Course:
Math 54, Linear Algebra & Differential Equations (Course Catalog)Course Description:
Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; linear transformations, symmetric matrices. Linear ordinary differential equations (ODE); systems of linear ODE. Fourier series.Credit Hours:
4Prerequisites:
Math 1A-1B, Math 10A-10B or equivalent.Textbook:
Linear Algebra and Differential Equations by Lay-Nagle-Saff-Snider, Pearson Learning Solutions; 2nd Custom Edition for UC Berkeley.This special version is prepared specifically for UC Berkeley Math 54, ISBN 10: 0-137-11403-6, ISBN 13: 978-0-137-11403-0. If you use a different edition, please be sure to match the assigned homework problems carefully, as exercise numbers may differ between editions.
Homework:
Homework assignments will be announced on the Homework page.- Homework is generally due on Gradescope on Monday 11:59 pm (Pacific Time). Please see these submission instructions for information on how to upload your work.
- To accommodate unforeseen circumstances and technical difficulties, we will accept homework submitted within 24 hours from the due date without a penalty.
- Homework assignments must be handwritten.
- There will be 13 problem sets. Your cumulative homework grade will be based on the best 11 of 13 scores.
- In view of the above arrangement, NO late homework will be accepted more than 24 hours after the due date.
- If you experience problems submitting your work, please contact your GSI promptly.
- Homework will be graded for completeness, with 3 points awarded for completing all assigned problems.
- You are encouraged to discuss homework problems with your classmates, but the work you submit must be your own. Copying another person's solutions is not permitted and is considered academic misconduct.
- A good portion of the quizzzes and exams will be based on the weekly hoemework sets, so it is essential that you understand how to solve each problem.
Discussion sections and Quizzes:
Discussion sections take place Monday, Wednesday, and Friday. You are expected to attend the discussion section that you are enrolled in. If you need to switch discussion sections, then please contact enrollment@math.berkeley.edu. We (the instructor and GSIs) have no influence on the enrollment process.- Quizzes will take place during your discussion sections, typically on Wednesdays. Please refer to the course calendar for the quiz schedule.
- Your cumulative quiz grade will be based on the best 7 out of 10.
- There will be no makeup quizzes. If a student misses a quiz for any reason, it will count as one of the dropped quizzes.
- Cheat sheets and electronic devices, including calculators, are NOT allowed during quizzes.
- Each quiz will last approximately 15 minutes and will be closely related to the homework due on Monday of the same week.
- You are not allowed to share quiz content or solutions with classmates until after Thursday of the same week.
- To ensure fairness across all discussion sections, quiz grades may be normalized across sections at the end of the semester.
Exams:
There will be two midterm exams and a final exam. All exams will be held in person.- Midterm 1 is scheduled for Wednesday, September 30 (45 minutes during lecture)
- Midterm 2 is scheduled for Wednesday, November 4 (45 minutes during lecture)
- Final Exam for LEC 001 (8 am on MWF lecture) is scheduled for Monday, December 14, 7:00-10:00 pm (Location: TBA)
- Final Exam for LEC 002 (10 am on MWF lecture) is scheduled for Monday, December 14, 8:00-11:00 am (Location: TBA)
It is your responsibility to make sure that you do not have any scheduling conflicts with the exams. Makeup exams will not be offered. As per university policy, if you do not take the final exam, you automatically fail the course. Please check the dates now to make sure that you have no unavoidable conflicts.
- You may use one 3 x 5-inch index card (front and back) of handwritten notes for the midterm exams. Electronic devices may not be used to prepare the notes unless you have a registered disability that permits typed or otherwise specially prepared notes.
- Details regarding permitted notes for the final exam will be announced in Week 13.
- Calculators or electronic devices of any kind are NOT allowed during exams and quizzes.
- Please bring your student ID to the exams.
- Academic Integrity violations will be taken seriously, and will be reported to the Center for Student Conduct for disciplinary action.
- Please check the announcement on bCourses for more details regarding exams.
