發(fā)送驗(yàn)證碼
發(fā)送驗(yàn)證碼
UCLA的全稱(chēng)是University of California, Los Angeles的Topology，即加州大學(xué)洛杉磯分校拓?fù)鋵W(xué)，下面將詳細(xì)介紹UCLA的的項(xiàng)目特點(diǎn)/院系介紹、UCLA的的研究領(lǐng)域、UCLA的的研究生申請(qǐng)要求。
加州大學(xué)洛杉磯分校
Topological research at UCLA began with the arrival of Robert Sorgenfrey in 1942, soon after he earned a Ph. D. at the University of Texas under the legendary topologist R. L. Moore. High points in the research accomplishments of topologists at UCLA include the solution by Robion Kirby, who was at UCLA from 1965 to 1971, (with Laurence Siebenmann) of four of the seven problems listed by John Milnor in 1963 as the most important in topology at that time. Kirby first presented his famous "torus trick", the key to the solutions, in a UCLA seminar in the summer of 1968.
1、the Casson invariant
2、Khovanov homology
3、Khovanov-Rozansky homology
4、 Reshetikhin-Turaev-Witten invariants
5、rational homotopy theory
1、卡松不變
2、Khovanov同源性
3、Khovanov-Rozansky的同源性
4、Reshetikhin-Turaev-Witten不變量
5、有理同倫論
托福87分，單項(xiàng)最低要求寫(xiě)作25，口語(yǔ)24，閱讀21，聽(tīng)力17或雅思7分，GRE，GPA：MA本科綜合不低于3.0，數(shù)學(xué)專(zhuān)業(yè)課不低于3.2,PhD本科綜合不低于3.0，本科數(shù)學(xué)專(zhuān)業(yè)課不低于3.5，研究生不低于3.5（如已讀研），學(xué)費(fèi)：PhD$30,410，MA$30,390，申請(qǐng)截止日期12月15日
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