While there are many math majors who will lament that math majors are too specialized, too deep, and too basic, and thus change careers halfway, there are many more who choose to continue on in this field. Some of them are forced by the pressure of employment and hope to get the golden brick of employment through graduate school, while some of them are motivated by their strong interest in mathematics and have found the fun and method of delving into this field. In particular, a small number of students who switched from the more applied engineering majors to mathematics majors, but also as a scientific research ideal to look at mathematics.
In recent years, math majors have also been slowly warming up, and the admission scores for graduate school seem to be getting higher by the year. In this issue, we interviewed dozens of graduate students in different directions of mathematics, and asked them to talk about the situation and prospects of mathematics majors in graduate school. To go to graduate school or not to go to graduate school? Do they go to graduate school because of the pressure of employment, or do they go to graduate school out of interest? I hope you can be inspired by their narratives, so as to find the right orientation.
Basic mathematics: the foundation of the foundation
Professional outline
Mathematics is a basic subject, basic mathematics is the foundation of the foundation. It has a broad field of study and is highly theoretical. It mainly refers to geometry, algebra (including number theory), topology, analysis, equations, and some mathematical subdisciplines developed on this basis, specific branch directions include: projective differential geometry, Riemannian geometry, integral differential geometry, harmonic analysis and its applications, wavelet analysis, partial differential equations, applied differential equations, algebra, and so on.
[Keywords] Prospects
Tobia (Ph.D. student in Computer Science, 2007, Basic Mathematics track): Basic Mathematics has been attracting a lot of attention internationally, with a number of significant research results, but unfortunately has not been as well developed as the other 4 secondary disciplines which are more application-oriented in China. This can be seen from the comparison of the impact factors of the top domestic and foreign journals. In terms of the various branches of basic mathematics, the domestic development in geometry is relatively good, close to the international level of development, while the other branches are not as satisfactory.
Basic mathematics is not as mysterious as many people think, and it has so many directions that it is hard to summarize in one or two sentences. Most people who choose basic math do so out of interest, so most people's choice for the future will probably be to go on to a PhD, though of course there are some people in the algebraic geometry direction who will go on to do computer or applied math.
Buick (Ph.D. in Basic Mathematics, Class of 2006): Basic mathematics is of course very tiring, but it does not mean that life is no longer fun or that there are no other possibilities in life. Basic math students have a strong foundation in math, and as long as they are interested in making a foundation and finding a direction that they are interested in and can excel in, there are unlimited possibilities for the future, such as economics, finance, and other popular fields are all directions that can be developed.
[Keywords] Research Hot Spots
Tobia (PhD in Computer Science, 2007, Basic Mathematics): There is no doubt that those who choose Basic Mathematics as their research direction will be the ones who really take Mathematics as a career, because the work they are doing is often ten or even a hundred years ahead of the Applied Mathematics of the era, which is unbelievable to some people but still they are determined to do it. still have no hesitation. The hottest thing right now is the mathematical physics direction, which is really the use of all kinds of mathematical tools to solve hard physics problems. And the hottest of these mathematical tools is algebraic geometry. Because of the strong connection to physics, it can be expected that this direction will always be a popular area of study.
Aqii (PhD in Basic Mathematics, Class of 2005): I think algebraic representation theory and algebraic coding will be hot, and I'm doing something in the algebraic direction now, which should be hot because it's more application-oriented. Buick (PhD in Basic Mathematics, Class of 2006): My main research interests now are the navier-stokes equations, Schr?dinger's equations, wave equations, and measure theory, among which the navier-stokes equations and Schr?dinger's equations are both hot at the moment.
Institutions Recommended
The Department of Mathematics at Zhejiang University, founded in 1928, has a long and glorious history, and the "Chen-Su School" founded by the famous mathematicians Prof. Chen Jianguong and Prof. Su Buqing was once famous all over the world. In 2007, the Mathematics Department of ZJU was recognized by the Ministry of Education as one of the national key disciplines, and the head of the discipline is Prof. Liu Kefeng, an internationally renowned mathematician. Basic Mathematics is one of the first doctoral degree-granting programs and postdoctoral mobile stations in China, and is part of the first national key disciplines (joint with Applied Mathematics), and has a national science talent cultivation base in Mathematics. Basic mathematics discipline strength of the institutions are also Fudan University, Nankai University, Peking University, Tsinghua University, Sun Yat-sen University, Nanjing University, Sichuan University and so on.
