School of Mathematics Science

Department of Mathematics

Department of Computer and Information Science

The Department of Mathematical Statistics and Actuarial Science

The School of Mathematics and Science contains the Department of Mathematics, the Department of Information Science, and the Department of Mathematical Statistics and Actuarial Science.

Department of Mathematics

Objectives:

This department aims to equip students with fundamental knowledge to acquire and study any mathematical subjects which interest them, and to a certain extent, to apply what they have learned. Courses prescribed are divided into three categories: fundamental, core, and applied courses. Core courses provide students with the preliminaries needed to be a man of mathematics. In addition, emphasis is put on subjects such as information science, management science, economics, and the actuarial approach to provide solid training for future policy-makers and computer language designers.

General Courses Credits

English	4
English Lab Drills	2
Constitution: The Foundation Spirit of R.O.C	4
Basic Concepts of Computer	4
Military Training	2
Physical Education	4

Major Courses Credits

Calculus	8
Linear Algebra	6
Fundamentals of Mathematics	6
Advanced Calculus	8
Algebra	6
Probability and Statistics	6
Differential Equations	4
Mathematical Programming	6
Topology	6
Complex Analysis	6
Differential Geometry	6

Elective Courses Credits

Physics	4
Economics	4
Military Training	2
Mathematics for Insurance	4
Numerical Analysis	6
Discrete Mathematics	4
Physical Education	4
Regression Analysis	3
Experimental Design	3
Analysis	6
Seminar	4
Series Theory	4
Algebra Ⅱ	6
Real Analysis	6
Decision Theory	6
Mathematical Statistics	6
Insurance	6

Course Description:

English (Credits 4)

This course is designed as to give the students an adequate command of the English language to enable him or her to read works of fiction and non-fiction, newspapers and magazines. In class, emphasis is placed on text explanation in English, reading, listening and group discussion.

English Lab Drills (Credits 4)

The course is designed for use as part of freshman English training, covering two types of drill materials: (1) Conversation Topics, including some specialized conversation in different tenses, intonation and sound. The coordinated reading which follows presents the subject matter for reference and enjoyment. (2)Audio-Visual Approach, taught with film strips on various subjects, designed for the practice of the expressions of daily usage. The strips emphasize the students' participation in the talks on the film subject.

Basic Concepts of Computers (Credits 4)

This is an introductory course on modern computer concepts. It presents the up-to-date computer technologies to students, which includes hardware and software applications. The hardware contains CPU, memory, input and output devices. The software contains compiler and other translator programs, software applications, and system software.

Calculus (Credits 8)

Calculus includes two fundamental concepts: the derivative and definite integral. The concepts of derivative and definite integral are defined by limiting processes. The notion of limit is the initial idea that separates calculus from elementary mathematics. The course is designed to develop the student’s understanding of the theoretic of calculus and its application.

Linear Algebra (Credits 6)

Each theme is developed first for system of linear equations and matrices, then for vector space and Euclidean space, determinant and finally for linear transformation between vector space and diagonalization of matrices.

Fundamentals of Mathematics (Credits 6)

This course covers the materials necessary for students to succeed in the further study of advanced mathematics. The topics include elementary logic, method of proof, set theory, relations, functions, cardinality, and Boolean algebra.

Physical Education (Credits 0)

This course aims to help students to acquire common sense of sports rules and skills. Sports like basketball, volleyball, baseball, table tennis, badminton and soccer are instructed in different classes.

Advanced Calculus (Credits 8)

To present elementary classical analysis in a concrete setting, emphasizing specific techniques important to classical analysis and its applications.

Algebra (Credits 6)

Each theme is developed first for integers, then for polynomials and finally for rings and groups. This enables students to see where many abstract concepts come from, why they are important, and how they relate to one another.

Differential Equations (Credits 4)

This course introduces methods in solving deferential equations. The topics include first order differential equations, higher order differential equations, series solutions of linear equations, Laplace transfon-n, and systems of linear first order differential equations

Economics (Credits 4)

The course include demand and supply, elasticity, utility and preference, production and cost, markets for goods and services, markets for factors of production, public economics, environment and resource, gross national product, employment, investment, aggregate supply and aggregate demand, macroeconomics fluctuation, growth, fiscal policies and monetary policies, and international economics.

Mathematical Programming (Credits 6)

This course is designed to develop the student's understanding of the importance of implemented mathematics programming. Mathematics problem is the application of s scientific approach to solving management problems in order to helps managers make better decisions.

Topology (Credits 6)

This course is mainly designed to provide the student with a sound background in point-set topology, so that he has the mathematical maturity to go on studying other more advanced mathematical courses. Apart from repeatedly exercising the concepts compactness and etc., main topics of point-set topology, we will also introduce some basic notions of algebraic topology should time permit.

