math257: Linear Algebra with Computational Applications

For a detailed schedule of lectures, discussions, and their locations, see courses.illinois.edu. For the difference between the in-person section A3 and the online section A4, please see the sections on In-person sections and Online section below.

• Lecturer: Yuliy Baryshnikov
• Lectures: Mondays and Wednesdays, 2-2:50pm, in CIF-3039
• Online labs: Fridays via Zoom; lab instructors and their office hours, see the course LMS site.
• Office hours: Tuesdays, 12:30-1:30pm.

Course LMS Site

The course site can be found on Canvas at canvas.illinois.edu/courses/*

If you have just registered for the course, you will automatically be given access within a few hours. Only if you do not have access 48 hours after registering should you contact your instructor.

In-Person Sections

In-person lectures are twice weekly on Mondays and Wednesdays. You are expected to read the lecture slides and/or watch the lecture videos before attending the in-person lectures. The content of the in-person lectures is not identical to that in the slides/videos. The in-person lecture will highlight several of the concepts introduced in the slides/videos and provide further examples.

Notes from the in-person lecture will be available at the course site the next day. Recordings of in-person lectures will also be made available on Canvas. Unless otherwise noted, students are responsible for all material presented in both the slides/videos and in-person lectures.

Attendance is mandatory for the in-person sections. Attendance will be taken via iClicker. You can either use the iClicker device or the iClicker app on your phone (available for Apple and Android smartphones). Every in-person lecture will feature a certain number of iClicker questions.

Your iClicker responses will be graded for completion only, not for correctness: you get a point for each answered question, regardless of whether you gave the correct answer. Your attendance score for that lecture is the percentage of answered questions.

Online Section

During the first two weeks students can move from any in-person section to the online section freely. Students can move from the online section to in-person sections subject to availability of seats.

Students in the online section will complete weekly checkpoint quizzes in lieu of attendance. Your attendance score for your final grade will be the average of your weekly checkpoint quiz scores, after applying the drop policy outlined in the grading section.

Email Format for Online Students

All listed lecture instructors are instructors for the online section. Email about any issues that online students face should be copied to all listed lecture instructors. The subject line of the email must start with [ONLINE] written exactly as shown. This helps instructors manage email requests from online students in a timely fashion.

Lecture Notes and Videos

Lecture notes (slides) and module videos are available at the Canvas page of this course. An interactive version of the slides with fill-in boxes is also available. If you would like to use this feature, print out the fill-in slides and fill them out on your own or while watching the videos. Video errata may be found at the video link on the course site under the appropriate week’s tab.

Additionally, there are associated weekly module checkpoint quizzes consisting of several conceptual questions with unlimited attempts. These quizzes can be found on PrairieLearn under the section “Check Point Quiz”, numbered CPQ1–14.

• Optional for students in the in-person sections
• Required for those in the online section OL1 — due by end of Tuesday of the following week

Since these are conceptual questions, precision is important, so read the lecture notes and the questions carefully. Most questions are True/False but allow unlimited attempts.

Additional Learning Material

We will post extensive lecture notes for all lectures and practice problems online. For many students these notes are enough. Here are some more learning resources:

Textbooks Not required

• Philip N. Klein — Coding the Matrix: Linear Algebra through Applications to Computer Science, 1st ed., Newtonian Press
• Feryal Alayont & Steven Schlicker — Linear Algebra and Applications: An Inquiry-Based Approach, scholarworks.gvsu.edu/books/21
• David Cherney, Tom Denton, Rohit Thomas & Andrew Waldron — Linear Algebra, math.ucdavis.edu/~linear
• Stephen Boyd & Lieven Vandenberghe — Introduction to Applied Linear Algebra — Vectors, Matrices, and Least Squares, web.stanford.edu/~boyd/vmls
• Gilbert Strang — Linear Algebra and its Applications, 4th ed., Cengage

You are not required to buy any of these textbooks. Please note the coverage and order of topics for these resources may differ from our course.

