He joined Konigsberg where he learned under Friedrich Richelot and Franz Neumann both former students of Jacobi. Despite Jacobis death ten years ago, Weber started his studies and his contributions were very influential. Most of Webers work was derived from Jacobis style of mathematics. Another potential student who made significant contributions was Wangerin who studied for his doctorate around the same period Weber developed his rehabilitation from (http://www-groups. dcs. st-and. ac. uk/history/Chronology/index. html).
In 1866, Weber became a privatdozent at Heidelberg at the same time his habilitation was adopted. He then spent the next twenty five years teaching at various universities. In Zurich he taught at the university of Konigsberg and Eidgenossische Polytechnikum. In Charlottenburg he taught at Technische Hochschule. The last post was in Strasbourg in the year 1895. Weber mainly concentrated in algebra, number theory which involved analysis and applications of analysis to mathematical physics.
Much of Webers work can be characterized by its contributions to different varieties of topics. To a certain point most of his influences can be attributed to other colleagues who worked by his side. The tremendous development in the applications to mathematical physics was made possible from Franz Neumanns input in Konigsberg. Although, Jacobis influence can not be left out particularly those from teacher Friedrich Richelot, which enabled Weber to make commendable progress on algebraic functions.
Weber is best known for his text Lehrbuch der Algebra documented in 1895 and other contributions in number theory and algebra (Kline, 1990, p. 43). Erik Ivar Fredholm is another person who is greatly acknowledged for his contributions on integral equations and spectral theory. Born in Klara at Stockholm City, Fredholm grew to be a very brilliant student at the Beskowska School in Stockholm and on 16th may 1885 he was presented with the baccalaureate. Just after the award, Fredholm joined the Royal Technological institute in Stockholm.
After completing his period at Royal Technological Institute, Fedholm joined the University of Uppsala. It was in Uppsala that he got his Masters of Science degree in the year 1888. Fedholms first publication was on a special class of functions while at the Royal Swedish Academy in the year 1890. On 30th May 1893 and 31st May 1898 he was awarded a PhD and a degree from the University of Uppsala respectively. Fredholms work quickly spread around the world when Holmgren made presentation in 1901 on the Fredholms theory at Gottingen.
Hilbert noted the significant of Fredholms theory, and on the first quarter of the 20th century, the theory of integral equations became a core research topic from (http://www-groups. dcs. st-and. ac. uk/history/Chronology/index. html). He documented papers with extra care and attention thereby producing high quality work. Fedholm was greatly commended for his work through out Europe. He had also studied actuarial science and most of his time was passed studying many questions surrounding this area. As a young boy he enjoyed playing flute and later started playing the violin.
He was able to incorporate his mathematical skills to music and mathematics. Until his death he was developing the mathematics of the acoustics of the violin, although today, his unfinished work still remains a mystery (Stanford, 1995, p. 67).
Index for the Chronology. Retrieved on 30th January 2009 from http://www-groups. dcs. st-and. ac. uk/history/Chronology/index. html Kline Morris, 1990, Mathematical thought from ancient to Modern Times, Oxford, Oxford University Press; pp. 43 Sandford R. Mariellen, 1995, Happenings and Other Acts. London: Routledge; pp. 67