To see the other types of publications on this topic, follow the link: Mathematics-Geometry.
Dissertations / Theses on the topic 'Mathematics-Geometry'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Mathematics-Geometry.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Ho, Chiu-chi. "The use of computer software in geometry learning." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20135944.
Full text
2
Le, Tuan Anh. "Applying realistic mathematics education in Vietnam teaching middle school geometry /." [S.l.] : [s.n.], 2007. http://opus.kobv.de/ubp/volltexte/2007/1348.
Full text
3
Le, Tuan Anh. "Applying realistic mathematics education in Vietnam : teaching middle school geometry." Phd thesis, Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2007/1348/.
Full textAbstract:
Since 1971, the Freudenthal Institute has developed an approach to mathematics education named Realistic Mathematics Education (RME). The philosophy of RME is based on Hans Freudenthal’s concept of ‘mathematics as a human activity’. Prof. Hans Freudenthal (1905-1990), a mathematician and educator, believes that ‘ready-made mathematics’ should not be taught in school. By contrast, he urges that students should be offered ‘realistic situations’ so that they can rediscover from informal to formal mathematics.
Although mathematics education in Vietnam has some achievements, it still encounters several challenges. Recently, the reform of teaching methods has become an urgent task in Vietnam. It appears that Vietnamese mathematics education lacks necessary theoretical frameworks. At first sight, the philosophy of RME is suitable for the orientation of the teaching method reform in Vietnam. However, the potential of RME for mathematics education as well as the ability of applying RME to teaching mathematics is still questionable in Vietnam. The primary aim of this dissertation is to research into abilities of applying RME to teaching and learning mathematics in Vietnam and to answer the question “how could RME enrich Vietnamese mathematics education?”. This research will emphasize teaching geometry in Vietnamese middle school.
More specifically, the dissertation will implement the following research tasks:
• Analyzing the characteristics of Vietnamese mathematics education in the ‘reformed’ period (from the early 1980s to the early 2000s) and at present;
• Implementing a survey of 152 middle school teachers’ ideas from several Vietnamese provinces and cities about Vietnamese mathematics education;
• Analyzing RME, including Freudenthal’s viewpoints for RME and the characteristics of RME;
• Discussing how to design RME-based lessons and how to apply these lessons to teaching and learning in Vietnam;
• Experimenting RME-based lessons in a Vietnamese middle school;
• Analyzing the feedback from the students’ worksheets and the teachers’ reports, including the potentials of RME-based lessons for Vietnamese middle school and the difficulties the teachers and their students encountered with RME-based lessons;
• Discussing proposals for applying RME-based lessons to teaching and learning mathematics in Vietnam, including making suggestions for teachers who will apply these lessons to their teaching and designing courses for in-service teachers and teachers-in training.
This research reveals that although teachers and students may encounter some obstacles while teaching and learning with RME-based lesson, RME could become a potential approach for mathematics education and could be effectively applied to teaching and learning mathematics in Vietnamese school.Seit 1971 wurde an dem renommierten Freudenthal Institut in Utrecht ein als Realistic Mathematics Education (RME) bezeichneter mathematikdidaktischer Ansatz entwickelt. Die Philosophie von RME beruht auf Hans Freudenthals Auffassung von Mathematik als menschlicher Aktivität. Der Mathematiker und Didaktiker Prof. Hans Freudenthal (1905 – 1990) plädierte dafür, dass Mathematik an den Schulen nicht als Fertigprodukt unterrichtet werden sollte. Im Gegensatz dazu forderte er, den Schülern an ‚realistischen’ Situationen nicht-formale und formale Mathematik wieder entdecken zu lassen. Obwohl die mathematische Schulbildung in Vietnam in den letzten Jahrzehnten schon einige Fortschritte gemacht hat, steht sie noch vor großen Herausforderungen. Derzeit ist die Reform der Unterrichtsmethoden eine dringliche Aufgabe in Vietnam. Augenscheinlich ermangelt es der Mathematikdidaktik in Vietnam an dem dazu notwendigen theoretischen Rahmen. Die Philosophie von RME eignet sich grundsätzlich als Orientierung für die Reform der Unterrichtsmethoden in Vietnam. Allerdings ist die Potenz von RME für die mathematische Schulbildung in Vietnam und die Möglichkeiten, RME im Mathematikunterricht anzuwenden, noch zu klären. Das Hauptziel dieser Arbeit war zu erforschen, wie RME beim Mathematik-Lernen und -Lehren in Vietnam eingesetzt werden kann und die Frage zu beantworten: Wie kann RME den Mathematikunterricht in Vietnam bereichern? Dazu wurde insbesondere der Geometrieunterricht in der Sekundarstufe I betrachtet. Im Einzelnen beinhaltet die Untersuchung: • eine Analyse der vietnamesischen Mathematikdidaktik in der ‘Reformperiode’ (etwa von 1980 bis 2000) • die Konzeption, Durchführung und Auswertung einer Befragung von 152 Mittelschullehrern aus verschiedenen vietnamesischen Provinzen und Städten zum Mathematikunterricht in Vietnam • eine Analyse von RME einschließlich der Freudenthalschen Sicht von RME und der Charakteristika von RME • die Diskussion, wie man RME-basierten Unterrichtseinheiten gestalten und diese in den Mathematikunterricht in Vietnam integrieren kann • Test solcher Einheiten in vietnamesischen Mittelschulen • Analyse der Rückmeldungen anhand der Schülerarbeitsblätter und der Lehrerberichte • Diskussion der Chancen und Probleme von RME-basierten Unterrichtseinheiten im Geometrieunterricht vietnamesischer Mittelschulen • Diskussion von Vorschläge zur Entwicklung und zum Einsatz RME- basierter Unterrichtseinheiten in Vietnam, einschließlich von Hinweisen für Lehrende und der Konzeption von Ausbildungs- und Fortbildungskursen zu RME Die Untersuchung zeigt, dass – obwohl Lehrer wie Schüler zunächst einige Hindernisse beim Lehren und Lernen mit RME- basierten Unterrichtseinheiten zu bewältigen haben werden – RME ein mächtiger mathematikdidaktischer Ansatz ist, der wirkungsvoll im Lehren und Lernen von Mathematik in vietnamesischen Schulen angewandt werden kann.