Videos

• Essence of Linear Algebra by 3Blue1Brown, on YouTube — highly recommended!
• MIT lectures by Gilbert Strang, MIT OpenCourseWare
• Coding the Matrix videos by Philip Klein, on YouTube

Online Labs

Online labs are held via Zoom on Fridays, with the detailed schedule available in Course Explorer. Zoom links can be found on Canvas.

Only attend the online lab you are signed up for. No credit is given otherwise.

During the online lab you will use computational tools in Python to solve linear algebra problems in real-world applications in science and engineering. You will be working together in small groups on a Python Jupyter notebook. Though the first session is a Python tutorial, students are assumed to have prior experience in Python or be able to familiarize themselves quickly.

Students without the requisite programming background have struggled to complete the course and should consult their advisor.

Attendance

Attendance will be taken in the first 10 minutes via a code provided by the TA. You are responsible for entering the code in a timely manner. If there is an issue entering the code, your TA needs to be notified before the end of the session. Note that it is not enough to just be present — you have to be actively working with your group on the project.

Requests to be excused should be submitted to the relevant teaching staff before the start of the session. Due to the available drops in various assessment categories, we generally do not grant excused absences or extensions for short-term illnesses, but rather only in exceptional circumstances (e.g., university athletic participation or letter from Office of the Dean of Students).

Online Homework

Each week there are two sets of homework (lab and non-lab), both delivered through PrairieLearn. This course is listed in PrairieLearn as:

MATH 257: Linear Algebra with Computational Applications → Fall 2026
Students must self-enroll by the end of the add/drop period (Monday of Week 3). Self-enrollment code:

TBA

Homeworks are mandatory for both in-person and online sections. Both sets of homeworks are open-notes and you may collaborate with other students.

• The non-lab homework associated with each module provides opportunity to practice the computations and algorithms covered in the module.
• The lab homework is based on the most recent activity in the online labs.

Workspace / Help Sessions

Starting Week 2, TAs will offer in-person tutoring Mondays to Thursdays 5–7pm. See the Office Hours tab on the course site for more details. At least one TA will be present during this time to answer your (non-Python related) questions.

You don’t have to come only if you have a question. You can just go there and work — either alone or with your fellow students. We highly recommend that you form study groups and make use of this room!

For Python-related questions, undergraduate course assistants (CAs) will hold online office hours via Zoom throughout the week starting Week 2. See the course site for details.

Weekly Assignment Schedule

Regular weekly assignment due dates are as follows:

• PrairieLearn (non-lab) Homework (covering modules from previous week), due Tuesdays 11:59 PM at 100%
• PrairieLearn lab Homework (covering lab from previous week), due Thursdays 11:59 PM

For example, PrairieLearn Week 1 non-lab homework is due (at 100%) on Tuesday of Week 2.

Students participating in in-person sections are strongly encouraged to complete the optional, ungraded checkpoint quizzes (covering modules from current week). For students in the online section these checkpoint quizzes are mandatory and graded by completion.

PrairieLearn

We will use PrairieLearn for homework. This course is listed in PrairieLearn as follows:

MATH 257: Linear Algebra with Computational Applications
Self-enrollment code:

(Non-lab) Homework (at 100%) will be due on Tuesdays at 11:59 PM. The first homework is due on Tuesday of Week 2. The PrairieLearn homework will lean towards computations, while the checkpoint quizzes will focus more on conceptual problems.

How Points Are Given on PrairieLearn

PrairieLearn places emphasis on mastery. The idea is to keep doing questions until you master the underlying concept or method. Each question has a value, a point total, and a point maximum.

If you answer a question correctly, two things happen:

• The point total increases by the value, until you reach the point maximum.
• The value increases.

If you answer a question incorrectly, one thing happens:

• The value goes back to what it was originally.

This system rewards repeated correct answers, which tend to demonstrate mastery. There is no penalty (other than resetting the value) for answering a question incorrectly, so don’t be afraid to submit an answer. Similarly, don’t be afraid to keep doing a question after you reach the point maximum — your point total will never go down!

