Summary, paraphrase, and quotation.

This is primarily a list of Greatest Mathematicians of the Past, but I use birth as an arbitrary cutoff, and two of the "Top " are still alive now. Click here for a longer List of including many more 20th-century mathematicians. Click for a discussion of certain omissions.

Please send me e-mail if you believe there's a major flaw in my rankings or an error in any of the biographies.

Obviously the relative ranks of, say Fibonacci and Ramanujan, will never satisfy everyone since the reasons for their "greatness" are different. I'm sure I've overlooked great mathematicians who obviously belong on this list. Please e-mail and tell me! Following are the top mathematicians in chronological birth-year order.

By the way, the ranking assigned to a mathematician will appear if you place the cursor atop the name at the top of his mini-bio. Earliest mathematicians Little is known of the earliest mathematics, but the famous Ishango Bone from Early Stone-Age Africa has tally marks suggesting arithmetic.

The markings include six prime numbers 5, 7, 11, 13, 17, 19 in order, though this is probably coincidence. The advanced artifacts of Egypt's Old Kingdom and the Indus-Harrapa civilization imply strong mathematical skill, but the first written evidence of advanced arithmetic dates from Sumeria, where year old clay tablets show multiplication and division problems; the first abacus may be about this old.

By years ago, Mesopotamian tablets show tables of squares, cubes, reciprocals, and even logarithms and trig functions, using a primitive place-value system in base 60, not Babylonians were familiar with the Pythagorean Theorem, solutions to quadratic equations, even cubic equations though they didn't have a general solution for theseand eventually even developed methods to estimate terms for compound interest.

The Greeks borrowed from Babylonian mathematics, which was the most advanced of any before the Greeks; but there is no ancient Babylonian mathematician whose name is known. Also at least years ago, the Egyptian scribe Ahmes produced a famous manuscript now called the Rhind Papyrusitself a copy of a late Middle Kingdom text.

It showed simple algebra methods and included a table giving optimal expressions using Egyptian fractions.

Today, Egyptian fractions lead to challenging number theory problems with no practical applications, but they may have had practical value for the Egyptians. The Pyramids demonstrate that Egyptians were adept at geometry, though little written evidence survives.

Babylon was much more advanced than Egypt at arithmetic and algebra; this was probably due, at least in part, to their place-value system. But although their base system survives e.

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The Vedics understood relationships between geometry and arithmetic, developed astronomy, astrology, calendars, and used mathematical forms in some religious rituals.

The earliest mathematician to whom definite teachings can be ascribed was Lagadha, who apparently lived about BC and used geometry and elementary trigonometry for his astronomy. Apastambha did work summarized below; other early Vedic mathematicians solved quadratic and simultaneous equations.

Other early cultures also developed some mathematics. The ancient Mayans apparently had a place-value system with zero before the Hindus did; Aztec architecture implies practical geometry skills. Ancient China certainly developed mathematics, in fact the first known proof of the Pythagorean Theorem is found in a Chinese book Zhoubi Suanjing which might have been written about BC.

Thales may have invented the notion of compass-and-straightedge construction. Several fundamental theorems about triangles are attributed to Thales, including the law of similar triangles which Thales used famously to calculate the height of the Great Pyramid and "Thales' Theorem" itself: The other "theorems" were probably more like well-known axioms, but Thales proved Thales' Theorem using two of his other theorems; it is said that Thales then sacrificed an ox to celebrate what might have been the first mathematical proof in Greece.

Thales was also an astronomer; he invented the day calendar, introduced the use of Ursa Minor for finding North, invented the gnomonic map projection the first of many methods known today to map part of the surface of a sphere to a plane, and is the first person believed to have correctly predicted a solar eclipse.

His theories of physics would seem quaint today, but he seems to have been the first to describe magnetism and static electricity.Homework is Silly - Homework has been an integral part of education since children started to be educated.

Recently however, homework has begun to be assigned more and more often to students, especially in the United States, as it has begun to fall further and further behind countries like China, Singapore, and Japan.

denotes the number of subsequences T of S having sum σ(T) = g and length |T| = k (counted with the multiplicity of their appearance in S). Then N g (S) = X k≥0 Nk(S), and N+(S) = X k≥0 N2k(S) resp. N−(S) = X k≥0 N2k+1(S) denote the number of subsequences T of S having sum σ(T) = .

There are a number of RNNs, but it is the LSTM that delivers on the promise of RNNs for sequence prediction.

It is why there is so much buzz and application of LSTMs at the moment. DOWNLOAD SEQUENCE FOR ACADEMIC WRITING 5TH EDITION sequence for academic writing pdf Journal of Instructional Pedagogies Supporting the development, page 4 ROLE OF WRITING IN THE mathematicians and number enthusiasts since well before BC when Pythagoras wrote about his famous "theorem".

The Hundred Greatest Mathematicians of the Past. This is the long page, with list and biographies. (Click here for just the List, with links to the tranceformingnlp.com Click here for a . In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and order matters. found in WPA: Writing Program Administration /2 (): ) A Sequence for Academic Writing’s approach provides students with ample practice in those areas that the WPA has identified as important outcomes: rhetorical knowledge; critical thinking, reading and writing; writing as a process; and knowledge of conventions.

At some point a longer list will become a List of Great Mathematicians rather than a List of Greatest Mathematicians. I've expanded my original List of Thirty to an even Hundred, but you may prefer to reduce it to a Top Seventy, Top Sixty, Top Fifty, Top Forty or Top Thirty list, or even Top Twenty, Top Fifteen or Top Ten List.

A3: Accurate, Adaptable, and Accessible Error Metrics for Predictive Models: abbyyR: Access to Abbyy Optical Character Recognition (OCR) API: abc: Tools for.

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Sequence - Wikipedia