4
Snead, Cynthia. "Development of computer graphics materials for teaching topics in informal geometry to high school remedial mathematics classes /." Access Digital Full Text version, 1987. http://pocketknowledge.tc.columbia.edu/home.php/bybib/10779334.
Full text
5
Porter, Leon K. "Critical reflective thinking in Euclidean geometry for grade nine mathematics students /." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0001/MQ42423.pdf.
Full text
6
Strassfeld, Brenda Carol. "An investigation about high school mathematics teachers' beliefs about teaching geometry." Thesis, University of Plymouth, 2008. http://hdl.handle.net/10026.1/1701.
Full textAbstract:
There continues to exist a dilemma about how, why and when geometry should be taught. The aim of this study was to examine high school mathematics teachers' beliefs about geometry and its teaching with respect to its role in the curriculum, the uses of manipulatives and dynamic geometry software in the classroom, and the role of proofs. In this study belief is taken as subjective knowledge (Furinghetti and Pehkonen, 2002). Data were collected from 520 teachers using questionnaires that included both statements that required responses on a Likert scale and open-ended questions. Also an intervention case study was conducted with one teacher. A three factor solution emerged from the analysis that revealed a disposition towards activities, a disposition towards an appreciation of geometry and its applications and a disposition towards abstraction. These results enabled classification of teachers into one of eight groups depending on whether their scores were positive or negative on the three factors. Knowing the teacher typology allows for appropriate professional development activities to be undertaken. This was done in the case study where techniques for scaffolding proofs were used as an intervention for a teacher who had a positive disposition towards activities and appreciation of geometry and its applications but a negative disposition towards abstraction. The intervention enabled the teacher successfully to teach her students how to understand and construct proofs. The open-ended responses on the questionnaire were analysed to obtain a better understanding of the teachers' beliefs. Four themes, the formal, intuitive, utilitarian and the mathematical, emerged from the analysis, which support the modal arguments given by Gonzalez and Herbst (2006). The findings reveal a disconnect between some high school teachers' beliefs about why geometry is important to study and the current position of the Standards Movement; and between whether geometry should be taught as part of an integrated curriculum or as a one-year course.
7
Gardiner, John. "Dynamic geometry, construction and proof : making meaning in the mathematics classroom." Thesis, Sheffield Hallam University, 2002. http://shura.shu.ac.uk/6479/.
Full textAbstract:
The overall aim of this study was to investigate mathematical meaning making in relation to the areas of construction and proof through the use of a dynamic geometry environment (Cabri II as available on the TI 92 calculator). The experimental work was carried out with 11-14 year old pupils in four schools in the North of England between 1996 and 1999. The research involved working with whole classes and a range of groups of varying sizes. The research methodologies adopted were drawn from various areas (an approach advocated as suitable for classroom research by Klafid, 1998). The researcher acted as both teacher and participant observer. The study was conducted over several cycles, with previous cycles of analysis and reference to the literature being used to inform subsequent stages. After a pilot phase when recording methods and technical approaches were clarified, there were four cycles of investigation. Data collection was by means of participant observation, with audio recording of dialogue. Screens generated by pupils were recorded in field notes. There was emphasis from the outset of the study to relate the findings to classroom practice. This led to a consideration as an ongoing part of the study, of ideas of classroom and group dynamics and how these could be combined with, and related to, the use of the technology. The study illuminated two key areas; the processes of immediate individual and group meaning making and wider aspects of social dynamics in the mathematics classroom. Socio-cultural analysis of classroom and group discourses identified progression from spontaneous to scientific concepts, illuminating the development of pupils' powers of intuition and sense of conviction. The dynamic geometry environment was used to investigate constructions stable under drag, illuminating the way in which the dynamic aspects afforded by the technology affect pupils' appreciation of the relationship between construction and proof. Various aspects of proof were highlighted and in particular the function of proof as explanation was seen to be an important aspect in the development of pupils' mathematical meaning making. Further analysis illuminated a distinction between the immediate individual sense making of pupils and the way this sense making is brought to social and consensual meaning making. At the wider classroom level the study identified issue of transparency the importance of the social use of argumentation to take forward the 'taken as shared' and the development of socio-mathematical norms and whole-class zones of proximal development. These aspects of individual and group meaning-making and whole class dynamics are advanced as ways of promoting local communities of mathematical practice as advocated by Winbourne and Watson( 1998).
8
Henry, Greg B. "The main challenges that a teacher-in-transition faces when teaching a high school geometry class /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1971.pdf.
