HACKER Q&A
📣 TheAntiEgo

What math course should I take?


I would like to learn more foundational mathematics. I am a business professional who also knows some software development. My goal is ultimately to have a more nuanced understanding of statistics, economic theory, and principles that will help me better understand the sciences. The last math class I took was in high school (13 years ago) and was probably geometry.

I'd like to determine where to start and, if possible, what list of online (preferably free) courses I should look into taking.

Any feedback would be much appreciated.

  👤 hackermailman Accepted Answer ✓
Try Terence Tao's book Analysis I, start at chapter 2 if you forgot trig. Defines naturals, integers, rationals and reals from scratch teaching you how a proof works at the same time. When you get to the calculus chapters watch Gilbert Strang videos with the book if you want extra insight but Tao's book is clear enough without needing secondary resources. There's a free sample of the first few chapters and the excellent appendix on basics of math logic https://math.unm.edu/~crisp/courses/math401/tao.pdf

All those proofs in probability and stats/linear algebra classes will make sense after imo

👤 LolWolf
Definitely start with Khan academy for pretty much everything up to calculus (or even including it). Then Linear algebra—as usual, I highly recommend Boyd’s text: https://web.stanford.edu/~boyd/vmls/ as it’s very approachable and practical, and then going on to statistics and probability.

You’ll need linear algebra and probability to formalize most concepts in economic theory among many other fields, but both are incredibly practical and will be useful throughout.

👤 sloaken
Basic probability will really grow your understanding of a lot of things. I would follow that with a standard statistics class. I am surprised as a 'business professional' you did not have these. For economics I really enjoyed macro economics. Mirco econ I did not hate, but macro was almost fun. But definitely AFTER probability.
👤 painintheazz
Like the others said you want to know basic linear algebra and probability. Another thing very helpful in general is mathematical analysis. From elementary real analysis up through measure theory and Lebesgue integral, at least. From here a lot of advanced math will open up to you: for example, big-boi probability theory and statistics.

Here below is an intro to how math people think (FREE):

* Book of Proof by Hammack: https://www.people.vcu.edu/~rhammack/BookOfProof/

For intro linal and probability, try

* Introduction to Probability by Bertsekas, Tsitsiklis: https://www.amazon.com/Introduction-Probability-2nd-Dimitri-...

* Linear Algebra by Kuldeep Singh: https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh-ebo...

Both (clear and easy to read) books above are on l#ibgen, I believe. Also, there's a free online course based on Bertsekas'/Tsitsiklis' book on edx if I recall correctly.

I prefer textbooks to online stuff when it comes to math (especially analysis). The many elementary analysis books that I know (and like) are print-only.

Although, you could probably do the following one after the other:

For pre-analysis, try

* From Calculus to Analysis by Schinazi: https://www.google.com/books/edition/From_Calculus_to_Analys...

For modern analysis, try

* Measure, Integration and Real Analysis by Axler: https://link.springer.com/content/pdf/10.1007%2F978-3-030-33...

The one by Schinazi is on l#ibgen and the one by Axler is available free.