Lam, Ho Yin Theodore. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 59-60). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Shift spaces and Symbolic Dynamical systems --- p.8 / Chapter 2.1 --- Shift spaces --- p.8 / Chapter 2.2 --- Symbolic dynamical systems --- p.10 / Chapter 3 --- β-expansion --- p.12 / Chapter 3.1 --- Expansion of real numbers --- p.12 / Chapter 3.2 --- Ergodic theory of f-expansion with independent digits --- p.16 / Chapter 3.3 --- β-expansion --- p.22 / Chapter 3.3.1 --- Ergodic theory of β-expansion --- p.22 / Chapter 3.3.2 --- Properties of β-expansion --- p.28 / Chapter 3.3.3 --- The normalizing function F(β) --- p.34 / Chapter 4 --- Symbolic Dynamics of β-expansion --- p.40 / Chapter 4.1 --- The symbolic dynamical system Sβ --- p.40 / Chapter 4.2 --- Classification of β and properties of Sβ --- p.42 / Chapter 5 --- Sizes of the classes --- p.49 / Chapter 5.1 --- Sizes of C1 and C2 --- p.49 / Chapter 5.2 --- "Sizes of C3, C4 and C5" --- p.50 / Bibliography --- p.59

Treatise (D.M.A.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

If a1, a2, . . . , an are nonnegative real numbers and fj(x) = paj + x, then f1o f2o· · · fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n ! 1 of such an expression is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the Cantor set.

In this study, problem solving provided deeper meaning and understanding through the implementation of a structured problem solving strategy with the teaching of rational numbers. This action-research study was designed as a quasi-experimental model with a control closely matched to an experimental group using similar demographics and number of economically disadvantaged students. In comparison to the control group, the experimental group received their instruction in rational numbers with the addition of a structured problem solving strategy, and a pre/posttest on problem solving with proportionality between similar geometric figures, converting fractions to percents, proportionality with a given ratio, expression of a ratio, and appropriate application of ratios. The study indicates that a structured problem solving strategy can improve the mathematical accuracy, approach and the explanation of rational numbers that are focused on rates, ratio, proportion, and percents. Results showed a statistically significant difference in the performance of these two groups. Effect sizes and 95% confidence intervals (CIs) were reported to support the findings. When examining subgroups, the study showed the structured problem solving stratey not only improved students' ability to understand and use rational numbers but also improved students' problem solving skills and their attitude towards problem solving. The experimental group showed the most improvement in the approach to solving problems with rational numbers indicating deeper understanding of rates, ratios, proportions and percents.

Thesis--Bonn. / Extra t.p. with thesis statement inserted. Includes bibliographical references (p. 39-41).

Thesis (Ph.D.)--University of Central Florida, 2009. / Adviser: Juli K. Dixon. Includes bibliographical references (p. 251-259).

Thesis (M.S.)--Mississippi State University. Department of Aerospace Engineering. / Title from title screen. Includes bibliographical references.

Thesis--Ph. D., University of Hong Kong. / Mimeographed.

Thesis (Ph. D.)--Ball State University, 2009. / Title from PDF t.p. (viewed on Feb. 08, 2010). Includes bibliographical references (p. 183-190).

Thesis (M.S.)--West Virginia University, 2003. / Title from document title page. Document formatted into pages; contains v, 30 p. Includes abstract. Includes bibliographical references (p. 29-30).