### College of Natural Sciences

#### Introduction

Mathematics is applied in almost every academic subject and it is a basic discipline that is expected to be used in much more areas in the future.

From this perspective, the educational objectives are to improve the ability to deal with mathematical subjects in strict logics, consistent systematics and simple abstraction and to foster human resources that are able to solve the problems presented in the society. The following are sub-objectives.

First, we help students understand basic and intermediate mathematical theories based on mathematics learned in high school and develop creative mathematical thinking abilities.

Second, based on mathematical abilities, we develop problem-solving skills that can be creatively applied to various academic disciplines.

Third, we develop the abilities for math teachers to provide creative education to teach mathematics more strictly and easily.

Fourth, we develop the qualities needed to become pure and applied mathematicians who can play an important role to improve mathematics for the next generation.

#### History

The Department of Mathematics was first installed and authorized within the College of Liberal Arts in 1967, which was changed to the College of Sciences after restructuring of the university in 1980. Graduate school courses were opened in February 1974. As of March 2010, 1,821 undergraduates, 116 masters and 40 Ph. D. were graduated. Graduates are currently active in parts of society such as in educational institutes including secondary school and universities, as well as in processing centers of financial institutions.

#### Job Fields

After completing teacher courses, students can become math teachers. Students can also find employment in processing centers at companies, financial institutes and public organizations. Students can also enroll in various application fields in graduate schools and there are more opportunities for students having double majors.