Applied Mathematics: The Popularity of the Cold
Professional Outline
Applied Mathematics is one of the broadest connotations of the five secondary disciplines of mathematics. Strictly speaking, computation, operations research, statistics are applied mathematical disciplines, but we now refer to the meaning of applied mathematics is much narrower, basically only divided into two general directions: computer graphics image (CAGD) and wavelet analysis. CAGD mainly refers to the use of modern mathematical methods for the study of image graphics theory and its applications, specifically in the direction of the image transformations and compression, deformation of the graphic and the generation of the direction of the image, also includes differential equations, geometric equations, and the generation of the graphic, and so on. It also includes the directions of differential equations, computational geometry and scientific computing. Computer graphics mainly includes image processing, computer graphics, computer-aided geometric design, scientific computing, medical image reconstruction. Wavelet analysis means fractal geometry and wavelet analysis, and approximation theory.
[Keywords] Prospects
sy1133 (Ph.D. in Applied Mathematics, Class of 2004): Applied Mathematics is a cross-disciplinary subject, so I think that any mathematical problem with an applied background can be seen as a development of the subject, and from this point of view, Applied Mathematics is thriving.
Lin Binbin (Master of Applied Mathematics, Class of 2007): Applied Mathematics started late in China, but it is very popular, although there is still a gap between the domestic development level and the international level. Applied mathematics graduates of the development of many directions, involving IT, information, computer graphics industry are good choices.
[Keywords] research hotspots
Lin Binbin (2007 Master of Applied Mathematics graduate students): Speaking of the research hotspots of applied mathematics, it should be said that there are a lot of hot topics in each direction, such as the processing of three-dimensional graphics. In the future, image searching and building image database to create software in image should be more popular, while reconstructing three-dimensional models using two-dimensional information and linking computerized automatic processing with artistic creation in graphics should be mainstream.
sy1133 (PhD in Applied Mathematics, Class of 2004): Applied Mathematics as a cross-discipline, the driving force is the engineering applications, biological computation, and the research direction related to it will also be popular in the future.
[Keywords] Suggestions
sy1133 (2004 PhD in Applied Mathematics): Although the word "application" is used, as a basic discipline, applied mathematics is still different from the engineering disciplines that are directly applied to the production of machinery and chemical industry, and the inputs and outputs are not necessarily proportional to each other. Just hold a "try" mentality to go to graduate school students need to carefully consider, if you really want to make some achievements in this area, you need to have a good mind and love of mathematics.
Lin Binbin (2007 Master of Applied Mathematics): In the study, we should lay a good foundation and focus on the development of all aspects of the ability, especially the programming ability and the ability to learn quickly. Because people who do CAGD need to program correctly in a very short time to verify their own hypothesis test, these programs are to do it themselves, it is impossible to go to the computer science department to help, so programming is a basic skill. Usually to learn more about the institutions of the professional information, to determine their own goals, in order to find their own favorite direction, because the examination is different from the college entrance examination, in addition to personal volunteers and tutors and other factors in which the ability to grasp the opportunity to fully depend on personal efforts.
Institutions recommended
Xinjiang University School of Mathematics and Systems Science is responsible for the national key disciplines "applied mathematics" and Xinjiang University "211 project" key disciplines "applied mathematics and systems engineering". Systems Engineering". In the national enrollment of master's degree in applied mathematics, Xinjiang University of Applied Mathematics in more than 200 institutions, Xinjiang University of Applied Mathematics disciplinary strength, followed by Peking University, Tsinghua University, Fudan University, Zhejiang University, Nankai University, Sichuan University, ranked seventh. The reason why I particularly recommend Xinjiang University is because Xinjiang University and the seven previously mentioned prestigious universities are the same as the key advantage of the discipline of applied mathematics units, but as a non-autonomous line of the three regions of the institution, the admission score line is much lower than the prestigious universities, the application of cost-effective.
Computational mathematics: making calculations for physics and engineering
Professional outline
Since the 20th century, because of the wide application of computers, computational mathematics has developed greatly, and the development of the theory of computational mathematics has contributed to the progress of computer and information science. Although computational mathematics has not been given enough attention at home, it is one of the hottest subjects abroad. The main research directions of computational mathematics include numerical generalized analysis and continuous computational complexity theory, numerical partial calculus and finite elements, nonlinear numerical algebra and complex dynamical systems, numerical solution of nonlinear systems of equations, numerical approximation theory, computer simulation and information processing, etc., and mathematical modeling and computation of engineering problems. Currently the best developed direction has been merged with the CAGD direction of applied mathematics, because the core of both is numerical computation and computer programming as a means.
