The Three-Year MATHCOUNTS Marathon

To be upfront, I was sent a free copy of the book in exchange for writing a review. I gave the book to my math team to look over as I was too busy to read it at the time.My kids loved it right away. My MATHCOUNTS teams have been state champs 14 of the last 15 years and I've coached the national champs twice, so I've seen and written a lot of material. My students found that the book addressed a lot of problems they hadn't seen before and more importantly techniques neither they nor I had seen. After about 2 weeks of them taking turns with the book during math team practice and enrichment meetings, I had to buy 3 more copies of the book so more kids could use it.I would say that this is not the book for kids that are hoping to do well at Chapter or AMC8 though. It is great for kids for whom those tests are easy and who need a leg up on the tougher problems they would see at MATHCOUNTS states/nationals, AMC10/12 and AIME. This book can help get them to the next level.

Every book has a target audience. With this title, it is the advanced middle schoolers who are at MathCounts national level, as well as earlier high schoolers. I agree the questions tend to be hard, but the quality (examples and questions) is superior so I'm happily using it for competitions like AMC10/12, or AIME, beyond MathCounts. There are many more basic MathCounts books at the AOPS site, if you are disappointed with this one. But this one definitely is one of the best competition books I,ve seen in years.

Excellent book. Very well selected topics. This book is not just for competition math. A must read for any student interested in math.

If boggles my mind why someone would put solutions right after the question with almost no space between them. If you don't read with index cards and paper covering the remaining problems, your eyes WILL see the solution and bias your thinking. Arranging papers and cards to block the solutions is incredibly annoying. Detailed solutions are already in the back of the book, so why did you make basic solutions right next to the problem? Destroys the experience for me, but the problems are mostly good and very interesting. A good collection of principles and problems if you can deal with the annoyance of the solutions being visible.

Excellent book. Wish the solutions were separate from the problems.

For national mathcounts competition.

A decent math book but not proper for preparing mathcounts. Some problems after chapter review are way too difficult (comparing to the last 5 of the sprint national problems). It's ok to practice using harder problems such as AIME, but may not be a good idea to tackle IMO (or equivalent) problems just for mathcounts.Hard to believe the book was complied by a middle school student (the only author of the book). Also some solutions (or tricks) are not well explained.

The short review: for content: excellent. For value, pretty good. For all but the top-level math contest competitors (who already know most of this stuff) you will learn a lot of good math by reading this book and working through its carefully selected problems. It is well-written and I recommend the book to middle- and high school students looking to improve their contest mathematics skills.The long review:I have been a math team coach for over twenty years, and have had teams successful at state and national levels In addition, I write the ARML Power contest and have written for AMC/AIME in the past. So I can recognize a valuable resource for preparing for math competitions when I see one, and this book definitely is in that category.The way to learn mathematics is by doing problems. Lots and lots of problems. Ms. Ge has assembled a huge database of competition problems from all levels of competition, and shares part of that database with her readers in this book. Each of the fifteen chapters on this book treats a different area of math that might come up in a contest, broken down into sections that tackle specific principles or topics, such as the inclusion-exclusion principle, or cyclic quadrilaterals. You can see the range of topics by using the "Look Inside" feature on the Amazon page. Each section covers one or two principles that can be used to solve particular types of problems, together with carefully chosen, fully worked examples that elucidate both the topic of the section and how a top-notch competitor goes about thinking about the problems. The chapter ends with at least twenty wonderful problems at varying levels of difficulty, all with complete solutions that again show not only the mathematics, but the way a competitor might go about thinking through the problem to achieve its solution.Content-wise, this book is hard to beat. It is great to find so many math competition techniques explained and demonstrated all in one place. As a resource for math team students and coaches this will be invaluable. Even experienced competitors working their way up the ranks in AIME, USAMO, HMMT, and perhaps even Putnam will find something of value--a little nugget or trick they didn't know before or at least a great supply of problems to practice.I was impressed with the quality of the writing as well. Occasionally the prose shows Ms. Ge's tender age, but she has the makings of a master expositor. The mathematical writing is excellent, with generally well-chosen notation, clear formatting, unambiguous exposition, and clean development. Many mathematical writers with more experience do not write as well as she!Lest you think I am just shilling for Aquahouse (my payment for this review amounted to one free copy of the book) I do have a few quibbles. There are a few editorial slips (I didn't keep track of pages where they occurred, as I was more interested in doing a mathematical review) such as a missing subscript or noun-verb mismatch. Not enough to be distracting, but noticeable because of the quality of the rest of the work. Perhaps about three or four in the book--not surprising for a first printing. I personally would have liked to see a larger type size, and perhaps more space or wider margins for annotations. Finally, I hate paying over $20 for paper-bound books. This one is worth the money content-wise, but I bet they could sell enough extra books at $19.95 to more than make up the difference in profit from charging the lower amount. (Edit: after I originally posted my review, the publisher took notice and took me up on the recommendation to lower the price--now it's an even better value, so feel free to help prove me right!)Two final thoughts. 1) I highly recommend that the publisher start an online forum for this book, or that students who read it create a forum on a site like Art of Problem Solving. Some of the problems I would have tackled in totally different ways than the author, and a great way to learn even more mathematics is to do the problems and then discuss different techniques for solving them. 2) Since Ms. Ge lives in the Chicago area I am definitely looking forward to having her on the Chicago All-Star ARML team this year!