**Department
of Mathematics**

required (4 ─ 4)

This course introduces the basic theory and applications of calculus. Main contents are limit, continuity; derivative, integral, methods of integration of functions of single variable, infinite series, and partial derivatives, differentiability, multiple integral of functions of multivariables.

required (3 ─ 3)

This course covers vectors, matrices, solving linear equations, vector spaces, determinants, eigenvalues and eigenvectors, linear transformations, canonical forms and inner product spaces.

required (2 一 0)

This course covers logic, methods of proof, sets, relations, functions, finite and infinite sets and so on.

**BMA107 INTRODUCTION TO COMPUTER
SCIENCE Ⅰ**

required (0 一 3)

This course introduces the computer hardware, number systems and codes, programming design and languages. It also covers the basic concept of operating system, application softwares and networks.

**BPS103
GENERAL PHYSICS**

required (3 一 3)

The goal of the course is to introduce rudimentary, but broad, knowledge of physics to freshmen. The contents of the course include mechanics, thermodynamics, electromagnetism, optics, and modern physics, …etc. Calculus is usually employed in lectures to enhance students, abilities to understand andanalyze various physical phenomena in depth, and thus to enlighten them on developing their potential and interest in learning about nature.

**BPS102 GENERAL PHYSICS LABORTORY**

elective (1 ─ 1)

Complements General Physics, illustrating basic concepts and training students in correct laboratory attitude and basic methods of physical measurement.

required (4 ─ 4)

This course introduces the real number system, Euclidean space and metric space, continuous functions, differentiable functions, integral, sequence and series of functions, the inverse and implicit function theorems and their applications.

Prerequisite : CALCULUS.

required (3 ─ 3)

This course covers groups, subgroups, permutation groups, cyclic groups, abelian groups, normal subgroups, factor groups, isomorphisms of groups, rings, ideals, fields, polynomial rings, factor rings, and their applications.

required (3 ─ 0)

This course covers probability spaces, random variables, expectations, law of large numbers, central limit theorem, moment generating and characteristic functions, statistical inferences for binomial distributions and normal populations, sample mean and analysis.

required (0 ─ 3)

This course introduces the definition of random sample, likelihood function and some estimators.

required (0 ─ 4)

This course covers methods of solving first order differential equations, higher order linear equations with constant coefficients, and systems of first order linear equations with constant coefficients; series solutions; Laplace transform; numerical solutions.

Prerequisite : CALCULUS, LINEAR ALGEBRA.

elective (3 ─ 0)

This course covers differential calculus of scalar and vector fields; multiple integrals, line and surface integrals; Green’s theorem, Stokes’ theorem, and Gauss’ theorem.

Prerequisite : CALCULUS.

**BMA2 INTRODUCTION TO COMPUTER
SCIENCE Ⅱ**

elective (3 ─ 0)

This course emphasizes the techniques of algorithm construction, structured programming design, debugging and testing, and software developments.

Prerequisite : INTRODUCTION TO COMPUTER SCIENCE I.

elective (3 ─ 0)

This course is an introductory survey of topics in number theory with emphasis on combinatorial aspects. Topics include well-ordering property, induction, Greatest common division, least common multiple, factorization, fundamental theorem of arithmetic, congruences, Wilson's theorem, Fermat's theorem, Euler theorem, congruence equations, quadratic reciprocity, Diophantine equations, Fermat's Last Theorem and sum of squares.

elective (3 ─ 0)

This course introduces two Mathematics softwares, MATLAB and MATHEMATICA. It presents the powerful numerical / symbolic computing, and graphic functions of these two math.

tools in Calculus and Linear Algebra. There is a priority rule to take this course because of the size of our computer laboratory.

elective (0 ─ 3)

Topics include abstract data types, algorithm analysis (loop, recurrence), fundamental data structure : arrays, stacks, queues, lists, trees and graphs, and advanced searching, sorting algorithms.

required (3 ─ 3)

This course introduces the basic theory of complex analysis and some of its applications. Main contents are analyticity, path integral and contour integral, series representation of analytic functions, residue theory and concept of comformal mapping.

required (3 ─ 3)

Topics include Frenet-Serret formula, isoperimetric inequalities, fundamental forms, parallel transport, geodesic and Gauss-Bonnet Theorem.

