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Paper-and-Pen Homework  

(Updated 17 February 2026)

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.

    • Homework 0 (Reading Assignment) Note: The password can be found in item 6. of the email that was sent to students on Friday, 12/26/2025.
    Note: Please complete this reading assignment by 02/03/2026. If you have any questions, please come to my office hours.

    Note: I know that diving into real analysis can sometimes feel challenging, especially if it’s been a while since you’ve worked on some of the prerequisite topics. To help you brush up on key concepts, I’ve included links to some excellent resources below. Feel free to explore them whenever you need a refresher—understanding the basics is an important step toward mastering the material in this course.

    Note: Please carefully read the syllabus. If you have any questions about the syllabus, please come to my office hours.
    Homework 1     (Due Friday, February 6, 2:00 pm)(Due Tuesday, February 10, 12:00 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 130.

      Note: The purpose of this homework assignment is to make sure that you know the terminology and specific methods discussed in class. All problems should be solved using terminology, ideas, and methods that were introduced in lecture.

      Note: Please carefully read the syllabus. If you have any questions about the syllabus, please come to my office hours.
    Special Extra Credit
      There are two standard approaches for constructing the set of real numbers (i.e., the ordered field that satisfies the least-upper-bound property) from the set of rational numbers. One method introduces real numbers as certain equivalence classes of Cauchy sequences of rational numbers, while the other method uses Dedekind cuts. For more detailed discussions, please consult the references below. You will earn extra credit if you come to any of my office hours to teach me either of these methods.

    • Robert Strichartz, The Way of Analysis, Chapter 2

    • Ethan D. Bloch, The Real Numbers and Real Analysis, Chapter 1
    Homework 2 (Due Tuesday, February 17, 12:00 pm)
    Homework 3 (Due Saturday, February 21, 11:00 pm)