Mathematical Olympiad Challenges 2nd Edition by Titu Andreescu (PDF)

Description

Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theoryHistorical insights and asides are presented to stimulate further inquiryEmphasis is on creative solutions to open-ended problemsMany examples, problems and solutions, with a user-friendly and accessible styleEnhanced motivatioReferences

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The concepts and techniques covered are all excellent, with great problems to practice with that have good range in difficulty.However, there are usually only 1 or 2 examples given for each chapter section which are well done, but in my opinion not enough to help a student get a good grasp. Yes, I can work through the problems to improve but a few more examples would make my use of this book more efficient I think. Motivations for solutions could be fleshed out, also.For an already strong contest student, this will be another excellent resource for problems and techniques. I will speak from an American perspective (sorry to other countries), you probably won’t get much out of this book if you haven’t made it to USA(J)MO level yet.

⭐I found this book challenging yet interesting, as you truly need to think in order to answer some of these questions. Great book and am still in the middle of enjoying it

⭐The book, Mathematical Olympiad Challenges”, is a delightful book on problem solving written by two of the leaders of the craft. Mathematical problem solving is a skill that can be honed like any other and this book is an ideal tool for the job. Problem solving usually involves elementary mathematics; this does not mean “easy mathematics”. An elementary mathematical problem is one that is easily stated and can be understood by anyone who has had basic training in the subject (up to calculus). The solution, though, may be quite hard and may require a great deal of ingenuity and thought.It should be noted that being an exceptional problem solver does not necessarily make one a good mathematician, but it helps. This is certainly true of the second author who is also a renowned mathematician in the field of knot theory and three dimensional topology.As mentioned the two authors have a sterling record in the arena of problem solving and in coaching would be problem solvers. I am more familiar with Razvan Gelca who led the University of Michigan team to a top five finish in the highly competitive and extremely challenging Putnam exam. This exam is administered yearly and is open to all college students in North America; usually around 430 universities and colleges send teams to compete in the Putnam. The exam has been offered since the thirties and finishing at the top carries a great deal of prestige. Razvan’s superior abilities led to the spectacular success of the Michigan team which was no mean feat.My own experience with the book has been one of revelation with each passing page. I used the book to teach the problem solving course at the University of Michigan, Ann Arbor, and it helped me immensely. The book possesses a variety of topics in elementary mathematics, ranging from algebra to geometry to trigonometry to number theory. Each chapter is divided into sections and each section has a theme. In keeping with the theme, the authors mention some useful formulae and/or facts that may be used in that section. This is followed by a demonstration of some dazzling problem solving techniques applied to a couple of problems. This is then followed by a list of challenging problems of varying levels of difficulty, all related to the theme of the section. There are roughly 18 such sections and many, many problems to think about. The rest of the book, which is the bulk of it, is dedicated to providing elegant solutions to every problem posed in the first part. Occasionally a problem merits more than one solution and sometimes the way is pointed to some interesting mathematics. The authors also acknowledge the source of many of the problems in the book which is a good indicator of the pedigree of the problem. Almost every solution is a gem and each problem demands its own style of solution. As noted earlier, problem solving is a skill and the authors try and succeed in conveying that idea in the problems and solutions they present.Here is a sample problem from the book; if you can’t do it and want to know how, check out the book:”Show that any cube can be divided into ‘n’ cubes for any integer ‘n’ bigger than 54.”In summary if you are interested in figuring out puzzles, if you are a problem solver of elementary mathematical problems, or if you are just plain curious how a large fraction of mathematicians got hooked on mathematics, I would highly recommend you give this book a try. You may learn something and may even enjoy yourself in the process.

⭐I have spent many entertaining hours going through the book only to realize how rusty I became in these last 25 years that passed since I was faighting a hopeless battle in the Romanian solvers’ contest against the first author.The book is centered around a number of tools, tricks, techniques, as you want to name them, which are then used to solve a number of problems depending on them.The problems are carefully arranged in increasing order of difficulty (maybe that’s the reason I was able to solve some of the first entries!), so that the reader is not immediately discouraged by problems too hard to solve.The actual selection of the problems clearly reflects the taste of the authors. Not a bad taste, I would say, if one notices that Titu Andreescu was the man behind the brilliant success of the USA olimpic team in 1994 (all whose members got then the maximum possible number of points).I was one of the coaches of an olimpic team myself and I know how fast one goes through a list, I would say through *any* list of problems with these gifted guys. From this point of view, the book is an essential instrument for all who contemplate being involved in problem solving training.But the book is a good teaching tool for high school teachers who wish to challenge their best students with more interesting problems. As another potential pool of customers, I would say that those old sea wolfs as myself, who get bored from time to time of the technicalities of professional maths will find this book a nice companion.Yes, I like this book and I warmly recommend it to all lovers of problem solving.

⭐I remember the first time I touched this book, i fell so in love with it that it was very hard for me to remember how many other things I had to do during my day. It really illustrated how every problem you solve (or at least try really hard) can be an entire lesson you can use later on.It is very well organized, even the problems in each section are set in a way that each one helps with the previous one in case a more creative solution doesn’t show up…I love this book, and I really recommend it for any student studying for any math contest around the world. It really helped me, and I’m sure it will do the exact same thing to anyone with the desire to spend countless hours solving beautiful math problems. Good luck, God bless you all :)Pura vida.

⭐Este é o melhor livro que já vi sobre olimpíadas de matématica, comparando-se com o Winning Solutions e Problems Solving Strategies que também são vendidos pela Amazon.com, que é sem dúvida a maior e melhor livraria do mundo. Este livro cita vários problemas conhecidos de importantes olimpíadas como IMO e ASIAN PACIFIC além de outras, além de abordar interessantes técnicas de como resolver problemas como substituição de variáveis trigonométricas. Pode ser considerado realmente um incomparável e imperdível livro que todos os alunos e professores de olimpíada de matemática deveriam ter… É realmente um tesouro matemático !

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