Grading:
There are two methods to determine your course grade.- Method 1: 7% Homework (Best 11 out of 13), 13% Quizzes (Best 7 out of 10), 22% Midterm 1, 22% Midterm 2, 36% Final Exam
- Method 2: 7% Homework (Best 11 out of 13), 13% Quizzes (Best 7 out of 10), 30% Better Midterm, 50% Final Exam
Your grade will be calculated under both methods, and the better grade will be used to determine your course grade.
Grade Adjustment:
If the class median M is below 81% on a midterm exam or the final exam, we will apply the following method to curve the exam. Your exam score S (%) will be adjusted to a new score S* to shift the median to 81%.
If \( S < M \), then \( S^* = \dfrac{81S}{M} \)
If \( S \ge M \), then \( S^* = \dfrac{100(S-M)+81(100-S)}{100-M} \)
Extra Credit:
- We will use Poll Everywhere occasionally during lectures. If you participate in more than 60% of the Poll Everywhere activities, you will receive 1% extra credit toward your final course grade. If your participation is below 40%, no extra credit will be awarded. For participation between 40% and 60%, extra credit will be awarded proportionally. The Poll Everywhere extra-credit opportunity may be reconsidered or discontinued if participation does not accurately reflect class attendance (for example, if students submit responses without attending lecture).
- Also, if at least 75% of the class completes the course evaluation, you will all receive 1% extra credit.
After your weighted average is calculated, approximate final grade cut-offs are given in the table below.
| A+ | A | A- | B+ | B | B- | C+ | C | C- | D+ | D | D- | F |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 98 | 93 | 90 | 87 | 83 | 80 | 77 | 73 | 70 | 67 | 63 | 60 | < 60 |
The exact final grade cut-offs will be finalized by the instructor at the end of the semester.
Please note that external considerations-such as the need for a particular grade for admission or retention in an academic program, scholarship eligibility, transfer credit, graduation requirements, or personal preference-are not part of the grade criteria and therefore do not affect your final course grade.
Students who have substantially completed the course but are unable to complete the remaining course activities due to serious extenuating circumstances may request an Incomplete grade. This request must be submitted in writing to the GSI and instructor. You must provide verifiable documentation for the seriousness of the extenuating circumstances. Refer to the Office of the Registrar's website for more information on the university's policy on Incomplete Grades.
Accommodations:
If you require course accommodations due to a physical, emotional, or learning disability, contact UC Berkeley's Disabled Students' Program (DSP). Notify the instructor and GSI through course email of the accommodations you would like to use. You must have a Letter of Accommodation on file with UC Berkeley to have accommodations made in the course. UC Berkeley is committed to providing robust educational experiences for all learners. With this goal in mind, we have enabled the ALLY tool for this course. You can now automatically generate "Alternative Formats" for course files and bCourses Pages. Depending on the context, these formats can include Tagged PDF, HTML, BeeLine Reader, Electronic Braille, ePub, Immersive Reader, MP3, and translated versions. For more information, watch the video entitled, "Ally Tutorial for Students at UC Berkeley."
Questions about your DSP accommodations:
- HW and Quizzes: Contact your GSI in advance.
- Exams: We will make sure that you can take advantage of the extended time for midterm and final exams as specified in your Letter of Accommodation. This means that you can either take your midterm or final exam with the DSP proctoring service or that we will provide an additional room where you can take your exam. Our HGSI, Robert Schütz (rschuetz@berkeley.edu) will provide more information in Week 2. If you want to take advantage of any accommodation beyond this, then please contact the Head GSI at least two weeks before each exam.
- If your accommodation concerns have not been resolved, contact the professor.
Regrades:
Regrade requests will be made using the built-in regrade request feature in Gradescope. There will be a limited window of time after your graded work is made available during which the regrade request feature will be active. This time window will be announced when the scores are released to the students. Please be advised that the regrade request window is usually brief, and if you want to request a regrade, it is your responsibility to make the request during the allowed time. Please understand that while we will correct errors in the grading, we will not modify the grading rubric or negotiate over partial credit after graded papers are returned to students.
