IITPAL

  Combinatorics is not difficult, it's different.  We deal it very similar to other branches of mathematics, i.e.  use the equation/formulae  to get an answer. And this fails. in some sense, every problem in combinatorics requires a different formula. My conclusion is " you can not master combinatorics by remembering a few set of formulae."  Combinatorics can be treated as SCIENTIFIC COUNTING.  To b egin with, combinatorics the most basic part is the fundamental theorem of counting, create your own logic of connecting information given in the problem, and practice a lot more problem. Every good combinatorics problem requires a new road map, create it. The biggest confusion for beginners is in fact when to apply  Permutation and when to apply Combination.  Here is an easy way that can clear you concept: With permutations, every little detail matters. Ali, Bobby and Charl is different from Charl, Bobby, and Ali. Combinations, on the other hand, are ...

We all know the easy way to solve the quadratic equation,           a x²+bx+c =0. W e use the quadratic formula for roots. We also have access to similar formulae for roots of cubic equations and quartic equations. The formula for roots of a cubic equation  ax 3 +bx 2 +cx+d=0 is  A similar complex looking formulae exist for roots of a quartic equation. But myster i ously we do not have any such formula for roots of 5 or higher degree polynomials. It seems as if, we can not construct the solutions of a degree 5 or higher degree polynomials just by using addition, subtraction, multiplication, division, and radicals in its coefficients.  Why so? what is so special in this 5-degree polynomial? These were questions that haunted the young Frenchman  Evariste Galois  in the 18th century. He developed a new mathematical object called a “group” that solved this issue in a surprisingly cool way. Galois being shot in a duel.  Image from...