Full text
9
Knapp, Andrea K. Barrett Jeffrey Edward. "Prompting mathematics teacher development through dynamic discourse." Normal, Ill. : Illinois State University, 2007. http://proquest.umi.com/pqdweb?index=0&did=1417799381&SrchMode=1&sid=8&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1207665349&clientId=43838.
Full textAbstract:
Thesis (Ph. D.)--Illinois State University, 2007.Title from title page screen, viewed on April 8, 2008. Dissertation Committee: Jeffrey Barrett (chair), Nerida Ellerton, Sharon Soucy McCrone, Cynthia Moore, Michael Plantholt, Agida Manizade. Includes bibliographical references (leaves 200-215) and abstract. Also available in print.
10
Ó, Buachalla Réamonn. "Quantum groups and noncommutative complex geometry." Thesis, Queen Mary, University of London, 2013. http://qmro.qmul.ac.uk/xmlui/handle/123456789/8675.
Full textAbstract:
Noncommutative Riemannian geometry is an area that has seen intense activity over the past 25 years. Despite this, noncommutative complex geometry is only now beginning to receive serious attention. The theory of quantum groups provides a large family of very interesting potential examples, namely the quantum flag manifolds. Thus far, only the irreducible quantum flag manifolds have been investigated as noncommutative complex spaces. In a series of papers, Heckenberger and Kolb showed that for each of these spaces, there exists a q-deformed Dolbeault double complex. In this thesis a comprehensive framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully at quantum homogeneous spaces. A number of basic results are established, producing a simple set of necessary and sufficient conditions for noncommutative complex structures to exist. It is shown that when applied to the quantum projective spaces, this theory reproduces the q-Dolbeault double complexes of Heckenberger and Kolb. Furthermore, the framework is used to q-deform results from Borel{Bott{ Weil theory, and to produce the beginnings of a theory of noncommutative Kahler geometry.
11
Delil, Huseyin. "An Analysis Of Geometry Problems In 6 - 8 Grades Turkish Mathematics Textbooks." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/3/12607251/index.pdf.
Full textAbstract:
The purpose of this study was to analyze geometry problems in a widely used sixth-, seventh-, and eighth-grade Turkish elementary mathematics textbooks series based on the cognitive assessment frameworks of the most recent TIMSS, the Trends in International Mathematics and Science Study 2003. To compare geometry problems in the textbooks and TIMSS 1999, in which Turkish students poorly performed, the cognitive behaviors that the problems required were determined and categorized. After the analysis, it was found that the two most frequent behaviors that the problems require are computing and applying with a total percentage of 72, in case of the textbooks. In TIMSS 1999 geometry problems case, however, applying and analyzing are the most frequent cognitive behaviors with a total percentage of 47. It was also found that a great majority of 22 behaviors of the framework were either not represented or underrepresented by the textbooks geometry problems. When we consider the four major categories of behaviors, 86 percent of the textbooks geometry problems required behaviors belong to two cognitive domains: Knowing Facts and Procedures or Solving Routine Problems. TIMSS 1999 geometry problems, however, mostly belong to Solving Routine Problems or Reasoning with a percentage of 65. In both the textbooks and TIMSS 1999 cases, a relatively small part of the problems required behaviors belong to Using Concepts. The results are discussed in the light of Turkey’
s performance in TIMSS 1999 and some suggestions related to the textbook problems were given.
12
Fauzan, Ahmad. "Applying realistic mathematics education (RME) in teaching geometry in Indonesian primary schools." Enschede : University of Twente [Host], 2002. http://doc.utwente.nl/58707.
Full text
13
Stephanus, Gervasius Hivengwa. "Exploring teaching proficiency in geometry of selected effective mathematics teachers in Namibia." Thesis, Rhodes University, 2014. http://hdl.handle.net/10962/d1013012.
Full textAbstract:
Quality mathematics education relies on effective pedagogy which offers students appropriate and rich opportunities to develop their mathematical proficiency (MP) and intellectual autonomy in learning mathematics. This qualitative case study aimed to explore and analyse selected effective mathematics teachers' proficiency in the area of geometry in five secondary schools in five different Namibia educational regions. The sample was purposefully selected and comprised five mathematics teachers, identified locally as being effective practitioners by their peers, Education Ministry officials and the staff of the University of Namibia (UNAM). The schools where the selected teachers taught were all high performing Namibian schools in terms of students' mathematics performance in the annual national examinations. The general picture of students' poor performance in mathematics in Namibia is no different to other sub-Saharan countries and it is the teachers who unfortunately bear the brunt of the criticism. There are, however, beacons of excellence in Namibia and these often go unnoticed and are seldom written about. It is the purpose of this study to focus on these high achievers and analyse the practices of these teachers so that the rest of Namibia can learn from their practices and experience what is possible in the Namibian context. The mathematical content and context focus of this study was geometry. This qualitative study adopted a multiple case study approach and was framed within an interpretive paradigm. The data were collected through individual questionnaires, classroom lesson observations and in-depth open-ended and semi-structured interviews with the participating teachers. These interviews took the form of post lesson reflective and stimulated recall analysis sessions. An adapted framework based on the Kilpatrick, Swafford and Findell's (2001) five strands of teaching for MP was developed as a conceptual and analytical lens to analyse the selected teachers' practice. The developed coding and the descriptive narrative vignettes of their teaching enabled a qualitative analysis of what teachers said contributed to their effectiveness and how they developed MP in students. An enactivist theoretical lens was used to complement the Kilpatrick et al.'s (2001) analytical framework. This enabled a deeper analysis of teacher teaching practice in terms of their embodied mathematical knowledge, actions and interactions with students. procedural fluency (PF) and productive disposition (PD), were addressed regularly by all five participating teachers. Evidence of addressing either the development of students' strategic competence (SC) or adaptive reasoning (AR) appeared rarely. Of particular interest in this study was that the strand of PD was the glue that held the other four strands of MP together. PD was manifested in many different ways in varying degrees. PD was characterised by a high level of content knowledge, rich personal experience, sustained commitment, effective and careful preparation for lessons, high expectations of themselves and learners, collegiality, passion for mathematics and an excellent work ethic. In addition, the teachers' geometry teaching practices were characterised by making use of real-world connections, manipulatives and representations, encouraging a collaborative approach and working together to show that geometry constituted a bridge between the concrete and abstract. The findings of the study have led me, the author, to suggest a ten (10) principles framework and seven (7) key interrelated factors for effective teaching, as a practical guide for teachers. This study argues that the instructional practices enacted by the participating teachers, who were perceived to be effective, aligned well with practices informed by the five strands of the Kilpatrick et al.'s (2001) model and the four concepts of autopoesis, co-emergence, structural determinism and embodiment of the enactivist approach. The study concludes with recommendations for effective pedagogical practices in the teaching of geometry, and opportunities for further research.
