Second, the content is selective and the book does not attempt to cover all of applied mathematics. Third, the number of page locators is not necessarily a good measure of importance. However, the index was prepared by a professional indexer, so it should reflect the content of the book fairly objectively. Where does one draw the line between an algorithm and a technique?
For a simple example, is putting a rational function in partial fraction form an algorithm? In compiling the following list I have erred on the side of inclusion. This top ten list is in decreasing order of the number of page locators. Note that JPEG and PageRank were youngsters in , but all the other algorithms date back at least to the s.
There is a remarkable agreement between the two lists! This comparison suggests that Dongarra and Sullivan did a pretty good job, and one that has stood the test of time well. Finally, I point readers to a talk Who invented the great numerical algorithms? The next biggest leap forward in the history of algorithms came in the s with the work of the great George Boole. Many others push algorithms forward in the 19th and 20th centuries, including Giuseppe Peano and Ada Lovelace, to name but a few.
But algorithms would get a major upgrade with the work of Emil Post and Alan Turing in the s that would ultimately give rise to the modern computer.
Nothing would be the same again. And so, without further ado, here are some examples of the most important algorithms of all time. The list includes ancient examples as well as some of the most groundbreaking computer science algorithms and programming algorithms in history. The following list of algorithms is far from exhaustive and is in no particular order.
Although there is some evidence of early multiplication algorithms in Egypt around BC , the oldest written algorithm is widely accepted to have been found on a set of Babylonian clay tablets that date to around BC. Their true significance only came to light around , when computer scientist and mathematician Donald E. Knuth published the first English translations of various cuneiform mathematical tablets. Here are some excerpts from his manuscript that explain these early algorithms The tablets also appear to have been an early form of instruction manual Thus the Babylonian procedures are genuine algorithms, and we can commend the Babylonians for developing a nice way to explain an algorithm by example as the algorithm itself was being defined The Euclidean algorithm is a procedure used to find the greatest common divisor GCD of two positive integers.
It was first described by Euclid in his manuscript Elements written around BC. It is a very efficient computation that is still used today by computers in some form or other. Euclid's algorithm requires the successive division and calculation of remainders until the result is reached. It is best described by use of an example:. Step 3 - Continue step 2 until no remainders are left in this case it's a simple 3 step process This algorithm is widely used for reducing common fractions to their lowest terms and in advanced mathematics applications such as finding integer solutions to linear equations.
It allows you to find all the prime numbers in a table of given numbers as many as you want to include. To perform it , you find all the numbers greater than 2, then cross out the ones divisible by 2. Then you do the same for non-crossed out numbers greater than 3, so on so forth ad infinitum until all composite non-prime numbers are crossed out. It is still in use today, especially in computer circuitry. You might be familiar with the term Boolean from mathematics, logic, and computer coding.
Boolean algebra is a branch of algebra in which a variable can only ever be true or false - so-called truth values usually binary 1 or 0. Boolean algebra is widely credited as being the foundation for the Information Age. Ada Lovelace spent the best part of a year translating one of Charles Babbage's lectures that had been transcribed into French by an Italian engineer into English.
During this process, she dutifully added additional explanatory notes of her own. Note G is now widely accepted as being the first recorded example of computer code - making her the first-ever computer programmer. The engine was never built, and so, her algorithm was never tested during her lifetime.
Her work was rediscovered in when her notes were republished. The fast Fourier transform FTT algorithm can trace its origins to Carl Gauss, who first created it to calculate the trajectories of asteroids. The formula was later expanded on by Joseph Fourier in But the more modern and widely used form of the algorithm was created, and published by, James Cooley and John Tukey in In compiling the following list I have erred on the side of inclusion. This top ten list is in decreasing order of the number of page locators.
Note that JPEG and PageRank were youngsters in , but all the other algorithms date back at least to the s. By comparison, the list is, in chronological order no other ordering was given. There is a remarkable agreement between the two lists! This comparison suggests that Dongarra and Sullivan did a pretty good job, and one that has stood the test of time well. Finally, I point readers to a talk, Who invented the great numerical algorithms?
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