Download bma105 linear algebra

Department of Mathematics
( 2004-2005 )
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 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.
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 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.
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.
continuous and discrete evolutional population models.
Some selected
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 Ⅲ
BMA430
UNDERGRADUATE RESEARCH Ⅳ
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.