Credit

There is no need to “submit” your homework. The system will record whatever your score is at that time. However, you’ll note the following line at the top of your screen:

Available credit: 110% until 11:59PM, Fri, 08/28

If you reach 100% prior to 11:59 PM on that Friday — i.e., complete the homework early — you will receive an extra 10% bonus. You will see this reflected in your score (the instant you reach 100%, it will jump to 110%).

For the first homework due in Week 2:

• You can receive 100% until 11:59 PM, Tuesday, 09/01
• You can receive 80% until 11:59 PM, Tuesday, 09/08

Your score will never go down. For example, if you achieve 90% by 11:59 PM on Tuesday 09/01, you won’t be able to increase your score after that time, but you won’t be penalized for not reaching 100% — your score will remain 90% forever. On the other hand, if you achieve only 70% by 11:59 PM on Tuesday 09/01, you will be able to increase your score after that time (to a maximum of 80%).

Lab Homework (at 110%) will be due on Thursdays at 11:59 PM. The first lab homework is due on Thursday of Week 2. Unlike the non-lab homework, the lab homework will only be offered at 110% and 80%.

Any changes to regular homework deadlines for either type will be announced on CampusWire.

In both lab and non-lab homework categories, your overall PrairieLearn score is capped at 100%. So even if you score 110% on every assignment, you will only receive 100% overall. The bonus is designed to help offset homeworks where you may not have received full credit.

Typos / Errors

If you believe there is a typo or an error in a question, or if you believe your answer was graded incorrectly, please take a screenshot and post to CampusWire. We have access to all of your submissions and can check to see what, if anything, went wrong.

CampusWire

All announcements will be posted on CampusWire at campuswire.com/c/G142011B2.

Please make sure you are signed up for CampusWire. The registration PIN is available under the Quick links at the top of the course site.

Posting Guidelines

Use the subject line wisely and post in the appropriate category. For example, if you ask something about matrix multiplication in Lecture notes 5, write "Lecture notes 5 - Matrix multiplication" and not just "Question about matrices". In addition, please post to the entire class whenever this is appropriate.

No question will ever be held against you. In fact, we encourage every student to make extensive use of CampusWire to ask questions both to your fellow students as well as the instructor team.

Because of the large number of students (~1800) and the limited number of teaching staff, please help us facilitate response times by observing the following:

• Please post all content questions and those of general interest regarding course material or organization to CampusWire rather than via email. Multiple course staff monitor CampusWire, and this allows all students to benefit from both the question and our reply.
• For private questions regarding special cases of course policy (e.g., DRES, absence from an exam, etc.) please use email and copy the relevant teaching staff (e.g., TA, lab TA, or course instructor). Please clearly indicate your lecture/discussion/lab sections in the email subject. We aim to have response times for emails generally in one or two business days.

Here is a summary of the grading scheme for this course, followed by drop and exemption modifiers, as well as percent-to-letter grade conversions and exam curving. Details about each category are given later in this document.

Grading Categories

#	Category	Weight
1	Syllabus quiz	2%
2	Class attendance (checkpoint quizzes for online section A3)	3%
3	Online lab attendance / completion (33% / 67%)	10%
4	PrairieLearn (non-lab) homework	8%
5	PrairieLearn lab homework	5%
6	Two Python quizzes (each 3%)	6%
7	Three midterms (16% each, 48% total) + Final Exam (18%)	66%

Syllabus Quiz

Because of the online format for much of this course, familiarity with course policies will be essential. All students will be required to complete a syllabus quiz by 11:59 PM Friday of Week 3 (February 6).

The quiz is located on PrairieLearn. It covers basic course policies. It is open-notes and unlimited attempts are allowed. Please complete this assessment as early as possible.

Given the extensive amount of time to complete this quiz, we will not grant extensions to complete it.

Exams

This course will have two Python quizzes, three midterms, and a final exam, all administered by CBTF.

Students register with CBTF for an exam slot during the below specified tentative windows. Details regarding administration of the final exam will be announced later in the semester.

