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Manuscript of De Morgan's introductory lecture delivered at the opening of classes in mathematics at University College London on 5 November 1828. Appended are notes for another lecture.

Mathematical fragments, letters, and papers.

Twenty-three manuscript notebooks on mathematical statistics which include 'The theory of deviation from an average', the introduction to 'An algebra of evolution', and 'Problems relating to the mathematical treatment of statistics: periodicity and deviation'.

3 letters from John Thomas Graves of 29 Grosvenor Place, Cheltenham to Augustus De Morgan, 28 Jan, 4 Feb and 4 Jun 1853. Relating to the works of Simon Stevin and other mathematical literature.

Autograph, with signature.

Letter from Wililam Wallace to Rev George Peacock, Dean of Ely, [1833]. Describing Wallace's part in the introduction of foreign mathematical notation to England and 'the Reformation .... the the Mathematical science in Britain'.

Autograph, with signature. Headed 'First Copy'. Inscribed in another hand: 'Found among Mr Thomas Galloway's papers'.

Papers of Professor Andrew Russell Forsyth, [1898-1921], comprising papers and lectures concerning mathematics, notably relating to Abels theorem, Abelian functions, binary forms, quintic equations and other modular functions, Fourier's and other series, algebraic functions, 1909, differential equations of mathematical physics, 1917-1921, elements of theory of functions, 1915-1916, elliptic functions, 1898, 1914-1915, spherical harmonic series, expansion in polynomials, expansion theorems, solid geometry, differential equations of dynamics.

Notebooks and papers of Benjamin Robins, consisting of a miscellaneous notebook primarily on gunnery and fortification (MS 39), a commonplace book (MS 46), a box of miscellaneous papers (MS 130) and a letter to Martin Folkes enclosing a written message from the Chevalier Ossorio, Envoy from the King of Sardinia, on the proper charge of cannon (MS 139).

Student's notes on lectures on Algebraic Geometry and the Calculus, given by Augustus De Morgan at University College London from 11 March to 13 May 1847.

Augustus De Morgan's mathematical tracts, copied by John Power Hicks from the original manuscripts in the Library of University College London.

Papers, 1840-1972, of and relating to Karl Pearson, comprising personal and family papers, 1844-1937 (Ref: 1-45); lectures and lecture notes, 1874-1972 (Ref: 46-84); papers relating to literary and scientific work [1870]-1936 (Ref: 85-229); papers relating to the history of the Department of Applied Statistics, University College London, 1895-1936 (Ref: 230-258); papers relating to the work of the Department of Statistics and of Pearson's colleagues, 1895-1962 (Ref: 267-346); papers relating to the journal Biometrika, 1900-1954 (Ref: 347-570); papers relating to Pearson's The life, letters and labours of Francis Galton, 1840-1931 (Ref: 571-598); papers relating to Pearson's wartime research (1914-1918), 1905-1923 (Ref: 599-612); acquired papers, 1842-1923 (Ref: 613-623); general correspondence [1843-1972] (Ref: 624-933). The collection also includes papers of Walter Frank Raphael Weldon (Jodrell Professor of Zoology and Comparative Anatomy at University College London), 1860-1935 (Ref: 259-266).

Letters of thanks from Augustus De Morgan to F Hendriks for sending him certain pamphlets and publications.

Undated lecture notes on geometry: two closely written sheets pasted onto an otherwise unused notebook.

'Elements of statics', a volume written for publication at the proposal of the Society for the Diffusion of Useful Knowledge, though it was never actually published. De Morgan used it as evidence of his work and knowledge when applying for the Mathematics Chair at University College London in 1827.

Some correspondence, papers, notebooks and publications of Sir James Hopwood Jeans. Early manuscripts in the series relate to Jean's education at Trinity College, Cambridge, in the form of early lecture notebooks, largely on mathematical topics. A collection of letters, 1901-1907, documents his treatment for tuberculosis at Ringwood Sanatorium, where he completed work on the theory of gases; correspondents included G H Hardy and Adam Sedgewick among others. Jean's engagements in popularizing science are represented by proofs and typescript of lectures and essays, especially those written for the BBC, 1934-1935, together with associated letters and press cuttings. The series contains collections of offprints, reprints, and extracts of published works by Jeans and others, notably from the Philosophical Transactions and the Philosophical Magazine.

The correspondence of Sir John William Lubbock, providing information on a wide range of Lubbock's contemporaries, not exclusively in the field of science. The largest collections of scientific letters are from George Biddell Airy (113 letters), John George Children (128 letters), Joshua Alwyn Compton, 2nd Marquis of Northampton (98 letters), G P D de Pontecoulant (67 letters) and William Whewell (87 letters). There are smaller but no less important groups of letters from Charles Babbage, Francis Baily, Francis Beaufort, Charles Darwin, John Couch Adams, J F W Herschel, Baden Powell and W H F Talbot.

Papers, 1931-1947, relating to the literary work of Ethel Maud Rowell, including offprints of published essays in journals such as the Hibbert Journal, The aryan path and Philosophy, as well as a published copy of her book Time and Time again: essays on various subjects (Allen and Unwin, London, 1941); newspaper cuttings comprising reviews of Rowell's published works, notably Time and Time again; typescripts and manuscripts of essays, stories and poems by Rowell. Correspondence, 1908-1954, relating to publication of Rowell's work, both before and after her death in 1951, including correspondence, 1951-1954, between Professor Elizabeth Marianne Blackwell, Head of the Botany Department at Royal Holloway College, and various publishing firms, concerning the possibility of the posthumous publication of 'Of memory and some other matters', a second collection of essays by Rowell. Miscellaneous documents relating to Rowell, notably a copy of a letter from the Rev Charles Lutwidge Dodgson (Lewis Carroll), 1895 and photographs of Rowell and other staff at Royal Holloway College, [1907-1939].

