It is a must read book for ANY math enthusiast and the math majors.After reading this book, you will possibly get a picture as to what is involved in solving higher level math problems especially the psychology of it.TRIZ (the Theory of Inventive Problem Solving) is a systemic approach for understanding and solving problems and is based on 40 principles of innovation.
Richly illustrated and easy to navigate, it pairs clear explanations of every design concept with visual examples of the concepts applied in practice.
From the “80/20” rule to chunking, from baby-face bias to Occam’s razor, and from self-similarity to storytelling, every major design concept is defined and illustrated for readers to expand their knowledge.
You need to know that as psychology is one of the greatest hurdles to over when it comes to solving contest problems.
Then you move on to "Thinking Mathematically" written by J. It has problems which are only few times too hard but most of the times, have just enough "toughness" for the author to make the point ONLY IF THE STUDENT TRIES THEM OUT.
CHAPTER 3 THINKING AROUND A PROBLEM Answering a different question A child’s-eye view Simple questions Starting at the end Listening to your daydreams Comparing and contrasting Reversing a problem Lateral thinking exercises INTERLUDE: THE MESSINESS OF CREATIVITY CHAPTER 4 GENERATING IDEAS Where do ideas come from?
Warming up your mind Patterns of thought Doing something totally different Seeking a second opinion Inspirational people Bending reality Figuratively speaking Old idea old idea = new idea Storing ideas Serendipity When words collide Picking a theme Having a Plan B CHAPTER 5 BEING CREATIVE WITH OTHERS Holding discussions Swapping ideas Working in large groups Brainstorming When differences get personal Suggest, don’t propose Finding three positives Looking for a third way Seeing the funny side CHAPTER 6 MAKING IT HAPPEN Setting a deadline Beating the mid-project blues Planning for the worst case Ten words for creativity Solutions Further reading Acknowledgments which are 1) open your eyes, 2) prepare the space, 3) play 4) use images, 5) do the opposite, 6) develop failure, 7) check-in, 8) use colour, 9) converse with blocks, 10) randomise, 11) cope nature, 12) lose the ego This is the top comprehensive, cross-disciplinary encyclopedia of design.
Most people simply sit and stare at the problem and don't go beyond that. In case you have ever wondered why, in spite of being lightning fast in solving textbook exercises in the 10th and 11th grade, you fail in being able to solve even a single problem from the IMO, you have to read this book.
Even the kids who are extremely fast with 10th grade math miserably fail. The ONE book which explains this is titled "Mathematical Problem Solving" written by Professor Alan Schoenfeld. I am surprised to see Polya's book getting mentioned so very often bu nobody ever mentions Schoenfeld's book.
It's a free online journal edited by Titu Andreescu.
They publish six times a year and their problems tend to reflect current olympiad trends.