**BMA311 MATHEMATICAL STATISTICS I**

elective (3 ─ 0) (0 ─ 3)

Intention in this course is to provide the mathematical aspects of statistical inference. Contents in this course include Probability distribution and expectations, point estimation, hypothesis testing, interval estimation, Bayesian theory, Linear model.

Prerequisite : INTRODUCTION TO PROBABILITY, INTRODUCTION TO STATISTICS.

**BMA314 FOURIER ANALYSIS II**

elective (3 ─ 0) (0 ─ 3)

This course introduces the convergence and divergence of Fourier series, and make application to solve partial differential equations.

Prerequisite: CALCULUS, LINEAR ALGEBRA.

elective (3 ─ 0)

Topics include permutations, combinations, binomial and multinomial theorems, Stirling numbers, ordinary and exponential generating functions, inclusion and exclusion theorems, recursive relation, Polya's theory of enumeration.

elective (0 ─ 3)

Topics include analysis of algorithms, introduction to graph theory, transport networks, coding theory, Boolean algebra, automata and formal language.

elective (0 ─ 3)

This course emphasizes the decompositions of matrix, such as LU decomposition, QR decomposition and singular value decomposition with their applications in the pseudo-inverse of a matrix, the least square problems and min-max principle.

Prerequisite : LINEAR ALGEBRA.

elective (3 ─ 0)

This course introduces the theory of error-correcting codes. Discuss encoding and decoding by algebraic methods and programming.

elective (0 ─ 3)

Selected some topics in combinatorial design and coding theory. And we will construct some codes in term of design theory and program them by computer.

elective (3 ─ 0)

Selected topics in algebra.

elective (1 ─ 0) (0 ─ 1)

Supervised by a faculty member, the student needs to work on a specific topic, write up a issertation.

Prerequisite : consent from the advisor is required before registration.

elective (4 ─ 0)

Topics include topological spaces, subspaces and continuity, product spaces, connectedness, compactness, separation properties, metric spaces. For examples, Tychonoff theorem, Urysohn’s lemma, and so on.

**BMA421 REAL ANALYSIS**

elective (0 ─ 4)

Topics include Lebesgue measure, Lebesgue integral, differentiation of an integral.

elective (4 ─ 0)

Topics include qualitative theory for the systems of first order ordinary differential equations, including the existence and uniqueness theorems, linear systems, and stability theory. Two-point boundary value problems of a second order linear differential equation.

elective (0 ─ 4)

Topics include first order linear equations, types of second order linear equations, wave equation, heat equation, Laplace’s equation, seperation of variables, and Fourier series.

elective (0 ─ 3)

Topics include the graphical solution of two variables LP, simplex algorithm, the big M method, algebraic methods, finding the dual of an LP, dual theorem, transportation simplex method, assignment, shortest path, maximum flow problems.

elective (3 ─ 0)

Topics include isomorphism theorems of groups, p-groups, Sylow theorems, finitely generated abelian groups, fields, algebraic extensions, splitting fields, finite fields, Galois groups.

Prerequisite : INTRODUCTION TO ABSTRACT ALGEBRA.

elective (0 ─ 3)

Topics include Galois theory, modules, projective modules, injective modules, structure of rings.

Prerequisite : INTRODUCTION TO ABSTRACT ALGEBRA.

elective (2 ─ 0) (0 ─ 2)

Introduction to Biostatistics, Analysis of Variances, Linear Regressions, ANOVA Table, Random Variables, Probability Density Functions, Normal Distributions, Chi-square Distributions, T-Distributions, F-Distributions; Design of Experiment, Comparisons of Variances.

elective (3 ─ 0) (0 ─ 3)

This course introduces the mathematical foundation of population genetics. Some selected continuous and discrete evolutional population models.

