## Sophomore Year

**40217 40218 Advanced Calculus (I)(II)**

Extends concepts and techniques of calculus and develops further applications. Topics include sets, functions, real numbers, Euclidean n-space and its topology, compact and connected sets, continuous mappings, differentiation and integration higher dimensional calculus, applications of vector analysis, uniform convergence of series, improper integrals and some special functions.

**40221 Probability**

This is a one-semester course. No previous study of statistics or probability is assumed, and a standard course in calculus provides an adequate mathematical background. In this course, we are going to mention some basic concepts in probability and several discrete and continuous distributions including their generating functions. Furthermore, we will introduce the essential material about some properties of random variables. The basic sampling distribution theory, including the central limit theory, is also considered here.

**40222 40372 Differential Equation (I),(II)**

Linear ordinary differential equations, solution in series, solutions using Laplace transforms, systems of differential equations and approximate methods of solving differential equations.

**40223 Linear algebra (II)**

Elementary matrix operations. The rank of a matrix. Matrix inverses. Systems of linear equations. Determinates. Eigenvalues and eigenvectors. Diagonalizability. Invariant subspaces. Cayley-Hamilton theorem.

**40224 Algebra (II)**

This course introduces the theory of rings and fields and covers the following topics: basic properties of rings, polynomial rings, ideals, fields of quotients, Fermat's theorem, principal ideal domains, unique factorization, Euclidean domains, field extensions, and finite fields. Prerequisite: Algebra I

**40225 Algebra(I)**

This course provides the study of Group theory. The main topics include equivalence relations, basic concepts of groups, subgroups, Symmetry groups, quotient groups, finitely generated abelian groups, and the Sylow theorems.

**40226 Introduction to Theory of Block Designs**

The aim of this course is to teach students some of the most important techniques used for constructing combinatorial designs. To achieve this goal, we focus on several of the most basic designs: Steiner triple systems, latin squares, and finite projective and affine planes. 1.Balanced Incomplete Block Designs. 2.Steiner Triple Systems 3.Kirkman Triple Systems 4.Mutually Orthogonal Latin Squares 5.Affine and Projective Planes

**40227 Advanced linear algebra**

Inner products. Norm. Gram-Schmidt orthogonalization process. The adjoint of a linear operator. Normal operators. Self-adjoint operators. Unitary operators. Orthogonal operators. Orthogonal projections. Spectral theorem. Bilinear and quadratic forms. Rayleigh quotient. Jordan form. The minimal polynomial.

**40228 Introduction to Graph Theory**

This course is intended as an introduction to graph theory. The aim has been to present the basic material, together with a variety of applications, both to other branches of mathematics and to real-world problems. 1.Graphs and Subgraphs 2.Trees 3.Euler Circuits and Hamilton Circuits 4.Adjacency Matrix of a Graph 5.Spectrum of a Graph 6.Regular Graphs 7.Strongly Regular Graphs

**40233 40234 Introduction to Analysis (I)(II)**

In this topic, we focus on problem solving in mathematics analysis. Techniques for attacking and solving challenging mathematics problems and writing mathematical proofs.

**40242 Statistics**

This is a one-semester course. Students should take the probability course in advance. Estimation, including point estimation and interval estimation, and tests of statistical hypotheses will be in this course. The t- and F-distribution are introduced for other applied statistical courses. The basic concepts of analysis of variance and regression analysis are also discussed in this course. We might be concerning the further topics, such as non-parametric method and quality assurance.

**40262 Data Structure**

An introduction is given to some useful data structure techniques for common database operations. The main part of the course studies the three main "models of data" -the relational model, the network model and the hierarchical model.

**40265 Assembly Language**

This course covers machine (assembly) language programming. Topics include the computer architecture, the internal representation of data, instruction sets, and addressing logic.

**40266 System Programming**

This course covers the internal structure of computers and machine (assembly) language programming. Topics include the logical design of computers, computer architecture, the internal representation of data, instruction sets, and addressing logic. Programming assignments will be in assembly language using the PC

**40273 Vector Analysis**

Elements of vector algebra, parametric equations of curves and surfaces, scalar and vector fields, line, surface and volume integral, divergence theorem, Green's theorem, Stokes' theorem.

40279 Vector Analysis

40279 Vector Analysis

Elements of vector algebra, parametric equations of curves and surfaces, scalar and vector fields, line, surface and volume integral, divergence theorem, Green's theorem, Stokes' theorem.

40286 English-listening and speaking Lab (Ⅰ)

40286 English-listening and speaking Lab (Ⅰ)

Required course, 1 credit, Fall semester, Prerequisite: none.

**40287 English-listening and speaking Lab (Ⅱ)**

Required course, 1 credit, Spring semester. Prerequisite: English-listening and speaking Lab I.

40288 Taiwan's History and Culture

40288 Taiwan's History and Culture

Required course, 2 credits, Fall semester, Prerequisite: none.

**40289 Chinese History and Civilization**

Required course, 2 credits, Spring semester, Prerequisite: Taiwan's History and Culture