Guest torquoiseworld Posted December 10, 2013 Share Posted December 10, 2013 Hi! I'm a new user here. I'm Valerie and I'm a high school girl trying to make it to MOP. I'm currently reading chapter 2 of geometry revisited and having a bit of trouble. Is there something slightly easier that is still olympiad geometry? Also, are there any books that I should prioritize? Quote Link to comment Share on other sites More sharing options...
EinsteinBlueprint Posted December 10, 2013 Share Posted December 10, 2013 Oh, that indeed is a great book. I used to fight over the lone copy with my fellow math teammates. But that was 20-something years ago... I think you are better off asking these questions on AoPS boards. Sorry. Quote Link to comment Share on other sites More sharing options...
Kathy in Richmond Posted December 11, 2013 Share Posted December 11, 2013 Hi Valerie, I agree that Geometry Revisited gets tough pretty fast. Without knowing what you've already done or what resources you're familiar with, here are some ideas. Have you already worked through the AoPS geometry text or the geometry chapters of the their Classic Problem Solving volumes 1 and 2? That's a good place to start since they go beyond what's in a typical high school geometry course. Geometry is a tricky subject in that concepts are easily mastered individually, but putting all the different ideas together at once in order to solve an olympiad problem can seem next to impossible and requires seeing the big picture, along with a touch of creative genius. AoPS does the best job at presenting geometry holistically that I've seen. I'm a mathematician, and I learned lots of new stuff from them. The AoPS online forums also are free & not only a good source of problems, but also a community where you can find other students who want to succeed in math like yourself. Plenty of geometry problems are available there! Look in the pre-olympiad, AMC, and olympiad geometry boards to start. My children (former math competition kids, one of whom attended MOP) also used these books, in rough order of difficulty: Gelfand's Trigonometry - His trigonometry is VERY geometrically motivated and gave us lots of new insights. The text is very well written & contains problem sets (no solutions, though). Gelfand's math texts are proof based and don't shy away from introducing real mathematics. The trig book contains ideas such as analytic continuation, linear combinations of functions, Fourier series, convergence of a series of functions, etc, all in a completely understandable way. It's a different take on trig from the standard school text, and a text that would benefit any future mathematician. Plane Euclidean Geometry: Theory & Problems by Gardiner & Bradley - This one might be good for you right now. It covers advanced geometry (many of the same topics as GR), but I think it's easier to read through than Coxeter. There are both instruction and problem sets, along with hints & solutions. Challenging Problems in Geometry by Posamentier and Salkind - no instruction, but lots and lots of non-routine problems and solutions organized by topic. It is a nice complement to the Coxeter book. If you want on online class, I'd highly recommend taking the AoPS Olympiad Geometry course from Richard R. Very advanced & challenging stuff! My kids both loved it & learned a LOT (grades 11/12). It's only offered occasionally, but I see that a section is scheduled to begin in Feb 2014. There's a placement quiz on the website. Honestly, though, what most improved my kids' geometry abilities in the intermediate years was just doing lots and lots of progressively harder problems. They used sources such as past AIME exams, USAMTS contests (probably one of the best sources for us; most rounds contain a geometry problem), and old HMMT geometry rounds. Also take a look at PUMaC and Duke math meet problems if that's not enough. Or buy an ARML or Mandelbrot practice book & pick out the geometry problems. When you're ready, old USAJMO & USAMO problems and solutions are online, too. Can you participate on a math team or attend a summer math camp? My kids loved Canada/USA Mathcamp, but there are many other camps available. Dd found out about an ARML team by posting inquiries on AoPS forums back when she was in high school. Their progress was light years faster when they had a motivated peer group & time set aside specifically to learn higher math. Good luck! Quote Link to comment Share on other sites More sharing options...
lewelma Posted December 11, 2013 Share Posted December 11, 2013 Wow Kathy! This list is great! Quote Link to comment Share on other sites More sharing options...
Guest torquoiseworld Posted December 11, 2013 Share Posted December 11, 2013 Hi Valerie, I agree that Geometry Revisited gets tough pretty fast. Without knowing what you've already done or what resources you're familiar with, here are some ideas. Have you already worked through the AoPS geometry text or the geometry chapters of the their Classic Problem Solving volumes 1 and 2? That's a good place to start since they go beyond what's in a typical high school geometry course. Geometry is a tricky subject in that concepts are easily mastered individually, but putting all the different ideas together at once in order to solve an olympiad problem can seem next to impossible and requires seeing the big picture, along with a touch of creative genius. AoPS does the best job at presenting geometry holistically that I've seen. I'm a mathematician, and I learned lots of new stuff from them... Thank you so much for answering with such depth! Right now my geometry level is between volume two and olympiad geometry. I just ordered Plane Euclidean Geometry, so I'll be waiting on that. This summer I attended IDEA Math's summer camp. It was really eye-opening, and that was what motivated me to start learning olympiad math. I qualified for JMO but only ended up with a 1. This year, I hope to get at least a 15. Quote Link to comment Share on other sites More sharing options...
Kathy in Richmond Posted December 11, 2013 Share Posted December 11, 2013 Thank you so much for answering with such depth! Right now my geometry level is between volume two and olympiad geometry. I just ordered Plane Euclidean Geometry, so I'll be waiting on that. You're welcome! I'm glad to share any time. At that level, I'd highly recommend adding USAMTS to your agenda, even if you just work the problems informally & don't enter the competition. Their geometry problems were the perfect bridge between AoPS vol 2 and olympiad geom for my kids. This summer I attended IDEA Math's summer camp. It was really eye-opening, and that was what motivated me to start learning olympiad math. IDEA Math is another excellent camp. It was MathPath that first opened our eyes to the world of Olympiad math. On the first day of camp, the kids were given a USAMO geometry problem to work on. I was sitting in the back of the auditorium totally stuck, thinking, "wow, this is tough stuff, but so interesting"...then the prof walked us through the solution & it seemed so elegant and almost easy in retrospect, ha! That was the start of much fun & rewarding math learning in our family. I qualified for JMO but only ended up with a 1. This year, I hope to get at least a 15. Good luck to you! I bet you'll reach your goal if you keep working this hard. :001_smile: Quote Link to comment Share on other sites More sharing options...
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