14
Helfgott, Michel. "A Sojourn Through Geometry and Algebra." Digital Commons @ East Tennessee State University, 2013. http://amzn.com/1492798894.
Full textAbstract:
This textbook is intended for college juniors or seniors majoring in mathematics, who plan to become high school teachers. It seeks to provide a deeper perspective on secondary mathematics, showing the interplay between plane geometry and algebra. A distinctive characteristic of the book is the frequent discussion of multiple paths to the solution of a problem or the proof of a theorem. Practically none of the topics covered in the book overlap with the content of courses taken by mathematics majors, say real analysis, abstract algebra, differential equations, combinatorics, probability and statistics, number theory, etc. These courses, and several others, provide indispensable mathematical maturity but are rather distant from the core of high school mathematics. Precisely, one of our main objectives is to bridge the gap between the latter and college-level mathematics.https://dc.etsu.edu/etsu_books/1084/thumbnail.jpg
15
Rippy, Scott Randall. "Applications of hyperbolic geometry in physics." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1099.
Full text
16
Zach, David. "Slicing the Cube." Kent State University Honors College / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ksuhonors1304703026.
Full text
17
Kemp, M. C. "Geometric Seifert 4-manifolds with aspherical bases." University of Sydney. Mathematics, 2005. http://hdl.handle.net/2123/702.
Full textAbstract:
Seifert fibred 3-manifolds were originally defined and classified by Seifert. Scott gives a survey of results connected with these classical Seifert spaces, in particular he shows they correspond to 3-manifolds having one of six of the eight 3-dimensional geometries (in the sense of Thurston). Essentially, a classical Seifert manifold is a S1-bundle over a 2-orbifold. More generally, a Seifert manifold is the total space of a bundle over a 2-orbifold with flat fibres. It is natural to ask if these generalised Seifert manifolds describe geometries of higher dimension. Ue has considered the geometries of orientable Seifert 4-manifolds (which have general fibre a torus). He proves that (with a finite number of exceptions orientable manifolds of eight of the 4-dimensional geometries are Seifert fibred. However, Seifert manifolds with a hyperbolic base are not necessarily geometric. In this paper, we seek to extend Ue's work to the non-orientable case. Firstly, we will show that Seifert spaces over an aspherical base are determined (up to fibre preserving homeomorphism) by their fundamental group sequence. Furthermore when the base is hyperbolic, a Seifert space is determined (up to fibre preserving homeomorphism) by its fundamental group. This generalises the work of Zieschang, who assumed the base has no reflector curves, the fibre was a torus and that a monodromy of a loop surrounding a cone point is trivial. Then we restrict to the 4 dimensional case and find necessary and sufficient conditions for Seifert 4 manifolds over hyperbolic or Euclidean orbifolds to be geometric in the sense of Thurston. Ue proved that orientable Seifert 4-manifolds with hyperbolic base are geometric if and only if the monodromies are periodic, and we will prove that we can drop the orientable condition. Ue also proved that orientable Seifert 4-manifolds with a Euclidean base are always geometric, and we will again show the orientable assumption is unnecessary.
18
Swann, Andrew F. "Hyperkähler and quaternionic Kähler geometry." Thesis, University of Oxford, 1990. http://ora.ox.ac.uk/objects/uuid:bb301f35-25e0-445d-8045-65e402908b85.
Full textAbstract:
A quaternion-Hermitian manifold, of dimension at least 12, with closed fundamental 4-form is shown to be quaternionic Kähler. A similar result is proved for 8-manifolds. HyperKähler metrics are constructed on the fundamental quaternionic line bundle (with the zero-section removed) of a quaternionic Kähler manifold (indefinite if the scalar curvature is negative). This construction is compatible with the quaternionic Kähler and hyperKähier quotient constructions and allows quaternionic Kähler geometry to be subsumed into the theory of hyperKähler manifolds. It is shown that the hyperKähler metrics that arise admit a certain type of SU(2)- action, possess functions which are Kähler potentials for each of the complex structures simultaneously and determine quaternionic Kähler structures via a variant of the moment map construction. Quaternionic Kähler metrics are also constructed on the fundamental quaternionic line bundle and a twistor space analogy leads to a construction of hyperKähler metrics with circle actions on complex line bundles over Kähler-Einstein (complex) contact manifolds. Nilpotent orbits in a complex semi-simple Lie algebra, with the hyperKähler metrics defined by Kronheimer, are shown to give rise to quaternionic Kähler metrics and various examples of these metrics are identified. It is shown that any quaternionic Kähler manifold with positive scalar curvature and sufficiently large isometry group may be embedded in one of these manifolds. The twistor space structure of the projectivised nilpotent orbits is studied.
