Learning Resources for Math 520

  • Class time. Come to class prepared to engage and ask questions. You will retain the material much better if it isn't totally unfamiliar the first time you see it in class.
  • Textbook. The book is an excellent place to look for more detailed discussion and for more practice problems. Take time to read sections specified in the syllabus, even if only to get some familiarity with the content before we discuss it in class.
  • 3Blue1Brown videos. 3Blue1Brown is the YouTube moniker of a person who has made some conceptually lucid and graphically stunning explanatory math videos, including a whole series on linear algebra. These videos are quite short and will provide you with some really valuable geometric intuition. These mental models are much more readily conveyed with the kinds of rich animation tools 3b1b is using. Highly recommended for everyone.
  • Course notes. Both the course head and Isaac are posting handwritten notes for their classes. These presentations are streamlined to the point of being not very useful as an exclusive source, but you might find them helpful as a supplement. They are available on the main course website and on Isaac's section website.
  • Cheat sheet. A list of each week's learning objectives, including a quick recap of the most important concepts, is available here. This document is helpful for refreshing your memory on the most important concepts before you tackle the homework, and it's also helpful for identifying examinable content.
  • Homework. Complete each homework question with the goal of understanding it thoroughly. Reflect on the principles you used to solve the question, how you recognized which principles would be useful, and the bigger picture the problem is trying to illuminate. If you sense that there are some things you aren't completely grasping, please attend office hours or the MRC (see last two items below) for more conversation. Also note that your MyMathLab account includes access to learning materials beyond just the problems you're required to complete, including question-specific help.
  • Quizzes. We will occasionally give you short quizzes to complete in class and self-assess. If you struggle to complete the quiz problems on time, take that as an indication that you should strive to learn the material more thoroughly while doing the homework. This might mean you need to solve additional problems.
  • Office hours. The course staff members' office hours are listed on the course page, and any Math 520 student is welcome to attend anyone's office hours. You do not have to have any pressing needs to attend office hours: you are welcome to come to chat about the course or go over problems you feel you already mostly understand or whatever.
  • Computer assistance. You will not benefit from doing every calculation by hand in this course. It is important to have enough facility with row reducing matrices, finding inverses, etc., to develop intuition about implications of these algorithms and to perform them correctly on an exam. However, when learning a new skill, it is a distraction from the key concepts if you have to do an inordinate amount of arithmetic every time you solve a problem. So, I suggest that you adopt some computational resource to help you work more efficiently. My top recommendation is the course Julia package, which was designed specifically for this purpose. It is a 5-minute, no-install, simple-instruction-following task to get up and running with this package in your browser, and it will help you save time and focus as you complete your homework and practice exercises.
  • Your fellow students. Collaboration on solving homework problems is encouraged (though the final write-up must still be your own!), because you can learn a lot from working through problems with one another.
  • Math Resource Center. The department provides learning support for a variety of undergraduate courses at Brown, including Math 520. Place & time: Foxboro Auditorium in the math department, 8 PM to 10 PM Monday through Thursday.
  • Tutoring. The office of co-curricular advising offers free group/individual tutoring on a weekly basis, which you sign up for in advance. The department also has a list of graduate students available for private tutoring (though that tends to be expensive).