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Saudi Elementary Mathematics Teachers’ Knowledge For Teaching Fractions, Mona Khalifah A Aladil
Saudi Elementary Mathematics Teachers’ Knowledge For Teaching Fractions, Mona Khalifah A Aladil
Dissertations
Recent reform efforts in Saudi Arabia attend to mathematics instruction with a great deal of emphasis to improve Saudi mathematics education. Studies in different countries have confirmed that teachers’ mathematical knowledge for teaching plays an important role in mathematical quality of instruction and students’ achievement (e.g., Ball, 1990; Baumert et al., 2010; Hill, Rowan, & Ball, 2005). Yet few studies about mathematics teachers’ knowledge for teaching have been conducted in the Saudi context. This study investigates Saudi elementary mathematics teachers’ knowledge for teaching in the content strand of rational numbers with an emphasis on fractions, which is an important step …
On The Local Theory Of Profinite Groups, Mohammad Shatnawi
On The Local Theory Of Profinite Groups, Mohammad Shatnawi
Dissertations
Let G be a finite group, and H be a subgroup of G. The transfer homomorphism emerges from the natural action of G on the cosets of H. The transfer was first introduced by Schur in 1902 [22] as a construction in group theory, which produce a homomorphism from a finite group G into H/H' an abelian group where H is a subgroup of G and H' is the derived group of H. One important first application is Burnside’s normal p-complement theorem [5] in 1911, although he did not use the transfer homomorphism explicitly to prove it. …
On Codes Over Rings: The Macwilliams Extension Theorem And The Macwilliams Identities, Noha Abdelghany
On Codes Over Rings: The Macwilliams Extension Theorem And The Macwilliams Identities, Noha Abdelghany
Dissertations
The MacWilliams extension theorem for code equivalence and the MacWilliams identities for weight enumerators of a code and its dual code are two of the most important results in classical coding theory. In this thesis, we study how much these two results could be extended to codes over more general alphabets, beyond finite fields. In particular, we study the MacWilliams extension theorem and the MacWilliams identities for codes over rings and modules equipped with general weight functions.
Extremal Problems On Induced Graph Colorings, James Hallas
Extremal Problems On Induced Graph Colorings, James Hallas
Dissertations
Graph coloring is one of the most popular areas of graph theory, no doubt due to its many fascinating problems and applications to modern society, as well as the sheer mathematical beauty of the subject. As far back as 1880, in an attempt to solve the famous Four Color Problem, there have been numerous examples of certain types of graph colorings that have generated other graph colorings of interest. These types of colorings only gained momentum a century later, however, when in the 1980s, edge colorings were studied that led to vertex colorings of various types, led by the introduction …