19
Pinsky, Nathan. "Mathematical Knowledge for Teaching and Visualizing Differential Geometry." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/hmc_theses/49.
Full textAbstract:
In recent decades, education researchers have recognized the need for teachers to have a nuanced content knowledge in addition to pedagogical knowledge, but very little research was conducted into what this knowledge would entail. Beginning in 2008, math education researchers began to develop a theoretical framework for the mathematical knowledge needed for teaching, but their work focused primarily on elementary schools. I will present an analysis of the mathematical knowledge needed for teaching about the regular curves and surfaces, two important concepts in differential geometry which generalize to the advanced notion of a manifold, both in a college classroom and in an on-line format. I will also comment on the philosophical and political questions that arise in this analysis.
20
Nystrom, Michel. "The Ambrose-Palais-Singer theorem in synthetic differential geometry /." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66260.
Full text
21
Barrott, Lawrence Jack. "Convergence of the mirror to a rational elliptic surface." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/285007.
Full textAbstract:
The construction introduced by Gross, Hacking and Keel in [28] allows one to construct a mirror family to (S, D) where S is a smooth rational projective surface and D a certain type of Weil divisor supporting an ample or anti-ample class. To do so one constructs a formal smoothing of a singular variety they call the n-vertex. By arguments of Gross, Hacking and Keel one knows that this construction can be lifted to an algebraic family if the intersection matrix for D is not negative semi-definite. In the case where the intersection matrix is negative definite the smoothing exists in a formal neighbourhood of a union of analytic strata. A proof of both of these is found in [GHK]. In our first project we use these ideas to find explicit formulae for the mirror families to low degree del Pezzo surfaces. In the second project we treat the remaining case of a negative semi-definite intersection matrix, corresponding to S being a rational elliptic surface and D a rational fibre. Using intuition from the first project we prove in the second project that in this case the formal family of their construction lifts to an analytic family.
22
Havens, Paul C. Havens. "The Rigidity of the Sphere." Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1461595829.
Full text
23
Marino, Nicholas John. "Vector Bundles and Projective Varieties." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1544457943307018.
Full text
24
Yu, Xiaojiang Gabardo Jean-Pierre. "Wavelet sets, integral self-affine tiles and nonuniform multiresolution analyses." *McMaster only, 2005.
Find full text
25
Hsu, Siu-fai, and 許紹輝. "Geometric quantization of fermions and complex bosons." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50434500.
Full textAbstract:
Geometric quantization is a subject of finding irreducible representations of certain group or algebra and identifying those equivalent representations by geometric means. Geometric quantization of even dimensional fermionic system has been constructed based on the spinor representation of even dimensional Clifford algebras. Although geometric quantization of odd dimensional fermionic system has not been done, the existence of spinor representations in odd dimension indicates that the geometric quantization is possible.
In quantum field theory, charge conjungation can be defined on complex bosons and fermions. Without interaction, the particles and anti-particles essentially have same physical properties.
In this thesis, we will first recall the setup of geometric quantization of even dimensional fermion and bosons. Then we will show how to quantize odd dimensional fermion. After that, charge conjungation on complex fermion and boson will be defined and the remaining effort will be put on how to identify the Hilbert spaces produced by different charge conjungations.published_or_final_version
Mathematics
Master
Master of Philosophy
26
Roux, Annalie. "Die invloed van taalvaardigheid op die meetkundedenke van graad 8 en 9 leerders / Annalie Roux." Thesis, North-West University, 2004. http://hdl.handle.net/10394/4482.
Full textAbstract:
Many authors have expressed concern regarding the extent of underachievement in mathematics. The role of language proficiency as a causal factor in this underachievement has been neglected. Researchers found sufficient evidence to conclude that language proficiency is related to mathematics achievement. In mathematics, symbolic language fills a dual role: It serves as an instrument of communication and as an instrument of thought by making the representation of mathematical concepts, structures and relationships possible (Esty & Teppo, 1996:45). According to Van Hiele (1988:5), language structure is a critical factor in the progression through the Van Hiele levels from the visual, concrete structures to the abstract structures. In this study, the influence of language proficiency on geometric thinking is investigated. 152 grade 8 and 9 learners completed two tests each. One test measured language proficiency in the learners' mother tongue. The second is a geometric test based on a Mayberry-type Van Hiele test for assessing learners' geometric thinking levels. Language proficiency was taken as the independent variable, and geometric thinking as the dependent variable. In the analysis of the results, the top 25 % and bottom 25% performers in the language proficiency test were chosen. Cohen's (1988) d-value was used to determine if there was a practical significant difference in the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels. Results showed a practical significant difference between the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels, but also with respect to the geometry test as a whole. In particular, two aspects of language proficiency, namely reading comprehension and vocabulary, appeared to be very strong predictors for geometric thinking on the first three Van Hiele levels
(d ≥ 0,8). Key terms for indexing: geometry, geometry learning, mathematics learning, geometric thinking, language, language proficiency, geometry and language, mathematics and language.Thesis (M.Sc. (Education)--North-West University, Potchefstroom Campus, 2004.