Assessment	Week	Tentative Dates
Midterm 1	Week 4	02/09 – 02/11
Midterm 2	Week 8	03/09 – 03/11
Python Quiz 1	Week 10	03/30 – 04/01
Midterm 3	Week 12	04/13 – 04/15
Python Quiz 2	Week 14	04/27 – 04/29
Final Exam	Finals	05/07 – 05/15

Students are responsible to ensure they register sufficiently early for availability of seats, are properly registered with CBTF, and sit for their exam at their registered time. There will be neither make-up exams nor extensions due to seat unavailability. To request exemption from a midterm exam, see “Special Cases” under the Grading section.

CBTF

This course uses the College of Engineering Computer-Based Testing Facility service CBTF Online for its exams: cbtf.illinois.edu

The policies of the CBTF are the policies of this course, and academic integrity infractions related to the CBTF are infractions in this course.

Important Information for DRES Students

If you have accommodations identified by the Division of Rehabilitation-Education Services (DRES) for exams, please upload your Letter of Accommodations (LOA) to the CBTF site at cbtf.illinois.edu/students/dres before you make your first exam reservation (at least five business days prior).

Issues During a CBTF Assessment

If you have any issue during a CBTF assessment, please inform the proctor or relevant CBTF staff immediately. Work with the proctor to resolve the issue at the time before logging off, and ask your proctor to file an incident report as record of your interaction.

If you do not inform a proctor of a problem during the test, then you forfeit all rights to redress.

We advise everyone to review all instructions on the CBTF website before your first exam: cbtf.illinois.edu/students/rules-copy.

Modifiers

• All assessments assigned in Weeks 1–2 (except the Syllabus Quiz due Friday Week 3) will not count towards your grade.
• From Week 3 onwards, the two lowest weekly scores in each of Items (3)–(5) above will be dropped.
• For in-person students, the lowest four lecture iClicker scores from Wednesday of Week 3 onwards are dropped. For online students, the lowest two weekly checkpoint quizzes from CPQ3 onwards are dropped.
• If your Final Exam is higher than one of your midterm scores, it will replace the lowest midterm score. A missed midterm exam will be counted as receiving a score of 0%.
• Any assignments for which you are “exempted” will be dropped. See below for the requirements for being “exempted.”
• If you were “exempted” for exactly one midterm, we will use the average of [the other two midterms + Final] as the score for the exam you were “exempted” from. Then, we will apply the midterm score replacement policy if applicable.

Example A

Student A is exempted for Midterm 2 due to traveling with a university sports team for the entire exam period, as confirmed by an official letter. Their scores for the other exams (M1, M3, F) are (70%, 90%, 95%). The exempted M2 is thus scored as 85% = (70% + 90% + 95%)/3. The final score of 95% is higher than M1 = 70% and thus replaces it. The scores used for computation of semester grades are then (M1, M2, M3, F) = (95%, 85%, 90%, 95%).

Example B

Student B is exempted for Midterm 1 due to illness during the entire exam window, as confirmed by a letter from the Office of the Dean of Students. Their scores for the other exams (M2, M3, F) are (70%, 80%, 60%). The exempted M1 is thus scored as 70% = (70% + 80% + 60%)/3. The final score of 60% is not higher than any of the midterm scores. The scores used for computation of semester grades are thus (M1, M2, M3, F) = (70%, 70%, 80%, 60%).

• If you were exempted for one of the two Python quizzes, it will be replaced by the other Python quiz score. There are no drops for the two Python quizzes.
• In the very unlikely event that you were exempted for more than one midterm or Python quiz, please contact your professor for grading details.

Special Cases

• Under certain special cases, the deadlines for assignments in categories (3)–(6) may be modified. See the “Absence Policy” document under Course Information on the course website.
• There are no exemptions for the syllabus quiz or for the Final Exam.
• To be “exempted” from a midterm, you need a letter covering the entire exam window from either:
  • the Office of the Dean of Students documenting absence due to illness, bereavement, etc.
  • a representative of a university sports team documenting traveling with a sports team; or
  • a faculty sponsor documenting academic travel.