Complex Analysis (Credits 6)

In this course, we study the theory of functions of a complex variable, together with some of its applications. Topics presented in this course will include Green's Theorem, Cauchy's Theorem and Cauchy's Formula, Residue Theorem, conformal mapping, harmonic functions, the Fourier transform and the Laplace transforms.

Numerical Analysis (Credits 6)

The emphasis of this course lies on the theory of numerical methods and its application to educate the learners by utilizing computers to solve all kinds of problems relating with mathematics with the aid of numerical analysis methods. It includes: Solution of Nonlinear Equation, Matrix Determinant and Simultaneous Equation Solution, Interpolation Methods, Approximation, Numerical Differentiation, Numerical Integration, and Numerical Solution of Ordinary Differential Equation.

Discrete Mathematics (Credits 4)

A major theme of this course is to study discrete objects and relationships among them. This course includes set theory, relations and functions, permutations and combinations, graph theory, recurrence relations, generating functions, boolean algebra, analysis of algorithms, coding theory, finite state machines, and designed theory.

Differential Geometry (Credits 6)

This course studies the differential geometry of curves and surfaces in Euclidean 3space, both in its local and global aspects. Apart from guiding the student to develop his geometrical intuition through concrete examples, we shall try to equip the student with basic techniques of doing rigorous differential geometrical analysis. Efforts will also be made to ensure that, near the end of the course, the notion of differentiable manifold is briefly introduced.

Department of Computer and Information Science

Objective:

ⅠThe Future Development of the Department

A. Human Management

The Department was established with the purpose of considering the teachers and the students as members of a family who may offer mutual assistance to each other. Apart from the learning and instructing of the professional knowledge, the Department is to provide students and teachers with the ambience of getting along with each others and being concerned with others.

B. The Instruction Emphasis Put both on Theory and Practicality

The development of this department is on the emphasis of theory and practicality to enter into the teaching and study of the information science. In teaching, the function of computing machines is completely utilized and the lecture theory is continually tested. The cooperation with other departments of the College is also executed by the Department.

It is the hope of the department that we may use our professional knowledge to offer solution to the problem of other departments which can be solved by computers. As a result, the teachers and the students of this department may have a chance to practice their ability of solving problems. By the time when the department is matured, in addition to equip students with professional skills, it is our hope that all graduates from this department may go straightforward to the society and devote themselves to the country.

General Courses Credits

English	4
English Lab Drills	2
Constitution: The Foundation Spirit of R.O.C	4
Basic Concepts of Computer	4
Military Training	2
Physical Education	4

Major Courses Credits

Calculus	8
Calculus Practice	0
Linear Algebra	6
Programming Design	4
Programming Design Practice	0
Foreign Languages	4
Probability and Statistics	4
Probability and Statistics Practice	0
Assembly Language	3
Data Structure	3
Programming Languages	3
Discrete Mathematics	3
Introduction to Design System and Labs	4
Computer Architecture	4
Chinese History	2
Special Information Topics Ⅰ	2
Special Information Topics Ⅱ	2
System Programming	3
Algorithms	3
Operation System	3
Compiler	3
Special Information Topics Ⅲ	2
Thesis Study	2

Elective Courses Credits

Physics	4
Computer Graphics	3
Database System	3
Electronics	3
Digital Integrated Circuits	3
Software Engineering	3
Artificial Intelligence	3
Master’s System	3
Computer Network	3
Network Program Plans	3
Linear Programming	3
Numerical Method	3
Formal Languages	3
Distributed System	3
Introduction to VLSI System Design	3

Course Descriptions:

Calculus (Credits 8)

Functions, limit, derivatives, chain rule, the derivatives of trigonometric function and it's inverse, exponential and logarithm ftmctions, mean value theorem, Hospital's rule, integrals, the fundamental theorem of calculus, indefinite integrals, improper integrals, infinite series, power series, Taylor's series, multi-variate functions, partial derivatives, directional derivatives, multiple integrals, iterated integrals, cylindrical coordinates, spherical coordinate.

Linear Algebra (Credits 6)

System of linear equations, matrix, vector spaces, the column and row spaces of a matrix, rank of a matrix, Gram-Schmidt process, orthogonal subspaces, least squares solution, determinant, linear transformation, representing matrix, diagonalization of a square matrix, eigen value, eigen vector, the power of a diagonalizable square matrix, recurrence relation, quadratic form.

Linear Programming (Credits 3)

Models of linear programming, basic solutions, fundamental theorem of linear programming, canonical forms, optimal solutions, criterion, pivoting, Simplex algorithm, two-phase method, revised Simplex method, duality, primal-dual algorithm, post-optimality analysis, transportation problem, game theory, network analysis.