27
Strawn, Nathaniel Kirk. "Geometry and constructions of finite frames." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1335.
Full text
28
Nivens, Ryan Andrew, Tara Carver Peters, and Jesse Nivens. "Views of Isometric Geometry." Digital Commons @ East Tennessee State University, 2012. https://dc.etsu.edu/etsu-works/293.
Full text
29
LAI, XUN. "¿¿¿¿¿¿GeometryEditor: A Web-based System for Authoring, Sharing and Support of Plane Geometry Manipulatives for Mathematics Education." Kent State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=kent1278997107.
Full text
30
Son, Do Nguyen. "McKay quivers and the deformation and resolution theory of kleinen singularities." Bonn : Mathematisches Institut der Universität, 2005. http://catalog.hathitrust.org/api/volumes/oclc/65375195.html.
Full text
31
Vincent, Jill. "Mechanical linkages, dynamic geometry software, and argumentation : supporting a classroom culture of mathematical proof /." Connect to thesis, 2002. http://eprints.unimelb.edu.au/archive/00001399.
Full text
32
Tucker, Thomas Marshall. "A new method for parametric surface registration." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/17114.
Full text
33
LaCroix, Tiffany Jo. "Resolving Apparent Inconsistencies in the Belief Systems of High School Geometry Teachers." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/105039.
Full textAbstract:
This qualitative research seeks to identify and understand the beliefs of 10 high school
geometry teachers that help resolve apparent inconsistencies between their espoused and
enacted beliefs. Data was collected using an initial interview, classroom observations,
and a follow-up interview to gather evidence of teacher beliefs based on what they say,
do, and intend respectively. Open coding, analytical coding, cluster identification, coding
memos, and analytical memos were used to analyze the data and write summaries of the
teachers' explanatory beliefs with beliefs as the unit of analysis. It was identified that
teachers consistently and inconsistently enact their espoused beliefs, but there are also
instances when teachers both consistently and inconsistently enact particular espoused
beliefs. This endeavor necessitates a shared understanding of terms, and it was found
what it means to "understand" needs to be clarified with a definition and examples from
teachers. When teachers appear to not enact their espoused beliefs, explanatory beliefs
were pinpointed that resolve the conflict and found the explanatory beliefs exist in at least
seven macro clusters. These explanatory beliefs interact with espoused beliefs by
overriding, limiting, or preventing the espoused beliefs to resolve the apparent
inconsistency in teachers espoused and enacted beliefs. The explanatory beliefs with
limiting and overriding interactions were found to coexist for some teachers around a teaching practice as overriding interactions are connected to constraints on the classroom
whereas limiting interactions are not. It was also found that belief clusters are nested
within clusters of beliefs, and these clusters allow for beliefs to cluster in isolation in
different ways. This work also shows empirically that some geometry teacher beliefs are
socially constructed due to the presence of common cultural artifacts and influence from
mathematics teacher educators. This work has implications and future research directions
in the areas of using beliefs as the unit of analysis, mapping teacher's belief systems,
considering the social construction of beliefs and role of community, connecting beliefs
to specific teaching practices, and educating teachers.Doctor of Philosophy
This research seeks to understand and interpret the beliefs of 10 high school geometry teachers that resolve apparent inconsistencies between what teachers say they believe and what they do in the classroom. Data was collected using an initial interview, classroom observations, and a follow-up interview to gather evidence of teacher beliefs based on what they say, do, and intend respectively. It was identified that teachers consistently and inconsistently enact their stated beliefs, but there are also instances when teachers both consistently and inconsistently enact their stated beliefs. When teachers appear to inconsistently enact their stated beliefs, it was found that teachers have logical reasons why they do so, and these reasons relate to specific teaching practices. It was also found that teacher beliefs interact with each other in different ways. Teachers' beliefs can limit or prevent the enaction of their other beliefs. In addition, school level constraints can override the enaction of some teacher beliefs. This research shows that some beliefs are held by different teachers from vastly different schools which suggests that some geometry teacher beliefs are held socially. The findings from this research have implications for teacher education
34
Liu, Stephen Shang Yi. "On the Asymptotic Behavior of the Magnitude Function for Odd-dimensional Euclidean Balls." Case Western Reserve University School of Graduate Studies / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=case1585399513964864.
Full text
35
Dobbins, Michael Gene. "Representations of Polytopes." Diss., Temple University Libraries, 2011. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/141523.
Full textAbstract:
MathematicsPh.D.
Here we investigate a variety of ways to represent polytopes and related objects. We define a class of posets, which includes all abstract polytopes, giving a unique representative among posets having a particular labeled flag graph and characterize the labeled flag graphs of abstract polytopes. We show that determining the realizability of an abstract polytope is equivalent to solving a low rank matrix completion problem. For any given polytope, we provide a new construction for the known result that there is a combinatorial polytope with a specified ridge that is always projectively equivalent to the given polytope, and we show how this makes a naturally arising subclass of intractable problems tractable. We give necessary and sufficient conditions for realizing a polytope's interval poset, which is the polytopal analog of a poset's Hasse diagram. We then provide a counter example to the general realizablity of a polytope's interval poset.
