Books with huge collections of hard, and original, problems on High School & Olympiad-level l Algebra?

Question

I'm searching for great and unknown books with huge collections of hard and original problems for my students on High School Algebra or Olympiad level Algebra, related (but not limited) to factoring polynomials and identities.

What I need is a huge collection of hard and unseen problems in high school algebra, because unfortunately most of the problems in these books below are well-known to my students and cannot feed their hunger. My students are about 13 and 14, are really talented.

Problem Solving Strategies by Arthur Engel
101 Problems in Algebra by Titu Andreescu and Zuming Feng
Introduction to Algebra by Richard Rusczyk

Over the past 15 years I've posted many such things in usenet and at Math Forum, and more recently at stackexchange. I don't have a full collection of these posts, but some that I could think of now are Some turbo-charged high school algebra (21 August 2008 sci.math post), minimizing quadratic/quadratic without calculus, and my answer to Is number rational?. — Dave L. Renfro, Feb 09 '15 at 19:15
Does this answer your question? Free introductory resources for learning algebra? — , Apr 29 '23 at 08:57

score 2 · Answer 1 · edited Apr 29 '23 at 02:40

2

Challenging Problems in Algebra (Dover) by Alfred S. Posamentier and Charles T. Salkind (Dover) would certainly fit your needs.

If not, then you can look at Problem-Solving Strategies by Engel. It has a section on polynomials which contains 82 problems.

Another option is 101 Problems in Algebra From the Training of the USA IMO Team by Titu Andreescu, Zuming Feng. You could also take a look at the IMO Compendium. It contains some interesting algebra problems.

edited Apr 29 '23 at 02:40

answered Feb 08 '15 at 19:48

Workaholic

6,763

I've seen this book I mean something different. sth like olympiad or pre-olympiad level algebra problems – souran Feb 08 '15 at 19:49
@mmahdit I suggested two other books in my recent edit. – Workaholic Feb 08 '15 at 20:21
thanks for both books I meant sth stranger because most of my students have read the second one. Engel's book is in hands of most of them and I myself enjoyed reading it years ago when I was student. Thanks again for your kind help :) – souran Feb 08 '15 at 20:23
@mmahdit What about the third one? – Workaholic Feb 08 '15 at 20:24
the 3rd one is a great book and I've read it when I was student. I mean sth like problems of the first chapter of this book. – souran Feb 08 '15 at 20:27
I'm collecting unseen and new problems... – souran Feb 08 '15 at 20:28
@mmahdit What about the fourth book I suggested? – Workaholic Feb 09 '15 at 11:50
Thanks a lot. I will check it soon. – souran Feb 09 '15 at 13:12
@mmahdit You're welcome, very happy to help! :-) – Workaholic Feb 09 '15 at 13:21

score 1 · Answer 2 · answered Feb 08 '15 at 20:34

1

I think you'll find Polynomials by E.J. Barbeau to satisfy your request very nicely indeed. It's probably the most exhaustive source on this topic for beginners and contains an enormous wealth of exercises. It's also extremely clear and gives many insights into the theory of polynomials at this level,mostly without abstract algebra.More sophisticated aspects of polynomials which require basic ring and field theory are discussed in optional sections.

I think you'll find this book just what the doctor ordered.

answered Feb 08 '15 at 20:34

Mathemagician1234

17,288

op's students might have seen it and may be aware of it. – abel Feb 08 '15 at 20:55
ok,but didn't see anything that indicated that. – Mathemagician1234 Feb 08 '15 at 22:58

Alex R. · Answer 3 · 2015-02-08T20:49:40.350

1

Have you looked at Art of Problem Solving's community? You can either search for "polynomial" and cherry pick the problems you like, or just go to the olympiad section for algebra. You'll find all levels there.

edited Feb 08 '15 at 20:49

answered Feb 08 '15 at 20:43

Alex R.

32,771

It's been years that I'm checking that website but it takes along time to cherry pick those problems.you asked about their age: they are about 13-14 and they are highly talented. some of them are really gifted and sometimes I find a genius among them. So I'm deeply responsible to those talents. – souran Feb 08 '15 at 20:57

score 0 · Answer 4 · answered Feb 09 '15 at 15:40

One resource that I use from time to time is Leonhard Euler's Elements of Algebra. There aren't a lot of practice problems, but some of the ones that he does have are somewhat difficult. As an example, take a look at problem 12 on this page. https://archive.org/stream/elementsalgebra00lagrgoog#page/n277/mode/2up

Books with huge collections of hard, and original, problems on High School & Olympiad-level l Algebra?

4 Answers4