know in the SI lessons you can ask your SI leader anything and they are more than willing to help you.
Your classmates are your best friends too. If you struggle or don't know what to do ask a classmate what's going on. More often than not, they can help you or at least get you started on a problem that you don't understand. Being able to bounce off ideas with someone is the best way to think and process a problem that you really don't understand.
Furthermore, I would start studying for the exams up to a week to two weeks early. What you can do to study is going over your notes and homework while creating a formula sheet along the way, this way you can have a sheet of paper that you can carry around everywhere that has the main points of the sessions you're going to be tested on. Another thing you can do to study is to do extra problems from the sessions along with the chapter review in the textbook. While it may seem to be a lot of work it really pays off and you'll see that the more practice you get the better you will do.
Lastly, the best way to over a lessons is to find a video on it. If you go to class, listen to the professor, go the SI lessons, and still don't understand the lesson then you need to find a different way to learn. It may be the format or way they're being taught that's difficult to you. What I did was look for math videos on youtube. A very helpful video I found that helped me review was Professor Leonard. His videos are super long but he goes over everything and beyond what you need to know for the class but it's great if you can't remember the lesson well or your notes just aren't helping you.
Me: Which sections are most difficult? How can you study them?
J.C.: The sessions that gave me the most problems were: Cylinders and Quadric Surfaces, Maximum and Minimum Values, and Triple Integrals.
What I did for these sessions was finding out what part of it I didn't understand and go from there. For example, for the cylinders and quadric surfaces I found out that I really didn't have a problem with how to do it, what I had problem was how to draw the surface. I realized very quickly that I knew how to do the problem if I had the surface already drawn out for me, but struggled if I didn't. So I went to other textbooks to help me review how to draw quadric surface along with the online drawing website that Professor Tran used in class to show us the surface. I also searched for videos that would help me recognize quadric surfaces. I utilized the same process for the other sessions that were giving me problems. Additionally, I would do extra practice problems on these sessions to make sure that I finally understood what was going on.
Me: How to achieve an A in MTH 2554? What is your advice to prospective students to be successful in this course?
N. Costa: To achieve and A in MTH 2554, the most important thing to do is to not fall behind schedule. After a lecture, do the assigned homework problems before the next lecture. Even if you do not completely understand the concept at first, it is better you get your feet wet and go back to it at a later time. Also, many concepts tend to grow from previous ones so if you fall behind it will take even more time to catch up.
Since your grade is composed of only exam grades, it is important to have efficient study methods. What helped myself out a lot was going back to all the homework problems assigned from the sections that were on each exam and redoing them. This allowed me to review concepts I learned earlier, while understanding the way the concepts were asked. The exams I did best on were the ones where I re-did every homework problem from those units and understood how to do them.
The last thing I recommend is attending SI sessions (if it is available for your class). This allowed me to work on problems with my classmates while often times led me to understanding topics better than I did before. If SI is not available, I recommend studying with people from your class or attending office hours.
Me: Which sections are most difficult? How can you study them?
N. Costa: The sections that I found most difficult were 13.4 (Motion in Space: Velocity and Acceleration), 14.2 (Limits and Continuity), 16.3 (The Fundamental Theorem for Line Integrals), and 16.4 (Green's Theorem).
For 13.4, the main issue was understanding the integrals/derivatives of vectors to solve the problems. In the SI sessions, many of my classmates had taken some physics and knew how to solve the problems with physics formulas. I however had never taken a physics class so I had to learn how to use calculus to solve them. My SI instructor went over many of these problems and I used Khan Academy to see these types of problems done.
For 14.2, it took me a while to understand the conditions of the tests to see if the limit does not exist vs. evaluating the limit. Professor Tran gave us a tip to help us choose which test to try first and that helped me understand the concept better.
For 16.3 and 16.4 the content was not extremely difficult. What was difficult was finding the time to learn this material while trying to review all of the other content I learned for the final exam. I suggest that you really work on managing your time towards the end of the semester and really focus on this last unit because it is really important!
Best of luck with MTH 2554 this semester :)
Me: How to achieve an A in MTH 2554? What is your advice to prospective students to be successful in this course?
D.P.: Calculus III can be a very tough course. While some people may say that it is easier than Calculus II, it does not mean at all that this class will be a breeze. It contained some tough concepts. You definitely can still get an A. What I did to achieve an A was several things. I attended all of the lectures and took notes during every one of them. I wrote pretty much everything down that my professor wrote, even though some things seemed unnecessary to include in the notes which I would look back in. This helped though when the professor wrote down trig. identities or formulas that were important to know and remember. It helped because it repeated those things in my head and helped me recall them. Also, a good addition to attending to the lectures every time is to attend the SI (Supplemental Instruction) as well. Personally, I did not do this for this course. However, I know from past experience (Calculus II) that it can be a great tool to reinforce the material you just learned, especially confusing material. Furthermore, I would try to do all of the homework. Like someone previously stated, this can be boring. Yet, it is actually very useful because it helps you to remember the information and not just forget it when you get onto the next topic you learn. When I did the homework, I used Chegg Study. This had solutions for basically every problem in the book. This was useful because it helped me on problems I was stuck on, and was a good tool to help me check my answers. Yes, you do have to pay for it after the free trial, but it is very useful for this class and other classes as well. I would recommend to try and understand the homework though, and not just copy it down from Chegg, because understanding it is just as important as getting it done. Also, a good tip to get an A in the class is to look up videos online. There a lot of great videos on Youtube by people such as Patrickjmt, Professor Leonard, Krista King, etc. I also recommend to go to the tutoring center. I also recommend to ask the professor questions during his office hours. The professor was always open to answering questions with his students, and wanted them to understand no matter what even if they came in numerous times such as me.