Prerequisite : LINEAR ALGEBRA, DIFFERENTIAL EQUATIONS, ADVANCED CALCULUS.

elective (4 ─ 0)

This course covers numerical methods and error analysis for the following topics : find the roots of f(x)=0, polynomial approximation and interpolation, direct / iterative methods for solving linear systems, numerical differentiation and integration, and initial value problem for ordinary differential equations.

elective (0 ─ 2)

This course focus the experiment with mathematics software (Mathematica) of numerical methods on the following topics : interpolation, approximation, eigenvalues / eigenvectors, solve system of nonlinear equations, solve Initial value, boundary value of ordinary differential equations.

Prerequisite : NUMERICAL ANALYSIS.

elective (3 ─ 0)

This course covers mainly the approximation by wavelets, including its theory, algorithm and application. We will emphasize the industry standard JPEG 2000 as our target. Fourier Analysis is prerequisite but not necessary.

elective (0 ─ 3)

The course "Coding" is a part of the project, improving Basic Science Education of the Ministry of Education for the years 2003~2006, which is conducted by the Dept. of Mathematics . This course introduces algorithms related to codes, such as graph, matrix and simulation. The recitation of the course exercises are programming and testing of algorithms.

elective (0 ─ 3)

Selected topics in graph theory, coding theory and combinatoral design are discussed and analyzed.

elective (2 ─ 0)

Selected topics in analysis.

elective (0 ─ 2)

Selected topics in mathematical statistics.

elective (2 ─ 0)

This course will include constructions of regular solids or crystal cells using compass, ruler, scissors, glue and construction paper. We will look into the limitation of the material and methods and proceed to develop abstract theory. The purpose is to learn by doing mathematics.

Prerequisite : DIFFERENTIAL GEOMETRY, INTRODUCTION TO ABSTRACT ALGEBRA.

elective (0 ─ 2)

We will investigate the physical phenomena, use computer as a tool to design simulations. We will deduce from the collected data a mathematical reasoning and finally , develop methodology and make comparison among all the methods.

Prerequisite : INTRODUCTION TO COMPLEX ANALYSIS.

elective (2 ─ 2)

Study the theory of numerical methods, experiment the methods in Programming language (Matlab) and discuss the output results. In the mean while, design the mathematical models for applications. All the contents of the experiments are implemented in web pages.

elective (1 ─ 0) (0 ─ 1)

Supervised by a faculty member, the student needs to work on a specific topic, write up a issertation.

Prerequisite : consent from the advisor is required before registration.

**BMA HISTORY
OF MATHEMATICS（1）（2）**

elective (2 ─ 0) (0 ─ 2)

The development of meditation originated from the three mathematics events: discovery of irrational numbers, definition of limit, paradox in set theory.

**BMA448 MATHEMATICAL
EPIDEMIOLOGY**

elective (2 ─ 2)

The course is intended to introduce the modern application of disease control with "mathematical model" to make predictions for a variety of infectious diseases and the development of disease control strategies. The concept of mathematical modeling is introduced to develop a variety of mathematical models of infectious diseases, including SI, SIS, and SIR, SID, SEIJR, SIJR, SICR ... and dynamic mathematical models of infectious diseases. Also, we will introduce some real-world applications of the mathematical models. Finally, some computer simulation experiments of the mathematical models will be given.

**BMA449 INTRODUCTION
TO MATHEMATICAL MODELING**

elective (2 ─ 2)

Objective: Students are familiar with mathematical modeling cycle of 6 steps

(1) analysis (A: analyzing);

(2) analog (S: stimulating);

(3) model of the relationship equation

(M: modeling with equations);

(4) experimental implementation

(W: working experimentally);

(5) Description (I: interpreting);

(6) interpretation (E: explaining).

Each student is able to use his or her mathematical knowledge to solve real-world problems by mathematical modeling approach.

Syllabus: Introducing some simple examples to explain the 6 steps of the mathematical modeling cycle. Solving some real –world problems where students need inter-discipline among natural sciences, biomedical, social sciences by mathematical modeling approach.