nLab Fred Richman

• MathGenealogy page

 Selected writings

See also the archive of Fred Richman’s Documents.

On constructive algebra:

• Ray Mines, Fred Richman, Wim Ruitenburg: A Course in Constructive Algebra, Springer (1988) [doi:10.1007/978-1-4419-8640-5]

On the fundamental theorem of algebra in constructive mathematics:

• Fred Richman, The fundamental theorem of algebra: a constructive development without choice. Pacific Journal of Mathematics 196 1 (2000) 213–230 [doi:10.2140/pjm.2000.196.213, pdf]

On constructive mathematics:

• Fred Richman, Constructive Mathematics without Choice,

  in: Reuniting the Antipodes – Constructive and Nonstandard Views of the Continuum, Synthese Library 306, Springer (2001) 199-206 [doi:10.1007/978-94-015-9757-9_17]

On the real numbers in constructive mathematics:

• Fred Richman, Real numbers and other completions, Mathematical Logic Quarterly 54 1 (2008) 98-108 [doi:10.1002/malq.200710024]

On algebraic functions on the real numbers:

• Fred Richman, Algebraic functions, calculus style. Communications in Algebra, Volume 40, Issue 7, July 2012, Pages 2671-2683 [doi:10.1080/00927872.2011.584337]

On a division algorithm for polynomials over reduced local rings:

• Fred Richman, A division algorithm. Journal of Algebra and Its Applications, Vol. 04, No. 04, pp. 441-449 (2005) [doi:10.1142/S0219498805001289]

On weak countable choice:

• Fred Richman, Douglas Bridges, Peter Schuster, A weak countable choice principle. Proceedings of the American Mathematical Society 128(9):2749-2752, March 2000. [doi:10.1090/S0002-9939-00-05327-2]

On whether 0.999… equals 1:

• Fred Richman, Is 0.999… = 1?. Mathematics Magazine, Volume 72, Issue 5, 1999, Pages 396-400, [doi:10.1080/0025570X.1999.11996777]

On Laurent series of real numbers:

• Fred Richman, Laurent series over $\mathbb{R}$. Communications in Algebra, Volume 48, Issue 5, 11 Jan 2020 Pages 1982-1984 [doi:10.1080/00927872.2019.1710166]

On polynomials and linear transformations:

• Fred Richman, Polynomials and linear transformations. Linear Algebra and its Applications, Volume 131, 1 April 1990, Pages 131-137. [doi:10.1016/0024-3795(90)90379-Q]

On uniform continuity and the fan theorem:

• William H. Julian, Fred Richman, A uniformly continuous function on [0,1] that is everywhere different from its infimum, Pacific Journal of Mathematics, 111(2), 1984, pp. 333–340. (10.2140/pjm.1984.111.333)

category: people