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Math 51
Spring 2018

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Course Description

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.

By the end of this course, you should be able to:
  • Solve and analyze systems of linear equations, and relate the solution set to properties of algebraic objects (matrix null space, column space) associated to the system.
  • Analyze the rate of change of a multivariable function in coordinate directions via partial derivatives. Aggregate partial derivatives (derivative matrix, gradients) to get local information such as: tangent planes, linear approximation, and directional derivatives.
  • Apply least squares and use differential calculus techniques such as critical points and Lagrange multipliers to solve for constrained local and global extrema.

For a detailed syllabus see the Syllabus page.

First Day Checklist

  • Enrollment in lectures and sections: Math 51 students attend lectures on MWF, starting April 2, and discussion sections on TTh, starting April 3. You will enroll in lectures and discussion sections on Axess. Please see the enrollment tab for more information.

  • Required materials:
    • The textbook is a special combined edition of Levandosky's Linear Algebra book and parts of Colley's Vector Calculus. (We will use Chapter 2 and 4 from the 4th edition of Colley.) 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.
    • iClicker2: Starting on Wednesday April 4, class participation will be recorded via the iClicker2 personal response system (PRS), used for answering questions in class and allowing the instructor to gauge your understanding and helping you actively engage in the learning process. Participation counts for 2% of your course average. You will be allotted two 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 note: Bringing a classmate's clicker to lecture and registering responses for him/her is an Honor Code violation, for both you and your classmate. Register your PRS as follows:
      • Please purchase the "iClicker2" from the bookstore or online or used.
      • Login to the Canvas site for your course.
      • Click the i>clicker link in the left-hand 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.
    • Calculators are neither required nor recommended for Math 51.

  • Check for exam conflicts right away and contact us: Except in case of emergency, you must inform us at least two weeks prior to the exam, together with a valid reason for the conflict. For midterm exams (evenings of Thursday April 26 and Thursday May 17), the allowable reasons are course-related or competition-related schedule. The time of the final exam (Friday June 8, from 7-10pm) is set by the University, and all students must take the exam then. See all exam details and policies here.

  • Students with documented disabilities: See 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, to provide us adequate time to arrange the accommodations.

Class Structure and Assessment

Math 51 has an "active learning" structure; research has shown that pre-class reading, combined with daily participation in class activities targeted to specific course objectives, improves student learning outcomes in math and science courses. Here's what this means for us:

Class sessions will be more interactive than traditional math lectures. Since students are expected to complete specific reading assignments before lecture, followed by twice-weekly questionnaire assignments on Canvas, we will not take up lecture time re-addressing every topic covered the text, leaving extra class time for the material that YOU have "voted" to be most needing of extra discussion. The goal of this is to make the lecture time more useful for learning the required topics. Discussion sections will encourage group collaboration on problems modeled after those found on homeworks and past course exams.

Canvas questionnaire assignments: A typical assignment will consist of about three to five "low-stress" questions. You needn't answer more than one or two sentences per question, and you will get full marks for ANY good-faith answer. These assignments are intended to give us feedback on how the reading has been going; think of them as "creative surveys" in which people are voting for which topics need more discussion in class (and which need less or none). Because we will have to review your feedback in a limited time period, the firm deadlines will be:

  • Thursdays at 11:59pm (typically about 3 questions); and
  • Sundays at 11:59pm (about 4-5 questions).
  • Exception: In the first week we'll have an ADDITIONAL assignment due on Tuesday, April 3 at 11:59pm. (It will be released Monday morning.)
Grading scheme: Your grade will be based on the following components:
  • 84%, Exam average: there will be two midterm exams and a final exam; see exams page for dates, policies, and previous exams. The breakdown of the 84% amongst exams will be approximately 24% for both midterms and 36% for the final.
  • 12%, Weekly written homework assignments (best eight of nine assignments)
  • 2%, Pre-class reading questionnaires on Canvas (total points earned divided by 75 percent of total possible points, not to exceed 100%)
  • 2%, Participation via iClicker2 PRS (fraction of lectures attended, not to exceed 100%; starts Wednesday April 4; two penalty-free absences)

Office hours and other resources for help

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.

Spring 2018 -- Department of Mathematics, Stanford University
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