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Math 51
Fall 2015

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Course Description, Prerequisites and Other Courses

Linear Algebra and Multivariable Calculus are two of the most widely used mathematical tools across all scientific disciplines. This course seeks to develop background in both and highlight the ways in which multivariable calculus can be naturally understood in terms of linear algebra.

This course assumes a strong understanding of differential calculus of one variable, as taught in the Math 41-42 series (or equivalent). For the linear algebra portion, we will start from the beginning and build up all concepts in lectures. However, this course is packed with information and moves very quickly. Students who are somewhat unsure of their mathematics background may want to consider courses in the 40 series. In particular, students missing the equivalent of Math 42 may find the portions of Math 51 that demand deeper conceptual understanding to be more difficult than those who have the experience of a full year of college-level calculus. (Students having quite a lot of experience with mathematical proof and who are looking for a more theoretical course may want to try Math 51H.)

For a detailed syllabus see the Syllabus page.

This quarter we are offering two options for the in-class format, which you choose by way of your Axess lecture registration: an "active-learning" (sometimes called "flipped") classroom style, or a more traditional lecture format. Either option involves the same calendar of topics (syllabus), the same exams, and the same weekly written homework assignments, but the weight carried by weekly homework on your course grade is heavier in the second option. Detailed information about these options is available on the active learning page.

Enrollment in lectures and sections

Math 51 students attend lectures on MWF and discussion sections on TTh.

The first step is to enroll in a MWF lecture on Axess. Consult the active learning page to determine which type of lecture you prefer and make sure you enroll in a section that will be taught in that format.

The second step is to enroll in a TTh section corresponding to your particular lecture in Coursework. Note that there are two sites on coursework. One is for the traditional lecture (F15-MATH-51-04), the other is for the active learning lectures. Please note that you will only receive credit for work turned into your discussion section leader, so make sure you select an appropriate section.

You will be able to join discussion sections by the first day of lectures. After logging into Coursework, select your Sp15-MATH-51 site. (You will automatically be a member as long as you've been registered for a lecture via Axess for about 24 hours.) Select the Section Info page on the Math 51 site and join one of the sections with space available.

A complete list of lecture/discussion section correspondences may be found here.


The textbook is a special combined edition of Levandosky's Linear Algebra Book and parts of Colley's Vector Calculus. Hard-copy versions of the text should be available at the campus bookstore. An electronic version is also available. If you are interested in one, read these instructions and then go to the publisher's site.

Calculators are neither required nor recommended for Math 51.


There will be two midterm exams and a final exam. Please check the exams page for dates, policies, and previous exams.


There will be weekly homework assignments. Please see the homework policy for more information.


Your grade will be based on the following components:
  • Homework: 16%
  • Total points earned on all exams, divided by total points possible: 84%

Points available on exams: The total points available on the exams will be in approximate proportion 2:2:3. That is, the first and second midterm exams will have approximately equal numbers of total points available, and the number of points available on the final exam will be approximately 1.5 times those available on a single midterm exam.

Office Hours

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.

Additional Help

Useful Links and Other Resources

Fall 2015 -- Department of Mathematics, Stanford University
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