Archives of the London Mathematical Society, 1853-1994, the bulk comprising c500 letters to Thomas Archer Hirst, 1853-1892, mainly in his capacity as a member of the LMS, including a letter inviting him to the first meeting of the Society, and also reflecting his travels in Europe, including letters from prominent European mathematicians. The letters include several from Henry M Bompas, 1865, 1874-1879; Arthur Cayley, 1858-1891 and undated; Michel Chasles, 1858-1871 and undated; Luigi Cremona, 1864-1892 and undated; Augustus De Morgan, 1861-1869; Georges-Henri Halphen, 1875-1879; Amédée Mannheim, 1866-1891; Julius Plücker, 1866-1868; William Roberts, 1859-1865 and undated; George Salmon, 1858-1878; [Hermann Cäsar Hannibal?] Schubert, 1877-1884; Henry John Stephen Smith, 1865-1876 and undated; William Spottiswoode, 1862, 1865, 1883; Cyparissos Stephanos, 1877-1887; Rudolf Sturm, 1874-1892; James Joseph Sylvester, 1859-1888 and undated; Barnaba Tortolini, 1858-1863; Richard Townsend, 1865-1878; John Van Voorst, 1864-1867; and there are a few letters from Hirst himself. The archive also includes a bound notebook containing a manuscript catalogue of the LMS library by R A Sampson, 1891-1893; miscellaneous administrative correspondence and papers, 1964-1975; membership lists, 1966-1972; binder of papers of H T J Norton on mathematics, with correspondence, largely to E H Neville, regarding their disposition in the LMS archive in c1938, and also including bibliographical material on elliptic functions, apparently compiled by Neville [1930s-1950s]; miscellaneous letters and papers on research, 1986, 1992-1994.

Undated mathematical fragments.

Notes for an introductory lecture in the Faculty of Arts and Laws at University College London.

Eight letters from Sylvester to his niece, Contessa Edith Gigliucci, 1865-1896, and two letters to Count Mario Gigliucci, 1896.

Papers relating to the history of the De Morgan family: genealogical notes, family trees, etc. Includes cuttings from newspapers, periodicals, and several letters.

Correspondence between Augustus De Morgan and George Boole, Professor of Mathematics at Queen's College Cork, dated 1842-1864. The collection also includes letters from John Stuart Mill, and letters from various correspondents mostly dated 1846-1848.

Letter from Matthew Collins of 40 Upper Pitt Street, Liverpool to Augustus De Morgan, 8 Apr 1853. Covering note, enclosing a pamphlet, On Clairaut's theorem ... (1853).

Autograph, with signature. A note in De Morgan's hand states that the content of the pamphlet, published in the Cambridge and Dublin Mathematical Journal, new series vol IX (1854), were plagiarized from a lecture given by Mr James MacCullagh in 1846.

Mathematical and scientific papers of George Boole.

Correspondence between De Morgan and Sophia Frend (two items), 1836 and undated; letter from De Morgan to Sir Jonathan Pollock, 1865; miscellaneous undated verses.

Papers of Professor Albrecht Fröhlich, 1916-2001, reflecting his mathematical research, publications and correspondence with colleagues. Papers are divided into six sections comprising biographical papers; research papers; publications; papers relating to visits, conferences and lectures; correspondence and theses and examinations.

Biographical papers include obituaries, memoirs and papers relating to memorials including a service in the Chapel of Robinson College Cambridge, 10 Feb 2002; autobiographical papers including copy of Fröhlich's entry for Personal Records of Fellows of the Royal Society; papers relating to Fröhlich's career, honours and awards including his Ph.D. thesis 'On some topics in the theory of representation of groups and in class field theory', and correspondence and papers relating to his university appointments and some of his principal honours, including election to the Fellowship of the Royal Society.

Research papers chiefly comprise mathematical workings, notes and drafts: notably relating to work on the decomposition of primes [1950] and work on Galois module theory and Gauss sums.

Publications comprise published material by Fröhlich, 1950-2000, drafts and unpublished drafts, including work with Charles Terence Clegg Wall on Brauer groups, 'Galois modules and the functional equation', and draft of a longer text entitled 'mathematical theory of ostensive and consequently of empirical predicates'.

Visits, conferences and lectures include papers relating to Fröhlich's conference attendance and overseas visits 1956-1998, documentation of his participation in mathematics meetings held at the Mathematisches Forschungsinstitut, Oberwolfach, Germany and papers relating to Visiting Professorships, including invitations, programmes, and texts or abstracts of lectures.

Correspondence,1950-2000, on subjects including progress of Fröhlich's research, discussions of problems with mathematical workings and drafts of papers. Notable correspondents include Fröhlich's Ph.D. supervisor Hans Arnold Heilbronn, colleagues Jean-Pierre Serre, Olga Taussky-Todd, Stephen Virgil Ullom and Charles Terence Clegg Wall, and former research students Colin J. Bushnell, Martin J. Taylor and Stephen Mark Johnson Wilson.

Theses and examinations comprise, theses of Ph.D. students supervised or examined by Fröhlich, including his research students at King's College London and examination papers, some with Fröhlich's manuscript calculations of answers, 1980-1990.