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Ask HN: What are the best general math workbooks?

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Ask HN: What are the best general math workbooks?

#1
By saying general math in the title I mean all of the following (in American way):

- 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.

Re: Ask HN: What are the best general math workbooks?

#4
I re-learned math via Kahn academy.

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.

Re: Ask HN: What are the best general math workbooks?

#5
Khan Academy fits most of your description. The number of exercises is not unlimited (because that’s an unusual requirement). It could supplement other material if you truly need a huge quantity of exercises. Once you’re into more advanced topics (calculus and above), mit opencourseware is probably the best quality material. Once again, the exercises are the quantity of a typical course.

Re: Ask HN: What are the best general math workbooks?

#8
This will take up some space in your home, but there are a ton of used textbooks on Amazon and eBay. The older ones that aren't used anymore are only a few dollars each. The books themselves may only have answers to the odd-numbered questions, but that's still a lot of questions. (Learning how to check your own work is also a good exercise, but if you need something guaranteed to be reliable, you can plug a lot of problems straight into Wolfram Alpha or even a good graphing calculator.)

Re: Ask HN: What are the best general math workbooks?

#10
My Linear Algebra https://hefferon.net/linearalgebra/index.html comes with lots of exercises in each section, from easy to (a few) pretty hard. There is a book of worked solutions that covers all exercises. It is free so if you download it (and the solutions) and you find that it doesn't suit then no harm done.

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.

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