(Subject code:0701)

Mathematics is a scientific system which researches the quantity relationship, the spatial pattern, and deductive system and so on. This is a collection of strictness, logic, abstraction, accuracy, creativity and imagination, and a vast intellectual treasure trove of resources which cover natural sciences, engineering technology, humanities and social sciences, etc. For human to recognize natural phenomenon and depict natural rules, mathematics subject plays a unique and irreplaceable role, besides, it’s the basis of all natural sciences.

Southwest Petroleum University (SWPU) received the qualification to offer the master’s degree in “Applied Mathematics” in 1998, and this discipline was approved as a “key discipline in Sichuan Province” in 2008 and was awarded the first-level master's degree in “Mathematics” in 2010. In 2003, the doctoral program of “Petroleum Engineering Computing technology" was set up for the first time in the country and the doctoral students were recruited. In 2018, it was successfully approved for a professional master' degree in “Applied Statistics”.

This discipline is tracking the mathematical frontier, based on the study of basic theory of mathematics, taking the mathematical problems in Petroleum Enterprises as the main research object. We pay attention to the intersection and integration of disciplines, mainly expands mathematics and applied mathematics research which focus on problem-oriented driving, and gradually form the following advantages and characteristics:          

(1) Carry on the innovation of basic theory following the frontier discipline: Research direction covers differential equations, optimization, system simulation and information processing, engineering computing theory and application, periodic solutions in differential equations, numerical format for fractional diffusion equations and its optimal control in anomalous diffusion, numerical solution of wave equation, Parameter inversion and identification of differential equations, non-elementary function constrained optimization, set-valued optimization, multi-level optimization and multi-constraint level optimization, nonlinear optimization problems on Hadamard manifolds, fractional optimal control, intelligent predictive control of complex systems, control of complex networks and stochastic fuzzy differential inclusions, etc.

(2) Developing question-driven mathematics research with the help of petroleum industry: By undertaking 117 projects of the national natural science-foundation of China and majoring scientific and technological projects (including sub-projects), etc.; and studying on the relatively basic theory and key technical problems of oil and gas ``Exploration-Development-Marketing". It's developed and enriched fundamental theory and methods in discipline such as Applied Mathematics, Computational Mathematics and so on.

(3) Multi-team coordination, theoretical research and cross application commonly development: School-level youth scientific research and scientific and technological innovation team led by Song Guojie and Wu Xinxing; the research team of pure mathematics represented by Yang Yan and Min Chao; and the Applied Mathematics team led by Liu Zhibin and Guo Dali, which is closely combined with other disciplines. All of them are spare no efforts to carry on mathematics theory and methods innovation and application, which form an academic atmosphere of respect, tolerance and equality, and coordinated research teams.       

 

1.      Target of Cultivating

Frist, recognizing and understanding Chinese basic conditions, having a rigorous style of study and certain ability of innovation. Secondly, mastering more solid mathematics basic theory and more systematic professional knowledge, having a certain understanding of the frontier progress and trend of the subject. And has received certain scientific research and training in one direction of applied mathematics, computational mathematics, operational research and cybernetics, probability theory and mathematical statistics. Ability to engage in scientific research or independently undertake specialized technical work. Thirdly, master a certain degree of Chinese, and be able to read professional foreign material skillfully. Finally, cultivating a high-level cross-composite talent and specialist in mathematical research who can apply mathematics knowledge to other relatively disciplines.

     

2.      Direction of Cultivating

According to target of cultivation, combined with the advantages and characteristics of the subject, there is the cultivation of a master’s degree in mathematics in four directions under the guidance of the key disciplines of ``Applied Mathematics” in Sichuan province.

（1）Applied Mathematics

Applied Mathematics is an important bridge between Mathematics and the Real World, it mainly researches mathematical questions in natural science and engineering technology, including information, economy, management and other important fields. To study mathematics theory and methods with actual background or application prospect, including to build relatively mathematical model and use mathematical methods to solve practical problems, etc. This research direction mainly engaged in ordinary Differential Equation, partial Differential Equation, Fractal and its Application, Power System, Information Network System and so on. The characteristics of this direction is applying mathematics theory and methods to social field such as finance, economy, petroleum exploration, development and other engineering technologies.

