How to Study
Research on learning points to a few techniques that reliably improve retention (and to several popular ones that feel productive but do little). A comprehensive review of the evidence rates two techniques as highest-utility: practice testing and distributed practice (Dunlosky et al. 2013).
Practice, don’t re-read. Retrieving an idea from memory strengthens learning far more than re-reading or highlighting, which the same review found to be low-utility despite their popularity (Dunlosky et al. 2013). Working on a problem or explaining a concept to others without looking at the answer is a great way to build knowledge. Use this book’s worked examples and end-of-section exercises to do this. Attempt each from memory before checking the solution.
Space it out. Several shorter sessions spread across days produce more durable learning than one long cram (Dunlosky et al. 2013). Start early and revisit often.
Take notes that make you think, not transcribe. Notes help most when they force you to select and rephrase ideas in your own words rather than copy them verbatim. In note-taking studies, students writing longhand understood concepts better than faster laptop transcribers (Mueller and Oppenheimer 2014). Whichever medium you use, process the material as you take notes. The process of summarizing, not copying, is what forces engagement with the material.
Often students say that they need all the slides because they can’t write fast enough. I disagree - you should not ever try to write everything down in a lecture. Prioritize the content that matters. In doing so, you will greatly strengthen your retention, and ability to use the material. Following along with my PPT is not the most effective way to engage with the material.
Come to Discussion and Office hours. Discussion sections and office hours let you practice with feedback. Coming to office hours having attempted homework problems and with concrete questions is a very effective way to learn the material. Be aware - we will help you, but we will not give you the answer, because that would deprive you of the joy of getting it yourself.