数学( Mathematics )是研究数量、结构、变化以及空间模型等概念的一门学科。透过抽象化和逻辑推理的使用,由计数、计算、量度和对物体形状及运动的观察中产生。数学的基本要素是:逻辑和直观、分析和推理、共性和个性。
自古以来,数学一直被广泛应用在各个不同的领域中,包括科学、工程、医学、经济学、金融学等。最近的几千年里,在不同的国度,数学都得到了发展。古埃及人写下了第一个方程。古希腊人则在许多方面都有贡献,比如几何和数秘术。中国数学家早就有了负数的概念。“0”这个数字则在印度首次被使用。接着在波斯伊斯兰教的黄金时期,数学家又跨越了一大步,书写了第一部代数学的书籍。在文艺复兴时期,数学与科学则共同欣荣发展。
专业背景
要求本科为数学或相关专业,上过高等微积分和复合变量、微分方程和线性代数、概率论和离散数学等数学相关课程。
先修课程
先修课程要求多为数学的基础课程和高阶课程为主,以康奈尔大学为例:
Prerequisites
Mastery of the material required for an undergraduate major in mathematics, including a rigorous course in advanced calculus and real variable theory that will serve as an introduction to measure theory and courses in linear algebra and modern abstract algebra at an advanced level. Applicants should also have some familiarity with applications of advanced calculus.
其他要求
需要注意,美国大学排名前20的学校很多强制要求学生在递交申请材料时,必须同时提交GRE Subject 数学的考试和GRE general 的成绩,但是关于托福和雅思成绩,学校一般给出的最低要求都不等,具体要以学校为主。
这里附上排名前十的美国院校:
2019年数学专业USNEWS排名
Ranking
|
University
|
Location
|
State
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#1
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Princeton University - Department of Mathematics
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Princeton
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NJ
|
#2
|
Harvard University - Department of Mathematics
|
Cambridge
|
MA
|
#2
|
Massachusetts Institute of Technology - Department of Mathematics
|
Cambridge
|
MA
|
#2
|
Stanford University - Department of Mathematics
|
Stanford
|
CA
|
#2
|
University of California--Berkeley - Department of Mathematics
|
Berkeley
|
CA
|
#6
|
University of Chicago - Department of Mathematics
|
Chicago
|
IL
|
#7
|
Columbia University - Department of Mathematics
|
New York
|
NY
|
#7
|
University of California--Los Angeles - Department of Mathematics
|
Los Angeles
|
CA
|
#9
|
California Institute of Technology - Department of Mathematics
|
Pasadena
|
CA
|
#9
|
New York University - Department of Mathematics
|
New York
|
NY
|
#9
|
Yale University - Department of Mathematics
|
New Haven
|
C
|