đź“– Syllabus

Welcome to Math 124, and to the University of Michigan! We’re so excited to have you in the course. Make sure to read the syllabus carefully so that you understand what is expected of you.

Overview

Course Staff

The course is taught by a staff of two instructors (who you may think of as the “professors”), one graduate TA (called a “GSI”, for “Graduate Student Instructor”), and one undergraduate TA (called an “IA”, for “Instructional Assistant”). See the Staff page for contact information and to learn more about us!

Content

Math 124: Vectors, Matrices, and Applications is an introduction to linear algebra built around vectors, matrices, geometry, computation, and applications in science and engineering. This course builds geometric intuition and algebraic skill in linear algebra for beginners, emphasizing vectors, matrices, orthogonality, linear systems, linear transformations and computational tools. It focuses on conceptual understanding, real-world applications and software use rather than proofs. Students gain practical experience connecting linear algebra concepts to engineering and data-driven problems.

Credit

This course is worth 4 credits. Math 124 is part of a brand-new two-course sequence for first-year students in the College of Engineering, along with Math 125.

Click here to read more about the course and how it fits in the College of Engineering curriculum.

The College of Engineering is piloting these two courses through an initiative to eventually update the general math requirement for all Engineering undergraduates. With the increasing importance of computational approaches (such as AI) across all engineering disciplines, there is a growing need for all engineers to be fluent in linear algebra, which is the mathematical backbone of such approaches. Furthermore, there are advantages for calculus topics to be taught in a way that highlights computational approaches, engineering-based examples, and analytical methods most relevant to engineering. Therefore, you have the opportunity to take this updated math sequence that is specially designed for engineering students (and co-taught by College of Engineering faculty) to provide benefits beyond the traditional sequence for your subsequent engineering studies.

  • Math 124 and Math 125 are unique in that they have been designed from scratch to introduce students to mathematical theory and to show how it is applied to solve real engineering problems.
  • For students in programs that don’t currently require linear algebra, Math 124 will nevertheless give them a deeper understanding of how their field works – every single engineering discipline relies on linear algebra. For students in programs that do require linear algebra courses – like Math 214, Math 217, or EECS 245 – Math 124 will provide a strong foundation for success in those courses.
  • Both pilot courses will be small and co-taught by Michigan Math and Engineering professors, giving you a tighter-knit experience than in the existing calculus courses.
  • In Math 124, rather than teaching students how vectors, matrices, and systems of equations work just in theory, they will be taught those same fundamentals while understanding how they power machine learning, physics, aerodynamics, circuits, cryptography, fluid mechanics, and more.

Prerequisites

Students should have a strong background in high school algebra and geometry. Quiz 0, administered in the second week of the class, will assess your knowledge of these topics.

Websites

Your source of truth for all things Math 124 is this course website, math124.org. All course content will be linked from this website, so make sure to bookmark it and check it regularly for updates.

In addition, we will be using a variety of platforms to facilitate Math 124, some of which you will need an account for.

Ed

Ed is our course message and discussion board. This is where all announcements will be made, not Canvas. More details are in the Communication section below. If you didn’t already receive an invitation to Ed, sign up here.

If you have a question about anything to do with the course — if you’re stuck on a problem, didn’t understand something from lecture, want clarification on course logistics, or just have a general question about mathematics or engineering — please ask on Ed! We know that generative AI tools can answer your questions, and while we encourage you to use those tools responsibly as well, part of the benefit of attending a school like Michigan is the ability to form connections with your instructors and peers. We only ask that if your question includes some or all of an answer (even if you’re not sure it’s right), please make your post private so that others cannot see it. You can also post anonymously to other students if you prefer.

Course staff will regularly check Ed and try to answer any questions that you have. You’re also encouraged to answer questions asked by other students. Explaining something is a great way to solidify your understanding of it!

Pensive

Pensive is where you’ll submit your homeworks, and where we will show you your grades on exams. As is discussed below, all homeworks must be handwritten, scanned into a PDF, and submitted to Pensive. If you didn’t already receive an invitation to Pensive, please let an instructor know. Pensive is like Gradescope – a tool you may use in other classes – but it allows for AI grading of handwritten work, with human review and the ability to ask for a regrade. Not only does this enable faster and more accurate grading, but it also frees up instructor time to spend working with students one-on-one, which AI cannot do. Pensive has been approved by the College of Engineering, who ensured that it meets the necessary privacy and accessibility standards; rest assured, Pensive does not train AI models on your work.

Canvas

Canvas will only be used for accessing lecture recordings. All other content will be posted on the course website.

