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Math 51
Autumn 2020

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Please check out the Jamboard links to some of our office hours. We advise you open the teaching staff's Jamboard on your web browser during their respective office hours.

Office hours and other resources for help

Mathematics courses taught at universities (not just at Stanford) are harder than those taught in high school. This is due to two reasons: (i) the material is cumulative in way that high school math is not, (ii) the expectations on your level of understanding and problem-solving skills with the material are much higher. The benefit of this hard work is a greater degree of confidence and accuracy when confronted with new situations in your later coursework in any quantitative field.

Don't hesitate to work with peers and ask questions in class and in office hours! We allow and encourage students to work with each other, and the course staff, in the preliminary stages of completing homework assignments. Even if you generally did your math homework in high school largely on your own, it is strongly recommended not to "go it alone" in math classes at the university level. Discussing the material and the homework problems with peers is strongly recommended, for students at all levels.

Plan to spend more hours on math than you did in your math classes in high school, regardless of how well you did in your math classes before arriving at Stanford. A rule of thumb is that you should spend at least 2 to 3 hours working outside of class for each in-class hour. Since Math 51 meets for approximately 5 hours each week, this means you should expect to spend 10 to 15 hours each work outside of class working on the course material: studying the textbook and your notes, and working on problems, perhaps even more exercises than those assigned (or working through detailed examples in the book).

  • Your first resource for help with the course are the office hours of the instructors and TA's. You may attend the office hours of any instructor or TA, and no appointment is ever necessary.

    A google calendar with the office hour schedule is given below. Please consult Canvas for Zoom links.

  • Peer Tutoring The Stanford University Mathematics Organization (SUMO) works with the Stanford Math department to provide free drop-in tutoring services for Math 51. The tutors are Stanford undergraduates available to answer any questions you have about the material and homework in Math 51. You will need to first self-enroll in the Fall 2020 SUMO Tutoring Canvas Course in order access the tutoring Zoom meetings. Just show up and the tutors will help you out. Feel free to come and work on your homework there even if you don't have any specific questions. Many students work on their homework during tutoring, asking questions when they encounter difficulties.

    Starting the second week of each quarter, tutoring for Math 51 is on Mondays and Wednesdays 6-8PM and 10PM-12AM on Zoom. Tutoring continues through Week 10 but excludes university holidays.

  • Vice Provost for Teaching and Learning (VPTL) offers free drop-in and appointment tutoring for Math 51, in addition to tutoring for a number of other courses. For more information and to schedule an appointment, visit tutoring appointments and drop-in schedule page.
  • We encourage you all to take a look at this excerpt from the Introduction of the Math 51 textbook -- these tips may be useful to keep in mind to help orient yourself in the learning process, especially once the workload picks up (in general, not necessarily for Math 51 itself) in the middle of the quarter. These tips are useful for future mathematics-related courses as well.
  • Some answers to frequently asked questions by Math 51 students can be found here.
  • Some advice on going through the course is given below the calendar.
Calendar of office hours will appear here shortly before the start of quarter.

Advice to Math 51 students:

  • Math 51 lectures introduce new concepts and discuss some examples and applications, whereas in discussion sections students primarily work through worksheets of exercises that reinforce the material from lecture. Assigned homework problems are not worked out in the discussion sections, but sometimes a worksheet exercise has features in common with a homework problem.

  • To do well on exams and be able to apply what you are learning in later courses, it is important that you truly understand the material, and do not just memorize mechanical techniques. A very large number of students at Stanford complete Math 51 each year. Many of them go on to study advanced topics in computer science, economics engineering, statistics, natural sciences, mathematics, and so on. The Math 50 series courses are designed to make that possible, but a student who gets by in a foundational course (in any subject) by just memorizing will not be successful at applying the course content in more advanced settings elsewhere down the road.

  • Read and take notes on the chapter associated to the exercises before completing them. Reading math takes longer than reading a novel; it is a genuinely new skill for many students. Be prepared to spend some time studying each section, with pencil (or pen) and paper nearby to take notes, write down questions, or fill in any steps omitted in the book.

  • Write up your solutions to homework neatly, not as a collection of scrap work that magically resulted in the right answer. Be critical of your own solutions: Is each step clearly explained? Is the reasoning sound? Most homework problems are calculations, but sometimes you are asked to explain what is going on. Such explanations should be a clear sequential argument, using what you have learned to reach the desired conclusion (sometimes via a calculation, other times by applying general facts or principles in the course). To write a satisfactory explanation, it always helps to make sure you understand the definitions.

  • It is a very good idea to learn and understand the definitions of terms as they come up in the course. The central role of definitions in university-level math is very different from the role of definitions in virtually any other subject, and is also a big change from math as taught in high school. If you fall behind in understanding definitions, it can be extremely difficult or impossible to understand ideas later on in the course. Don't let that happen to you! Spend some time comprehending the new definitions that come up in each section of the textbook, and thinking through the worked examples that illustrate them. Homework also helps with this, via working out explicit situations and computations.

  • Office hours of both the TA's and instructors are an opportunity to discuss any difficulties you are having with concepts, examples, or homework problems. You will get much more out of coming to office hours if you have spent time beforehand trying to do the problems or thinking about what is puzzling you. All students may go to the office hours of any of the instructors or TA's. These are arranged to take place at a wide variety of days and times.

  • Even if you discuss the homework with peers or course staff, you must write up the submitted solutions in your own words. To just copy solutions from someone else is an Honor Code violation. Stanford's Honor Code and Fundamental Standard are taken very seriously.  By Math Department policy, any student found to be in violation of the Honor Code on any assignment or exam in this course will receive a final course letter grade of NP.

  • 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.

Autumn 2020 -- Department of Mathematics, Stanford University
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