Homework

Weekly homework and solutions will be posted on this page.

Logistics for handing in homework

The homework is due on Wednesdays at 9:00 a.m. Pacific Time. NO LATE HOMEWORK IS ACCEPTED. (see explanation below)
Homework submissions will be handled electronically via the Gradescope platform, that is now linked through canvas.

Gradescope accepts only electronic submissions, so you will need to scan your homework before uploading it. Details on how to use Gradescope can be found below.

Assignments will be posted one week before they are due. Any change (e.g., to fix a typo) to a posted assignment will be announced in class and via email.

Untagged problem policy: Untagged homework problems will not be graded by the graders. Once you submit a regrade request due to a problem tagged incorrectly, there will be between 10% and 50% penalty for that problem. (penalty progressing from Hw2).

To account for unforeseen circumstances, in the final course average calculations the homework score will be calculated as a percentage (not to exceed 100%) of 80% of the total homework points on offer. For example, if there are 100 total homework points across all assignments, a student with 82 points would get a homework score of 100% and a student with 75 points would get a homework score of 75/80 = 93.75%.

It is always recommended that students submit partially-completed assignments even if they are not able to finish the full assignment by the deadline.

The purpose of education

We urge you to think for yourself on assignments. Thinking is hard; it is how you learn and make progress. You may consult lecture notes, textbooks, teaching staff during office hours, SUMO/CTL tutors, and your peers (preferably after trying a problem by yourself). Sensible use of AI tools (more on this below) can devise new examples to explore, and probe your grasp of ideas. However, you must write homework solutions in your own words, expressing your own thoughts, after consultations are done.

Expressing ideas and methods in your own words is how to judge what you truly understand, and real understanding is what makes a Stanford degree worth more than the paper on which it is printed. Just as watching cooking shows while sitting on a couch does not actually give you the ability to cook, if you rely on AI to do your academic work and merely read (and perhaps memorize) its output then you will never learn how to ``do the math'': to use course content in substantive reliable ways in the future.

Avoid over-reliance on AI: Using AI to do your work prevents you from developing problem-solving skills and conceptual understanding needed to succeed in this course and any future quantitative courses, which will lead to poor performance on exams. Math builds on itself, and gaps in your understanding will accumulate over time. There is no substitute for your own hard work.
The only way to truly learn math is to engage actively with the material and work through problems on your own. If you use AI to generate practice problems for yourself, beware that AI can be wrong. When you are stuck, ask instructors or teaching assistants for help. Unlike AI, which often provides solutions without helping you to genuinely learn the material, the course teaching team will guide you through the thought process in a way that strengthens your understanding.

It is prohibited without explicit instructor permission to share, upload, or reproduce copyrighted course materials -- including lecture notes, readings, homework assignments, practice exams, and exams -- on AI platforms (or any websites) apart from asking it to explain or illustrate a screenshot of a limited part of the material (e.g., for clarification, learning purposes, asking AI if your own work has errors, or illustrating similar -- not identical -- examples). Since AI output is generated by probability rather than intelligence, it is entirely {m your responsibility} to judge its correctness via your own intelligence. The blind-faith excuse ``but AI told me this is correct'' is never acceptable.

AI Disclosure Policy:

The purpose of homework is to reinforce your learning and prepare you for exams to assess mastery of the course material. Apart from circumstances when the instructor explicitly indicates otherwise, if you outsource to AI any part of your work on an assigned task (to get ideas, to try out a similar but not identical task, etc.) then you must abide by the math department AI Disclosure Policy:

If you are unsure about policies regarding the use of AI tools in this course, seek clarification from the instructor(s). Students in math department courses have been found responsible for Honor Code violations in recent years when their homework and/or exam answers clearly resemble AI output and are distinct from their usual style of writing.

Responsibility for understanding

You are expected to understand your submitted work in homework and exams and to be able to verbally explain to your instructor (upon request, and without advance notice) any work you submit. When you apply for jobs, you will be interviewed by professionals who instantly recognize a lack of real understanding due to over-reliance on AI; we hold you to the same standard. Do not submit what you do not understand. The response ``I don't understand what I was writing but I know it works'' is never acceptable when asked to explain a submission. If your verbal explanation is inadequate in that you clearly do not understand what you wrote down or you cannot solve a similar problem using the same techniques, your grade for that portion of the assignment or exam will be assigned (or reassigned) to be 0. Your instructor may also file an Honor Code concern if your work contains solutions resembling AI output that you cannot adequately explain in-person in your own words when asked to do so.

Logistics for handing in homework

The homework is due on Wednesdays at 9.00 am Pacific Time.
Homework submissions will be handled electronically via the Gradescope platform, that is now linked through canvas.

Gradescope accepts only electronic submissions, so you will need to scan your homework before uploading it. Details on how to use Gradescope can be found below.

Assignments will be posted one week before they are due. Any change (e.g., to fix a typo) to a posted assignment will be announced in class and via email.

