Abstract
This chapter comprises definitions, notation, and basic results related to set theory, real and complex numbers, and linear spaces.
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Notes
- 1.
Max August Zorn, German mathematician, 1906–1993.
- 2.
Greek mathematician, known as father of Geometry, born around 330 BC, presumably in Alexandria, Egypt.
- 3.
Otto Stolz, Austrian mathematician, 1842–1905; Karl Weierstrass, German, known as father of modern analysis, 1815–1897.
- 4.
Richard Dedekind, German mathematician, 1831–1916.
- 5.
Georg Cantor, German mathematician, 1845–1918; Charles Méray, French mathematician, 1835–1911.
- 6.
August-Louis Cauchy, French mathematician, engineer and physicist, 1789–1857.
- 7.
Archimedes of Syracuse, 287–212 BC.
- 8.
Bernard Bolzano, Bohemian mathematician, logician, philosopher, and theologian, 1781–1848.
- 9.
René Descartes, latinized Renatus Cartesius, French mathematician, philosopher, and scientist, 1596–1650.
- 10.
Niels Henrik Abel, Norwegian mathematician, 1802–1829.
- 11.
Viktor Y. Bunyakovsky, Russian mathematician, 1804–1889; Karl Hermann Amandus Schwarz, German mathematician, 1843–1921.
- 12.
Jorgen Pedersen Gram, Danish actuary and mathematician, 1850–1916; Erhard Schmidt, Baltic German mathematician, 1876–1959.
- 13.
Leopold Kronecker, German mathematician, 1823–1891.
- 14.
Carl Friedrich Gauss, German mathematician and physicist, 1777–1855.
- 15.
Carl Gustav Jacob Jacobi, German mathematician, 1804–1851.
- 16.
James Joseph Sylvester, English mathematician, 1814–1897.
- 17.
Charles Hermite, French mathematician, 1822–1901.
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Marsden, J.E., Hoffman, M.J.: Elementary Classical Analysis, 2nd edn. W. H. Freedman & Co., New York (1993)
Moroşanu, G.: Elements of Linear Algebra and Analytic Geometry. Matrix Rom, Bucharest (2000, in Romanian)
Rosenlicht, M.: Introduction to Analysis. Dover, New York (1968)
Rudin, W.: Principles of Mathematical Analysis, 3rd edn. McGraw-Hill, New York (1976)
Yosida, K.: Functional Analysis, 3rd edn. Springer, Berlin (1971)
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Moroşanu, G. (2019). Introduction. In: Functional Analysis for the Applied Sciences. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-27153-4_1
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