Temple University--Theses
36
Hoyt, Christopher. "On the Landscape of Random Tropical Polynomials." Scholarship @ Claremont, 2018. https://scholarship.claremont.edu/hmc_theses/114.
Full textAbstract:
Tropical polynomials are similar to classical polynomials, however addition and multiplication are replaced with tropical addition (minimums) and tropical multiplication (addition). Within this new construction, polynomials become piecewise linear curves with interesting behavior. All tropical polynomials are piecewise linear curves, and each linear component uniquely corresponds to a particular monomial. In addition, certain monomial in the tropical polynomial can be trivial due to the fact that tropical addition is the minimum operator. Therefore, it makes sense to consider a graph of connectivity of the monomials for any given tropical polynomial. We investigate tropical polynomials where all coefficients are chosen from a standard normal distribution, and ask what the distribution will be for the graphs of connectivity amongst the monomials. We present a rudimentary algorithm for analytically determining the probability and show a Monte Carlo based confirmation for our results. In addition, we will give a variety of different theorems comparing relative likelihoods of different types of tropical polynomials.
37
Zharkov, Sergei. "Conic structures in differential geometry." Thesis, Connect to e-thesis, 2000. http://theses.gla.ac.uk/1005/.
Full textAbstract:
Thesis (Ph.D.) -- University of Glasgow, 2000.Includes bibliographical references (p.86-88). Print version also available. Mode of access : World Wide Web. System requirements : Adobe Acrobat reader required to view PDF document.
38
Rogers, Virginia Lee Copper. "Teaching geometry in the elementary classroom." CSUSB ScholarWorks, 1995. https://scholarworks.lib.csusb.edu/etd-project/1044.
Full text
39
Duran, James Joseph. "Differential geometry of surfaces and minimal surfaces." CSUSB ScholarWorks, 1997. https://scholarworks.lib.csusb.edu/etd-project/1542.
Full text
40
Johnson, Jamie. "Continued Radicals." TopSCHOLAR®, 2005. http://digitalcommons.wku.edu/theses/240.
Full textAbstract:
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.
41
Praggastis, Brenda L. "Markov partitions for hyperbolic toral automorphisms /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/5773.
Full text
42
McClain, Nichola Sue. "A study in geometric construction." CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/1811.
Full text
43
Gokce, Semirhan. "A Structural Equation Modeling Study: Factors Related To Mathematics And Geometry Achievement Across Grade Levels." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/3/12606697/index.pdf.
Full textAbstract:
The factors related to mathematics and geometry achievement were modeled in this study. It was based on the data obtained from the Student Assessment Program carried out by Ministry of National Education. Mathematics achievement tests and student questionnaires of each grade were analyzed by using principal component analysis to obtain different dimensions that are expected to be related with student achievement. Before the principal component analysis, a content based evaluation of the content of the mathematics achievement tests was actualized and the items were grouped as mathematics and geometry. Regarding the student questionnaire socio-economic status, perception of success and interest toward mathematics and science, student-centered activities and teacher-centered activities in the classroom were identified as factors through the principal component analysis. Thereafter, three models were designed and tested by structural equation modeling technique (SEM) using LISREL 8.54. Path analysis with latent variables was used for testing the models. The following results were obtained in the study. In all of the models, socioeconomic status had a positive impact on the mathematics and geometry achievement of the students for all the grade levels examined. Teacher centered activities were found to be positively related with the students&rsquosuccess of mathematics and geometry. On the other hand, student centered activities intended to have a negative relation with mathematics and geometry achievement. As the other variables were considered, an increase on the mathematics and geometry scores of the students&rsquo
was observed in all grade levels with the increase in the perception of success and interest toward mathematics and science.
44
Bulut, Aykut. "Investigating Perceptions Of Preservice Mathematics Teachers On Their Technological Pedagogical Content Knowledge (tpack) Regarding Geometry." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614704/index.pdf.
Full textAbstract:
The aim of this study is to investigate perceptions of preservice mathematics teachers&rsquotechnological pedagogical content knowledge (TPACK) regarding geometry. In addition, the purpose is to examine the relationships among the components of TPACK. Moreover, possible gender and year of enrollment differences related to preservice mathematics teachers&rsquo
technological pedagogical content knowledge dimensions are examined. This research study has been conducted with 780 preservice mathematics teachers who are enrolled in elementary mathematics education department of Education Faculties of seven public universities located in Central Anatolia. Perceived TPACK regarding geometry instrument has been developed to collect data. In order to determine the levels of preservice mathematics teachers&rsquo
perceptions related to TPACK in geometry, descriptive information have been used. The results indicate that preservice mathematics teachers&rsquo
perceptions of TPACK related to geometry is higher than moderate. Furthermore, correlational analysis was conducted to identify the relationship among dimensions of TPACK. Positive significant correlations among the components of the TPACK framework were found in correlational analysis. Besides, two-way MANOVA has been conducted to investigate a possible relationship between demographic information of preservice elementary mathematics teachers and their perceptions of TPACK. According to the MANOVA results, there are statistically significant differences between male and female preservice mathematics teachers in favor of male participants in three components of TPACK, namely technological knowledge, technological pedagogical knowledge and technological pedagogical content knowledge in favour of males.
45
LIN, CHIEH-LING, and 林芥菱. "The Performance of Mathematics Reading and Mathematics Conception on Geometry for Third Graders." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/23830790325361703485.