（2）Computational Mathematics

Computational mathematics is a numerical solution method and theory to research mathematical problems in science technology fields, especially concentrate on the research of efficient and stable numerical algorithm. Numerical algorithm has already used to reduce or even replace some large-scale experiments that are costly or even difficult to achieve. In recently years, relying on the characteristics and advantages of ``Petroleum and Natural Gas range”, ``Geophysics” and their supporting subject groups in our university, and on the basis of new theories and viewpoints arising from the theoretical breakthroughs in numerical algebra and numerical solutions of differential equations. The research directions of seismic wave field numerical simulation, oil and gas reservoir numerical simulation, image processing and application are formed.

（3）Operational Research and Cybernetics

Operational Research and Cybernetics are closely related and intersecting disciplines such as mathematics, management science, system science and so on. By developing and solving various optimal and control model in system, its provides theoretical basis to different system planning, design, management, optimal control decisions. Our university gives full play to the characteristics and advantages of the double first-class specialty of "Petroleum and Natural Gas Engineering" and its supporting subject groups. it is based on the theoretical research of system optimization and control, combined with computer simulation and experimental research. In the field of system simulation predictive control of oil and gas exploration, development and management, the professional direction characterized by operational research and cybernetics application research has been created.

（4）Probability Theory and Mathematical Statistics

Probability Theory and Mathematical Statistics is a discipline to study stochastic uncertainty. It provides scientific data processing and statistical inference methods for natural science and social science by studying essence and connotation in various stochastic phenomenon. Relying on the advantages of the subject of "Oil and Gas Engineering" and based on advanced statistical analysis theories and methods, this paper studies the important problems involved in the oil and gas field development industry chain, such as geological statistics, data monitoring, fault diagnosis, optimization decision-making and risk management, and provides theoretical support for oilfield exploration, development and management decision-making in uncertain environment. A series of unique research directions of probability and statistics have been formed.

 

3.      Basic Requirements

According to the ``basic requirements for doctoral and master’s degrees in first-tier discipline”, it’s better for students who got the master’s degree in this discipline to have a noble character and humanistic comprehensive quality, and to possess the ability of strong language expression, cooperation, communication, adaption, and innovative spirit. To master the basic theory and methods, to have a good mathematical science literacy. Students should have preliminary mathematical ability to study scientifically research and solve several practical problems by computer. Besides, they also should know the relatively frontier trends in fields of the discipline, to obtain a wide knowledge structure, to have the ability of comprehensive application of foreign languages and proficient in computer application, and to meet the prescribed requirements. They are all as follows:

 

3.1  Basic Knowledge Requirements

The master students of this subject should master the core conceptions and basic knowledge system of analysis, statistics or calculation in mathematics, and then study all direction of the subject about the basic knowledge and some professional knowledge and new progress.

(1)   Applied Mathematics

The basic knowledge involved includes: Partial Differential Equation Theory and Application, Fuzzy Mathematics, etc.

(2)   Computational Mathematics

The basic knowledge involved includes: Higher Numerical Calculation, Numerical Solution of Differential Equation, Modern Optimization Technology, etc.

(3)   Operational Research and Cybernetics

The basic knowledge involved includes: Optimization Theory and Method, Non-linear Analysis, Modern Optimization Technology, etc.

(4)   Probability Theory and Mathematical Statistics

The basic knowledge involved includes: Higher Mathematical Statistics, Random Process, etc.

 

3.2  Basic Quality Requirements           

(1)    Students are required to have a good scientific and mathematical quality, a rigorous academic attitude, a strong extending spirit, what’s more, are good at accepting new knowledge, arising new thinking, exploring new tasks and having a good teamwork spirit.  

(2)    Students should advocate the scientific spirit, abide by the law, rigorous style of study, good conduct, have a strong dedication to work and dedication to science.

