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Thesis (Ed.D.)--Boston University.

The aim of this research was to look at the strategies used by children when doing mental addition problems of the varying levels of complexity. An authentic arithmetic task was designed for use in a school environment. The central aim was to study developing fluency in mental arithmetic as achieved through recruiting various strategies into solving more complex problems than those studied by existing research. The nature of mental addition strategies was inferred from children's solution times when doing sequences of sums. Three studies were carried out on 7-11 year-old children from two local schools.

Thesis (Ed.M.)--Boston University

In many areas of engineering and applied mathematics, spectral methods provide very powerful tools for solving and analyzing problems. For instance, large to extremely large sizes of numbers can efficiently be multiplied by using discrete Fourier transform and convolution property. Such computations are needed when computing π to millions of digits of precision, factoring and also big prime search projects. When it comes to the utilization of spectral techniques for modular operations in public key cryptosystems two difficulties arise; the first one is the reduction needed after the multiplication step and the second is the cryptographic sizes which are much shorter than the optimal asymptotic crossovers of spectral methods. In this dissertation, a new modular reduction technique is proposed. Moreover, modular multiplication is given based on this reduction. These methods work fully in the frequency domain with some exceptions such as the initial, final and partial transformations steps. Fortunately, the new technique addresses the reduction problem however, because of the extra complexity coming from the overhead of the forward and backward transformation computations, the second goal is not easily achieved when single operations such as modular multiplication or reduction are considered. On the contrary, if operations that need several modular multiplications with respect to the same modulus are considered, this goal is more tractable. An obvious example of such an operation is the modular exponentiation i.e., the computation of c=m[superscript e] mod n where c, m, e, n are large integers. Therefore following the spectral modular multiplication operation a new modular exponentiation method is presented. Since forward and backward transformation calculations do not need to be performed for every multiplication carried during the exponentiation, the asymptotic crossover for modular exponentiation is decreased to cryptographic sizes. The method yields an efficient and highly parallel architecture for hardware implementations of public-key cryptosystems. / Graduation date: 2006

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 149-169).

Thesis (Ph. D.)--Lehigh University, 2001. / Includes vita. Includes bibliographical references (leaves 131-141).

Thesis (M.S.)--Central Connecticut State University, 2003. / Thesis advisor: Philip Halloran. " ... in partial fulfillment of the requirements for the degree of Master of Science in Mathematics." Includes bibliographical references (leaves 36-41). Also available via the World Wide Web.

Thesis (Ph. D.)--University of Adelaide, Dept. of Pure Mathematics, 1985. / Includes bibliographical references (leaves 121-123).

Thesis (Ph. D.)--University of Toronto, 2007. / Source: Dissertation Abstracts International, Volume: 68-06, Dec 2007. Includes bibliographical references (leaves 193-209).