[Keywords] Research Hot Spots
Cai Xiaohao (2006 Master's Degree in Computational Mathematics): Computational Mathematics is a very important discipline both domestically and internationally, which mainly researches problems such as scientific engineering calculations. There are many new research directions in computational mathematics because of the crossover of disciplines. The hottest directions now would be numerical solution of differential equations, numerical algebra, and flow learning, especially flow learning which has been hot for several years and is expected to continue to be hot.
Pan Yili (2007 master's degree in computational mathematics): computational mathematics is a science major formed by the cross-pollination of mathematics, physics, computer science, operations research and control science and other disciplines. As a cross-cutting discipline, it has a broad development prospect. A lot of research with practical physical applications (such as fluid dynamics, optical waveguides, photonic crystals, etc.) and a lot of problems that need to be solved, engineering people are often due to the lack of practical mathematical computational skills on the mathematical problems can not begin, do not know how to solve, which is just the need for the Department of Mathematics students to use their mathematical background to start to solve these problems.
Sophia (M.Sc. Computational Mathematics, Class of 2006): In short, computational mathematics is a field of study that does computations for physics and engineering. Personally, I think finite element is the hot direction now and in the future.
Recommended Institutions
Xi'an Jiaotong University is one of the first three institutions of higher education to establish a major in Computational Mathematics, and the discipline of Computational Mathematics is a national key discipline. On the basis of maintaining the advantages of the main research direction of Applied Mathematics and Computational Mathematics, XJTU attaches importance to and strengthens the research of mathematical foundation of information science, scientific computation, modern optimization, data analysis and statistical computation, numerical simulation of electronic systems, mathematical modeling of biological systems, etc., and possesses a group of experts and scholars such as Zhiping Chen, Zhengxing Cheng, Yanren Hou, Yidun Ma, and Kecun Zhang. Other institutions with strong computational mathematics disciplines include Peking University, Jilin University, Dalian University of Technology, Shanghai University, Shandong University, Xiangtan University, Northwestern Polytechnical University, Hunan University, etc.
Operation and Control Science: Providing New Ideas and Methods for Modern Science and Technology
Professional Outline
Operation and control science is a very practical discipline. Operations research and control are two related aspects, both centered on system optimization. The main research areas in operations research are mathematical finance, financial risk management, control theory, algorithm design and analysis, and mathematical planning. Cybernetics is the study of the regulation and control laws of all kinds of systems, which is a transversal discipline formed by the interpenetration of a variety of science and technology, such as automatic control, communication technology, computer science, mathematical logic, neurophysiology, statistical mechanics, behavioral science. Operations research cybernetics embodies the development trend of modern science as a whole and provides new ideas and scientific methods for modern science and technology. Our country from the early 1960s began to translate the introduction of cybernetics writings, but only in recent years began to carry out extensive and in-depth research on it, and in the economy, population, energy, production management and other aspects of cybernetics began to use cybernetics to establish mathematical models, such as input-output model, population model, etc. in the use of good results.
[Keywords] Research Hot Spots
Wang Songjing (2007 master's degree in operations research and cybernetics): I know that the direction of operations research is about engineering control models, financial models, logistics planning, etc. The hottest is financial mathematics, and it will be even hotter in the future, and the combinatorial optimization has not been paid attention to now, but it will be very hot in the future. Operations research direction employment prospects are broader, but for the average company, operations research and cybernetics majors to learn far more than the actual need, so the choice of research centers is a better way out.
[Keywords] Advice
Yang Zhichang (Master of Science in Operations Research and Cybernetics, Class of 2007): The application of operations research is very wide, and the good operation of any system requires operations research and optimization. In addition to operations research optimization ideas and methods, but also need to master some basic skills, such as graduate students in the cybernetics class to solve a large number of equations, because the equations can be solved is the key to the problem can be solved. Learning operations research brain to live, but the basic skills should also be solid. In addition, operations control is a very strong application of the discipline, so it is best to have more opportunities for practical operation.
Wang Songjing (2007 master's degree in operations research and cybernetics): We should pay more attention to the basics, and it's best to start contacting professional papers as early as possible. You can choose a specific direction according to your own situation. If you are really interested in math, you should study the fundamentals; otherwise, you'd better choose the application, and there will be more ways out in the future.
