Department of Mathematics

 

BMA101  CALCULUS

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.

 

BMA105  LINEAR ALGEBRA

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.

 

BMA106  INTRODUCTION TO FUNDAMENTAL MATHEMATICS

required  (2 0)

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

 

BMA107  INTRODUCTION TO COMPUTER SCIENCE

required  (0 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 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.

 

BMA201  ADVANCED CALCULUS

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.

 

BMA302  INTRODUCTION TO ABSTRACT ALGEBRA

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.

 

BMA202  INTRODUCTION TO PROBABILITY

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.

 

BMA203  INTRODUCTION TO STATISTICS

required  (0 3)

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

 

BMA204  DIFFERENTIAL EQUATIONS

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.

 

BMA211  VECTOR ANALYSIS

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

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.

 

BMA213  INTRODUCTION TO NUMBER THEORY

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.

 

BMA212  MATHEMATICS SOFTWARES

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.

 

BMA217  DATA STRUCTURES

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.

 

BMA301  INTRODUCTION TO COMPLEX ANALYSIS

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.

 

BMA303  DIFFERENTIAL GEOMETRY

required  (3 3)

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

 

BMA311  MATHEMATICAL STATISTICS I

BMA312  MATHEMATICAL STATISTICS II

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.

 

BMA313  FOURIER ANALYSIS I

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.

 

BMA315  COMBINATORIAL MATHEMATICS

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.

 

BMA316  DISCRETE MATHEMATICS

elective  (0 3)

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

 

BMA214  APPLIED LINEAR ALGEBRA

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.

 

BMA439  ALGEBRAIC CODING

elective  (3 0)

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

 

BMA440  COMBINATORIAL CODING

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.

 

BMA422  TOPICS IN ALGEBRA

elective  (3 0)

Selected topics in algebra.

 

BMA428  UNDERGRADUATE RESEARCH I

BMA427  UNDERGRADUATE RESEARCH II

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.

 

BMA420  INTRODUCTION TO TOPOLOGY

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.

 

BMA413  THEORY OF ORDINARY DIFFERENTIAL EQUATIONS

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.

 

BMA414  INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS

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.

 

BMA415  LINEAR PROGRAMMING

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.

 

BMA435  MODERN ALGEBRA I

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.

 

BMA443  MODERN ALGEBRA II

elective  (0 3)

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

Prerequisite : INTRODUCTION TO ABSTRACT ALGEBRA.

 

BMA431  BIOSTATISTICS I

BMA432  BIOSTATISTICS II

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.

 

BMA437  MATHEMATICAL BIOLOGY I

BMA438  MATHEMATICAL BIOLOGY II

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.

 

BMA424  NUMERICAL ANALYSIS

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.

 

BMA425  COMPUTING MATHEMATICS

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.

 

BMA441  COMMERICAL CODING

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.

 

BMA442  CODING

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.

 

BMA426  TOPICS IN COMBINATORICS

elective  (0 3)

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

 

BMA4    TOPICS IN ANAYSIS

elective  (2 0)

Selected topics in analysis.

 

BMA4    TOPICS IN STATISTICS

elective  (0 2)

Selected topics in mathematical statistics.

 

BMA4    EXPERIMENT IN MATHEMATICS I

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.

 

BMA4    EXPERIMENT IN MATHEMATICS II

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.

 

BMA436  EXPERIMENTS IN NUMERUCAL COMPUTATIONS

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.

 

BMA429  UNDERGRADUATE RESEARCH

BMA430  UNDERGRADUATE RESEARCH

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 MATHEMATICS1)(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.