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**NOTES ON RESEARCH METHODOLOGY FOR THE NET EXAMINATION--click here **

click here: Automata, Algorithms and Analysis of Algorithms

click here for GATE CSE PPT BOOK

click here for ADDITONAL MATERIAL

MATERIAL FOR

CSE GATE - 2017

SOLUTIONS TO ALL GATE CSE PAPERS 1987-2016 IN USER FRIENDLY PRESENTATIONS

FOR ALL BRANCHES OF GATE THE QUESTION PAPERS FROM 2013-2016 ARE ESPECIALLY RELEVANT AS THEY HAVE THE OFFICIAL KEY DECLARED

EARLER GATE PAPERS DO NOT HAVE AN OFFICIAL KEY SO ONE HAS ONLY EDUCATED GUESSES AS TO THE CORRECT ANSWERS

THE PRESENTATIONS ALONG WITH CURRENTLY FREELY AVAILABLE YOU TUBE VIDEOS ALLOW SELF-STUDY IN GROUPS RATHER THAN EXPENSIVE COACHING FEES TO BE SPENT

THE ROO-POOH-TIGGER STUDIES

THE FOUNDATIONS REVISITED

OWL, PIGLET and LUMPY standing on the shoulders of the great and mighty giant EULER behold a Silver Bullet to tackle many expoential time complexity problems. This yields polynomial time complexity algorithms for the integer facatorisation. discrete logarithm, elliptic curves discrete algorithm and the sum of sunsets decision problems using the Piglet Transform!!

(Note:- The integer factorisation algorithm has been implemented for the RSA-100 number but the P=NP queston suffers severely from the Tom and Jerry syndrome. So a lot of time must pass before we can accept Owl's point of view.)

Once we accept the existence of the mighty Euler constants e and gamma and their relationship to Harmonic numbers as in the great formulas given by Euler in the above postage stamp the decision problem of the Sum of Subsets problem and the integer factorisation problem can be resolved in polynomial time!

Why is the Piglet Transform so powerful that it can resolve the integer factorisation problem and seemingly the discrete logarithm prohlem, the elliptic curve discrete logarithm problem and the P=NP question? It turns out that any periodic function can be described as the interaction of weighted sine and cosine waves as shown by the great French mathematician Fourier. The Fourier series depends on Analysis. Anything in Analysis has an equivalent in Arithmetic. The independently discovered Piglet Transform is nothing but a restatement of the Fourier Series in Arithmetic. Piglet uses weighted interacting harmonic series and the sine and cosine waves are replaced by the factors of composite integers. So in a way Piglet's Integer Factorisation algorithm is nothing but a recasting of Shor's algorithm using Fourier Series in its Arithmetic equivalent. The existence of the mighty Euler constants e and gamma and their relationship to the harmonic numbers pulverises the exponential. We end up using the naive binary search rather than the still more primitive linear search and the exponential time complexity becomes polynomial time complexity.