- Algebra 1, 2
- Geometry
- Precalculus
- Calculus 1, 2, 3
- Statistics and Probability
- Discrete Math
- Linear Algebra
- Differential Equations
But especially these two:
- Calculus 1, 2, 3
- Linear algebra
I am currently studying at a non-english university in a technical specialty involving math (Calculus and Linear Algebra, to be exact). Right now the workload is 3-4 hours of classes a week, which is painfully low. And after a second year, apparently even less time will be spent on it. My English is good enough to consume math content, so that's not an issue. As well as explanations: I have already found and used resources (both in English and my mother tongue) to self-study fast enough to submit my homework.
What actually is an issue are workbooks (or exercise books, whatever you call it). All the workbooks by which we study vary in quality and there are library shortages. The authors are almost always dropping easy exercises right after the start of the paragraph in favor of much more complex ones.
Since I can buy books on Amazon or acquire PDFs using other methods I am asking for your advice on picking general math workbooks that fall under all of the following criteria:
1. There is a shit ton of exercises in the book, varying greatly in their complexity. You can't solve the book in a month or two even if you study 24/7. This way it's suitable for spaced repetition.
2. The author does not sacrifice easy stuff for hard stuff and vice versa.
3. The answers are given to all of the exercises, no matter the complexity.
4. The solutions, however, are unnecessary.
5*. The workbook itself may actually be some online platfrom like Grasple.
https://tutorial.math.lamar.edu
He's got a healthy amount of exercises for each topic with worked out solutions, both inside the notes (as examples) and as practice/assignment problems. I've found that his exercises/examples don't pull punches.
There is no platform, no way of having the computer check your answers (if that is what you mean). For things like proofs, I don't think the technology can do that at this point.
While I had a good math education, that was two decades prior. My child was starting to study the Calculus AB curriculum, and I wanted to have some basis for helping them (or at least encouraging them).
I found I literally had to start with adding/ multiplying fractions. I did get through the Calc, but stopped during that section because of time constraints.
But I found the basic math portions of the exercises to be quite helpful and feel like it was a good progression. There are a lot of exercises and it is free.
I have two books that satisfy criteria 1 through 4, but they are full textbooks with explanations not just exercises. Lots of exercises though (easy) and lots of problems too (hard). Links in my profile.
In the meantime I will share with you the concept maps from the two books, since they might be helpful to "situate" you on the journey towards all these topics: https://minireference.com/static/conceptmaps/math_and_physic... and https://minireference.com/static/conceptmaps/linear_algebra_...
A fellow hacker with a strong math education background spent most of the last decade building this and it's quite impressive (more exhaustive than anything I've seen). I don't know of a better way to learn math than this.
It leads the reader from basic arithmetic all the way up to complex analysis, one exercise at a time.
A pdf can be obtained legally from the Internet Archive: https://archive.org/details/advancedcalculuswoods
Skills Practice Workbook with Full Solutions
By Chris McMullen
Cannot recommend highly enough. Comprehensive, rigorous, and well written. Amazing community around them too. Can take you all the way to the IMO, if you want.