Challenge and Thrill of Pre-College Mathematics (, New Age International Publishers) - Free ebook download as PDF File .pdf), Text File .txt) or read book . It's not actually available as pdf but you can find it here: Challenge and Thrill of Pre-College Mathematics Edit 1: A newer version of the book can be found here. challenge and thrill of pre college mathematics pdf free download.
|Language:||English, Spanish, French|
|Genre:||Business & Career|
|Distribution:||Free* [*Registration needed]|
Challenge and thrill of pre-college mathematics, co-authored by dr v krishnamurthy, c r pranesachar, b j venkatchala, and k n rananathan was written to help. Challenge And Thrill Of Pre-College Mathematics Is An Unusual. Enrichment Text For Mathematics Of Classes 9, 10, 11 And 12 For Use By Students And. thrills and challenges of pre college mtn-i.info FREE PDF Challenge And Thrill Of Pre-College Mathematics Is An Unusual Enrichment Text For.
Nonetheless, there was nobody with whom to discuss my overall Olympiad preparation plans and strategies.
During the months of May-June, apart from the formality of attending the VMC lectures and doing some of their problems, I focussed on Olympiad mathematics.
As I already mentioned, I had neither any Olympiad senior nor any peer to discuss my progress with, so I had to find my own way. I'll describe some specific instances. The methodology of research has been classified into theory building and problem solving. By nature, I'm more of a theory builder: during my tenth class, I used to make notes to try to fit a pattern into what was being taught in school, and in junior classes, I had tried to create new axiomatic theories of geometry.
When I wanted to master a particular area, i wouldn't try to solve a hundred problems in it, rather, I would solve just a few and try to stare at the linking ideas of the theory. Olympiad problems, on the other hand, are famous for the lack of pattern and its intractability even with knowledge of the theory.
But I wanted to have a theory-centered approach to the preparation, in addition to practising lots of problems. There were two reasons. One, I felt correctly that today's insights are tomorrow's theories. Two, I believed that since my ultimate aim is to study mathematics, knowing the theory will be helpful in later study. From Challenge and Thrill, I picked up Ceva's and Menelaus' Theorem, and did a lot of practice questions on these results. There were some questions, specially in the last exercise, that I just couldn't solve at the time.
However, coming back to them in a few days, I was able to crack them, and the solutions remained etched in my mind. I converted all the difficult problems into important theorems, and framed them in my mind. I would open a random page from the Penguin's Dictionary, see a definition or a result, and try to prove it. Many of the results which seemed simple to state were hard to prove, and I got stuck over a number of them. Again, it was a matter of getting them eventually after a long struggle.
On the theory side, I was keen to build a reasonable "theory of quadrilaterals". Quadrilaterals are a lot more messy than triangles, and there are all sorts of special kinds of quadrilaterals. After analyzing the many special kinds of quadrilaterals, I came up with the following scheme.
Let a,b,c,d be the sides of the quadrilateral. Analogously, define q,r,s. Thus, the quadrilateral is a "kite". Thus, the quadrilateral is a "parallelogram".
And I feel that this is an indication that I have research potential. This was a completely problem-oriented book, but each problem contained a new morsel of the theory. I worked on the first chapter, trying each problem, looking at the solution, and augmenting my theoretical understanding. I also created heuristics lists. Although I probably never used those heuristics lists explicitly, the process of creating the heuristics itself helped me clarify my thinking.
I also attempted the puzzles in Mathematical Circles. These taught me some elementary combinatorial tricks and also made for good puzzles to discuss with others. The simple and elegant proof of Fermat's Little Theorem was one factor that hooked me to number theory early on. I finished the first chapters of Burton's books, getting stuck at the quadratic residues part.
I was to later return to quadratic residues with a vengeance. The clear notation and notion of congruences helped me give neat solutions to problems where I had hitherto given ad hoc solutions. I also had the book by Niven and Zuckermann, but I did not read it during the summer holidays. At the time, I was not too interested in algebra per se, though I liked to use algebraic methods and tools in general.
Besides, the VMC maths classes already had a reasonable amount of algebra in them. On the whole, the months of May and June were crucial in kickstarting me into the world of Olympiad mathematics. Right uptil class ninth, I stayed a class or two ahead of school. I also exposed myself to some hobby math and popular math books.
I didn't follow all the details at the time, but did get intrigued by a result called Fermat's little theorem. Devlin's book stated that this was a piece of elementary but ingenuous mathematics, and I always believed that any "elementary problem" could be solved with enough time and dedication. So I took the problem with me to the dentist's appointment but came back empty handed.
The problem was -- I had nothing to chew upon. With no approach, no idea of how to start, no knowledge of what can be used, I was completely clueless. All I knew was that x - 1 divided xn - 1, and that is not sufficient in itself. I was always keen on mathematics.
During my seventh and eighth standards, I set myself the less taxing goal of being a math school teacher. I even used to rehearse in my mind a scene where I was teaching a class.
I visualized how I would arrange and organize the curriculum. I thought of setting up my own school. Interestingly, when I was in seventh standard, I dreamed of being a seventh standard teacher, and when I reached eighth standard I dreamed of being an eighth standard teacher. You can imagine what happened when I reached ninth standard. By the time I reached tenth standard, I realized that my dream of being a teacher and elucidator of the subject could be best met if I took up the line of research.
Then, I could teach in colleges and spread the word for mathematics in schools. Which meant that I should take up "mathematical research". But what did that mean? Would I become a musty old professor in a college?
Or would I be a cutting edge thinker, an explorer into the world of knowledge? Another question that plagued me was: where to study? Should I take up an undergraduate course in mathematics? A mixture of these concepts are also observed at times. Number Theory : This topic again carries a weightage of 1 or 2 questions or near about 17—34 marks. We need to learn Number Theory by heart, for that purpose there should be a co-ordination of books and videos simultaneously.
I will give a brief summary of boos and the links to directly order them from site at the end, meanwhile the questions can be from Remainders. They might even come from an inspired previous year problems, so previous year problems must be learned by heart too. What else? Well allow me to store some suspense in the store or I would run out of words.
Get A Copy. Paperback , pages. More Details Friend Reviews. To see what your friends thought of this book, please sign up. How to get hard copy of this book? Lists with This Book. This book is not yet featured on Listopia. Community Reviews. Showing Rating details. Sort order.
May 24, Nageshwar Mitkar rated it it was amazing.
So how can I read this book. View 2 comments. Apr 13, Sabyasachi Mukherjee rated it liked it. This book is exceedingly well-written with an enormous amount of geometry in it I did not really read the geometry part in great detail but it was very good. The sections on number theory and combinatorics offer a variety of innovative techniques.
Sep 03, Tejas Oke rated it it was amazing. It is very good.
Jan 21, Umang Srivastava rated it really liked it. Soumya Das rated it it was amazing Mar 01, Gautam Khona rated it it was amazing Sep 05, Harjot Singh rated it really liked it Jan 09, Shikha Sharma rated it really liked it Mar 21,