Institutions recommended
Shandong University mathematics discipline in 2007 was evaluated as "national key disciplines", its operations research and control science disciplines are in the China Science Evaluation and Research Center rankings (2006-2007) in one fell swoop over Tsinghua University, Fudan University, Zhejiang University, Nankai University and other prestigious schools, ranking the first in the world's top 100 universities, and the second in the world's top 100 universities, Nankai University and other famous schools, topped the list. Prof. Peng Shiguo has achieved world-leading original results in the research of the maximum principle of stochastic optimal control systems, the theory of inverse stochastic differential equations, and the theory of nonlinear mathematical expectation, which have been highly evaluated by domestic and foreign counterparts. Professor Wu Zhen is both a major theoretical subject in stochastic analysis and has a strong application background in financial mathematics and stochastic control, with his main research interests in the theory of forward and backward stochastic differential equations. Operations Research and Control Science discipline strength of the institutions are also Fudan University, Shanghai University, Chongqing University, Beijing Jiaotong University, Harbin Institute of Technology, Northeastern University, East China Normal University and so on.
Probability and Mathematical Statistics: Exploring Laws in Random Phenomena
Professional Outline
Random phenomena are very common in nature and human's daily life, such as the winning numbers of every welfare lottery. Probability theory is based on the statistical laws of a large number of random phenomena of the same kind, to make an objective scientific judgment on the possibility of a certain outcome of the random phenomena, to make an objective scientific judgment on the possibility of such occurrence, and to make a quantitative description; to compare the size of these possibilities. Mathematical statistics is the application of the theory of probability to study the regularity of a large number of random phenomena, to give strict theoretical proofs of the statistical methods obtained through a certain number of scientifically arranged experiments, and to determine the conditions for the application of the various methods, as well as the reliability and limitations of the methods, formulas, and conclusions, so that people can determine from a set of samples whether or not a certain judgment can be guaranteed to be correct with a fairly large probability, and that it is possible to control the probability of an The probability of error.
[Keywords] Research Hot Spots
Luo Yan (2007 master's degree in probability theory and mathematical statistics): Now the research in the direction of applied statistics is getting hotter and hotter, and applied statistics is closer to life, so it is more and more being emphasized by all walks of life. But we should not forget that the basis of statistics is probability. The research on probability is still worthy of attention.
Song Gao Yang (2007 probability theory and mathematical statistics master's degree): the main direction of statistics has a stochastic theory, data analysis, financial statistics, and so on, in the present situation, data analysis and data mining will be more popular, because the application of the scope of the wider. If you choose to work after graduate school, the more applied disciplines are the best choice.
[Keywords] Suggestions
Song Gao Yang (2007 master's degree in Probability Theory and Mathematical Statistics): Many universities in China categorize statistics and finance into one category, set up the School of Finance and Statistics or directly statistics into the Department of Economics. This is very understandable, because economics and finance are both based on statistics as the basic method. However, the scope of statistics as a secondary discipline of mathematics is very far from financial statistics, and the academic component is a bit higher. Statistics is based on probability theory, which is more theoretical and requires more basic knowledge of stochastic processes, probability limits, regression analysis, and so on. In fact, statistics is not only in finance only have a place, back to the beginning of the mentioned "biostatistics", is the popular "headline", which requires candidates to pay attention to when applying for their own choice in the end of the School of Economics statistics, or the Department of Mathematics statistics. The first thing you need to do is to get your hands on a new one, and you'll be able to do that.
Institutions recommended
The probability theory research group at Beijing Normal University has been through three generations, has 40 years of tradition and accumulation, with Chen Mufa, Li Zenghu, Zhang Yuhui, Wang Fengyu and other famous experts and scholars. This research group has been recognized as the "Chinese School of Ma's Processes" or the "Beijing School" by two major international mathematical journals. The main research directions include interacting particle systems, stochastic analysis, measure-valued martensian processes, and so on. Probability theory and mathematical statistics discipline strength of the institutions are Nankai University, Central South University, Northeast Normal University, Wuhan University, Huazhong University of Science and Technology, University of Science and Technology of China.
The tree of mathematics has flourished over the years. General key universities in the Department of Mathematics will have dozens or even hundreds of professors or lecturers, each of the research direction is different, they are different from each other as if Da Vinci's eggs, coupled with a variety of disciplines and the development of the intersection, but also produced more new branches of direction. Because of this, the discipline of mathematics is so rich and colorful.