Reddit reviews Differential Equations, Dynamical Systems, and Linear Algebra (Pure and Applied Mathematics)

I would check out Differential Equations, Dynamical Systems, and Linear Algebra by Hirsch and Smale (note this is different from Differential Equations, Dynamical Systems, and an Introduction To Chaos by Hirsch, Smale, and Devaney, which is a less self-contained, less rigourous, and more application-driven sequel).

The former book does rigourous proofs of all the results. It does applications as well, and is actually good at explaining things intuitively as well as rigourously. If you're okay with multivariable calculus, then I think you'd be okay with this book. While it's definitely easier if you already know linear algebra and analysis, this book doesn't assume those as prerequisites (the necessary linear algebra is mostly contained in the book, but the analysis results are usually stated without proof before being used to prove something else). That said, generally I would recommend that one knows linear algebra and real analysis, in addition to multivariable calculus, before reading this book or any other serious book on dynamical systems. They say in the introduction that a strong sophomore could handle this book, but that it's written more for an upper level undergrad or even graduate course.

I've been reviewing topics in Hirsch & Smale's Dynamical Systems text.

it might be very dated, but I remember being deeply impressed by Hirsch & Smale's "Differential Equations, Dynamical Systems, and Linear Algebra", a beautiful and seminal book: http://www.amazon.com/Differential-Equations-Dynamical-Mathematics-Academic/dp/0123495504/

Like the other comments say, polynomial division is closely related to Jordan form for linear maps (see pages 12-13 of this lecture for instance https://see.stanford.edu/materials/lsoeldsee263/12-jcf.pdf), and although this has no immediately obvious connection with statistical data, this description of what linear transformations can be like, and has generalizations to non-linear phenomena as in this book https://www.amazon.co.uk/Differential-Equations-Dynamical-Systems-Mathematics/dp/0123495504/ref=pd_sbs_14_t_0/258-1780192-4312467?_encoding=UTF8&pd_rd_i=0123495504&pd_rd_r=30e40ed0-89f8-4fbc-9b41-d4d065c63d73&pd_rd_w=aukE3&pd_rd_wg=W7tNp&pf_rd_p=e44592b5-e56d-44c2-a4f9-dbdc09b29395&pf_rd_r=7CC41Q1EX6Z0J2AS7P43&psc=1&refRID=7CC41Q1EX6Z0J2AS7P43 or others.

 

Also, polynomial division is the main element of the polynomial-time primality test of AKS.

 

The tacit assumption that you can understand phenomena by exclusively applying least-squares analysis (regression, correlation, ANOVA, t-test, f test, etc etc) occurs even in parts of "Freakonomics" and damages and weakens that otherwise wonderful text. Polynomials, complex numbers, Laplace transforms etc etc are indeed weirdly and unfortunately specific, but the aim should not be to discard particular conceptual tools and make things more specific, rather to try to widen and connect together the conceptual tools we do have. And, crucially, to learn not to over-depend on any particular one.