马上就要开始正式申请，在选择学校的同时，专业也要选择了。貌似有很多时候，中介代劳了填表工作。我觉得基本的信息可以让中介帮忙填写。专业的选择还是自己做做功课比较好。因为这里面的细分太多，其实每个学校还有各种不同，即便是同样的名词，认真阅读，可以发现每个学校是不一样的。专业里面还有一些细分，了解下，对以后职业发展也可以有个初步定义。
我先呈上UCLA的数学专业的细分， 在UCLA数学系，这些都是有可能可以选择的方向。为了保持原汁原味，我保留了英文, 文章最后会有简单的翻译。
Mathematics Designed for students who are interested in the theory of mathematics. Pure mathematicians often pursue master and doctorate degree in mathematics in order to prepare for a career in research or university level teaching.
Applied Mathematics Designed for students who are interested in the classical relationships between the physical sciences and engineering. They often seek employment in the industry utilizing their skills to solve engineering and computer related problems.
Financial Actuarial Mathematics Designed for students interested in financial mathematics and its applications. Graduates typically go on to MFE/MBA programs, the actuarial field, banking and/or and business.
Mathematics of Computation Designed for individuals who are interested in the mathematical theory and the applications of computing. These students often seek employment in areas similar to the applied mathematicians.
Mathematics for Teaching Designed for students who have a substantial interest in teaching mathematics at the secondary level. Visit the Curtis Centerwebsite for more information about other undergraduate teacher preparation programs such as the Joint Mathematics Education Program and the Subject Matter Preparation Program.
Mathematics/ Applied Science The Mathematics/Applied Science major is intended for students who are interested in applications of mathematics to other areas. Students majoring in Mathematics/Applied Science often pursue careers in medical professions, professional programs, or graduate programs in business or law.
Mathematics/Economics Designed to give students a solid foundation in both mathematics and economics, stressing those areas of mathematics and statistics that are most relevant to economics and the parts of economics that emphasize the use of mathematics and statistics. It is ideal for students who may wish to complete a higher degree in economics.
Specialization in Computing The Department of Mathematics offers a Specialization in Computing, which can be added to all of the majors with the exception of Mathematics of Computation.
另外，我拉了UCB的信息，UCB把数学分为，纯数（mathematics）和应用数学（Applied mathematics）, 如果你选择应用数学，在后面的选课过程中又有以下细分，学生要和自己的顾问讨论，最后选择一个方向， 然后根据选择的方向上相应的课。
Actuarial Science: Mathematics 128B, Statistics 134 or 140, 135, 151A, Economics 141
Classical Mechanics: Mathematics 123, 189, Physics 105, Mechanical Engineering 104
Computer Science: Mathematics 128B, Computer Science 164, 170, 172, 174, 184, 188, 189
Data Science: Computer Science C100, 188, 189, Mathematics 170, Statistics C100, 133, 134 or 140, 154
Economics: Economics 103, 104, 141, Mathematics 103, 170, Statistics 134 or 140, 155
Fluid Mechanics: Required: Mechanical Engineering 106; Elective: 2 of Mechanical Engineering 163, Chemical Engineering 141 or Engineering 115, Mathematics 126, Mathematics 128B
Geophysics: Required: Geophysics 108 and 121; Elective: 1 of Geophysics 104, 122, 130 or 145
Life & Physical Sciences: Generally: Mathematics 123, 126, 128B
Mathematical Biology: Required: Mathematics 127; Elective: 2 of Mathematics 170, 172, 126 or 128B
Numerical Analysis: Mathematics 123, 126, 128B
Operations Research: Statistics 134 or 140, Indust. Engnr. & Oper. Research 130, 160, 161, 162
Probability Theory: Mathematics 105, Statistics 134 or 140, 150
Quantum Mechanics: Mathematics 126, 189, Physics 137A, 137B
Relativity: Required: Math 140 and Physics 139; Elective: 1 of Math 126 or Math 141
Social Sciences: Generally: Statistics 134 or 140, 135, 150, 151A, 151B, 153
Statistics: Mathematics 128B, Statistics 134 or 140, 135, 150, 153, 154, 155, 156
Systems Theory: Electrical Engineering and Computer Science 104, 120, 122, 123
每个学校的数学系基本都会有纯数，应数，但是细分，并不是每个学校都有的，有也是不相同的。比如UCLA的数学系在财务精算方面其实就比较强大，他们数学系的孩子考证很在行。 UCB的数学系和计算机专业结合的略紧。另外，大U的选择方向和细分比较多，文理学院，或者私立学校小可能就没有分的这么细，相对比较笼统了。
其实我是蛮喜欢UCLA对数学专业的细分,基本可以看出数学系的出路
纯数-研究方向
应数-工程和计算机方向
财务和精算-四大，投行和保险公司为目标择业方向
计算数学-类似应用数学的就业方向
数学&教育-以后做数学教育方向
数学&应用科学-数学在交叉学科里的应用
数学&经济-适合以后在经济方面继续发展的孩子
即将选择数学专业或者已经录取数学专业的孩子，都可以仔细研读和考虑下，哪个方向是你真正想追求的。爹妈也可以给孩子一些职业方面的简单介绍，各个方向是干啥的。各个行业的基本概念。也许认知并不能一天造就，但是给孩子一个启蒙，总比说简单的数学系好吧。
另外，天底下最复杂的数学系大概要算滑铁卢大学，大家要面面俱到，细细研究可以去扒滑铁卢的官网。