# Workbooks for advanced high school math topics

I'm looking for advanced workbooks and exercises for working in class (math high school/undergraduate level) covering the following topics (or some of them):

1. Logic and sets (propositional calculus, predicates, relations between predicates and sets, constructing of sets)
2. Addition and subtraction (associativity, commutativity, additive identity, etc.), multiplication and division, comparison
3. Natural numbers
4. The Pythagorean theorem visually
5. The Binomial theorem visually
6. Commensurability, the Euclidian theorem
7. Straight-line mathematics (motion, shift, the composition of shifts, group).
8. Reflection
9. Cayley table for line shifts
10. Chasles' theorem (lemma about three nails).
11. Circle movements, group of circle movements, Chasles' theorem
12. Integers, ring.
13. Greatest common divisor and the Euclidian theorem
14. Prime numbers and the Fundamental theorem of arithmetic
15. The object symmetry, the symmetry of the equilateral triangle, the symmetry of the regular polygon.
16. Subgroups of the circle movements.

Can you help me with authors/keywords in your country? We have already put up the theoretical material, we need only to collect exercises for them.

UPD: Question needs an additional clarification: we've put together the theoretical material for advanced high school kids / undergrads, you can check it here: https://github.com/nkrishelie/mathempire/blob/master/250/250le%C3%A7ons.pdf

It's in Russian, but you can use Google Translate on PDF document to get the basic idea. Actually, the problem is that we have one-two problems per chapter, but we need to get some more covering our theory with practice. So, I need a collection of books/articles (just name and title) with collections of problems matching topics we try to cover. Something like this. The most critical for us now is to cover Chapters 9 - 15. Permutations, linear algebra, continuum, algebraic numbers and elements of analysis. For the beginning of the book I've already found some materials to work on.

The goal for all of this is simple: to collect better problems and avoid cheating by using non-googleable materials from other countries.

• For what level? Elementary, high school, college?
– JRN
Jun 16, 2020 at 8:15
• It's an advanced math high school.
– paus
Jun 16, 2020 at 8:18
• Have you seen Art of Problem Solving? Jun 19, 2020 at 0:40

This seems like a quite peculiar assortment of topics, and I do not imagine that any existent text addresses all of these. I think you will need to either write your own materials (if you want a coherent treatment), or just cobble together textbook treatments from a diversity of sources.

• It's not required to cover all of them. Even one/two workbooks per topic would be enough. The goal of this question is more about comparing different materials and it's quality from other countries (ideally) and choosing better fitting in our curricula. That's it.
– paus
Jun 18, 2020 at 14:32
• @paus Maybe you want to clarify this goal in the question. Also, define workbook. Is it a book of worksheets with multiple choice questions or write-ins, or it is a problem book? Jul 6, 2020 at 16:15
• @RustyCore I added few more details making things clear. What we're looking for is a set of problem books for our sketched up course materials to collect some more problems to give as a homework handout.
– paus
Jul 6, 2020 at 21:41

For Advanced High School math, I'd consider looking at "IB Further Math" materials.

If you look it up on Wikipedia, you'll find that it's been discontinued but if you search online for pdfs then you could find some materials that could cover your topics. For example, this book.