Financial Mathematics
1. Program Description
The Financial Mathematics is the application of mathematical methods to the solution of problems in finance. It draws on tools from probability, statistics, stochastic processes, and economic theory. The methods of financial mathematics are widely used by investment banks, commercial banks, hedge funds, insurance companies, regulatory agencies, etc. The undergraduate program of Financial Mathematics in Nanjing Normal University aims to cultivate students’ abilities, which are adapted to the Jiangsu’s and national economic and social development needs of high quality in theory and application research on financial mathematics.
Successful graduates of this program are expected to master the analytical methods and quantitative skills. After graduation from this program, the students should become high-level professional with certain international vision, and be well-positioned to advance careers in public, private, and governmental financial institutions, etc. In addition, most of them should be graduate students in high-level universities and research institutions both at home and abroad.
2. Program Duration and Credit
This is a four-year undergraduate program, which can be completed within a minimum of three years and a maximum of seven years.
A total of 162 credits are required upon the completion of the program.
3. Curriculum
Three modules of courses are offered for the program: Basic Curriculum, Essential Curriculum, and Elective Curriculum. The Basic and Essential curricula are compulsory for a Bachelor’s degree.
The Elective Curriculum in the list includes extended disciplinary courses offered by the school into which an individual student is admitted, as well as cross disciplinary courses offered by other schools. Students can choose the extended and cross disciplinary coursesaccording to their personal interests and career plans; however, credits should be approved by the School.
(1) Basic Curriculum
|
Course Code |
Course |
Credit |
Semester |
Remark |
|
100701062110 |
Mathematical Analysis(Ⅰ)* |
7 |
1 |
|
|
100701062111 |
Advanced Algebra (Ⅰ)* |
6 |
1 |
|
|
100701062112 |
Analytic Geometry |
3 |
1 |
|
|
100701062113 |
Mathematical Analysis(Ⅱ)* |
7 |
2 |
|
|
100701062201 |
Mathematical Analysis(Ⅲ)* |
7 |
3 |
|
|
100701062202 |
Advanced Algebra (Ⅱ)* |
6 |
2 |
|
|
100701062203 |
Mathematical program introduction and discussion |
2 |
1 |
Including 2 practice credit |
(2) Essential Curriculum
|
Course Code |
Course |
Credit |
Semester |
Remark |
|
100701063018 |
Stochastic Differential Equations |
3 |
5 |
|
|
100201152202 |
Microeconomics |
6 |
3 |
|
|
100201152201 |
Macroeconomics |
5 |
4 |
|
|
100712063001 |
Probability Theory * |
3 |
3 |
|
|
100701063001 |
Ordinary Differential Equations * |
3 |
3 |
|
|
100712063002 |
Mathematical Statistics * |
4 |
4 |
|
|
100712063004 |
Actuarial Science of Insurance |
3 |
4 |
|
|
100712063005 |
Applied Stochastic Processes* |
3 |
4 |
|
|
100701063006 |
Real Variable Function* |
3 |
5 |
|
|
100701063019 |
Operations Research |
3 |
5 |
|
|
100203063001 |
Econometrics |
4 |
6 |
Including 1.5 practice credit |
|
100203063002 |
Graduation Practice |
2 |
8 |
Including 2 practice credit |
|
100701063011 |
Graduation Thesis |
4 |
8 |
Including 4 practice credit |
(3) Elective Curriculum
|
Course Code |
Course |
Credit |
Semester |
Remark |
|
100712164001 |
The Principle of Accounting |
3 |
2 |
|
|
100010191003 |
Programming in C |
4 |
2 |
Including 1 practice credit |
|
100701194003 |
Database Developing Language |
3 |
3 |
Including 1 practice credit |
|
100203064002 |
Stochastic Calculus for Finance |
3 |
6 |
|
|
100712064006 |
Stochastic Control |
3 |
6 |
|
|
100701063004 |
Functions of Complex Variable |
3 |
6 |
|
|
100701063007 |
Mathematical Physics Equations |
3 |
6 |
|
|
100701064009 |
Research of Mathematical Analysis |
3 |
7 |
|
|
100701064005 |
Research on Advanced Algebra |
3 |
7 |
|
|
100203153005 |
Monetary Finance |
3 |
3 |
|
|
100203153010 |
Investments |
3 |
5 |
Including 0.5 practice credit |
|
100203154005 |
International Finance |
3 |
4 |
|
|
100203064003 |
Financial Statistics Analysis |
3 |
6 |
|
|
100712064010 |
Foundations of Security Investment Analysis |
3 |
6 |
|
|
100712064004 |
Risk Theory |
2 |
5 |
|
|
100712063007 |
SAS and Statistical Analysis |
4 |
5 |
Including 1 practice credit |
|
100712064003 |
Options and Futures Pricing Theory |
3 |
6 |
Including 1 practice credit |
|
100712064008 |
Statistical Modeling and Data Analysis |
3 |
6 |
Including 1 practice credit |
|
100203064001 |
Topics of Mathematical Finance |
3 |
7 |
|
|
100701064003 |
Algebra |
4 |
7 |
|
|
100701064013 |
Modern Analysis |
4 |
7 |
|
|
100712064001 |
Foundations of Measure and Probability |
4 |
7 |
|
(Note: 1. Odd-number semesters are the fall semesters and even-number semesters are the spring semesters in each academic year.
