Division of Science






Department of Mathematics
The City College of New York
160 Convent Avenue
New York, NY 10031

Phone: (212) 650-5346
Fax: (212) 650-6294

Math 392 1XB - Summer 2019

Course Syllabus and CLO

Video Recordings of Lectures

Click here for video recordings of the lectures posted on YouTube. These lectures were recorded in Spring 2018. The course content has not changed.

Quiz and Quiz Answer Keys


Be careful using the answers. It is often the case that students view the answers prematurely and in the end it doesn't help. Blank versions are provided here as well. If you did poorly on a quiz, do not look at the answers right away. Print out THE VERSION YOU TOOK, go over this version slowly. No help at first. If you still do poorly after going over it slowly, then use your text/notes to help. If that still doesn't go well, go see a tutor. Only after this point should you look at the answers--after you've made several attempts on your own and then got human help. At the end of this cycle, print out the OTHER version, the one you didn't take, and then go through that, no help, under timed conditions. The grade you get then will accurately represent what you understand.


Quiz 1

Quiz 2

Quiz 3

Quiz 4

Quiz 5

Quiz 6

Reviews for Tests

Test 1 Review


The most important assessment metric is what you can do correctly by yourself. If you did not get a problem correct entirely by yourself, assume you don't understand that problem. Whether you get help from looking at a written solution, or an answer, or a hint from another human, or by watching virtual Jhevon on YouTube, any help you get indicates that there's something you don't understand. Strive to be able to do a problem correctly all by yourself. When you can get several problems for some topic correct, back to back, while almost being bored, then you can say you understand that topic. At all times, prioritize what you can do on your own.

I am not saying don't get help (you should!), but don't confuse the help for your own understanding. I will give you instructions on how/when to get help in this section. Be sure to distinguish between what you originally did vs what you got help with. Use a different writing color, or use a different paper all together. You need to save your original work, and don't copy the help you got from somewhere else in the same place as your original work. Your original attempt must be kept in its original form. Do not contaminate this. Any time you get help, write it somewhere else or write it in a different color ink, etc.

Don't practice the same problems over and over. It is easy to confuse "understanding" with "remembering". If you need more practice on a certain problem type, consult your textbook for new problems.

A. Do some preliminary studying, as I've been describing in class and have been suggesting by quizzes (know general formulas, methods, concepts, etc.) This should not take you too long, assuming you've been studying for quizzes. But take some time to really sharpen up on these. Work out all the kinks, so you can recall a fact quickly and accurately, by rote, on command.

B. Save all the scrap paper that you use for studying. Distinguish between anything that you did on your own, and anything that you got help with from any other source. That way, when getting help or assessments from me, or a tutor, we would be able to see what you understand written on the paper and thus would be able to help you better.

C. Below you will see problem sets to complete, taken from past finals. Do one problem set at a time, in its entirety, under test conditions. The time you should take will be indicated. Do not go beyond this. If you run out of time before you complete a problem, write "ran out of time" in the space where you'd normally write the solution. You may do the solution afterwards (somewhere else, or with a different color ink) just to see that you could do it if you had not ran out of time. After each set, assess how you did, using any source--but a tutor or teacher is best.

D. Pay attention to the type of problems you're really good and/or fast at doing. These should be the problems that you do FIRST on the actual test. Do not do a test in order. Do what is easiest first. This builds momentum, confidence, and ensures that you don't lose points by running out of time when you could have done a problem. A slight variation on this is to start by doing the test in order, but the moment you realize you're stuck, just move on quickly and come back later.

E. Go here to access the final exams mentioned. Do the indicated problems within the indicated time. After each set, fill in the gaps with your notes, or the help of a tutor, etc. Then, once confident you understand, move on to the next set. The goal is, by the time you get through all problem sets, all your major gaps would have been filled. But you must do the work by yourself first, BEFORE getting help. It's OK if you leave something blank or half done at the first run through. Just fill in the gap afterwards, and again, make sure you don't confuse your original attempt (or lack thereof) with the help that you get! Keep these separate! You (or I) will need this to assess (and fix) your weaknesses later.