Untagged problem policy: Untagged homework problems will not be graded by the graders. Once you submit a regrade request due to a problem tagged incorrectly, there will be between 10% and 50% penalty for that problem. (penalty progressing from Hw2).
Due January 14th Homework 1 Solution
Due January 21st Homework 2 Solution
Due January 28th Homework 3 Solution
Due February 4th Homework 4 Solution
Due February 11th Homework 5 Solution
Due February 18th Homework 6 Solution
Due February 25th Homework 7

Logisitcs of Homework

Mathematics is a cumulative subject, with many concepts building on prior ones. Homework assignments reinforce concepts and prepare students for upcoming material. Solution sets are posted shortly after submission deadlines so that students can promptly see where they had misconceptions and alternative approaches. Release of such solutions also supports exam preparation. Extensions of additional time on homework assignments beyond the release of solution sets are not granted because this would fundamentally alter the course and its cumulative nature.

Logistics for Weekly Homework: The weekly homework submission is handled electronically via the Gradescope platform that is now linked through your canvas coursesite. Gradescope accepts only electronic submissions, so you'll need to scan your homework before uploading it. Make sure to allot plenty of time to follow the submission instructions below before each deadline. Assignments will be posted no later than a week before they are due, and it is strongly recommended that you begin assignments promptly.

Students are encouraged to examine their graded homework assignments promptly. Usually only a portion of each week's assigned problems will be graded (and the selection of problems chosen to be graded will not be announced in advance); as a result, be sure to look over the posted solutions to check over your solutions to the ungraded problems when your graded assignment is returned. It is ultimately your responsibility to look over your graded assignment while consulting the posted solutions, not only to check your understanding but also to find any grading errors.

Homework regrades

If there is a problem where you believe you deserve more credit based on the visible work in your original submission and the grader's rubric, submit a regrade request through Gradescope explaining why you should earn more credit. All requests for homework regrades must be submitted within two weeks of the original due date (each HW will be graded within one week of the due date) or March 13th, whichever comes first.

Please note that if a problem was missing from your submission (whether you accidentally skipped it, did the incorrect problem, or forgot to upload the relevant scan), you will not receive any credit for that problem.

Gradescope overview

Gradescope is an online platform for grading exams and homework. For each problem, you will be able to see clearly which rubric items your solution satisfied and any additional comments the grader has for you.

Two important notes:

  • Homework assignments will still be graded by members of the Math 21 instructional team. You are not being graded by an electronic system.
  • Students are still responsible for scanning and uploading their homework each week.

How do I actually upload my homework?

For each homework assignment, you must

  • Produce a legible PDF of your complete solutions to each problem. Make sure your problems are clearly labeled!
  • Upload the PDF to Gradescope by the deadline (9AM on Wednesday mornings)
  • Select the page(s) that contain the solution to each of the assigned problems. Note: Failure to do this finalizing step will mean that some or all of your problems will not be graded! Once you submit a regrade request due to a problem tagged incorrectly, there will be between 10 to 50% penalty for that problem (the penalty will progress, starting with Homework #2.)

An example of the PDF submission process is depicted in this video.

Note: It is also possible to choose to take a picture of each question and upload each question individually, though this is less recommended.

Gradescope has its own mobile app for submitting homework (though the website is still the only way to view feedback and submit online/timed assignments).

How do I produce a PDF of my homework?

This does not mean you have to do your homework on a computer. It just means you have to scan your handwritten work and create a PDF. The first thing to be aware of is that the scan will come out much better if you write in a darker pencil or pen.

To actually scan your homework, there are a number of mobile/tablet apps for various platforms recommended by Gradescope that will allow you to turn photos into multi-page PDFs. Note: GeniusScan is also available for iPhone and some may find it preferrable to Scannable.

Alternatively, there are traditional scanners in many (theoretically all) computer clusters in campus residences and many (theoretically all) campus libraries. Contact the Residential Computing help desk for details.

MOST IMPORTANT POINT: Make sure to preview your scan before you upload it to Gradescope! You want to make sure that every bit of work is visible and readable so that the graders can provide accurate feedback on your solutions.

What if I notice an error in my solution or forgot a page of my homework when I submitted it?

If the deadline has not passed, you can resubmit your homework. Simply go to Gradescope and click on the relevant assignment to view your submission. In the bottom right hand corner of your browser, you should see a "resubmit" button. This will allow you to update your submission to correct the error you noticed. Only your final submission will be graded.

Important note: Choosing to resubmit your assignment will completely erase your current submission, meaning you will have to reupload your entire solution again. Gradescope does not currently allow you to just update a single question.

How do I see how I did on the homework assignment?

Once the submission deadline has passed, your homework will be graded. This usually takes about a week. Therefore, around the following Tuesday, you will receive an email saying that your graded work is available for viewing. Your score as well as grader feedback on your homework will be available in Gradescope.


Winter 2026
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