加州理工學院數(shù)學

The graduate program in mathematics is designed to prepare students for research careers in universities, industry, or government. Accordingly, only those students seeking the Ph.D. degree are admitted. In the past fifteen years, Caltech has awarded doctorates in mathematics to about 90 students, many of whom have moved into attractive positions as members of university faculty and in industry and government research.
Graduate students are encouraged to engage in creative research work after passing their qualifying exams. As a result of the informal atmosphere, small size of the department, and the large faculty to student ratio, graduate students have ample opportunity to interact closely with the faculty in research.

1、Real and Complex Analysis

2、Abstract Algebra

3、Topology and Geometry

4、 Elliptic Curves

5、Statistics

6、Mathematical Logic and Axiomatic Set Theory

7、Computability Theory

8、 Combinatorial Analysis

9、Group Theory

10、Information Theory

11、Algebraic Geometry

12、Functional Analysis

13、Number Theory

14、Ordinary and Partial Differential Equations

1、實數(shù)和復數(shù)分析

2、抽象代數(shù)

3、拓撲和幾何

4、橢圓曲線

5、統(tǒng)計學

6、數(shù)理邏輯和公理集合論

7、可計算性理論

8、組合分析

9、群論

10、信息論

11、代數(shù)幾何

12、功能分析

13、數(shù)論

14、普通和偏微分方程