Discussion – Advice from the Past

For the past several years I have taught this same course in the Fall semester (until last year, it had the course number MAT 2071).   At the end of each course, I give my students the following assignment:

Imagine that you are invited to speak on the first day of MAT 2071, to give advice to entering students.  Write at least three sentences … describing what you would tell them.

To see the assignment and the students’ responses, follow this link for Fall 2019 (this class was very small, only 5 students), this link for Fall 2018, and this link for Fall 2017.

Your assignment, due at the beginning of class on Tuesday, September 8th, is to:

  1. Read through ALL the responses (there are about 30 of them altogether).
  2. Write a reply to this post (1 paragraph) responding to all of the following:
    1. What advice seemed most relevant to you personally? Why? (you can copy/paste a short statement, or put it in your own words)
    2. Based on this advice, what changes can you make right now to help you succeed in this course?

Extra Credit. For extra credit, write a response to one of your classmates’ comments.  Do you have any advice?  Be kind.


  1. Irina Chernyavskiy

    The advice from years past has been wonderful but there are some that are my favorites. A knowledge of algebra as stated by some of the students in 2018 is very useful to be aware of since there are some proofs that will require algebraic manipulation. Not everything about this course will be radically different from what you have seen before it’s nice to be reminded of it. Another comment I especially like what one student from 2017 said about succeeding in this course they had a shorthand the two P’s practice and participation. In this course it seems like there will be a lot of concepts thrown at you later on in the semester that really make the beginning look much easier as suggested by the students’ comments in multiple years. I would like to add from what I’ve heard of higher level courses you can’t escape understanding why something works like you maybe can in maybe some other courses it really makes a distinction now more than ever.

    I can improve y chance of success in this course by interacting more with the class in general or with the professor via email/office hours. I’d rather send an email or go to office hours since it gives me more time to actually figure what is causing the confusion. While I’m in class I’m usually trying to get all the notes as quickly as possible ( I tend to write rather slowly) as well anything the professor particularly emphasizes. Something else that would really help me is to start doing more practice problems even if they haven’t been assigned for homework I’ll worry less come exam time if I do that and it will be easier get a good grade that way.

    • Ihn Lee

      I like the two P’s. I agree with participation and practice! I should take advantage of office hours when I have a question.

    • Jonas Reitz

      This makes a lot of sense to me – it’s important to know your own habits and methods of working, and adapt to them (just as it’s important to try to adapt to your students!).

  2. Denyese Gonsalves

    Re: Advice from the Past
    2. a. I enjoyed most of the past students’ responses. I am aware I can’t quote all. I especially liked the students’ advice which pertained to staying on top of the work by doing the assignments on time and reading the textbook as well as all the material given by Professor Reitz. As one student said, it is like building a house where a firm foundation is needed…However, this student’s response personally resonates within me.
    “In order to well in this class I recommend you to do the two P’s. The two P’s stand for practice and participate. In Professor Reitz class, he does assign homework on paper and on Webwork. You might think it might be overwhelming but believe me it will pay off to do your homework assignments. By doing your homework it will help you understand the theorems better and it will help you do well on the tests. So practice, practice, practice!
    Now participation might not be easy to do for some students, I know because I don’t like participating myself. Don’t stay quiet if you are having trouble understanding something, Professor Reitz is always happy to receive your questions. If you still don’t feel comfortable enough to participate, you can always email him and he will help you with any issues you are having in class. Overall, you will learn to enjoy the class, especially with the help of Professor Reitz patience, kindness and happy energy to teach the class.” Written by Evelin. As Evelin has stated, a student has to practice, practice, practice.

    b. All I can do is practice more and when I am tired of doing that practice even more. As much as the work may seem familiar (at this stage) I owe it to myself to feel comfortable with the material by familiarizing myself with the theorems etc. To not fall behind, I will continue doing what I do, try to get the homework in before the given deadline date, read everything Professor presents and ask a question or email Professor if I don’t understand something.

    • Jonas Reitz

      These really sound like good strategies, Denyese. I would add, if you reach the point of feeling tired of practicing, that finding alternative ways to wrestle with the material can be a nice change – for example, set up a zoom call with a classmate and go over homework together!