Letter Grades

100.00% – 98.00%A+

97.99% – 93.00%A

92.99% – 90.00%A−

89.99% – 87.00%B+

86.99% – 83.00%B

82.99% – 80.00%B−

79.99% – 77.00%C+

76.99% – 73.00%C

72.99% – 70.00%C−

69.99% – 67.00%D+

66.99% – 55.00%D

54.99% – 0.00%F

Exam Curves

We will curve each of the midterms and the Final Exam score such that the distribution of letter grades coincides with historic grade distributions for this course. No further curve will be applied at the end of the course.

In particular, there will be no individual extra credit opportunities after class instruction ends, and closed assessments do not reopen. Make sure to work hard for every assessment!

Rescoring

Please check each week that your scores were entered correctly on Canvas. With so many students, it can happen that your grade is entered incorrectly. If, after an assessment, you find an error in the grading, please email the relevant course staff immediately. All rescoring requests must be made via email.

• Except for exams, rescoring requests will only be considered within a week of the assessment due date.
• For exams, rescoring requests will only be considered within a week of the posting of exam scores.
• Requests must be received before Reading Day. Don’t wait!

Final Grades

As this is a very large course, there are always many cases where students are close (sometimes even very close) to the next letter grade, and at the end of the semester make the case that they should receive higher grades. Unfortunately, in almost all cases we cannot grant the request without being unfair to other students — even if we would like to!

Many aspects of this course will be conducted online. Each student will be assumed throughout the semester to have the necessary technical equipment to participate in course activities:

• A computer/laptop/tablet with a microphone
• A stable internet connection with sufficient bandwidth and data allowance for using Zoom
• In-person section students will need iClicker access (either via app or remote)

We do not grant accommodations due to technical issues accessing or completing assignments. Please contact the Student Assistance Center (helpdean@illinois.edu) immediately if you are missing any required technology.

This is a first course in linear algebra. It covers basic definitions and algorithms of the subject needed in higher-level (engineering, science, and economics) courses and more sophisticated mathematical techniques such as the Singular Value Decomposition.

In this course you learn the mathematical theory and how to implement it in Python. You will discover many of the striking modern applications of linear algebra, such as Google’s PageRank algorithm, image and audio compression schemes such as JPEG and MP3, automatic face recognition, and other data science and machine learning algorithms.

The course covers the same mathematical theory as MATH 415, but adds a focus on the computational and large-data aspect of linear algebra through the lab sessions.

What you will achieve:

• Familiarity with the core concepts of linear algebra
• Insight into modern applications of linear algebra in a variety of fields
• Experience of linear algebra computing (on Python).

Be aware that course credit is not given for both MATH 257 and any of MATH 125, MATH 225, MATH 227, MATH 415, or ASRM 406. Any enrollment-related questions should be sent to mathadvising@illinois.edu.

This is not a course that only teaches you how to compute stuff. A computer will always be faster. Modern applications of linear algebra require a sophisticated understanding of theory and methods, and learning these is the purpose of this course. Through the applications we cover in discussions, you’ll realize that this indeed is applied linear algebra.

If you already know some linear algebra, this course might look easy at the beginning. Don’t be fooled into thinking it will stay like that. Even familiar material will be covered in more depth here. Exams will require a deeper understanding of the concepts. Take this course seriously from the beginning.

To err is human. If you find a typo or an error in any part of this course, please let us know by sending an email to the instructors. We appreciate your help, and are also happy to hear any further comments or suggestions. Thank you!

etiquette

Since this course has a substantial online component, please be respectful of your fellow classmates and teaching staff in all online communications. Fostering a helpful learning environment requires everyone’s cooperation. Remember that forum posts are visible to all students and staff in the course (over a thousand people). So please double-check your posts before submitting them.

Cheating

No books, notes, cheat sheets, or electronic devices are allowed during the exams except the CBTF-provided scientific calculator. We take cheating very seriously!

A more detailed description of the University policy on cheating and plagiarism may be found at: las.illinois.edu/students/integrity