Information and Computing Science
1. Program Description
The undergraduate program for Information and Computing Science in Nanjing Normal University is designed to provide students with an education that prepares them for careers as research in high-level university, scientific research institutions and enterprise with practicing mathematicians or further study. In order to accomplish this aim, certain objective have been incorporated into the curriculum as follows:
To give students a solid foundation in fundamental mathematics upon which to build their understanding of mathematical applications and creativity; to provide a broad-based applied mathematics education and a certain introduction in the field of information; to integrate computing literacy and algorithm design ability throughout students’ studies because computers are indispensable tools for solving mathematical problems; foster in students an eagerness to solve scientific, industrial and commercial problems of concern to the local community and beyond; to give students a thorough knowledge in numerical methods, numerical analysis, and modeling for practical computing in a broad range of disciplines and applications; to provide students rigorous research and analytical skill to evaluate research techniques, methodologies and to interpret results in their own field and research.
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 160 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 courses according 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 |
|
100701063001 |
Ordinary Differential Equations* |
3 |
3 |
|
|
100701063012 |
Discrete Mathematics* |
3 |
3 |
|
|
100712063001 |
Probability Theory |
3 |
4 |
|
|
100701063004 |
Functions of Complex Variable |
3 |
4 |
|
|
100701063013 |
Computational Methods(Ⅰ)* |
4 |
4 |
Including 1 practice credit |
|
100701063006 |
Real Variable Function* |
4 |
5 |
|
|
100701063014 |
Optimization Method |
3 |
6 |
|
|
100701063015 |
Computational Methods(Ⅱ)* |
4 |
5 |
Including 1 practice credit |
|
100809063001 |
Data Structure and Algorithm |
3 |
5 |
Including 1 practice credit |
|
100701063007 |
Mathematical Physics Equations |
4 |
6 |
practice course |
|
100701063016 |
Numerical Partial Differential Equations |
4 |
7 |
Including 1 practice credit |
|
100701063017 |
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 |
|
100701064001 |
Mathematical Modeling |
3 |
4 |
Including 1 practice credit |
|
100010191003 |
Programming in C |
4 |
|
Including 1 practice credit |
|
100010072101 |
College Physics B（1） |
3 |
|
|
|
100010072102 |
College Physics B（2） |
2 |
|
|
|
100010072103 |
College Physics Experiments 1（1） |
0.5 |
|
Including 0.5 practice credit |
|
100010072104 |
College Physics Experiments 1（2） |
0.5 |
|
Including 0.5 practice credit |
|
100701064009 |
Research of Mathematical Analysis |
3 |
7 |
|
|
100701064005 |
Research on Advanced Algebra |
3 |
7 |
|
|
100712063002 |
Mathematical Statistics |
3 |
5 |
|
|
100701063003 |
Abstract Algebra |
3 |
4 |
|
|
100701063009 |
Functional Analysis |
4 |
6 |
|
|
100701064015 |
The Finite Element Method |
3 |
7 |
Including 0.5 practice credit |
|
100701064011 |
Design and analysis of algorithms |
2 |
6 |
Including 1 practice credit |
|
100701064008 |
Matrix Theory |
2 |
6 |
|
|
100701194001 |
Java Programming |
4 |
6 |
Including 1 practice credit |
|
100701194002 |
Operating System |
3 |
6 |
|
|
100701194003 |
Database Developing Language |
3 |
3 |
Including 1 practice credit |
|
100809064001 |
Computer Networks |
2 |
6 |
Including 0.5 practice credit |
|
100701064002 |
Fundamental Measure Theory |
3 |
6 |
|
|
100701064003 |
Algebra |
4 |
7 |
|
|
100701064013 |
Modern Analysis |
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.
100701062111 Advanced 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.
100701062202 Advanced 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.
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.
100701063012 Discrete Mathematics (3.00 cr.)
Prerequisites:
Discrete mathematics is the basic part of mathematics devoted to the study of discrete (as opposed to continuous) objects. It mainly includes mathematical logic foundation, set theory, and introduction of combinatorial mathematics, graph theory and related algorithms. A course in discrete mathematics provides the mathematical background needed for all subsequent courses in computer science (a example is data structure) and for all subsequent courses in the many branches of discrete mathematics, for examples, number theory, abstract algebra etc.
1. Ability to read, understand, and construct mathematical arguments and proofs.
2. Know well the techniques for counting of different kinds and objects.
3. Understand the abstract mathematical structures that represent objects and the relationships between them. Examples are sets, permutations, relations, graphs and trees.
4. One ability to solve related problems is to specify an algorithm.
5. Develop the ability to structure new models in various domains using discrete mathematics.
100701063013 Computational Methods(Ⅰ) (4.00 cr.)
Prerequisites:
The main task of this course is to learn the basic ideas and theories of the commonly used numerical algorithms. After the course, the students can master the main concepts and theories of numerical computing, have good abilities of programming and debugging, possess certain abilities of analyzing and solving problems in the real world, and have enough foundation for further studying and researching.
The course of computational methods is a compulsory and core curriculum for the undergraduate students majoring in information and computational science. It is a significant branch of modern mathematics, which is closely related to the engineering technology and scientific researching. In this course, students will learn to propose numerical algorithms for certain problems, to write programs to obtain approximate solutions via computers, and study the basic concepts and theories of the numerical methods.
100701063006 Real Variable Function (4.00 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.
100701063015 Computational Methods(Ⅱ) (4.00 cr.)
Prerequisites:
The main task of this course is to learn the basic ideas and theories of the commonly used numerical algorithms. After the course, the students can master the main concepts and theories of numerical computing, have good abilities of programming and debugging, possess certain abilities of analyzing and solving problems in the real world, and have enough foundation for further studying and researching.
The course of computational methods is a compulsory and core curriculum for the undergraduate students majoring in information and computational science. It is a significant branch of modern mathematics, which is closely related to the engineering technology and scientific researching. In this course, students will learn to propose numerical algorithms for certain problems, to write programs to obtain approximate solutions via computers, and study the basic concepts and theories of the numerical methods.