  3. Ihn Lee

    You need to be able to be responsible enough to read the textbook. It gives plenty of examples and even more practice problems. The Prof can’t go over everything so it’s up to you to pick up the lack and choose to succeed.

    I happen to be a person who jump right into solving problems. I don’t read the textbook. I use the note from the lecture instead. I don’t practice a lot. I just review the homework, questions and examples that the professor show us. The advice above says that read through the text book and practice. I totally agree with that. I should read the textbook and practice more. I believe If we do, we all can pass.

    • Jack Berner

      I’m very much the same way, Ihn. Usually I don’t have to spend too much time with the textbook and am still able to do well on homework and tests. One of the past students said to read the textbook before the class rather than after. Maybe that would work well for you since you’re not used to going to the text after lectures.

    • Nina Melendez

      I used to be the same way, but in the past year I have become better at using the textbook. Not only that, but if I’m struggling with a topic I will find different explanations to become better versed on the topic.

    • Jonas Reitz

      I do think that that you tend to use the textbook more (and you learn to use the textbook more) as you progress in Math – for myself, I think I rarely used the textbooks (except for homework) up through the end of the Calculus sequence, but after that I came to rely on them much more!

  4. hanzhang

    I thought I made a mistake to mark the comment under the Agenda 2. so I copied it from there to here and sorry to make you read twice.
    Thanks for professor to introduce us to ready the past student’s advices for this course. we could learned a lot from them. There are only 3 classes passed and I feel easy at the beginning but some students said that the coming prove section will be difficult which we will use direct proof or contraposition proof or contradiction proof. that is funny and I am curious of that.
    refer to the study method. I get some suggestions like: ready the text books and do more practice from the book, make a good note that will help us for the tests and exams. prepare lessons from class…… those are all helpful. but I thought everyone should find their own way to learning. I like to say ” practice thinking”, think more, think deeper. whether you are holding a book or not, whether you are walking or cooking, just thinking, use the brain anywhere when you want to, then you can save time and solve problems by accident.this is very interesting, you will feel the sense of success and pleasure unconsciously.
    and also Professor Reitz is very professional educator he provide us a lot of opportunities to ask questions, guide us how to study, and listen to our voices constantly as there are lot of place that we could add a comment or ask questions just like my comments in Agenda 2 and here. the students could communicate with the professor through many different channels, that is great.

    • Jonas Reitz

      I did indeed see your comment first under the Agenda post – thanks for re-submitting it here, that definitely helps me keep things organized! But in general, I will try to keep on top of all the various communication methods we have – I want to be as accessible as possible to you all.

  5. Allison Kirshner

    Advice from the Past was an interesting read. It was great to get the students’ thoughts after the course was over. I learned a lot by reading their comments. The main points I got was the following: Read the textbook, ask a lot of questions, do the homework ontime, practice practice practice!, pay attention to sets, and Induction and proofs are the most difficult areas. For Induction, follow steps closely to master the problems.

    The advise was very good advise. I always tend to practice problems whenever homework is assigned or whenever given a review for an exam. Repedative practing has always helped me in the past. I am very happy the lectures are being recorded because I can always go back when a topic isn’t clear to me the first time. So far, I am enjoying this course. Thank you professor for making this course enjoyable and the topics easier to understand!

    • Chris

      Yes! I also felt like all of the advice from the prior students added up to Study, work hard, do what you are tasked to do and do not be afraid to ask questions, all this combined and you will succeed. Of course that paired with a professor that sets us up to be successful pretty much gives us the choice of whether we take advantage and pass or slack off and fail.

      Good luck in the Semester Allison.

      • Allison Kirshner

        Thank you! You too!

    • Luis lora

      Allison you make a very good point mentioning recorded videos as a way of reviewing content this is the first class ive ever been a part of were i can review a video instead of taking notes . I notice i miss far more staring down and writing then staring up and listening .

      • Allison Kirshner

        Yes! I really like this method of learning. It is so nice to be able to review the video when a subject isn’t clear the first time, as opposed to just reviewing hand-written class notes.

        • Jonas Reitz

          This is great feedback for me as well, as I am definitely trying things (like recording lectures) for the first time in this class. I plan to send another survey (about things like this) in the next few weeks. Thanks!