Ed Discussion:
The GSIs, the Head GSI, and I will be offering help on Ed Discussion Monday through Friday. Only comments/questions pertaining to the mathematical content of the course are allowed. Any postings that do not meet these criteria will be deleted and Ed Discussion privileges may be removed. However, during the first two weeks of the course, we will also do our best to answer logistical questions. As a diverse community of learners, students must strive to work together in a setting of civility, tolerance, and respect for each other and for the instructor. Conflicting opinions among members of a class are to be respected and responded to in a professional manner. There are to be no offensive comments or language.
Late Add Policy:
If you are on the waitlist for a course, you are expected to attend class and complete assignments. If a student does not take a quiz or does not turn in assignments before the due dates, the student will receive a 0 on all missed assignments. No exceptions will be made. Similarly, a student not on a waitlist who adds the class late will not be given additional time, nor will they be excused from the assigned work.
Rules regarding absences and missed exams, assignments, etc.:
Attendance in class or in the discussion section is highly recommended, but not required. If you miss a class, then you can catch up by watching the Course Capture recordings. If you miss a discussion section, then we recommend asking a classmate for the missed material. If you miss one of the midterm exams (for example due to illness or family emergency), then your course grade will be computed using grading method 2.
We will also drop a few of the lowest quiz and homework grades. These rules will be applied automatically and you do not need to inform us about your absences.
We are aware that a number of students will miss a midterm exam, quiz or a homework assignment due to a variety of reasons. This is why we have implemented generous replacement or dropping rules. The purpose of these rules is precisely to alleviate the impact of such absences. So we will not be able to offer further accommodations like make-up exams or further drops. If you think that these rules did not fully cover your absences, then you can email us at the end of the semester and we will review your case.
Please do not share doctor's notes with us or any other documents containing private information. For privacy reasons we cannot ask for doctor's notes. Therefore, we also cannot accept them for equity reasons. Otherwise your classmates would be forced to release private information in order to receive the same accommodations. The only document that we accept is your official Letter of Accommodation issued by the DSP office.
Math 49:
If you are a student who wants to complete only part of this course (Math 49), please review the Math 54-49 instructions.
Academic Integrity:
Academic integrity is a cornerstone of scholarship at UC Berkeley. Upholding honesty in your work reflects your personal values and sustains the trust essential to our academic community. Acts of dishonesty undermine these principles and may lead to serious consequences under university policy, including administrative sanctions such as suspension or expulsion. By committing to integrity, you help foster a fair and meaningful learning environment for yourself and others. For more information about university policies on academic integrity, check UC Berkeley Center for Student Conduct.
Use of GenAI Tools:
In this course, our goal is to support your active learning, deepen your understanding of the material, and develop your mathematical reasoning and critical thinking skills. GenAI tools may be used as a learning aid-for example, to review concepts from lecture, ask for additional explanations or examples, or help clarify ideas related to homework. However, these tools should not be used to complete graded work for you. All submitted work should reflect your own understanding and reasoning. If the use of AI or other unauthorized online resources is suspected, the instructor may ask you to complete a brief oral or written follow-up to demonstrate your understanding of the relevant material. If you are unable to demonstrate that understanding, a zero may be assigned for the work in question.
Practical Study Advice:
- Teach to Learn: One of the most effective ways to master a topic is to teach it. Try explaining the material to a classmate, a family member, or a friend. Anticipate the questions they might ask -it is a great way to check your understanding and identify any gaps in your knowledge.
- Master the Details: True understanding comes from paying attention to the finer points. A superficial understanding of a topic is not sufficient; success comes from noticing the subtleties and understanding how they show up in problem-solving.
- Invest Your Time: Success in this course requires consistent effort. A 4-unit class typically translates to about 12 hours of work per week-time that will help you keep up with material, practice skills regularly, and deepen your understanding. Think of this time as an investment in mastering the subject.
- Practice for Success: I will provide practice problems and a practice test approximately 10 days before each exam. You may use them for additional preparation. Start working on them at least one week in advance.
External Support:
- For questions about enrollment, contact Marsha Snow or email enrollment@math.berkeley.edu.
- The Student Learning Center provides support for this class, including full adjunct courses, twice-weekly topic reviews, review sessions for exams, and drop-in tutoring.