Me: Which sections are most difficult? How can you study them?
D. P.: I thought that Limits and Continuity was one of the hardest topics during this course. It adds a different aspect to the understanding of limits that were developed from Calculus I. Therefore, it can be hard to comprehend the differences. Also, to prove whether a limit exists or does not exist in 3D is not so technical. There are useful procedures that the professor explains well, however they take some thinking and practice to get better at. I also thought Triple Integrals were a bit hard at first. Similar to the Limits and Continuity, I got better at them with practice and understanding that they are really just double integrals but with a third dimension attached. You pretty much knock out one dimension, which is generally the hardest, and then draw the other two dimensions in a 2D plane. This can help a lot because we are used to seeing which function is on top of the other (or which one is right and left) in 2D. I didn't always write out the domain part of setting up the integrals like the professor did, but it is preference, and he tells you that. Evaluating the integrals aren't very hard, but setting them up is the hard part. So yeah, this topic can be really confusing at first, however once you understand it, it is super easy when you look back at it. Going along with triple integrals, I think understanding how graphs look in 3D can strengthen how well you do in doing triple integrals. I think the more experience you get with what certain equations look in 3D and whether or not they can be negative due to their equation will help a lot in the whole course. Also, if you recall that the 3D coordinate system is just the 2D, XY plane, with the Z axis going through the middle (the origin), then this can help you because you may think that 3D is hard to interpret at first. All in all, good luck and I truly believe you can do it. Trust in God and yourself and don't give up!
Me: How to achieve an A in MTH 2554? What is your advice to prospective students to be successful in this course?
Amanda: To be successful in MTH 2554, you should attend class everyday and take notes. After class or when I had time, I would rewrite the class notes and put them into my own words. As well, I would write down all the equations and the main ideas for the chapter. If there was a particular idea I didn’t completely understand, then I would look through the book or any online resources I could find. Every time homework was assigned, I would complete it when I had the lesson fresh in my mind. When a test was approaching, I would review the notes I had rewritten earlier, the practice exam given out in class, and any homework problems that confused me earlier in the semester. If there was a topic I still wasn’t confident on, I would then go through the book and try to find similar problems done in class. That way, I could have extra practice and be more prepared for the exam.
Me: Which sections are most difficult? How can you study them?
Amanda: A few of the sections that involved 3-D drawing (ex: 15.7 Triple Integrals) were difficult for me because I could not visualize specifically how the equations were supposed to be drawn and thus, I got the wrong answer. To solve this, I did a lot of extra practice problems from the book, as well as a few worksheets I found online. I also tried to visualize the general shape and the relationship of the equations in my mind and tried to work through the problem from there. Another section that was difficult was the absolute min and max (14.7 Max and Min Values). For these types of problems, it is beneficial to graph the equation and then break down each section of the function. There, you can analyze each max and min within that particular section.
Me: How to achieve an A in MTH 2554? What is your advice to prospective students to be successful in this course?
Alexis: First, try really hard to do most of, if not all, the assigned homework and stay on top of it. The worst thing is having challenging material build up and trying to figure it all out right before the exam. Personally, I love Chegg because they give detailed explanations on the process of how to solve the problem. Make sure you understand the process to get to the right answer, and not just the right answer itself. When I came across a challenging topic, I worked through a problem with Chegg and then tried to do the rest on my own, and double checked my work with Chegg. It’s not very common for students in a math class, but I always create flashcards for each section as the exam approaches. Some equations are crucial to solving a problem and if you don’t know it, there’s no way to solve the problem. I create flashcards for equations and sometimes processes to solving a specific type of problem. Before exams, I choose problems from the assigned homework I believe are key problems that I might see on the exam. I redo those problems to review before the exam. Redoing key homework problems and studying my flashcards are how I study for exams
Me: Which sections are most difficult? How can you study them?
Alexis: A few challenging sections:
14.2 Limits and Continuity – There are different ways to prove a limit is continuous or discontinuous and it is usually not specified which method to try first. I had to do many practice problems to recognize patterns in the given equation to see which method would work best. Practice these a lot.
14.7 Maximum and Minimum Values – These problems are long, but they are repetitive. Memorizing the steps to solving is much easier than doing 10 of these problems.
15.9 Triple Integrals in Spherical Coordinates - This is one of the sections I heavily relied on flashcards. If you don’t know the correct variables that correspond to spherical coordinates, then this may be a very difficult problem to do. Also, recognize the patterns of when to use spherical vs. polar vs. general region. Using spherical could be way simpler when applied correctly. Chapter 16 – Make sure you do plenty of practice on the last chapter because it will be on the final exam. If you practice, the questions aren’t too challenging but if you choose to ignore these last sections, you’ll lose easy points.