2. The asterisk * marks a core course.)
4. Core Courses and Introductions
100701062110 Mathematical Analysis(Ⅰ) (7 cr.)
Prerequisites:
This course mainly introduces the theory of completeness of real numbers, the differential calculus of one-variable function and its applications. The main contents of Mathematical Analysis (Ⅰ) are as follows: sets of real numbers and functions, limits of number sequence, limits of a function, continuities of the function, derivatives and differentiations, mean value theorems of differentiation and their applications, and the theory of completeness of real numbers, and so on. The teaching of this course not only pays attention to integral introduction of its basic principles and major methods, but also emphasizes the abilities of abstract, logic and calculation.
The teaching of this course will make the students to correctly understand the basic concepts of Mathematical Analysis, to master the basic theories and basic techniques of Mathematical Analysis, to improve the ability of abstract thinking and strictly logical reasoning. To cultivate the students to have the ability to perform mathematical calculations and apply mathematics.
100701062113 Mathematical Analysis (Ⅱ) (7 cr.)
Prerequisites:
This course introduces the integral calculus of one-variable function, the theory of series, and their applications. The main contents of Principles of Mathematical Analysis(Ⅱ) are as follows: indefinite integral, definite integral, some applications of definite integral, improper integral, series of number terms, sequence of functions and series of function terms, power series, Fourier series. The teaching of this course not only pays attention to integral introduction of its basic principles and major methods, but also emphasizes the abilities of abstract, logic and calculation.
The teaching of this course will make the students to obtain an integrated knowledge of the integral calculus of one-variable function, the theory of series, and their applications. Students can master the methods and basic theories to study the analysis properties of one-variable function.
100701062201 Mathematical Analysis(Ⅲ) (7 cr.)
Prerequisites:
This course introduces the calculus differential and integral calculus of function of many variables and their applications. The main contents of Principles of Mathematical Analysis (Ⅲ) are as follows: limits and continuities of function of many variables, the differential calculus of multivariable function, implicit function theorems and their applications, integral depending on parameters, curvilinear integral and surface integral, multiple integral, the theory of field. The teaching of this course not only pays attention to integral introduction of its basic principles and major methods, but also emphasizes the abilities of abstract, logic and calculation.
The teaching of this course will make the students to obtain an integrated knowledge of the differential-integral calculus of function of many variables, and their applications. Students can master the methods and basic theories to study the analysis properties of function of many variables.
100701062111Advanced Algebra (Ⅰ) (6 cr.)
Prerequisites:
This textbook is designed to teach the university mathematics student the basics of the subject of linear algebra. The text has two goals: to teach the fundamental concepts and techniques of matrix algebra and abstract vector spaces, and to teach the techniques associated with understanding the definitions and theorems forming a coherent area of mathematics. So there is an emphasis on worked examples of nontrivial size and on proving theorems carefully.
(1) The basic theory of the polynomials over the number fields. (2) The properties of the determinants and some computing skills, Cramer’s rule. (3) The basic concept of system of linear equations and Gaussian elimination. (4) The operations of matrices, the determinant and rank of matrices multiplication, and the inverse of the matrix, the block of matrices, elementary matrix. (5) The basic theory of quadratic form, the properties and applications of the positive definite quadratic forms.
100701062202Advanced Algebra (Ⅱ) (6 cr.)
Prerequisites:
This textbook is designed to teach the university mathematics student the basics of the subject of linear algebra. The text has two goals: to teach the fundamental concepts and techniques of matrix algebra and abstract vector spaces, and to teach the techniques associated with understanding the definitions and theorems forming a coherent area of mathematics. So there is an emphasis on worked examples of nontrivial size and on proving theorems carefully.
(1) The concepts and theory of linear spaces and linear mappings. (2) The properties of operations of linear transformations, the definitions and computings of eigenvalues, eigenvectors, and characteristic polynomials. (3) The basic properties of Euclidean spaces, orthogonal bases, and Schmidt orthogonalization method, the definitions of the least squares method and the unitary spaces.
100712063001 Probability Theory (3.00 cr.)
Prerequisites:
Through learning, students are required to grasp the basic concepts, theories and methods of probability theory, learn how to processing method of random phenomena, master the basic ability to use probability method to solve practical problems and make a good foundation for the study on some subsequent professional statistics courses.