Full textAbstract:
碩士國立臺中教育大學
數學教育學系在職專班
104
The purpose of this study aims at investigating the performance on mathematics reading which embedding with history context of mathematics. The subjects all of 153 person include third graders from an elementary school in Taichung City, Taiwan. The assessment “Mathematics Reading Test” is designed by the researcher. According to responses based on constructed-response item, this study analyzes the thinking and error types related to geometry. The study result is reading comprehension and specific mathematics skills and background mathematics knowledge, Their relationships exist significantly positive relation. The main results of the study are as follows. The frist. 1. According to the performance of mathematics reading, the students perform best in reading comprehension. Specific mathematics skills graded 2 and the background mathematics knowledge is the lastest. 2. The insufficient reading ability influences the text comprehension and generates erroneous concepts. And second. 1. Some students can effectively distinguish and answer the internal and external in a plane graphical. But quite a few students are unclear structure on the graphical, leading to the perimeter defined is not understanding in the subject, that the perimeter attributable to the internal or external graphics. 2. Some students can write the proper perimeter, that actual measurement and draw the length of it. They will be able to measure the perimeter of complete graphic and combined the segments for perimeter, but a few students unable to piece together the full graphic of perimeter. Therefore, the concept understanding of perimeter, there will be gap of the segment and the overall graphic. 3. Some students can identify the center and circumference of a circle in correctly. But the radius resolution easy to have ideas unclear or conceptual confusion with diameter, that the centimeter unit can not distinguish with millimeter. 4. Some students can compare and judge the size of angle conceptual in correct for answer, but a few students weak construction of angle concepts results, that makes the judgment angle error of constitute the angle insufficient concept. For Example: They mistaken closed figure is the angle. ; They mistaken the both sides of the arc-graphics is the angle. 5. Some students can operate the graphics easier, that separate is converted to different appearance of the same areas graphical, or through text guide were measured and then tell the size of the graphics. But a few students weak construction of reading and prior knowledge concepts , that makes the judgment in error.
46
Kao, Wan-Hua, and 高菀華. "Scanimation and Hologram Applied to Geometry Teaching inElementary Mathematics." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/78530368969681357003.
Full textAbstract:
碩士崑山科技大學
視覺傳達設計研究所
99
In elementary mathematics, geometry curriculum teaches the children elements of geometry. It is always using 2D images to explain three-dimensional geometry images in textbooks. However, geometry teaching has some problem of storage, so we try to use the scanimation and hologram to show stereo images of geometric shapes, providing a continuous changing and multi-angle images. The study begins with the analysis and integration of geometry, geometry teachings,scanimation and hologram, and then explores the design principle of scanimation and hologram through two experiments. The experiment conclusions are used to create three products. The conclusions are shown below: 1. Yellow is the best color of represent scanimation images. 2. For children, line spacing 0.6mm is best of represent scanimation images.It’s different from adults who just see line spacing 0.3mm, or 0.4mm to build a complete image. 3. Three or four pictures are best number of scanimation images. 4. For the reflection holographic, the bottom of geometry virtual images with 40% luminance and the bottom of geometry real images with 0% luminance are the most clear holographic. And the children prefer to the show of geometry virtual images.
47
Wei, Wu. "Projective Geometry." Thesis, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-85306.
Full textAbstract:
Projective geometry is a branch of mathematics which is foundationally based on an axiomatic system. In this thesis, six axioms for two-dimensional projective geometry are chosen to build the structure for proving some further results like Pappus' and Pascal's theorems. This work is mainly in synthetic geometry.
48
Xu, Feng. "Geometry of SU(3) Manifolds." Diss., 2008. http://dukespace.lib.duke.edu/dspace/bitstream/10161/826/1/D_Xu_Feng_a_200808.pdf.
Full text
49
Chang, Chih-Chieh, and 張志傑. "Investigate Mathematics Reading and Metacognition of Geometry among Fifth Graders." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/dn97q9.
Full textAbstract:
碩士國立臺中教育大學
數學教育學系
103
The purpose of this research was to investigate the relationship between mathematics reading and metacognition of geometry among fifth graders. The subjects were 261 fifth graders from five elementary schools in Taichung City. Using a self-developed “Mathematics Reading Test for Fifth Graders”, this research evaluated the fifth graders’ performances in mathematics reading and metacognition of geometry and further explored the relationship between mathematics reading and metacognition among them. The analysis showed the following findings: 1.In mathematics reading, the students performed best in the “prior knowledge of mathematics” dimension, followed by the “reading comprehension” dimension and then the “mathematics-specific skills” dimension. 2.In metacognition, the students also performed best in the “prior knowledge of mathematics” dimension, followed by the “reading comprehension” dimension and then the “mathematics-specific skills” dimension. 3.A significant and positive correlation between performance in mathematics reading and performance in metacognition was observed among the students. 4.Performance in metacognition significantly explained performance in mathematics reading, suggesting that students with better metacognition tended to perform better in mathematics reading. Results and findings of this research could be a reference for teachers and future researchers.
50
Osinenko, Anton. "The two-legged K-theoretic equivariant vertex." Thesis, 2019. https://doi.org/10.7916/d8-ze3v-0g40.
Full textAbstract:
In this work we study K-theoretic Donaldson-Thomas theory. We derive an explicit formula for the capped vertex with two legs in a certain gauge. Using this result we obtain an explicit formula for the operator corresponding to relative geometry of the resolved conifold with two nontrivial legs. As a consequence, we prove polynomiality in the Kahler variable of the operator for the corresponding absolute geometry.