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Math 51
Fall 2014

Home Syllabus Homework Office Hours Exams Useful hints Errata Coursework (for members)



If you've heard of Math 51, you know that it is a difficult class that goes at a breakneck pace. We will be covering the same material in 8 weeks that would normally take 10, so as you can imagine that requires hard work. You can expect to learn a good deal of linear algebra, but not everything that would be covered in a full linear algebra course, either abstract or applied; and enough differential vector calculus to be able to do further learning on your own, or to succeed in classes such as physics (mechanics, or electromagnetism). You will also be introduced to "thinking like a mathematician", or, theoretical proofs.

As you may infer from the other sections, the staff, course books and websites are here as resources for you to learn. As a college student, you are expected to take responsibility for your own participation, and be pro-active in seeking help for your own benefit. That means that you must check websites, keep up-to-date on course news, and know deadlines and attend exams without needing reminders. It means I won't take attendance at classes, and I don't expect you to come if you are sick, can't concentrate, and so on. It also means that I may not check up on you: if you miss a homework, if you miss class and want to know what happened, you should come to my or Megan's office hours and/or contact me separately.

We would like to support all our students as best we can, with the hope that everyone can get something out of this course besides a grade. To that end, I must emphasize that many students struggle in the class; this can be due to lack of time to put into it, or because you fall behind a week and then are lost; it can be because they are used to learning on their own, and these course textbooks may be hard to read by yourself. So please seek out your fellow students and come to office hours. But be aware that there is only 1 instructor and 1 course assistant for 72 students, thus some of the inflexible deadlines and so on are due to the necessity of managing our work. On homework and on exam questions, it is usually not sufficient to simply answer the question: you should explain your answer. That can mean showing work in a presentable way that a classmate (and therefore an instructor) should be able to read and understand; it can mean correctly writing a proof, using a combination of mathematical symbols and words to explain your reasoning. We will give you examples to show how you can meet this standard.

Honor code

Stanford has an honor code, which you and I should follow: link. When you do homeworks, you are free to work problems out with each other or check answers. However, solutions involve work, not only answers; each person should write up solutions in your own words. In addition to this being necessary for you to fairly earn your homework grade, it is useful for you to be sure that you can solve such problems on the exam, and for you to re-read your own work while studying.

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.

Teaching staff and meeting times

A list of instructors and TA's. Email addresses are in parentheses and should be with the "" ending.


Rafe Mazzeo (mazzeo):
MWF, 11 - 11:50 am, 380-380Y
Office: 383-R

Hilaf Hasson (hilaf):
MWF, 11 - 11:50 am, 380-380C
MWF, 1:15 - 2:05 pm, EDUC128
Office: 382-Q1
Davi Maximo (maximo):
MWF, 10 - 10:50 am, 200-205
MWF, 1:15 - 2:05 pm, 200-205
Office: 382-Q2
Jennifer Wilson (jchw), ACE:
MWF, 10 - 10:50 am, 380-380Y
MWF, 2:15 - 3:05 pm, MCCULL115
Office: 382-H

Teaching Assistants

Chris Henderson (chris):
"Uber" TA - email for all logistical questions
Office: 380-N

Seung Ki Kim (kimsk):
Office: 380-H
Chao Li (rchlch):
Office: 381-B
Christos Mantoulidis (c.mantoulidis):
Office: 381-K
Khoa Nguyen (khoan), ACE:
Office: 380-U1
Ho Chung (Soarer) Siu (siuhc):
Office: 380-L
Jacek Skryzalin (jskryzal):
Office: 381-A
Gergeley Szucs (gergelys):
Office: 381-B
Graham White (grwhite):
Office: 380-R


  • Weeks 1-4: Linear Algebra, by Levandosky - Errata
  • Weeks 5-8: Differential Vector Calculus (Revised 2013 Edition), by Licata
Hard-copy versions of both texts should be available at the campus bookstore; if you have problems finding either text, please contact your instructor. There is not an electronic alternative for the Levandosky textbook, but the Licata textbook can be ordered in electronic form. Please go to the Materials section of Coursework and download the "instructions for Licata reader" link.

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.

No calculators are allowed for any of the exams.


Homeworks are due at the beginning of class on Mondays of the course (first homework is due Monday, June 30). If you can't come on time to class you may have a friend turn it in for you, or you may scan it and email it to me; however, I need to have the scanned pages by noon in a PDF format for ease of printing, and I need you to email me, or, by Sunday night to let me know this is your plan.

Solutions will be posted on Coursework by 4pm on Mondays after the homeworks are due. Graded homeworks will normally be given back on Thursdays, but we will have an earlier time before the midterm.

There will be 7 homeworks altogether, of which 6 homework grades will be counted: your lowest score, whether it is 0 or higher, will be dropped. This is because you really need to do the homeworks or you may not be able to keep up in the class. If an emergency situation arises, you can turn in an incomplete homework. Late homework will not be accepted.


Your grade will be based on the following components:

Office Hours

You are encouraged to attend the office hours provided by the instructors and teaching assistants.

Additional Help

Javier Stober, who has led many problem and review sessions for Math 51 in the past, is offering tutoring. Please contact him, stoberx at gmail dot com for instructions.

Useful Links and Other Resources

  • Prof Brumfiel's advice for Math 51 students
  • Common Errors in Undergraduate Mathematics
  • Math 51A students are part of the ACE program, short for "Accelerated Calculus for Engineers." More information about the program can be found here.
  • Statement from the Registrar concerning students with documented disabilities:
    "Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is being made. Students should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066)."
  • To apply this statement to the course precisely: I need at least a week's notice for all conflicts and for OAE letters for access needs. As soon as you know you are asking for an OAE letter, please send me (Elizabeth) an email before you receive your OAE letter. This is the "informal notice" mentioned in the syllabus, and is important so that I can schedule exams with only 2 instructors available.

Fall 2014 -- Department of Mathematics, Stanford University
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