Probability theory mainly introduces the mathematical theories and methods of statistical regularity of random phenomena, such as events and probability, random variables and their distributions, random vectors and their distributions, numerical characteristics and characteristic functions of random variables, law of large numbers and the central limit theorem and so on. Axiomatic definition of probability, the definitions of random variable, the distributions of random variable, numerical characteristics and characteristic functions of random variables and law of large numbers will be highlighted.
100712063002Mathematical Statistics (4.00 cr.)
Prerequisites:
Trough the study of the course, students are required to master the basic concepts, basic theories and methods of mathematical statistics, learn to use common statistical methods to solve some practical problems, and lay a good foundation for the follow-up courses.
Mathematical statistics is based on the Probability theory, which is a discipline about the collection, organization and analysis of the data. The main contents of this course are the basic concepts, statistics and distribution; parameter estimation, including point estimation, the evaluation criteria, sufficience and completeness, interval estimation; hypothesis test, including the basic concepts, hypothesis test about mean and variance, goodness-of-fit test of distribution function, test of independence, optimal test, other methods of hypothesis test; analysis of variance (ANOVA), including one-way ANOVA, two-way ANOVA; Bayesian statistics, including the estimation of Bayesian priori distribution and posterior distribution, Bayesianestimation,Bayesian inference.
100712063005Applied Stochastic Processes (3.00 cr.)
Prerequisites:
Stochastic processes is an important branch in the field of modern probability theory, through the study of the course of stochastic processes can further improve the mathematical ability of students' understanding the phenomenon of stochastic , preliminary master the control capacity of stochastic system ; through the study of this course, students have a preliminary knowledge ability to read the relevant literature. Basic requirements: students are required to understand the basic concepts and methods of stochastic processes, familiar with the basic theory of several stochastic processes, and can use them to solve some simple practical problems.
As one of the important branches of modern probability theory,the stochastic process theory provides us rich theoretical guidance and practical methods to explore the stochastic phenomena in the real world. Along with the progress of the society, more and more people need to understand and even to use the stochastic process theory in practice. The stochastic process theory is not only essential for professional experts in probability and statistics, but also for many others in mathematics, natural science, technology, economy, management, and even for researchers in social science. This course focuses on teaching students the basic concept, ideas and methods of the stochastic process theory. In this course we introduces the theories, methods and applications of the important processes such as Poisson process, renewal process, Markov chain, Martingale, Brown motion and stochastic integral. Students with higher mathematics and elementary probability theory can master the main content of the course without difficulties.
100701063006 Real Variable Function (3.00 cr.)
Prerequisites:
The Real Variable function is one of important basic courses in department of Mathematics for undergraduates. It is continuation and development of Mathematical Analysis. The theory of Lebesgue measure and Lebesgue integral are established by applying analysis methods in the space of n-dimension Euclid. The basic idea of abstract analysis must be understood by students. This course focus on cultivating students' thinking ability and logical reasoning ability, to lay a good foundation for the subsequent academic research.
The theory of Real Variable Functions is an important foundation of modern mathematics, the emergence of real variable function theory is as the main branch of modern mathematics - the birth of modern analysis mathematics. The main contents of this course are included as follows: (1). Set theory and related knowledge of point set (Chapter 1 and Chapter 2). (2). Measure theory and Measurable functions (Chapter 3 and Chapter 4): the definition of Lebesgue measurable set in the sense of Caratheodory and the notion of measurable functions, the relation between measurable functions and continuous functions, the relation of measurable functions and simple functions, the three convergences of measurable functions (almost everywhere convergence, uniform convergence and convergence in measure). (3). Lebesgue integration and its main properties (Chapter 5): the definition of Lebesgue integral and its basic properties, several important limit theorems of Lebesgue integral, etc.
100701063001 Ordinary Differential Equations (3.00 cr.)
Prerequisites:
The students could learn the elementary integral methods of the first order differential equations, and could solve the higher-order linear differential equations (systems) with constant coefficients, and understand the existence and uniqueness theorem, and know some qualitative and stable properties for differential equations. Finally, the students should have the ability of analyzing and solving problems.
Ordinary Differential Equations introduces how to solve the ordinary differential equations and investigates the qualitative properties of solutions. The main contents of this course are the Elementary integral methods; Fundamental theorems; First-order linear differential systems; Higher-order linear differential equations; Qualitative theories and stability theories; and Theories of the first-order partial differential equations, etc. After the systemic training, the students can master the fundamental knowledge and the necessary theories in the study of ordinary differential equations, and grasp the fundamental calculation methods. Based on these training, the students can also continue to learn the follow-up courses including physics, mechanics and others.