Ada Byron's notes on the analytical engine
From Academic Kids

In 1840 Charles Babbage was invited to give a seminar at the University of Turin about his analytical engine. Luis Menabrea, a young Italian engineer wrote up Babbage's lecture in French, and this transcript was subsequently published in the Bibliothèque Universelle de Genève in 1842.
Babbage asked Ada Byron (also known as Ada Lovelace) to translate Menabrea's paper into English. He then further asked Lady Ada to augment the notes she had added to the translation, and she spent most of a year doing this.
These notes, which are more extensive than Menabrea's paper, were then published in The Ladies Diary and Taylor's Scientific Memoirs (under the pseudonym A.A.L.).
Her notes were labelled A, B, C, D, E, F and G, the last one being the longest.
In note G Ada describes an algorithm for the analytical engine to compute Bernoulli numbers. It is generally considered the first algorithm ever specifically tailored for implementation on a computer, and for this reason she is considered by many to be the first computer programmer.
Note G could possibly also be said to be the first expression of the modern computer phrase "Garbage In, Garbage Out". Lovelace writes:
 "The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. It can follow analysis; but it has no power of anticipating any analytical relations or truths."
On the other hand, proponents of Artificial intelligence would dismiss the above quote as nonsense: Automated theorem proving could be cited as a counterexample.
According to Linda Talisman on [1] (http://www.cs.yale.edu/homes/tap/Files/adalovelacenotes.html) "Baum cites:
 Perl, Teri. The Ladies Diary or Woman's Almanac, 17041841, Historica Mathematica 6 (1979): 3653
 Wallis, Ruth and Peter. Female Philomaths, Historica Mathematica 7, (1980), 5764
There were indeed women in midcentury England who signed their names to mathematical articles in popular journals, and there were influential periodicals, such as the Edinburgh Review, that lent intellectual women psychological support.... Although the Ladies Diary ..., the most popular of the mathematical periodicals, encouraged women to join wit with beauty, it attracted serious amateurs of both sexes... [it] was a respectable place to pose mathematical problems and sustain debate... since there were few science periodicals in England until the 1830s, technical articles often appeared in general periodicals like the Ladies Diary. It may have been something similar that originally sparked Mrs. Somerville's interest in mathematics. At a tea party one afternoon, she recalled years later, young Mary Fairfax had been given a ladies' fashion magazine that contained a puzzle, the answer to which was given in strange symbols. These symbols turned out to be algebra. And that magazine became her introduction to the world of Euclidean geometry and number.
Baum, p. 35" Submitted to [2] (http://www.cs.yale.edu/homes/tap/Files/adalovelacenotes.html) by Linda Talisman
External links
 Sketch of The Analytical Engine Invented by Charles Babbage by L. F. Menabrea with notes upon the Memoir by the translator Ada Augusta, Countess of Lovelace (http://www.fourmilab.ch/babbage/sketch.html)
 Ada Lovelace's Notes and The Ladies Diary (http://www.cs.yale.edu/homes/tap/Files/adalovelacenotes.html)