I designed the Mathematical Foundations Series to help adults efficiently master all the middle and high school material (including calculus) necessary for university-level math.
It starts with fractions and goes as far as calculus, basic linear algebra, & random variables.
I'm often asked which high-school topics were excluded from the Foundations series. We decided to leave some topics out either because (a) they're not important for university-level study or (b) we plan to include them in the university-level course where they're most needed.
Here's a summary of topics that didn't make the cut:
* Some Geometry topics: All of the essential geometry is covered. However, we removed topics on inscribed angles, Thales' Theorem, Triangle congruence, the SSS and SAS similarity criteria (we kept AA, as this crops up in Calculus), midpoint and triangle proportionality theorems, some solid geometry (though we kept what's fairly standard for calculus, such as volumes and surface areas of spheres, volumes of cones), lots of stuff on different types of quadrilaterals.
* Conic sections: Both pathways (high school and foundations) cover the essentials. However, in the high school path, we go into a little more detail about foci, directrices, and eccentricity and utilize their geometric definitions (e.g., focus-directrix properties).
* Trig Identities and Equations: Both pathways cover these, but the high-school versions go into more detail and consider more cases.
* Other arbitrary Prealgebra topics: Delving deeper into 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. These will be covered in our Real Analysis when we get to that, but other than infinite geometric series (which is covered in Foundations), these tests don't appear very 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 and real analysis courses for anyone wishing to take that course when ready. The foundations series does cover second-order Taylor polynomials.
If anyone has any questions about the Foundations Series, I'd be happy to answer them.
You can find the course descriptions (including a list of all 989 topics here:
mathacademy.com/courses/math…
mathacademy.com/courses/math…
mathacademy.com/courses/math…