  • Spring 2005: 4(b), 5(a), 6, 7, 8, 9(a) (1 hour)

  • Fall 2005: 5, 6, 7, 8, 9(a)(1 hour)

  • Spring 2006: 4, 6, 7, 8, 9(a) (1 hour)

  • Fall 2006: 4, 5, 6, 7, 8(a) (1 hour)

  • Spring 2008: 3, 4, 8, 9, 10(a)(1 hour)

  • Spring 2010: 3(a), 5, 6(a), 7, 8(a) (45 minutes)

  • Spring 2016: 1, 2, 4, 8, 9 (1 hour)

  • Fall 2016: 1, 3, 4, 8, 10 (1 hour)

  • Spring 2017: SKIP THIS! Do not look at this, save this for the final review.

F. AFTER doing the above problem sets, do these two tests. They are the tests I gave my class last year. Your test 1 will cover the material across tests 1 and 2 from that semester.

  • Test 1 Spring 2018 - Do in its entirety, 1 hour and 15 minutes. You may skip the bonus problems.

  • Test 2 Spring 2018 - Do in its entirety, 1 hour and 15 minutes. You may skip the bonus problems.

Were I you, I'd only attempt to get the bonus problems if I've taken this course before, or it's clear that I'm already VERY good at the topics on the actual test. If you're new to the course and/or a bit shaky on the material, stick to the plan. Don't try to be a hero and go ahead.

G. You may also want to try Matthew Grayson's Test 1 prep for his class, by clicking here.

H. In the interest of time, you may complete several (2 or 3) problem sets before seeing me or a tutor. But you should do so BEFORE getting through the last problem set. You should be checking your work with a tutor (or some other way) intermittently. And after each such occasion, you should practice new problems to see if what you were told has sunk in.

Test 2 Review

  • Follow the advice/instructions from the test 1 review.

  • Do all problems from the past finals NOT appearing in the review for test 1, giving yourself 15 mins per complete problem and 6 minutes per part of a problem. Complete the problem set for each final in one sitting under timed conditions. (You may also decide how much time to give yourself by taking 2 hours and 15 mins and subtracting the quoted times in Review 1.)

  • A specific list of problems will appear here shortly for those of you who don't know how to recognize what you have and haven't done. But that would be a red flag, just so you know. You show know the differences between problem types well enough to know what to choose. You should also be able to, by process of elimination, know what to choose.

  • You might also find it helpful to complete tests three and four from my Spring 2018 class. DO NOT LOOK AT THESE BEFORE YOU'RE READY TO ATTEMPT THEM UNDER TEST CONDITIONS! Complete each in 1 hour and 15 minutes (No longer). Test conditions! Review with a tutor after your attempts, and be sure to distinguish between your work and that of the tutor's.

  • Test 3 Spring 2018

  • Test 4 Spring 2018

Final Review

Do the following in the order shown.

  • On the last day of the class, studying for the final as you have been instructed to study throughout the course. Learn your main definitions and formulas, learn the manipulations, learn the Dos and DONTs, learn the typical problems and the strategies for how to do them, and the differences between each problem type (how is finding a surface integral over a scalar field different from one over a vector field?), etc. I've given a lot of advice on how to study and how to know you're doing it right and how to know you're following up correctly. Hopefully you paid attention, wrote it all down and started putting it into practice when I gave the advice. By now, all the kinks should be worked out and you should be good at studying this way. I won't go into all the advice here, but the second sentence in this paragraph is to give you an idea of what I mean by "study".

  • Within one days of the last class, go here and do the Fall 2016 final, in its entirety, under timed conditions (2 hours and 15 minutes, and yes, timing yourself while doing this is important). If you can't find the time to sit for 2 hours and 15 minutes all at once, break it up, but keep timing yourself. For each break, deduct 5 minutes from your total time. For example, say you want to break the exam up into three parts that you will sit separately, you should give yourself 2 hours instead of 2 hours and 15 minutes to complete the exam, and so you should complete it in three sessions, 40 minutes each. Doing a final in a single session is ideal though, so if it is at all possible to do that, make the sacrifice and do it.

