Linear Algebra and Multivariable Calculus are two of the
widely used mathematical tools in quantitative work across all fields of study. This
course develops conceptual understanding and problem-solving skills in both, highlighting how
multivariable calculus is most naturally understood in terms of
linear algebra, and the course text addresses a variety of real-world applications.
Our focus is on teaching you skills that underlie a wide array of applications and preparing
you for all courses involving advanced quantitative work (across all sciences, engineering, economics, computer science, statistics, and so on).
By the end of this course, you should be able to:
- relate the algebra of systems of linear equations to the geometry of vectors, acquiring the ability to "see" in dimensions far beyond 3 (thinking is seeing!);
- analyze the behavior of multivariable functions via partial derivatives, and combine that information with tools of linear algebra (such as matrices and eigenvalues) to solve optimization problems;
- apply your newly acquired visual skills in high dimensions to gain insight into a variety of real-world applications across data science, natural sciences, and economics.
For a detailed syllabus see
the Syllabus page.
First Day Checklist
- Enrollment in lectures and sections:
Math 51 students attend lectures on MWF, starting on the first Monday of the quarter, and discussion sections on TuTh, starting on the
first Tuesday of the quarter.
Enroll in lectures and discussion sections on Axess.
Please see the enrollment tab for more information.
- Required materials:
- The textbook has been specially created by the Stanford Math department in consultation with colleagues in many other departments; it is free and electronic-only. To get the book using your SUNet ID, visit the textbook page by clicking here or selecting the Textbook menu item at the top of this page.
- iClicker2: Starting on Wednesday January 8, class participation will be recorded via the iClicker2 personal response system (PRS), used for answering multiple-choice questions in class and allowing the instructor to gauge student understanding and helping you to actively engage in the learning process. Participation (not correctness) counts for 3% of the course grade.
Note: Don't bring a classmate's clicker to lecture and register responses for him/her; that is an Honor Code violation
(for you and the classmate).
You are allotted four lecture absences without penalty, including absences due to late enrollment, illness, oversleeping, dead batteries, forgetting your iClicker2, athletics, job interviews, not registering your PRS device in Canvas, etc.
Please register your PRS as follows:
- Purchase the "iClicker2" from the bookstore or used (or online). (See below for financial aid information.)
- Login to the Canvas site for your course.
- Click the i>clicker link in the left-side navigation list on Canvas.
- Enter your iClicker2 registration number following the instructions on the i>clicker Canvas page.
- If you have already registered your iClicker for some other course, your registration should carry over. However, you should check the registration number against your name on Canvas, just to be sure.
- Calculators are neither required nor recommended for any exams in Math 51 (we keep the numbers simple on exams). There are a small number of homework problems for which any basic scientific calculator (even a free online one) is useful to convert some expressions into decimal approximations (and such calculations never arise on exams). There is no programming anywhere in the course.
- Check for exam conflicts right away and contact us: Except in case of emergency, you must inform us of exam conflicts at least two weeks prior to the exam, together with a valid reason for the conflict.
For midterm exams (evenings of Thursday January 30 and Thursday February 20; see details given on the Exam page or by clicking the Exam menu item at the top of this page), the allowable reasons are course-related or competition-related schedule. The time of the final exam (Tuesday March 17, 12:15-3:15pm) is set by the University, and all students must take the exam at that time. See all exam details and policies here.
- Students with documented disabilities:
See the Registrar's page on academic accommodations. You must provide
an accommodation letter, dated in the current quarter, at least two weeks prior to
an exam, for us to have adequate time to arrange the accommodations. Please email your accommodation letter.
Math 51 has an "active learning" structure; research
has shown that pre-class reading, combined with daily participation in class activities targeted to specific learning goals, improves student
learning outcomes in math and science courses. Here's what this means for us:
Both MWF class sessions and TuTh discussion sections are more interactive than traditional math classes:
- Twice each week (exception on weeks with midterms) there will be a modest amount of reading in the course text to introduce
some of the motivation behind the topic(s) to be discussed in class, along with an associated questionnaire
on Canvas to be completed before class. The responses to the questionnaire (which are not
graded for correctness, just for a good-faith effort) inform
how the instructor organizes the classroom time around the learning goals for that day.
- The TuTh discussion sections focus on small-group collaboration with worksheets consisting of
problems designed around the learning goals and themes in the homework and exam questions.
The goal is to engage with the new skills and concepts, and to learn from your peers as well as from the guidance of a graduate student
who answers questions. The work in discussion sections is aimed at giving practice with the material
recently learned in the course; it is not graded, and complete solutions are provided later in the day for each TuTh worksheet.
Canvas questionnaire assignments on the twice-weekly pre-class reading: a typical questionnaire consists of 3 to 5 "low-stress" questions. You needn't answer more than one or two sentences per question, and you get full marks for ANY good-faith answer. These assignments are intended to give the instructor feedback on how the reading went and how the course is going; think of them as surveys in which students are voting for which topics need more motivation in class (and which need less or none). Because we will have to review your feedback in a limited time period, the firm deadlines are:
The course grade is based on the following components:
- Thursdays at 11:59pm (typically about 3 questions) except on exam weeks (where there is no pre-class reading for the Friday class); and
- Sundays at 11:59pm (about 4 or 5 questions).
- Exception: As a "warm-up," in the first week we'll have an ADDITIONAL pre-class reading questionnaire, due on the first Tuesday at 11:59pm. (It will be posted in Canvas on the first Monday morning.)
- 80% for exams, with the breakdown of approximately 23% for both midterms and approximately 34% for the final (see exams page for dates, policies, and previous exams);
- 13% for weekly written homework assignments (best 8 out of 9 assignments);
- 4% for pre-class reading questionnaires on Canvas (total points earned divided by 85% of total possible points, not to exceed 100%);
- 3% for participation via iClicker2 PRS (fraction of lectures attended, not to exceed 100%; starts the first Wednesday of the quarter, and there are four penalty-free absences)
You are encouraged to attend the office
hours provided by the
instructors and teaching assistants. You
may attend the office hours of any teaching staff member, and no appointment is ever necessary.
The office hours page also lists some other help resources.
While cell phones are not prohibited in lecture, recording or taking pictures in class is strictly prohibited without the consent of your instructor. Please ask before doing.
The Stanford Math Department does not use Piazza or similar platforms in its courses. This decision is based on a careful review of a variety of issues. We strongly encourage students working with and assisting one another, as well as with TA's and instructors. But we believe that (despite FERPA compliance) Piazza does not sufficiently protect student privacy, and there are other potentially adverse effects that give us additional concern.
Affordability of course materials: All students should retain receipts for books and other course-related expenses, as these may be qualified educational expenses for tax purposes. If you are an undergraduate receiving financial aid, you may be eligible for additional financial aid for required books and course materials if these expenses exceed the aid amount in your award letter. For more information, review your award letter or visit the Student Budget website.