The primary purpose of this study was to investigate experimentally the following questions: (1) What is the relative effectiveness of the vector approach and the traditional approach to teaching certain topics in plane analytic geometry to high school students in terms of achievement and understanding? (2) Does teaching these topics in plane analytic geometry via vectors produce more transfer to other topics in analytic geometry (mainly solid analytic geometry) than teaching these topics via the traditional approach? / Typescript. / "December, 1968." / "Submitted to the Department of Mathematics Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: E. D. Nichols, Professor Directing Dissertation. / Includes bibliographical references.

Thesis (doctoral)--Universität Jena, 1911. / Vita.

Thesis (doctoral)--Universität Bern, 1911.

Thesis (Ph. D.)--Columbia University, 1922. / Vita.

Thesis--Technische Hogeschool te Delft. / Bibliography: p. 175-176.

Thesis (Ph. D.)--Columbia University, 1922. / Vita.

Thesis--Universität Bern, 1911.

Thesis--Friedrichs-Universität, 1910.

"Litteratur-Nachweisungen und Zusätze" : p. 488-508.

The aim of this thesis is to explain some basic facts, examples, ideas and results in Tate’s theory and its applications. / In the first chapter, we will introduce some preliminaries of Banach algebras over k. The Tate algebra (resp. affinoid algebra) is analogous to the power series defined on the unit disc (resp. analytic set of unit disc). There are some properties of its algebraic structure. / In the second chapter we will construct the rigid analytic variety X, the topology on it, and the structure sheaf Oₓ. Tate found an interesting property, now called Tate’ Acyclicity Theorem, which makes analytic continuation stand. Moreover, by using G-topology, we define rigid analytic spaces, and we are able to paste them. The Tate curve is a good example. / In the last chapter, we introduce Schottky group and Mumford curve. A Mumford curve is obtained from P¹ discarding a compact set quotient by a group action, and it can be characterized as an algebraic curve with totally split reduction. The converse is also true. / 這篇文章的目的是闡釋Tate理論中的一些基本事實、例子、想法和結果，以及一些應用。 / 在第一章中，我們會介紹一些關於k上的Banach代數的初等事實。Tate代數（affinoid代數）類似於定義在單位圓（單位圓的解析集）上的冪級數。關於它的代數結構有一些結論。 / 在第二章中，我們會構造剛性解析簇，它的拓撲，以及它的層結構。Tate發現了一個它的有趣的性質，現在被稱為Tate Acyclicity Theorem；這個性質使得我們可以做解析延拓。此外，通過使用G-拓撲，我們構造剛性解析空間，並且我們可以將幾塊剛性解析空間“粘”起來。Tate曲線是它的一個很好的應用。 / 在第三章中，我們將介紹Schottky群和Mumford曲線。一條Mumford曲線是P¹挖掉一個緊集后除掉一個群作用而得到的，並且可以被表徵為擁有totally split reduction的代數曲線。反之亦然。 / Yuan, Zhiri. / Thesis M.Phil. Chinese University of Hong Kong 2015. / Includes bibliographical references (leaf 65 ). / Abstracts also in Chinese. / Title from PDF title page (viewed on 13, September, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.