Norman Macleod Ferrers (11 August 1829 – 31 January 1903) was a British

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and university administrator and editor of a

mathematical journal In academic publishing, a scientific journal is a periodical publication designed to further the progress of science by disseminating new research findings to the scientific community. These journals serve as a platform for researchers, schola ...

Career and research

Ferrers was educated at

Eton College Eton College ( ) is a Public school (United Kingdom), public school providing boarding school, boarding education for boys aged 13–18, in the small town of Eton, Berkshire, Eton, in Berkshire, in the United Kingdom. It has educated Prime Mini ...

before studying at

Gonville and Caius College, Cambridge Gonville and Caius College, commonly known as Caius ( ), is a constituent college of the University of Cambridge in Cambridge, England. Founded in 1348 by Edmund Gonville, it is the fourth-oldest of the University of Cambridge's 31 colleges and ...

, where he was

Senior Wrangler The Senior Wrangler is the top mathematics undergraduate at the University of Cambridge in England, a position which has been described as "the greatest intellectual achievement attainable in Britain". Specifically, it is the person who achiev ...

in 1851. He was appointed to a

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at the college in 1852, was called to the bar in 1855 and was ordained

deacon A deacon is a member of the diaconate, an office in Christian churches that is generally associated with service of some kind, but which varies among theological and denominational traditions. Major Christian denominations, such as the Cathol ...

in 1859 and priest in 1860. In 1880, he was appointed Master of the college, and served as vice-chancellor of

Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

from 1884 to 1885. Ferrers made many contributions to mathematical literature. From 1855 to 1891, he worked with J. J. Sylvester as editors, with others, in publishing

The Quarterly Journal of Pure and Applied Mathematics ''The Quarterly Journal of Pure and Applied Mathematics'' was a mathematics journal that first appeared as such in 1855, but as the continuation of ''The Cambridge Mathematical Journal'' that had been launched in 1836 and had run in four volumes ...

. Ferrers assembled the papers of George Green for publication in 1871. In 1861 he published "An Elementary Treatise on Trilinear Co-ordinates". One of his early contributions was on Sylvester's development of Poinsot's representation of the motion of a rigid body about a fixed point. In 1871 he first suggested to extend the equations of motion with nonholonomic constraints. Another treatise of his on "Spherical Harmonics", published in 1877, presented many original features. In 1881, he studied Kelvin's investigation of the law of distribution of electricity in equilibrium on an uninfluenced spherical bowl and made the addition of finding the potential at any point of space in zonal harmonics. He died at the College Lodge on 31 January 1903.

Integer partitions

Ferrers is associated with a particular way of arranging the partition of a natural number ''p''. If ''p'' is the sum of ''n'' terms, the largest of which is ''m'', then the

Ferrers diagram In number theory and combinatorics, a partition of a non-negative integer , also called an integer partition, is a way of writing as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same ...

starts with a row of ''m'' dots. The terms are arranged in order, and a row of dots corresponds to each term. Adams, Ferrers, and Sylvester articulated this theorem of partitions: "The number of modes of partitioning (n) into (m) parts is equal to the number of modes of partitioning (n) into parts, one of which is always (m), and the others (m) or less than (m)." The proof, attributed to Ferrers by Sylvester in 1883, involves flipping a Ferrers diagram about a diagonal line. In 1951 Jacques Riguet adopted this manner of ordering to the rows of a

logical matrix A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets. It is an important tool in ...

. Alignment of rows of ones along the right side of a matrix is used, instead of the alignment of dots on the left. The logical matrix corresponds to a

heterogeneous relation In mathematics, a binary relation associates some elements of one set called the ''domain'' with some elements of another set called the ''codomain''. Precisely, a binary relation over sets X and Y is a set of ordered pairs (x, y), where x i ...

of Ferrers type.Jacques Riguet (1952) "Les relations de Ferrers", ''Comptes Rendus'' 232: 1729-3
pdf link at archive.org
/ref> Green-3

Family

On 3 April 1866, he married Emily, daughter of John Lamb, dean of Bristol cathedral. They had four sons and one daughter.

Bibliography

* 1861
An Elementary Treatise on Trilinear Coordinates
(London), link from

Internet Archive The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including web ...

* 1871
Mathematical papers of the late George Green
Edited By N.M. Ferrers * 1877
An elementary treatise on spherical harmonics and subjects connected with them
(London) from Internet Archive

References

External links

*
The National Archives , National Register of Archives , Person details , Archive Details
at www.nra.nationalarchives.gov.uk *http://www.macleodgenealogy.org/ACMS/D0035/I2304.html {{DEFAULTSORT:Ferrers, Norman Macleod 1829 births 1903 deaths 19th-century British mathematicians Alumni of Gonville and Caius College, Cambridge Combinatorialists Fellows of Gonville and Caius College, Cambridge Fellows of the Royal Society Masters of Gonville and Caius College, Cambridge People educated at Eton College Senior Wranglers 19th-century English Anglican priests Vice-chancellors of the University of Cambridge