Norman Macleod Ferrers

D.D. A Doctor of Divinity (D.D. or DDiv; la, Doctor Divinitatis) is the holder of an advanced academic degree in divinity. In the United Kingdom, it is considered an advanced doctoral degree. At the University of Oxford, doctors of divinity are ra ...

(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, structure, space, models, and change. History On ...

and university administrator and editor of a

mathematical journal In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. Content Articles in scientific journals are mostly written by active scientists such as s ...

Career and research

Ferrers was educated at

Eton College Eton College () is a public school in Eton, Berkshire, England. It was founded in 1440 by Henry VI under the name ''Kynge's College of Our Ladye of Eton besyde Windesore'',Nevill, p. 3 ff. intended as a sister institution to King's College, C ...

before studying at

Gonville and Caius College, Cambridge Gonville and Caius College, often referred to simply as Caius ( ), is a constituent college of the University of Cambridge in Cambridge, England. Founded in 1348, it is the fourth-oldest of the University of Cambridge's 31 colleges and one of th ...

, where he was

Senior Wrangler The Senior Frog 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 a ...

in 1851. He was appointed to a

Fellowship A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

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 churches, such as the Catholic Churc ...

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

Cambridge University , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

from 1884 to 1885. Ferrers made many contributions to mathematical literature. From 1855 to 1891 he worked with

J. J. Sylvester James Joseph Sylvester (3 September 1814 – 15 March 1897) was an English mathematician. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics. He played a leadership ...

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 b ...

. 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. His another treatise 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 Partition may refer to: Computing Hardware * Disk partitioning, the division of a hard disk drive * Memory partition, a subdivision of a computer's memory, usually for use by a single job Software * Partition (database), the division of a ...

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 positive 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 part ...

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 Jacques Riguet (1921 to October 20, 2013) was a French mathematician known for his contributions to algebraic logic and category theory. According to Gunther Schmidt and Thomas Ströhlein, "Alfred Tarski and Jacques Riguet founded the modern calc ...

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. Matrix representation ...

. 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 elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over sets and is a new set of ordered pairs consisting of elements in and in ...

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 digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...

* 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