Relearning math as an adult

As Justin mentioned, there are several criteria that we must meet in our high-school pathway that aren't needed for studying higher-level (e.g., undergraduate) math, or they can be postponed. We decided to remove some of these in the Foundations series.

The idea behind the foundations series is to provide adult learners with the most efficient path possible to get onto the higher-level material.

Examples of topics that were removed from the high-school series to create the foundations series include some of the following:

* Various Geometry topics: All of the _essential_ geometry is covered. However, we removed topics on inscribed angles, Thales' Theorem, Triangle congruence, and similarity criteria (apart from the AA, which is the only one that seems to come up in practice), midpoint and triangle proportionality theorems, a fair amount of solid geometry, except what's fairly standard for calculus (volumes and surface areas of spheres, volumes of cones), lots of stuff on different types of quadrilaterals.

* Conic sections: The essentials are covered in both pathways. But in the high-school path, we go into a little more detail about foci, directrices, eccentricity, and utilizing their geometric definitions (e.g., focus-directrix properties).

* Trig identities and Equations: Covered in both pathways, but the high-school versions go into more detail and consider more cases.

* Some word problem/modeling topics.

* Other arbitrary Prealgebra topics: Divisibility rules, going into more detail about ratios in contextual settings, scientific notation, and some basic data representation topics that one would normally meet in Prealgebra.

* Slope fields. This will be covered in our upcoming differential equations course.

* Some analytical applications of differentiation that are quite specific to the BC Calculus exam: Identifying and removing point, jump, and infinite discontinuities and analyzing graphs of first and second derivatives.

* There are also fewer topics on related rates and optimization, though these topics are still covered.

* Some contextual applications of integration, like volumes of revolution and volumes of known cross-sections.

* Convergence tests for infinite series. When we get to that, these will be covered in real analysis, but other than infinite geometric series (which _is_ covered in Foundations), these tests don't show up too often anywhere else.

* Some ODE models, such as exponential and logistic growth and decay. We cover ODE basics in the foundations course, but particular models will be covered in the differential equations course.

* Taylor series. Again, this can be covered in the differential equations course for anyone wishing to take that course when it's ready.

Happy to answer any further questions you may have.

If you could find a book just going through the relevant bits you wouldnt really have to "learn math again", it can be translated into english straightforwardly -- very very few ML papers relevant to industry have extended proofs, etc. that require eg., even being able to differentiate anything yourself.

90% of it is: here's the domain (ie., type) of our variables, here's the formula of our functions, we're taking a weighted average with some inner products involved.

It might sound like a lot of math, but it's really all doable in semester-1 of an undergrad course, were it focused enough.

Luckily, soon after the decision was made, I finally got my first full time job in Finland. I could easily support the two of us and give her an uninterrupted life to focus on grinding up for the math exam. We took the last ~10 years' worth of math exams online, turned their problems into Anki cards, and set her nose to the grindstone. I had had tremendous success with this in college with abstract algebra and real analysis, so I figured the same methodical approach + a very stable living situation was bound to work for algebra through basic calculus.

Five months later, she retakes the high school exam and gets the highest score possible! Her rapid success at this convinced her to give CS a serious try, and indeed her improved math exam was the differentiator - without it she would not have been accepted to the CS program. She got top marks in her first semester at CS as well, I couldn't be more proud. My wife is truly an incredible person.