One of the things that I regret the most is that I didn’t start my graduate career with a firmer foundation in mathematics. Sure, I have always been good at math, but mathematics is something that is simply not stressed in social science curricula. I think that this is unfortunate. Even though I still have a lot to learn, the more I read about the underlying mathematics of the methods I use on a regular basis, I am increasingly amazed by their elegance and unity. I cannot speak for other students, but it seems that many students simply do not have sufficient training in mathematics to appreciate this – I sure as hell didn’t and I still have a LOT to learn. But I take comfort in the fact that we all still have a lot to learn.
In this post, I am going to share some of the resources that have been tremendously helpful in understanding and visualizing some of the concepts that are otherwise not all that intuitive. The first of which is John Fox’s (2008) fantastic (and very affordable) work “A Mathematical Primer for Social Statistics.” As he states in the introduction (as does the series editor in the preface), this work is meant to help students establish a basic understanding of a lot of the concepts that underlie the methods that we use, including matrices, linear algebra, vector geometry, a brief introduction to calculus, and probability and estimation (as well as all of the subtopics, such as properties of estimators, maximum likelihood estimation, etc.). I cannot say that I fully grasp everything in this text, but I can say that it has helped me gain a bit better intuitive understanding of a lot of the material.
Fox’s book also pairs well with some videos that I found on Youtube. I have always appreciated multimedia content when learning, and thankfully, a YouTuber (Grant Sanderson) has created a series on linear algebra and calculus that some might find helpful for for understanding these topics in a more intuitive way. Sanderson also has a lot of other interesting videos on a variety of other topics at his channel 3Blue1Brown.
The appendices (A, B, and C, to be specific) of Gujarati’s (2008) “Basic Econometrics” are another great resource. I haven’t read the rest, but the appendices seem to have a lot of helpful information (Appendix B and C address matrix algebra and its application in linear regression). These appendices cover a lot of the fundamentals and is a great for reference when you need a bit of a refresher.