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 Member ID: 47

## Karan Sahni

Email
k6346589@rediffmail

Profile: I am a Junior Year student of Computer Information Systems at Ansal Institute of Technology, affiliated to Coastal Carolina University.

 Course Semester Grade Add New Course Algorithm Design - I Fall 2002 View Update Course Probability & Statistics Spring 2003 View Update Course Algorithm Design - II Spring 2004 View Update Course

### Projects (1)

 Project ID: 45Course: Algorithm Design - IITopic: Sorting Algorithms VisualizationUpdate Project Description: My Part of the project was to create working C++ Sorting programs from the various Algorithms. We had decided to make the project comprehensive. So, we included all the sorting algorithms we knew: Bubble Sort Insertion Sort Selection Sort Merge Sort Quick Sort Batcher's Odd-Even Merge Sort Shell Sort Heap Sort Radix Sort Bucket Sort Team Manifesto The first (and probably the most important) thing that any computer programmer learns are the various algorithms for SORTING data. They are absolutely critical for a complete understanding of the whole computer science field itself. But it can get quite confusing at times. Especially, when one wants to understand how each one of them works? Or, How each one of them is different from the other? We think we have an answer to that. Suppose you wish to introduce somebody to the game of FOOTBALL. A verbal discription would not be very helpful. The best solution would be to show a visual of the football game to that person. Same is the case with Sorting Methods. Through this project, we give a visual discription of the various Sorting Algorithms, with the aim of making learning easy and fun. But the solution also gives rise to a more complex problem. How do we represent the sorting algorithms visually. The solution is to create unique visualization schemes to represent the status of data elements at various instances of time. This method of representation gives rise to a more complex field in mathematics known as Dynamical Systems. After the main idea of the project was concieved, the elements of the project were distributed to the various team members. Team Members: Karan Sahni (Algorithms - Coding Sorting Algorithms into C++ Programs) Parul Yadav (Visualizations - Creating Visualization Schemes in OpenGL) Devina Sibal (Visualizations - Creating Visualization Schemes in OpenGL) Prakash (Win32 Integration - Integrating all components in Visual C++ Environment)

### Seminars (1)

 Seminar ID: 53Course: Algorithm Design IITopic: Mersenne PrimesUpdate Seminar Description: Many early writers felt that the numbers of the form 2^n-1 were prime for all primes n, but in 1536 Hudalricus Regius showed that 2^11-1 = 2047 was not prime (it is 23.89). By 1603 Pietro Cataldi had correctly verified that 2^17-1 and 2^19-1 were both prime, but then incorrectly stated 2^n-1 was also prime for 23, 29, 31 and 37. In 1640 Fermat showed Cataldi was wrong about 23 and 37; then Euler in 1738 showed Cataldi was also wrong about 29. Sometime later Euler showed Cataldi's assertion about 31 was correct. Enter French monk Marin Mersenne (1588-1648). Mersenne stated in the preface to his Cogitata Physica-Mathematica (1644) that the numbers 2^n-1 were prime for n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257 and were composite for all other positive integers n < 257. Mersenne's (incorrect) conjecture fared only slightly better than Regius', but still got his name attached to these numbers. Definition: When 2^n-1 is prime (where n is also a prime) it is said to be a Mersenne prime. It was obvious to Mersenne's peers that he could not have tested all of these numbers (in fact he admitted as much), but they could not test them either. It was not until over 100 years later, in 1750, that Euler verified the next number on Mersenne's and Regius' lists, 2^31-1, was prime. After another century, in 1876, Lucas verified 2^127-1 was also prime. Seven years later Pervouchine showed 2^61-1 was prime, so Mersenne had missed this one. In the early 1900's Powers showed that Mersenne had also missed the primes 2^89-1 and 2^107-1. Finally, by 1947 Mersenne's range, n < 258, had been completely checked and it was determined that the correct list is: n = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107 and 127. Are there infinitely many Mersenne primes? Equivalently we could ask: Are there infinitely many even perfect numbers? The answer is probably yes (because the harmonic series diverges). Another question that I am personally confused with is the fact that actually in the form 2^p-1, p has to be prime or just be an odd number?