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Paper-and-Pen Homework  

(Updated 29 November 2024)

Paper-and-Pen assignments should be submitted through Gradescope. You will be able to access Gradescope through the course Canvas page. If you are not familiar with Gradescope, you can find a video demonstrating the submission process at the following link:

https://gradescope.com/get_started#student-submission
Also Gradescope has provided a helpful guide to scanning and submitting your assignment as a PDF:
Guide to scanning and submitting your assignment
  • Late assignments will not be accepted.
  • Please keep all problems in the same order as the assignment list and ordered vertically on your page.
  • You must show all of your work.
  • All your solutions should be in a single pdf file before being uploaded, or as a picture for each question.
  • Please make sure your files are legible before submitting. Unreadable solutions will not earn credit.
  • Most word processors can save files as a pdf.
  • There are many tools to combine pdfs, such as here, and others for turning jpgs into pdfs, such as here.
  • As it will be announced in class, in addition to submitting your solutions to Gradescope, you will also be asked to bring a hard copy of your solutions to class. Both actions will be required.

    • Homework 0, Part I (Reading Assignment) Note: The password can be found in item 6. of the email that was sent to students on Wednesday, 08/14/2024.
    Note: Please complete this reading assignment by 08/28/2024. If you have any questions, please come to my office hours.
    Note: Please carefully read the syllabus. If you have any questions about the syllabus, please come to my office hours.
    Homework 0, Part II (Reading Assignment)
      Reading: Please carefully review Professor John M. Lee's invaluable guidelines on writing mathematical proofs. I encourage everyone to make their best effort to follow these principles.
    • Some Remarks on Writing Mathematical Proofs
    Note: Please complete this reading assignment by 09/09/2024. If you have any questions, please come to my office hours.
    Note: Please carefully read the syllabus. If you have any questions about the syllabus, please come to my office hours.
    Homework 1     (Due Friday, September 6, 2:00 pm)
      Note: Misconception: "Every homework problem must be directly analogous to an example or an exercise solved in class." NO! For some problems you may need to apply what you have learned to something new, make connection between various concepts discussed in class and think about concepts in different ways and from different angles. It is absolutely false (and dangerous) to think that you should be able to solve every homework problem in under 10 minutes, by directly applying algorithms/procedures taught in class. If you want to really learn the lecture topics, you need to work hard every single day.

      Note: If you have any questions about the homework problems, please come to my office hours. If any of the homework problems seems hard or impossible, that just indicates that there is a fundamental problem with your understanding of basics of mathematical analysis and mathematical reasoning. By experience I know that dealing with this through email is ineffective. It is not a good idea to answer any questions about homework via email. We should meet up in person (or in zoom) during my office hours to discover what the root of the problem is. Remember, the goal is not just solving the problem; we want to UNDERSTAND the problem and REFLECT on the solution. Please bring your questions to my office hours. There is nothing that I like more than answering your questions about the material covered in Math 230.

      Note: Please carefully read the syllabus. If you have any questions about the syllabus, please come to my office hours.
    Homework 2 (Due Saturday, September 14, 6:00 pm)
    Homework 3 (Due Saturday, September 21, 6:00 pm)
    Homework 4 (Due Saturday, September 28, 6:00 pm)
    Homework 5 (Due Saturday, October 5, 6:00 pm)
    Extra Credit
      Note: Please review the above PDF on the importance of the concept of compactness. If you visit any of my office hours to discuss the contents of this PDF, you will receive extra credit.
    Homework 6 (Due Sunday, October 20, 6:00 pm)
    Homework 7 (Due Sunday, October 27, 6:00 pm)
    Homework 8 (Due Sunday, November 10, 6:00 pm)
    Homework 9 (Due Sunday, November 24, 6:00 pm)
    Reading Assignment
      Note: Here are two useful facts about the limsup and liminf of sequences of real numbers and an example comparing the Root Test and the Ratio Test. Feel free to read through them at your own pace and bring any questions to my office hours.
    Homework 10