PrairieLearn and PrairieTest

PrairieLearn is the platform on which you will take practice quizzes, and is the same interface quizzes will use. If you didn’t already receive an invitation to PrairieLearn, please let an instructor know.

PrairieTest is used for scheduling quizzes. If you didn’t already receive an invitation to PrairieTest, please let an instructor know.

Both PrairieLearn and PrairieTest are discussed in detail in the Quiz Logistics page of the course website. Read this page ASAP: scheduling for Quiz 0 opens on August 31, and Quiz 0 is administered from September 8 to 11.

Google Colab

Most homework assignments will have accompanying code to run, hosted on Google Colab. More details are in the Running Code page of the course website.

Lectures

There are two types of regularly-scheduled class meetings in Math 124: lectures and labs.

Lectures are held on Tuesdays and Thursdays from 2:30-3:50PM in Room G127 of Angell Hall, and are co-taught by the instructors, Kartik and Suraj, who will each teach roughly half of the lectures throughout the semester.

Lectures are where we introduce core concepts. The term “lecture” makes it sound like you’re just going to sit and listen, but we will do our best to make them engaging and interactive. Expect to spend a lot of time working on activities and discussing approaches. Lectures will be recorded and posted on Canvas, but the recordings are intended for review and occasional absences rather than as a replacement for attending class.

Course Notes

Instead of relying on an existing textbook, we’ve written a set of notes specifically for the course, which you can find at notes.math124.org. Lectures will follow the notes very closely, and will contain additional examples and explanations. We will try our best to make the notes for each lecture available before the lecture, but we are actively writing them as we go, so there may be delays. (That is to say, you aren’t expected to read the notes before class, but you should read them after class.)

These notes aren’t optional readings, they’re mandatory. Reading course notes regularly will help you stay up to speed and succeed on assessments.

If you find any typos or ways to improve the notes, please fill out this form.

Attendance

Lecture attendance is required, and is worth 4% of your overall grade. How is this assessed?

  • There will be 28 lectures in total; each lecture you attend will earn you 1 “lecture point”, up to a maximum of 24 lecture points.
  • Your lecture score will be the number of lecture points you earn out of 24. This means you can miss up to 4 lectures for any reason (late add, extenuating circumstances, etc.) and still earn a full lecture attendance score.

Labs

The other type of regularly-scheduled class meeting is labs. While everyone in the course attends the same lecture section, there are two separate lab sections, each on Wednesdays for 2 hours, and you should attend the one that you are officially enrolled in.

Labs are run by our GSI, Aaron, and IA, Sanjana. During the first half of lab, you will work on a physical worksheet that reviews content from the previous two lectures (so bring a pencil!). Once you’ve finished the worksheet, you’ll spend the rest of lab getting a headstart on that week’s homework. Homeworks may involve writing code, so make sure to bring your laptop to lab.

To earn credit for a lab, you must show the GSI or IA a completed lab worksheet and meaningful progress on that week’s homework. This means that there is no option to receive credit for labs remotely. Labs are primarily completion-based and contribute 10% of your overall grade. Your lowest two lab scores will be dropped. On Wednesday evenings, we will post the lab worksheet and its solutions on the course website.

Homework

Weekly homework develops the ideas from lecture and lab in greater depth. Homework may include written mathematics and computational applications. Homeworks are normally due on Mondays; Homework 1 is due on Tuesday because of Labor Day. Other changes to this planned schedule will be announced on Ed and updated on the course homepage.

Homeworks must be handwritten on paper or tablet by each student individually, scanned into a single PDF, and submitted to Pensive. That is, no typing and no LaTeX, unless you have accommodations specifying otherwise. We believe that handwriting the material helps you learn it better, better prepares you for exams, and frankly is harder to cheat with AI.

Homeworks are worth 20% of your overall grade and is graded by accuracy. Your lowest two homework scores will be dropped.

Collaboration and Generative AI Policy

The majority of homework problems will involve writing solutions to math problems, but some will involve writing code in a Jupyter Notebook. The point of a homework problem is not really to “find the answer” – we know the answers, and ChatGPT can easily provide answers to any homework problem we could ask you. Rather, the point of a homework problem is to help you deeply understand the material, apply it to new problems, and build problem-solving skills along the way that will pay dividends in future courses and in your life as a graduate of the University of Michigan.

Think of it like this: driving 10 miles is a lot easier than running 10 miles, and in many cases, driving makes total sense. But, if you’re trying to exercise, driving 10 miles won’t really help you achieve your goals. If you buy that analogy, just think of driving as “copying the answers from someone else” and running as “thinking through problems yourself” – both may earn you the same score on homeworks, but only the latter will help you in the long run.

