Math 51 Autumn 2020


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 problemsolving 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 inclass
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 dropin 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 selfenroll 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 68PM and 10PM12AM
on Zoom. Tutoring continues through Week 10 but excludes
university holidays.
 Vice Provost for Teaching and Learning (VPTL) offers free dropin 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 dropin 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 mathematicsrelated 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.



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 universitylevel 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.