Numerical Method (Credits 3)

Solution of linear system of equations, the algebraic problem, solution of nonlinear equations, interpolation and approximation, numerical integration and differentiation, numerical solution of ordinary and partial differential equations.

Discrete Mathematics (Credits 3)

Sets and relations, counting method and pigeonhole principle, recurrence relations, graph theory, algebraic structures, automata, coding theory.

Physics (Credits 4)

Kinematics, dynamics, work and energy, conservation of momentum, conservation of angular momentum, Keplere law, relativity, thermodynamics, electric field and electric potential, magnetic field and magnetism, electromagnetic wave, modem physics.

Operating System (Credits 3)

Process management, concurrent job management, processor management, memory management, secondary memory management, protection, deadlock, distributed system, case study of Unix.

Data Structure (Credits 3)

Introduction, arrays, stacks and queues, linked lists, trees, graphs, internal sorting, symbol tables, heap and search structure(option) .

Algorithms (Credits 3)

Analyzing the efficiency of algorithms, divide and conquer, dynamic programming, greedy approach, backtracking, branch and bound, introduction to computational complexity:the sorting and searching problem, computational complexity.

Compiler (Credits 3)

In this course, we will introduce the major phases of a compiler including lexical analysis, syntax analysis, semantic analysis, data flow analysis, intermediate code generation, code optimization, and target code generation. We will present the topics of the major work, the designing method, the input/output requirements, and the data structure of each of these phases. We hope students will be able to understand the major work and possible problems of designing a compiler.

Programming Language (Credits 3)

The principle goal of this course is to provide students with the tools necessary for the critical evaluation of existing and future programming languages and constructs. We pay attention to the fundamental concepts of programming languages by defining the design issues of the various language constructs, examining the design choices for these constructs in some of the most common languages, and critically comparing the design alternatives.

Distributed System (Credits 3)

The contents of this course will mainly focus on the discussions of existing distributed systems and its designing method. We will discuss the technologies of identification, encryption, protection, service control, resource management, synchronization, concurrent control, backup and updating. The contents of file system management, job scheduling, shared memory management, programming language are also considered important topics in this course.

Software Engineering (Credits 3)

This course will be mainly focused on how to schedule and design a well engineered software that is reliable, understandable, and maintainable. The contents of this course will include technical aspects such as software requirement identification, software design, implementation, testing and debugging. In addition, this course also includes the human aspects of software engineering such as: the documentation, the design of user interfaces, and the software management.

Formal Language (Credits 3)

This course provides students understanding the use of language-theory concepts and the application of language-theory ideas. The contents of this course include Finite Automata, Regular Sets, Context-Free Grammars, Turing Machines and the Computational Complexity Theory.

Database System (Credits 3)

The purpose of this course is to introduce the fundamental concepts necessary for the design, use, and implementation of database systems. The presentation stresses the fundamentals of database modeling and design, the languages and facilities provided by database management systems, and the techniques for implementing database systems.

Probability and Statistics (Credits 4)

This course covered are: Probability space; Combinatorial analysis ; Discrete and continuous random variables; Expectation; Distributions of random variables; Distributions of functions of random variables; Limiting distributions; Estimation; Statistical hypotheses.

Master’s Systems (Credits 3)

This course is want to introduce into their programs anew and advanced software technology, An expert system generally includes a knowledge base, an inference engine, and user interface facilities. The knowledge base contains rules and facts, and the inference engine consists of search control and reasoning mechanisms.

Artificial Intelligence (Credits 3)

Artificial intelligence is a tool for complex problems. This course covered are: languages of Al; basic search techniques; gwne playing; automated reasoning; problem solving; computational linguistics; natural language processing; knowledge representation; pattern recognition; computer vision; machine learning.

Advanced Discrete Mathematics (Credits 3)

This course covered are: graph theoretic foundations; directed graphs, matching, and colorings; triangulated graph; Interval, Pennutaion, and Split graphs; Finite State machines; monodies and groups; Binary group codes; Lattices; Rings and ideals; Polynomial rings and Polynomial codes.

Computer Network (Credits 3)

This course is to let students have the computer network programming skills. We will

teach the students the programming methods in TCP/IP and the Internet. In this course,

students can have an exercise to transmit data from one computer to the other. And they

will be also taught to communicate the internet WWW server by program.

System Programming (Credits 3)

The purpose of this course is to introduce the fundamental concepts necessary for

the design, use, and implementation of system programs. We will teach the students

fundamentals and implementations of computer system program, and they include

assembler, interpreter, editor and compiler.