With that in mind, you can – and are actually encouraged to! – talk to other students in the class about the problems and discuss solution strategies. Talking and debating about challenging ideas is a great way to solidify your own understanding of the material. That said, you should not share any written communication. You can tell someone how to approach a homework problem if they’re stuck, but you cannot show them how to do it. One way to tell if you are respecting this boundary is to ask yourself whether your collaboration could take place over the phone. Additionally, the content of your verbal communication should involve the problem-solving strategy and approach, and you should not directly compare answers with classmates.

Similarly, you can ask generative AI tools like ChatGPT for help with concepts, because these tools can be genuinely useful. Just be cautious that they can also lead you astray. If you find a particularly useful explanation online, either on a website or from a generative AI tool, please let us know! You cannot ask generative AI tools to solve homework problems for you or to verify your answers. Doing so is only cheating yourself. Remember you will not be able to use these tools during the exams, which are worth 50% of your overall grade.

If we suspect that your homework answers are not the result of your own work, we reserve the right to interview you in-person and ask you to answer and explain similar questions, and submit a case to the LSA Honor Council.

You may post homework-related questions on Ed, though your questions and answers should be about approaches, not answers to specific problems. If your question includes some or all of an answer (even if you’re not sure it’s right), you must make your post private so that others cannot see it. We are not able to tell you whether your answer is correct.

One final thought: Demis Hassabis, the co-founder of Google’s DeepMind AI research organization and a 2024 Nobel Prize winner, said

Those people who understand the deep technical, they’ll be able to use these tools 10 times more effectively than people who don’t have that technical knowledge. (source)

While it’s true that generative AI tools can answer any question we’d ever ask you in the course, remember that the point is to gain independent critical thinking skills. Keep this at the back of your mind throughout the semester!

Late Policy, Slip Days, and Drops

All homeworks must be submitted by 11:59PM Ann Arbor time on the due date to be considered on time. If you make a submission after the deadline, your assignment will be counted as late.

You have 6 “slip days” to use throughout the semester. A slip day extends the deadline of a homework by 24 hours. You may use at most 1 slip day on any one homework assignment. Since lab worksheets must be submitted in person, they cannot be submitted late and cannot use slip days.

Slip days are designed to be a transparent and predictable source of leniency in deadlines. You can use a slip day if you are too busy to complete a homework on its original due date or if you forgot about it. Slip days are also meant for things like the internet going down at 11:58PM just as you go to submit your homework. Slip days are meant to be used in exceptional circumstances, so you probably should not need to use all 6, but if something in your life is impeding your ability to do your classwork on time, please reach out to us as soon as possible so we can work something out. The earlier you let us know that something’s going on, the more we can do to help.

Slip days are applied automatically at the end of the semester, and you don’t need to ask in order to use one. It’s your responsibility to keep track of how many you have left. If you’ve run out of slip days and submit an assignment late, that homework may still be graded, but you will receive a 0 on it when we calculate grades at the end of the semester.

In addition, your lowest 2 homework scores will be dropped from your final grade. This means that you can miss up to 2 homeworks for any reason and still earn a full homework score. You do not use any slip days on homeworks you don’t submit; for example, if you choose not to submit Homework 2, it costs you 0 slip days.

Regrade Requests

If you believe that we have made a mistake in applying the rubric shown to you on Pensive, you may submit a regrade request directly on Pensive within one week of the grades being released. If you do not submit a regrade request within one week, your original grade will be final. Part of your grade is clarity, so if your answer was mostly right but unclear you may still not be eligible for full credit.

Quizzes

There are five quizzes this semester, worth a total of 12% of your overall grade. Your lowest two quiz scores are dropped.

Quizzes are meant to be checks of your understanding of the basic computational ideas introduced in the class, while exams assess your deeper theoretical understanding of the ideas and problem-solving skills. Quiz 0 is designed to assess your understanding of high school-level algebra and geometry.

Quizzes are administered in person, but in the College of Engineering’s Engineering Testing Facility (ETF) on North Campus. Here are the key ideas:

  • You will take each quiz on a computer in the facility, rather than writing your work out on paper.
  • Quizzes are run on PrairieLearn, a website that allows us to provide randomized assessments.
  • Each quiz is open for a 4-5 day window, and it is your responsibility to schedule one 50 minute slot in which you will take the quiz, using PrairieTest.
  • You can only take each quiz once, but as we describe in the Practice Quizzes section of the Quiz Logistics page, you can take unlimited practice quizzes from home to prepare.
 Open FromScheduling Opens OnContent
Quiz 0September 8 to September 11August 31High school algebra and geometry
Quiz 1September 21 to September 25September 14Lectures 2–6
Quiz 2October 12 to October 16October 5Lectures 9–12
Quiz 3November 2 to November 6October 26Lectures 13–17
Quiz 4November 30 to December 4November 23Lectures 22–26

Read the Quiz Logistics page for more logistical information. Remember to do this ASAP, since Quiz 0 is very early on into the semester.

