Math 51
Spring 2024

Some Frequently Asked Questions:

How to use the textbook? How much of the textbook am I responsible for?

• We recommend that you read the Introduction to the textbook: pages ii through x, in particular the section "How you should read this book" on page iv and Table 1 on page v.
  • The material in the blue boxes is important: you are responsible for that material even though we may not cover all of it in class. You should also be reading the non-boxed portions, which give useful explanations of what is summarized in the blue boxes.
  • There are lots of real-world examples in green boxes. Don't feel you need to read all of them, but you should definitely read some. You can choose which ones to read according to your interests. You may wish to read more in future years when you encounter relevant applications in other courses or your work.
  • The material in gray boxes, plus some whole sub-sections with the heading "(Optional)," go a bit deeper into various topics. Read them if you're interested (and have time), but you should feel to skip any or all of those portions of the text.
• You are expected to read the assigned pre-class reading before class, but are not expected to fully understand it at that point (this is a first exposure, with class providing further discussion).
• For many of you, reading and digesting a math textbook will be a new learning experience. We strongly urge you to watch the instructional videos on How to read the course textbook before the first pre-class reading assignment. The intent of these videos is to help make the book more approachable, and to teach you good habits about how to approach your reading, which will serve you well in your future Stanford career.
• After each lecture, you should go over the blue boxes in the corresponding chapter and the page of chapter highlights (at the end of each chapter, immediately before the chapter's Exercises). Use the chapter highlights as a study guide (e.g. before doing the homework and when preparing for exams).
• We also recommend that you look at some of the examples in the chapter to reinforce your understanding of material.
• The green and gray boxes are for reading according to your interests (in specific applications and derivation details). You will not be tested on that material, but may find some application discussions to be helpful as motivation.

There are so many new terms and concepts to absorb. How can I handle it?

• Use the Chapter highlights page to keep track of where to read about key definitions, notations, concepts and results, and computational skills. The terminology and notation are used throughout applications of math in many fields, and with experience during the course you will digest it.

Are there solutions available for the end-of-chapter exercises in the textbook?

• Some portion of these exercises will be assigned for weekly homework. The particular problems that will be assigned for homework will have full solutions made available after the deadline, but the others aren't going to have published solutions. (You can always talk about them with a course staff member in office hours -- we're happy to give you feedback on whether you're on the right track.)

Besides worksheets, what else can I do to practice problems from a given chapter on my own and check my work against solutions?

• One thing you can do is go through the "examples" in each chapter -- they are all fully worked out, and you can treat these like the "problems with answers in the back of the book" that are in many textbooks.
• We are also in the process of building up another resource of "practice homework" problems and their solutions; it has only been partially completed due to short resources during the pandemic, but the supply that we can share thus far is located in the Additional practice textbook HW exercises folder of the "Files" section in Canvas.

Office hours are too crowded. Where else can I get help?

• Check out the weekly schedule of office hours, noting that office hours on Wednesdays, Thursdays, or Fridays are often not as crowded (since homework is due on Wednesdays). You can go to the office hours of any of the teaching staff, not just those of your own instructor or TA.
• SUMO peer tutoring is available on Sunday evenings 4-8PM in Room 380-381T; on Monday, Tuesday, and Wednesday evenings 6PM-10PM in Room 380-381T; as well as on Monday and Tuesday evenings 10PM-Midnight on Zoom. Students will need to first self-enroll in the SUMO Tutoring Canvas Course in order access the Zoom meetings for SUMO tutoring sessions. Wednesday ones are usually less crowded and so are a good time to address conceptual questions.
• The Center for Teaching and Learning (CTL) offers free drop-in and appointment tutoring.

What will the exams look like?

• We will post two practice exams in the format of an actual exam 2 days before each exam. Complete solutions will be available as well.
• To be useful for practice, please practice on the version without solutions before you look at the version with solutions.

What are some tips for writing math?

• You will be developing your mathematical writing skill in weekly homework assignments. Here is a 1-page handout on "Writing Mathematics Well".