(3)    Do not infringe upon the intellectual property rights of others; respect the facts and abide by academic norms in the signature of results, citation of works, collection and use of data, evaluation of results, etc.

            

3.3  Academic Ability Requirements

(1)   Ability to acquire knowledge

To have the ability of accessing literature materials personally, conducting literature reviews, the necessary ability of further learning mathematics and other related subjects.

(2)   Capacity for scientific research

Having the ability to carry out theory research independently and apply mathematics to solve actual problems, in professional direction, students should do some theory and practical meaning achievements.

(3)   Capacity to evaluate results

When evaluating the achievements of others, we can maintain the objectivity and fairness of academic evaluation on the basis of fully mastering the relevant materials, theories, application results and data at home and abroad, and strive to be comprehensive and accurate.

(4)   Ability to communicate academically

To have the ability to communicate academic exchanges with counterparts at home and abroad, be able to clarify question, exchange knowledge, and report on academic and scientific achievements.

(5)   Able to use computers and modern information tools to engage in scientific research, teaching, high-tech development or management.

 

4.      School System and training Mode

 

4.1 School System

The standard academic system for master students is 3 years and the longest limit of study is 5 years. Those who have excellent grades can graduate in advance, but the shortest length of study is not less than 2 years.

4.2 Training Mode

(1)   Implementation of mentor responsibility system. Mentor makes the feasible cultivation plan for each postgraduate under the degree regulations and training programs. The role of teacher is teaching and educating students, it’s necessary to regularly inspect, conscientiously guide, supervise, and care about the political thinking, professional study, scientific research work, and dissertations of postgraduate students. Cultivating students’ thinking in science, ability of work independently, creativity and enterprising spirit should be concerned. It’s better to organize the postgraduate periodically to carry out academic exchange activities, to know the progress and thinking in their research and find and adjust problems immediately. For students to understand the development trend of the field, the mentor should create conditions for them to join in academic exchange activities at different level.

(2)   The first school year is dominated by courses. We should not only master the solid theoretical foundation and systematic professional knowledge in the subject, but also be familiar with the basic methods of scientific research. With the guidance of mentors, postgraduate students should research the latest development trend and technical progress in direction of this subject, and cultivate research interest to prepare for dissertation opening report. The second and third school year are dominated by scientific research and dissertation work, besides, students should strengthen the practicing and cultivation of their self-study ability, scientific research ability and language expression ability.

 

5.      Cultivation Link

  

5.1 Learning of Course

Curriculum learning is an important link to ensure the quality of postgraduate training. The curriculum learning of master students emphasizes the consolidation of the theoretical basis of the subject, the study and practice of research methods, the cultivation of independent thinking and critical questioning ability, and the promotion of innovation and academic technology development ability. To strengthen the ability of self-study, to emphasize the equal importance of compulsory course learning, optional course learning and self-study, to attach importance to learning in scientific research practice and teaching assistant management, to practice while learning, and to cultivate humanistic quality, scientific spirit, team cooperation spirit and intellectual property awareness, abide by academic norms and academic ethics.

 

5.2 Practicing Link

In the scientific research practice of cultivating postgraduates, mentor or academic teams should activity create an atmosphere of innovation, cooperation and competition. Give full paly to the role of scientific research and practice bases inside and outside the university, and run through scientific experiments, scientific research training, academic training, and social practice throughout the whole training process. To cultivate the scientific experiment ability, scientific research ability, innovation ability, teamwork and organization ability of master students.

In addition to various forms of teaching practice, the content of practice may also participate in social investigation, undertake scientific research, design, investigation, consultation, technical development and service both inside and outside the school. The details of the implementation shall be carried out in accordance with the relevant provisions of the school and the school of science.

 

5.3 Dissertation

    The master thesis must be completed independently by the postgraduate student himself and under the guidance of the tutor, and meet the normative and quality requirements. The actual workload of the dissertation is not less than 1 year.