A Typical Week

To summarize the details above, here’s what a typical week looks like in Math 124:

MondayTuesdayWednesdayThursdayFriday
Homework \(N-1\) Due
Homework \(N\) Released		LectureLabLecture 

Office Hours

To get help on assignments and concepts, course staff will be hosting several office hours per week. In-person office hours will be held across a mix of Central Campus and North Campus locations, and we will also hold remote office hours depending on staff availability. See the Calendar tab of the course website for the most up-to-date schedule and directions. If you aren’t able to consistently attend at least one office hours slot a week, please email one of the instructors – we will try our best to move things around to get you the support you need.

We highly encourage you to attend office hours. Even if you don’t have specific questions, you will likely get a lot out of conversing about the material and hearing others’ questions. And even if you’ve mastered the material, still come and say hi – take advantage of the fact that this is a relatively small class!

You are required to attend at least two office hours with the instructors (Kartik or Suraj) – one before Fall Break and one after. This is worth 1% of your overall grade.

Exams

This class has two Midterm Exams and one Final Exam, all of which will be administered in-person and on paper. Together, exams are worth 50% of your overall grade.

ExamDate and TimeContentWeight
Midterm 1Monday, October 5, 7-9PMLectures 1-915%
Midterm 2Monday, November 16, 7-9PMLectures 10-1915%
Final ExamFriday, December 18, 4-6PMCumulative20%

If you have conflicts with any of the exams, please let us know on the Welcome Survey. We may provide alternate exam times for students with a valid, documented conflict with a required activity in another course or official university-affiliated activity, or to help students avoid negative academic consequences when their religious obligations conflict with academic requirements.

Exams are to be completed individually, with absolutely no collaboration allowed. Any suspected violations will be reported to the LSA Honor Council.

Index cards and calculators

  • For Midterm 1, you can bring 1 handwritten double-sided 4x6” index card. By handwritten, we mean that you physically write on the index card yourself; you cannot type a document or write one on your iPad and print it out.
  • For Midterm 2, you can bring 2 such index cards.
  • For the Final Exam, you can bring 3 such index cards.

This way, you can reuse your old index cards for future exams (if you want).

Additionally, calculators will not be allowed on any exams. We will design the questions such that the arithmetic is not very complicated, in order to have you focus on the conceptual ideas.

Redemption Policy

The specific lecture numbers in the table above are subject to change slightly. Midterm 2 is not cumulative. The Final Exam will be cumulative, and broken into three parts:

  1. Part 1 of the Final Exam will be based on Midterm 1 content. If you score higher on Part 1 than you did on Midterm 1, we will replace your Midterm 1 score with \(\frac{\text{Part 1 score} + \text{Midterm 1 score}}{2}\).
  2. Part 2 of the Final Exam will be based on Midterm 2 content. If you score higher on Part 2 than you did on Midterm 2, we will replace your Midterm 2 score with \(\frac{\text{Part 2 score} + \text{Midterm 2 score}}{2}\).
  3. Part 3 of the Final Exam will be based on the content introduced after Midterm 2.

This “redemption policy” for Parts 1 and 2 is designed to help you boost your Midterm 1 and Midterm 2 scores if you didn’t do as well as you’d hoped. This policy can only help your grade; it can’t hurt. To be clear, all three parts of the Final Exam are required and part of your Final Exam score.

Course Improvement Surveys

Math 124 is a new course. As a result, we will administer more surveys than you might normally receive in a course so that we can learn from your experience and improve future offerings. To account for the time you’ll spend completing surveys, completing surveys counts as 3% of your overall grade.

Some surveys will be “internal” surveys, run directly by the course staff through Google Forms. These will usually not be anonymous, because they involve questions where the instructors want to know your specific responses (e.g. whether you need alternate exams, or how much time you spent on recent homeworks so we know whether to reach out to you for support).

The other surveys are called FCI Surveys, which are designed to help track your experience in the course more broadly. FCI stands for “Foundational Course Initiative”, a program run by the University of Michigan to improve the quality of foundational courses, like this one. The responses to FCI surveys are not anonymous, but the instructors do not have access to your responses – only FCI staff does. FCI staff will summarize the responses and provide insights to us. (They will tell us who filled out the FCI Surveys, though, since we need that information to give you credit for them.)

