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.

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.

Letter from Michel Chasles of Paris to Augustus De Morgan, 8 Apr 1848. On algebraical formulae.

Autograph, with signature.

Scientific and other papers sent to the Royal Society, presented at meetings of Fellows, or commissioned by the Society. They form a complementary series to the Early Letters, both of which were superseded by the Letters and Papers. Many of these items, referred to as the 'Guard Books', are duplicated in the Register Book of the Society. The classification is a simplified form of the 'Philosophical Transactions' abridgment by John Lowthorp. This arrangement was completed in 1741 by Thomas Birch. The majority of the papers in these volumes are manuscript, but a few printed documents occur throughout the series. Some of the papers are earlier in date than the grant on 15 July 1662 of the First Charter to the Society. The Committee of Trades seems to have been associated with the earlier meetings of those philosophers who subsequently became Fellows, and produced a number of practical papers, some of which were written in 1639 and which are mostly found in Volume 3(i). There are still earlier documents, mostly in Volume 25, which may have been included in the gift, in 1667, of the Arundel Library.

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.

Letter from Baldassarre Boncompagni-Ludovisi, 1856 to [To Augustus De Morgan], asking for a copy of 'The Elements of the Mathematical art commonly called Algebra, expounded in two books, by John Kersey. 1717'.