5.3.1 Argumentation on the opening of Dissertations

(1)   Selection of Thesis Topic. It’s necessary to choose a topic with value in mathematics theory or mathematics application. What’s more, students should have new views on the topic, can show that the author has mastered a more solid basic theory and more systematic expertise in his subject, and own the ability to engage in scientific research or independently undertake specialized technical work.

(2)   Literature review and Problem analysis. More comprehensive reflection of the proposed research direction and related scientific fields of development and the latest results, basic understanding of domestic and foreign research status and existing problems, objective summary.

5.3.2 Reply on Dissertation

(1)   Qualification Examination

Before applying for paper reply, master students should examine whether they have the conditions to apply for paper reply through the pre-hearing and pre-reply organized by the institute (room, center) or the tutor team.

a)        The innovation and value of thesis.

To modify or supplement for the present theory and method; creatively to solve the actual problems and difficulties with the present theory and method, besides, to solve the difficult problem in engineering or economy field by new theory and new methods. The thesis and its achievements have certain influence and function on the subject direction and the technical progress of the industry.

b)        Basic knowledge and scientific research ability.

It shows that the author has a solid basic theory and systematic professional knowledge; has a strong ability of working on scientific research independently; and adopts advanced technology, method information to carry out thesis research work. The research of thesis is more difficult, and full workload in research, theoretical analysis, calculation and comprehensive assessment, etc.

c)        Paper writing and specification.

The citation chart and sentence are clearly marked; the structure of the paper is reasonable and logical; the text expression is accurate and smooth; the chart, terminology, unit symbols and so on conform to the relevant norms.

(2)   Reply

After submitting the dissertation, the student should actively prepare the dissertation reply. The main contents and innovative achievements and this paper should be clarified succinctly, the ideas are clear, the key points are prominent, the answers to the questions are targeted, and they have their own opinions.

(3)   Modification and Perfection

At the end of the paper reply, students should modify their dissertation seriously to meet the basic requirements of the paper archiving and sampling inspection based on the suggestions of mentors, review experts and reply experts.

 

6.      Curriculum System and curriculum

The postgraduate courses in mathematics should be divided into the basic theory courses, professional core courses and professional elective courses. Among them, the basic theory course includes the national conditions of China and the language course; the professional core courses should cover the basic knowledge of discipline which should be mastered in mathematics of the first-level subject, such as analysis, statistics, etc.; the professional elective courses cover the professional basic knowledge and professional knowledge that each research direction should master respectively.

(1)   Basic Theory Courses (6 credits)

   Take two courses. For details, see the list of requirements for curriculum and training links.

(2)   Professional Core Courses (4 credits)

Take two courses. For details, see the list of requirements for curriculum and training links.

(3)   Professional Elective Courses (10 credits)

Take five courses. For details, see the list of requirements for curriculum and training links.

 

7.      Degree Standard and Degree Award

The graduation results of mathematics students in Southwest Petroleum University should meet the conditions of “The basic requirements of Southwest Petroleum University on the academic Achievement of Master's degree Application” (Southwest Petroleum University [2011] No. 34). If postgraduate students graduate ahead of schedule, they will be carried out in accordance with the regulations of “Southwest Petroleum University on the early graduation of Master's degree students” (Southwest Petroleum University [2014] No. 19). The detailed rules for the implementation of the award of master's degrees in mathematics of Southwest Petroleum University shall be carried out in accordance with the rules for the implementation of the award of doctorates and master's degrees of Southwest Petroleum University (School Research [2009] No. 3). The instructor may independently determine the academic achievement requirements for the award of a degree by an international master's degree.

 

Appendix: a List with the requirements of Curriculum setting and cultivation link

 

Notes:

① Students who have studied in our school and have received "China profile" credits (the grades are valid for 5 years) may apply for exemption.

② Students who have received credits for the "Chinese" course at the time of admission (the results are valid for 5 years) or who have reached the new HSK level 5 in science and the new HSK6 level in the liberal arts may apply for exemption from the Chinese language level examination.