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):
- Logic and sets (propositional calculus, predicates, relations between predicates and sets, constructing of sets)
- Addition and subtraction (associativity, commutativity, additive identity, etc.), multiplication and division, comparison
- Natural numbers
- The Pythagorean theorem visually
- The Binomial theorem visually
- Commensurability, the Euclidian theorem
- Straight-line mathematics (motion, shift, the composition of shifts, group).
- Cayley table for line shifts
- Chasles' theorem (lemma about three nails).
- Circle movements, group of circle movements, Chasles' theorem
- Integers, ring.
- Greatest common divisor and the Euclidian theorem
- Prime numbers and the Fundamental theorem of arithmetic
- The object symmetry, the symmetry of the equilateral triangle, the symmetry of the regular polygon.
- 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.
Thank you for your help in advance!
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.