          • Allison Kirshner


  6. Chris

    The advice I often give myself and rarely follow through entirely is to practice what I may have difficulty with. I usually practice it until I get it, not until I master it. Which sometimes comes back to bite me in the backside. So I am glad to see some students mention that constant practice is one way to get ahead and succeed in this course. SO, from now on I need to make sure I follow through and try and MASTER the topics I see as most challenging to me. So I too can have some advice at the end of this course to help the next group of students pass.

  7. Jack Berner

    I found Kelly’s advice from 2017 particularly helpful. She recommended reading textbook sections before they are covered in class, because “understanding basic terminology and concepts will allow the student to absorb the information presented in class quicker.” This advice stood out to me because I often take the opposite approach as a student, finding the textbook easier to comprehend after I’ve already taken notes on a professor’s explanation of the topic. While Kelly’s approach definitely seems more time consuming (I’ll probably still have to look at the textbook after lectures), I can imagine it being really effective in making discussion/lecture time as educational and productive as possible. I don’t know if I’ll start doing it immediately, but I plan on using Kelly’s approach when our class moves out of basic set theory and into proofs.

    • Matthew Schwartz

      Jack, I have the same approach with you when learning a new topic. It is counter intuitive and hard to look ahead into subject matter because it feels like its taking away from whats ahead of you. And for me personally I find it hard to read a math textbook without taking notes.

  8. Luis lora

    Some great advice I found was the difficulty of certain topics such as proof by use of inductive reasoning. This topic may have been the most challenging but, students found that asking questions, reading the textbook, further content research, class discussions and professor guidance that may prove effective in understanding the course material. I believe preparing for the upcoming content, learn as much as one can and use the resources available are helpful in this scenario. This class is quite different than some of the previous as it is online therefore my advice is to also participate in the discussions comments and zoom chats as much as possible.

  9. Matthew Schwartz

    There are so many skills that are pre requisites to be successful in a class such as this, and in mathematics in general. Reading the book is completely essential and doing practice problems on your own really spoke to me- as someone who spent a lot of academic years disengaged doing the bare minimum was the name of my game. Just doing enough to get through a class means nothing in terms of understanding. When you read the book, when you do problems on your own…when you find yourself thinking about what it means for a set to be countably infinite versus uncountable, reading ancillary sources on your own- working through the examples in the book out of your own personal interest, that’s when you know you are going to succeed in a class such as this one. A lot of math is hierarchical, you need to develop basic understanding before being able to move on to higher concepts, you’ll even find yourself revisiting things and realizing they went even deeper than you had previously understood. Changes I would make based off this advice today would be reading the book in my spare time, even if only for a few minutes. Flipping through chapters ahead, getting a sense of where the class is going and looking up YouTube videos (as one does) to try and build out a conceptual framework before digging deep. As Lawrence Krauss says about Quantum Mechanics “the first time students get a hold of it, they have no idea what they’re looking at, but the second time they can say ‘I’ve seen this before’ “.

    • Jonas Reitz

      I love the quote from Lawrence Krauss! A great mathematician (von Neumann) once said “In mathematics you don’t understand things. You just get used to them. …” which seems to have a similar flavor. I often find that the first time I try a new type of problem, it takes forever – but after a few, they go much faster (even if they are still challenging). I think this is “getting used to” things!

  10. Nina Melendez

    What advice seemed most relevant to you personally? Why? (you can copy/paste a short statement, or put it in your own words)
    I found Silvana’s advice from 2018 to be personally relevant. She starts by stating:

    “My advice would be to always keep track of your work and try to avoid doing everything las minute. You must do all your homework. This will also prepare you for exams. There is much extra credit you can earn. Do all of them if possible to get maximum points.”

    This resonated with me as I tend to “put too many things on my plate” and end up with a mountain of work.

    A step for this is that I am creating a “to do” list (I’m putting it directly on my computer desktop with a notes application) with all that I need to complete. This will allow for this list to visually be in front of me when I turn on my computer.

    • Jonas Reitz

      Figuring out a method of self-organization that works for you is such a great (and ongoing) life task! I settled years ago on a running to-do list (just a Google doc, with the most important items at the top). Unfortunately, the doc is now about 15 pages long and I never really look at anything that’s not on the first page – so I clearly have more work to do in this area. No doubt there are very important items buried down in the lower reaches…I’m scared to look.

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