Basic Computer Concepts (Credits 6)

In this course, we introduce the fundamental computer knowledge to students. Many primary research fields and applications in computer science will be introduced. These fields include computer hardware, operating system, system software, computer network, multimedia, computer graphics and other applications.

Computer Program Design (Credits 4)

This course is to let student have fundamental ability in the computer program design. So we will teach the students the most popular C/C++ programming language. The C/C++ program structure, syntax, data types and data structure are stressed. And the students will be trained and ask to solve problems by computer programming language. So this course with contains many computer program exercises for practices and trains.

Assembly Language (Credits 3)

The purpose of this course is to make the students understand the inner operations in computers and have the ability to control computer hardware by assembly language program. This course stressed the computer hardware architecture, assembly language addressing modes and instructions, and the programming skills in assembly language.

Computer Graphics (Credits 3)

The course is designed to develop the student's understanding of various computer graphic algorithms. Students will have the knowledge of basic concept of computer graphics after studying the course. It includes straight line algorithm, circle algorithm, filled color algorithm.

Introduction to VLSI System Design (Credits 3)

The course is designed to develop the student's understanding of various VLSI design methods. Students will have the knowledge of basic concept of VLSI design after studying the course. It includes MOS transistor theory, CMOS processing technology, structure design, symbolic layout systems.

Computer Architecture (Credits 3)

The course is designed to develop the student's understanding of various digital computer architectures and applications of microcomputer. Students will have the knowledge of basic concept of computer architecture after studying the course. It includes center processing units, input devices, output devices, memory, micro-programming.

Introduction to Digital System Laboratory (Credits 4)

The course is designed to develop the student's understanding of various digital system design methods. Students will have the knowledge of basic concept of digital system after studying the course. It includes binary system, logic gates, combination logic, MSI system design, flip flops, sequential logic.

Digital Integrated Circuits (Credits 3)

The course is designed to develop the student’s understanding of various digital integrated circuits families. Students will have the knowledge of basic concept of integrated circuit after studying the course. It includes integrated circuit characteristics, NMOS integrated circuit, CMOS integrated circuits, transistor-transistor logic, emitter coupled logic.

Electronics (Credits 3)

The course is designed to develop the student's understanding of semiconductor devices and its circuit analysis. Students will have the knowledge of analog circuit design after studying the course. It includes semiconductor, diodes, breakdown, Zener diode, bipolar junction transistor, field effect transistor, amplifier.

English (Credits 4)

This course is designed as to give the students an adequate command of the English language to enable him or her to read works of fiction and non-fiction, newspapers and magazines. In class, emphasis is placed on text explanation in English, reading, listening and group discussion.

English Lab Drills (Credits 4)

The course is designed for use as part of freshman English training, covering two types of drill materials: (1) Conversation Topics, including some specialized conversation in different tenses, intonation and sound. The coordinated reading which follows presents the subject matter for reference and enjoyment. (2)Audio-Visual Approach, taught with film strips on various subjects, designed for the practice of the expressions of daily usage. The strips emphasize the students' participation in the talks on the film subject.

Computer Network Programming (Credits 3)

The purpose of this course is to give students the computer network programming skills. We will teach the students the programming methods in TCP/IP and the Internet. In TCP/IP network programming, students will learn how to use socket and remote procedure call in computer network. In Internet programming, students will study java language and how to use it to communicate with a WWW server.

Special Information Topics Ⅰ，Ⅱ，Ⅲ

This course is to give students training in the design and implementation of computer hardware and software. Such practical training is helpful to students who will e a researcher or an engineer after graduation. The whole course is from the beginning of the third tesr and lasted three semesters. In this course, students according to their interests are arranged in several groups. Every group will have a special topic with a goal in computer science, and is directed by a teacher who is good at the topic. Students are asked to complete their goals in the end of this course.

The Department of Mathematical Statistics and Actuarial Science

Objectives:

This undergraduate program, which focuses on the study of actuarial science, is the first of its kind that is established in Taiwan. The design of its curriculum, committed to the educational Idea of the University, aims at developing a student’s research ability and career potential in related fields, cultivating a well-rounded character through a sophisticated general courses; thus enabling. a student to substantially comprehend mathematics and its relationship with social sciences in life, annuity, and welfare issues, as well as to obtain reliable information via statistical analysis, and as a result to foster a mind that is independent, pluralistic, humble, and compatible.

In the meantime, special guidance and assistance in academic training are offered from the third year to enhance students’ performance in passing actuarial certificate examinations, and to guarantee a professional quality that leads to services in their prospective careers such as insurance, welfare, finance, and trust. Students are also encouraged to conduct further research in related areas in management science, applied mathematics, actuarial science, and statistics; after graduation.

The Department will have its first students in Fall 1998.