  • Grade yourself, and assess your weaknesses and strengths. Review your weaknesses with me or a tutor at the Marshak Tutoring Center.

  • Within two days after the last class, go here and do the Spring 2017 final, in its entirety, under timed conditions. Assess how you did on the final. Be honest!!! If you get anything wrong, even if it is for a "silly" reason, take it seriously and look over the topic. Work out the gaps in your knowledge. Let this inform the second round of your studying. Study based on these gaps. At this point, your studying will be very individual to you.

  • (Optional) You may want to do the last step in a mock final setting. In such a case, organize with a group and Jhevon to set something up.

  • Assess yourself again. Rinse and repeat with different problem sets, until your (objective) assessment shows that you are in the A range.

  • As much as is possible, rinse and repeat the bullet points above. Get several problem sets and work them out under test conditions. These should be as close to a final as possible. If you forgot the problems for the old finals, you can redo them (with less time). If you didn't do the review for the tests when you should have, now's your time to do them and make up for that. Do not cheat yourself, don't go easy on yourself, ask someone to make challenging tests and do them and honestly assess yourself. Revise your mistakes and do the process over again. Keep doing it until you're getting an A.

  • You MUST study and do the first two finals as instructed. If, after that, you REALLY don't have time. (More than likely you do even if you think you don't. You will lie to yourself to stop the discomfort, be aware of this!) But if you REALLY don't have time, then make problem sets consisting ONLY of problems you have a lot of difficulty with. Hopefully this is smaller than an entire final. Once you create a test full of your worst nightmares, give yourself ~15 minutes per problem (or whatever the allotted time is), and do this nightmare test under test conditions. Then follow up as I have been instructing you to.

  • Your assessment is not valid unless it is based on how you perform on a full length test by the numbers. Assessing yourself based on how confident you feel is silly. Assessing yourself based on whether you understand worked out solutions when reading them is even more silly. The only way to know how you will perform is to do unfamiliar problem sets under timed conditions (as described above or very similar), and then grading yourself and seeing what numerical grade you get. That number tells you how much you understand--nothing else does.

It may take you 3 cycles of studying and doing practice finals, it may take you 20. It does not matter. Whatever it takes, however long it takes, whatever it costs, whatever inconveniences arise, DO NOT STOP UNTIL YOU HIT THE MARK. This is how success is achieved. That's what it takes. It's uncomfortable and frustrating, which is why many are not successful. But the end result is SO rewarding. The end result is that you will be able to take on bigger challenges. Some will run from this frustration and challenge. You need to be different. What you want is on the other side. Keep pushing. At all cost, keep pushing. Your success is in YOUR hands, and no one else's. Not even mine. You will give yourself a grade at the end of this term, I'm just the guy recording it in CUNY first. Keep pushing!

Blank Tests and Solutions

How to use these tests and solutions

Remember, there is no substitute for your own work. If you just go straight to looking at the solutions, it will not be as helpful to you. Especially if you're not doing so well, and you feel like you didn't do so well on the test. Print out the blank versions first. Work through the version that you took and try to fill in the gaps on your own. First, work through it with no help, then you may use your notes to help you. If you still have gaps or insecurities, you can get help from a tutor. At this point, when seeing the tutor, you can print out the solutions and take them with you and have the tutor review them and help you understand them. Once you're confident your gaps are filled in, try the OTHER version under test conditions (with slightly less time), and you can check your work with the solutions then. Be sure to distinguish what you do on your own vs what you do with notes vs what you do with a tutor. Your metric of understanding is ALWAYS what you can do on your own.

Test 1

Test 2


  • Test 1 is on July 2.
  • Last day to withdraw is July 5.
  • Test 2 is on July 18.
  • The final is on Wed. July 24 at 10:30am.