Study multiple subjects at the same time or deep dive into one?

Question

I want to learn probability theory and discrete math. However, I also need to brush up on computational calculus and linear algebra. Would you recommend only studying one subject at a more intense pace for a shorter period of time or would you recommend taking on multiple subjects over a longer period of time- e.g. learning probability and discrete math whilst also reviewing calculus but like taking in less information about any given subject each time i learn, or doing subjects on alternating days.

Example of one subject- learning probability and only probability every day for 3 hours for one month until i finish a series of lectures

example of multiple- learning probability 3 days a week for 3 hours and reviewing for 3 hours the other 3 days

or

another example of multiple - learning probability for 90 minutes and reviewing for 90 minutes every day.

My goal is to maximize retention and understanding while still keeping a good pace. If I don't use it within a month I usually lose it.

What do you think?

Answer 1

I advise one, not two. The biggest danger with self study is quitting. Keep it simple and get an earlier victory. Will reduce quitting danger. Retention can be kept by periodic review. And/or really just brushing up, WHEN YOU NEED IT later in life. Nobody expects you to remember every trick, if you are not continuing to use the stuff and/or doing a follow-on course to use it. But it sure comes back quick when needed. Especially if you MASTERED (look up the concept) it at the time.

P.s. Note, I'm concerned about hearing you talk about getting through lectures. Don't. Get through a book and do lots of problems. Same thing with review. Review means a retest of your abilities, followed by corrective action to do some more drill and retest again. It does not mean more passive viewing/reading. See: https://www.scotthyoung.com/blog/2012/11/13/why-lectures/

Answer 2

Terms to search for include "blocked practice" and "interleaving"; the latter is also known as "mixed practice" or "varied practice".

For instance, see https://effectiviology.com/interleaving/ (excerpt below)

Interleaving is a learning technique that involves mixing together different topics or forms of practice, in order to facilitate learning.

Interleaving helps people retain new information, acquire new skills, and improve existing abilities in a wide range of domains, such as math, music, and sports. When deciding what kind of material to interleave, you should use logical criteria given the reason that you want to interleave material in the first place, and make sure that the items that you interleave aren’t too similar or too different.

The effectiveness of interleaving varies based on factors such as the type of material involved and the environment in which the material is learned, so you should assess the situation when deciding whether and how to interleave; if possible, you should also assess the effectiveness of the interleaving over time, and experiment with different approaches to it.

Interleaving can be hard, and people sometimes underestimate its effectiveness; this is important to keep in mind both when it comes to interleaving in your own learning and when it comes to interleaving while teaching others.

In your specific situation, you might want to look into any overlap between your courses that could reinforce your retention and understanding of concepts. Perhaps discrete probability comes up in discrete mathematics (some courses/books include it). Certainly, permutations and combinations are likely to be covered in discrete mathematics; these topics are also used in probability. Integrals (calculus) may also come up when studying probability. Linearity from linear algebra also shows up in the linearity of operations of differentiation and integration. Vector spaces in linear algebra can have "vectors" that are sequences or functions. Matrices can arise in the graph theory part of discrete mathematics. More generally, standard proof techniques might be needed in both linear algebra and discrete mathematics.