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Hamilton Mathematics Institute
Sir William Rowan Hamilton LL.D, DCL, MRIA, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the Andrews Professor of Astronomy at Trinity College Dublin, and Royal Astronomer of Ireland, living at Dunsink Observatory. Hamilton's scientific career included the study of geometrical optics, ideas from Fourier analysis, and his work on quaternions which made him one of the founders of modern linear algebra. He made major contributions in optics, classical mechanics and abstract algebra. His work was fundamental to modern theoretical physics, particularly his reformulation of Newtonian mechanics, now called Hamiltonian mechanics. It is now central both to electromagnetism and to quantum mechanics. Early life Hamilton was the fourth of nine children born to Sarah Hutton (1780–1817) and Archibald Hamilton (1778–1819),Bruno (2003) who lived in Dublin at 29 Dominick Street, later renumbered to 36. Hamilton's father, who was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dublin
Dublin (; , or ) is the capital and largest city of Republic of Ireland, Ireland. On a bay at the mouth of the River Liffey, it is in the Provinces of Ireland, province of Leinster, bordered on the south by the Dublin Mountains, a part of the Wicklow Mountains range. At the 2016 census of Ireland, 2016 census it had a population of 1,173,179, while the preliminary results of the 2022 census of Ireland, 2022 census recorded that County Dublin as a whole had a population of 1,450,701, and that the population of the Greater Dublin Area was over 2 million, or roughly 40% of the Republic of Ireland's total population. A settlement was established in the area by the Gaels during or before the 7th century, followed by the Vikings. As the Kings of Dublin, Kingdom of Dublin grew, it became Ireland's principal settlement by the 12th century Anglo-Norman invasion of Ireland. The city expanded rapidly from the 17th century and was briefly the second largest in the British Empire and sixt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system. Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics (stress, elasticity, fluid mechanics, moment of inertia, ...), electrodynamics (electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), general relativity ( stress–energy tensor, cur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Edwin Hamilton
William Edwin Hamilton (10 May 1834 – 17 March 1902) was the elder son of the Irish mathematician Sir William Rowan Hamilton and Lady Helen Maria Hamilton Bayly. Early life in Ireland William Edwin Hamilton was born at Dunsink Observatory, in the civil parish of Castleknock, Dublin. He graduated in 1857 from Trinity College Dublin and became a civil engineer, working for some years as a surveyor for railway purposes. In 1862 Hamilton left for Nicaragua with his aunt Sydney Hamilton on a venture scheme anticipating a canal project across the Isthmus of Darien. Realizing the futility of this venture, and not used to the diet and the climate, in 1864 he returned to the Observatory and lived with his parents until his father's death in 1865. In 1843 Hamilton's father had discovered the quaternions, a four-dimensional number system that extends the complex numbers, and he had published Lectures on Quaternions' in 1853. From 1858 until his death in 1865 he worked on a second book, ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cunningham Medal
The Cunningham Medal is the premier award of the Royal Irish Academy. It is awarded every three years in recognition of "outstanding contributions to scholarship and the objectives of the Academy". History It was which was established in 1796 at the bequest of barrister Timothy Cunningham of Gray's Inn. After a period of uncertainty and experimentation regarding the terms and conditions of the award, it was agreed in 1848 that the medals would be open to the authors of works or essays in the areas of Science, Polite Literature and Antiquities, published in Ireland or about Irish subjects. After 1885, the academy stopped giving the award, but it was revived in 1989 for the bicentennial of Cunningham's gift. Recipients The following persons have been awarded the Cunningham Medal: *1796: Thomas Wallace *1800: Theophilus Swift (writing, poetry) *1805: William Preston (poetry) *1818: John Brinkley (astronomy) *1827: John D'Alton (history) *1830: George Petrie (history) *1833: G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Medal
The Royal Medal, also known as The Queen's Medal and The King's Medal (depending on the gender of the monarch at the time of the award), is a silver-gilt medal, of which three are awarded each year by the Royal Society, two for "the most important contributions to the advancement of natural knowledge" and one for "distinguished contributions in the applied sciences", done within the Commonwealth of Nations. Background The award was created by George IV of the United Kingdom, George IV and awarded first during 1826. Initially there were two medals awarded, both for the most important discovery within the year previous, a time period which was lengthened to five years and then shortened to three. The format was endorsed by William IV of the United Kingdom, William IV and Victoria of the United Kingdom, Victoria, who had the conditions changed during 1837 so that mathematics was a subject for which a Royal Medal could be awarded, albeit only every third year. The conditions were chang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Guthrie Tait
Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook '' Treatise on Natural Philosophy'', which he co-wrote with Lord Kelvin, and his early investigations into knot theory. His work on knot theory contributed to the eventual formation of topology as a mathematical discipline. His name is known in graph theory mainly for Tait's conjecture. He is also one of the namesakes of the Tait–Kneser theorem on osculating circles. Early life Tait was born in Dalkeith on 28 April 1831 the only son of Mary Ronaldson and John Tait, secretary to the 5th Duke of Buccleuch. He was educated at Dalkeith Grammar School then Edinburgh Academy. He studied Mathematics and Physics at the University of Edinburgh, and then went to Peterhouse, Cambridge, graduating as senior wrangler and first Smith's prizeman in 1852. As a fellow and lecturer of his college he remai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John T
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope Joh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zerah Colburn (math Prodigy)
Zerah Colburn (September 1, 1804 – March 2, 1839) was an American child prodigy of the 19th century who gained fame as a mental calculator.W. W. Rouse Ball (1960) ''Calculating Prodigies'', in Mathematical Recreations and Essays, Macmillan, New York, chapter 13. Biography Colburn was born in Cabot, Vermont, in 1804. He was thought to be intellectually disabled until the age of six. However, after six weeks of schooling, his father overheard him repeating his multiplication tables. His father was not sure whether or not he learned the tables from his older brothers and sisters, but he decided to test him further on his mathematical abilities and discovered that there was something special about his son when Zerah correctly multiplied 13 and 97. Colburn's abilities developed rapidly and he was soon able to solve such problems as the number of seconds in 2,000 years, the product of 12,225 and 1,223, or the square root of 1,449. When he was seven years old he took six seconds to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cayley–Hamilton Theorem
In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex numbers or the integers) satisfies its own characteristic equation. If is a given matrix and is the identity matrix, then the characteristic polynomial of is defined as p_A(\lambda)=\det(\lambda I_n-A), where is the determinant operation and is a variable for a scalar element of the base ring. Since the entries of the matrix (\lambda I_n-A) are (linear or constant) polynomials in , the determinant is also a degree- monic polynomial in , p_A(\lambda) = \lambda^n + c_\lambda^ + \cdots + c_1\lambda + c_0~. One can create an analogous polynomial p_A(A) in the matrix instead of the scalar variable , defined as p_A(A) = A^n + c_A^ + \cdots + c_1A + c_0I_n~. The Cayley–Hamilton theorem states that this polynomial expression is equal to the zero matrix, which is to say tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Group
In group theory, a Dedekind group is a group ''G'' such that every subgroup of ''G'' is normal. All abelian groups are Dedekind groups. A non-abelian Dedekind group is called a Hamiltonian group. The most familiar (and smallest) example of a Hamiltonian group is the quaternion group of order 8, denoted by Q8. Dedekind and Baer have shown (in the finite and respectively infinite order case) that every Hamiltonian group is a direct product of the form , where ''B'' is an elementary abelian 2-group, and ''D'' is a torsion abelian group with all elements of odd order. Dedekind groups are named after Richard Dedekind, who investigated them in , proving a form of the above structure theorem (for finite groups). He named the non-abelian ones after William Rowan Hamilton, the discoverer of quaternions. In 1898 George Miller delineated the structure of a Hamiltonian group in terms of its order and that of its subgroups. For instance, he shows "a Hamilton group of order 2''a'' has quater ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hodograph
A hodograph is a diagram that gives a vectorial visual representation of the movement of a body or a fluid. It is the locus of one end of a variable vector, with the other end fixed. The position of any plotted data on such a diagram is proportional to the velocity of the moving particle. It is also called a velocity diagram. It appears to have been used by James Bradley, but its practical development is mainly from Sir William Rowan Hamilton, who published an account of it in the ''Proceedings of the Royal Irish Academy'' in 1846. Applications It is used in physics, astronomy, solid and fluid mechanics to plot deformation of material, motion of planets or any other data that involves the velocities of different parts of a body. See Swinging Atwood's machine Meteorology In meteorology, hodographs are used to plot winds from soundings of the Earth's atmosphere. It is a polar diagram where wind direction is indicated by the angle from the center axis and its strength by the di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of study. Basic idea In universal algebra, an algebra (or algebraic structure) is a set ''A'' together with a collection of operations on ''A''. An ''n''- ary operation on ''A'' is a function that takes ''n'' elements of ''A'' and returns a single element of ''A''. Thus, a 0-ary operation (or ''nullary operation'') can be represented simply as an element of ''A'', or a '' constant'', often denoted by a letter like ''a''. A 1-ary operation (or ''unary operation'') is simply a function from ''A'' to ''A'', often denoted by a symbol placed in front of its argument, like ~''x''. A 2-ary operation (or ''binary operation'') is often denoted by a symbol placed between its argum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