Read more about the Foundational Course Initiative here. This semester, Math 124 is partnering with the Foundational Course Initiative (FCI) at the Center for Research on Learning and Teaching (CRLT). FCI is a program to improve undergraduate experience and learning in large enrollment courses and involves a course design collaboration between instructional staff, former course students, and FCI consultants. Over the course of the term, outside observers may attend class sessions, and you may be asked to complete surveys and/or participate in focus groups aimed at evaluating the effectiveness of specific course elements. While this is an educational improvement project, it also has a research component to understand educational experiences and document the effectiveness of various course design strategies (IRB: HUM00150716). Your participation in surveys and focus groups will be voluntary, and at no time will your name or any identifying details be included in any research presented either within or beyond the University of Michigan.

More information on FCI can be found here.

Please feel free to contact crltfciteam@umich.edu if you have any questions or concerns about this project.

To start, there are two surveys we need you to fill out:

  1. The first is the Welcome Survey. This survey is designed to help us understand your background and whether you need any alternate exams. The responses are not anonymous.
  2. The second is FCI Survey 1, which asks slightly different questions about your background and experiences. (FCI Survey 1 opens on August 31.)

Both surveys are due along with Homework 1, on Tuesday, September 8th. Each one is worth 0.5% of your overall grade. We have tried to make them different enough so that you don’t feel that you are repeating yourself.

Grades

ComponentWeightNotes
Midterm 115%See Exams section above
Midterm 215%See Exams section above
Final Exam20%Cumulative
Homework20%• 2 lowest scores dropped
• 6 slip days available to use with a max of 1 per homework
Quizzes12%5 total; 2 lowest scores dropped
Labs10%2 lowest scores dropped
Lecture Attendance4%28 total; 4 lowest scores dropped
Course Improvement Surveys3% 
Office Hours1%See Office Hours section above

Grades will not be any stricter than the standard grading scale, where an A+ is a 97+, A is 93+, A- is 90+, etc. For instance, the threshold for an “A” will never be higher than 93%.

Student Support and Well-Being

Accommodations

If you need, or think you might need, an accommodation for a disability, please let us know during the first three weeks of the semester. Some aspects of this course may be modified to facilitate your participation and progress. As soon as you make us aware of your needs, we can work with the Services for Students with Disabilities (SSD) office to help us determine appropriate academic accommodations. SSD (734-763-3000) recommends accommodations through a Verified Individualized Services and Accommodations (VISA) form. Any information you provide is private and confidential and will be treated as such.

If you already have accommodations through SSD, please send both instructors your accommodations letter in the first two weeks of the term so that we can make arrangements. You should also make sure your accommodations information appears on PrairieTest, so that they are in effect for the quizzes, which are administered by the Electronic Testing Facility.

Diversity and Inclusion

It is our intention that students from all backgrounds and perspectives will be well served by this course, and that the diversity that students bring to this class will be viewed as an asset. We welcome individuals of all ages, backgrounds, beliefs, ethnicities, genders, gender identities, gender expressions, national origins, religious affiliations, sexual orientations, socioeconomic background, family education level, ability - and other visible and nonvisible differences. All members of this class are expected to contribute to a respectful, welcoming, and inclusive environment for every other member of the class. Your suggestions are encouraged and appreciated.

Campus Resources

As a student, you may experience a range of issues that can negatively impact your learning, such as anxiety, depression, interpersonal or sexual violence, difficulty eating or sleeping, loss/grief, and/or alcohol/drug problems. These mental health concerns or stressful events may lead to diminished academic performance and affect your ability to participate in day-to-day activities.

In order to support you during such challenging times, the University of Michigan provides a number of confidential resources to all enrolled students, many of which are listed here. Some particularly useful resources include:

Acknowledgements

Language in this syllabus has been adopted from EECS 245, Math 115/116, and other courses at the University of Michigan.

Disclaimer

While we try to do our best to plan ahead, unfortunately, sometimes circumstances do arise that necessitate a policy change. When this happens, the change will be announced, and this document will be updated with the new policy.

We appreciate any and all feedback, given that this course is new and evolving. If you’d like to provide us with anonymous feedback at any point, you can do so using this form. Thank you.

Note about Accessibility
It’s important to us that all students are able to fully engage with our course content. We’re working to ensure that all digital materials – the website, course notes, homework and lab PDFs, supplemental videos, etc. – meet WCAG 2.1 AA accessibility standards, as mandated by the federal government of all public universities in the United States. If you find any accessibility issues (hard-to-read colors, missing alt text, videos with missing captions, or anything else that makes the content difficult to access), please let Suraj know as soon as possible at rampure@umich.edu.