#### Faculty

sorted by the position and Korean name

#### Curriculum

##### Department Of Mathematics
• 1-1,2
1- 1 CALCULUS I Calculus(1) covers the following: Sequences, limits and continuity of functions of single variable, derivatives, properties of derivatives, differentiation rules, higher order derivatives, applications of derivatives, definite integrals, indefinite integrals, properties of integrals, integration rules, applications of integrals, infinite series power series. CONVERGENCE- AND INTEGRATION-BASED THINKING AND WRITING The ability of analyzing and solving problems is emphasized as one of the conditions for survival in the 21st century and one of the core elements of creative capabilities. This course was designed to cultivate convergence- and integration-based creative capabilities, which are integrated problem-solving capabilities to collect, analyze and process knowledge and information by reinforcing the ability of analyzing and solving problems, recreate it in a synthetic fashion, and express it effectively through speech and writing. The course will help the students cultivate their synesthesia thinking and communication skills based on sympathy with other human beings, understanding of the community, and positivity or Gongseong that is sought after by Yeungnam University. Its ultimate goals are to promote the students' creative knowledge development and reinforce their writing capabilities consistently through "convergence- and integration-based thinking and writing as a problem-solving approach." SEMINAR FOR ACADEMIC LIFE 1. Summary of the course This course is to assist university freshmen in CRM designing to adapt university life well through the instruction and counselling of supervising professor. (This course is composed of self analysis, personality type test, career research, instruction for the success of university life, career plan and direction setting, CRM designing method and CRM designing. The course should be teaching in classes of the students by supervising professor.) 2. Course objectives This course is to motivate the students before the mid term exam and provide students with self analysis, personality type test (MBTI or TCI) and career research (YAT test). Also, this course shall has a plan to instruct the students to enhance the efficiency of university life through career and time management. In addition, this course is to make a chance for the students to have practical assistance to university life by providing study method, report designing strategy and the information on academic system and various kinds of internal programs of the university. After the mid term exam, the students will be instructed to set the direction of career designing through continuous counselling of supervising professor and the students will be able to establish CRM designing and execution plan. SOCIAL CONTRIBUTION AND SERVICE This course is to cultivate community sense as members of society and the global village for students in order to develop the basic knowledge required as global citizens. Especially, this course is to foster the spirit of cooperation, sharing, service, and creativity and study the social contribution and leadership to solving the challenges the global community faces. As a liberal arts course, it is centered to nurture a leader having the global capability to contribute to community development through learning the knowledge and the case on the value & logic of social responsibility focused on environmental preservation, social contribution, and good governance(ESG). This course aims to foster a generous mind, learn knowledge and technology and build the capacity to contribute to building a society towards a safer and happier world through the study of theory and practice. SOFTWARE AND AI Software and AI (Artificial Intelligence) course aims to educate the basic concepts of software and computational thinking to use them in various applications. It allows students of various majors to experience the core technologies of the 4th industrial revolution, such as big data, machine learning, and AI. It also introduces various applications of AI so that students can easily apply these technologies to their field of study. This course classifies the lecture types into three categories, and adjust the lecture difficulty according to the student's academic ability. CALCULUS II Calculus(2) covers the following: vector valued functions, curves in spaces, limits and continuity of functions of multi variables, partial derivatives, properties of partial derivatives, partial differentiation rules, higher order partial derivatives, applications of partial derivatives, double and triple integrals, properties of multiple integrals, applications of multiple integrals, line integrals, Green's theorem, surface integrals, Stokes' theorem, divergence theorem. PYTHON PROGRAMMING The core competencies required in the era of the Fourth Industrial Revolution is the ability to come up with idea for solving a given problem and realize it in software. In this course, as the first step this, we will learn Python programming language. This course aims to cultivate basic programming skills and problem-solving skills based on creative thinking. The topics covered in this course are as follows. - Python language grammar (basic and advanced levels) - Python library for GUI programming (tkinter) - Python library for image processing (pillow) - Python libraries for data analysis (Matplotlib, Numpy, and Pandas) STATISTICS(1) This course defines events and probabilities, conditional probabilities and independence to evaluate probabilities. Elementary probability distributions such as binomial distribution, geometric distribution, Poisson distribution, and normal distribution are also introduced. The concepts of sample distribution of the statistic and the central limit theorem are introduced. The statistical inference including estimation and hypothesis testing of the mean and the standard deviation will be discussed.
• 2-1,2
2- 1 DIFFERENTIAL EQUATIONS This course introduces basic methods to solve elementary differential equations and examples applied to various scientific problems. The main topics of this course are method of separation of variables, exact equations, general solutions of linear equations and differential operators. LOGIC AND ESSAY WRITING IN MATHEMATICAL EDUCATION This course disciplines Logic and Essay writing in Mathematical Education PROBABILITY & STATISTICS Application of probability is playing an ever increasing role in a number of diverse fields in engineering and the natural science as well as statistics. In this course following topics will be treated; probability spaces, probability, measurable functions, random variable, Lebesgue integral, expectation, mgf, central limit theorem. COMPUTER PROGRAMMING PRACTICE FOR MATHEMATICS This course deals with programming skills in various programming languages such as C, C++, JAVA and Matlab based on the architecture of computer. LINEAR ALGEBRA This course are an advanced course of Matrices and Determinants. The main topics of this course are matrices, systems of linear equations, vector spaces, bases, linear mappings, and inner product spaces. CAREER DESIGN 1. Summary of the course This course is to let the students to set the career goal at the early stage of university life through systematic and continuous counselling and instruction on CRM achievement and change of career designed by the students after the admission to the university. This course is to let the students attain career management method and edit, complement and confirm the CRM in a systematic manner by self analysis and analysis of employment competence while the course is being taught. Also, this course is to utilize video lecture as the secondary teaching material to let the students have competency in employment. 2. Course objectives This course is to assist to the enrolled students in designing their own employment plan for themselves by the education of drafting application materials for employment (resume, statement of purpose and application forms), communication skills and presentation skills. Furthermore, the course ultimate goal of guiding the students to systematically design (manage) CRM at each grade of the university with the counselling by the supervising professor until the time of graduation. APPLIED DIFFERENTIAL EQUATIONS This course is a continuation of Differential equations(1). It treats well known techniques of solutions and some qualitative theory for differential equations. Topics include linear systems of ordinary differential equations, qualitative behavior of plane autonomous systems, Fourier series and boundary value problems and second order linear partial differential equations. It is primarily for students in disciplines which emphasize methods of solving. Proofs are not emphasized in this course APPLIED LINEAR ALGEBRA This course is the continuation of the previous course, Linear Algebra I. The main topics of this course are determinants, eigenvalues and diagnoalizations, bilinear and quadratic forms, linear operators, and multilinear products. NUMBER THEORY We extend the student’s knowledges on integers by using logical and algebraical analysis of them, and studying various properties of integers, Fermat’s theorem, systems of homogeneous equations and Fermat’s last theorem, etc. INTRODUCTION TO ANALYSIS As an introductory course to analysis, fundamental theories and various properties on limits and continuities of sequences and functions in real number system will be treated. NUMERICAL ANALYSIS This course gives an overview how mathematics and computers are related each other, and enhances programming skills in programming language. It also introduces some basic numerical computation techniques including floating point arithmetics and error estimations, bisection methods, Newton methods, fixed point methods for nonlinear equations, Gauss eliminations, Gauss-Seidel method for systems of linear equations and interpolations.
• 3-1,2
3- 1 ACTUARIAL MATHEMATICSⅠ It is an introductory course in the Actuarial Mathematics, covers parts of calculus, linear algebra, basic probability, basic statistics etc. that are used in the actuarial science. APPLIED NUMERIC ANALYSIS Basic knowledges of programming languages are required. This course introduces numerical methods to solve problems arising from various sciences and engineering. Mainly numerical integrations, numerical differentiations and numerical methods (Euler’s methods, Runge-Kutta methods) for differential equations are treated. COMBINATORICS Combinatorics is one of fast-growing area of modern mathematics. Much of the growth of it has gone hand in hand with the development of the computer. In this course, we study some basic counting rules in combinatorics, elementary graph theory, recurrence relations, the principal of inclusion and exclusion, the pigeonhole principal and their applications. INFORMATION AND MATHEMATICAL SCIENCES In this course, we introduce basic concepts and technologies of modern cryptography as well as coding theory with an emphasis on mathematics. This course focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. This course is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. INTRODUCTION TO MODERN ALGEBRA This course provides basic concepts of group theory and ring theory, and helps students to understand algebra as abstract and logical concepts. ANALYSIS Fundamental concepts of analysis will be treated on metric spaces. Especially, this course presents concepts of differentiation and integration, convergence of series of real numbers and sequences and series of functions. INTRODUCTION TO GENERAL TOPOLOGY Topology is an abstraction of geometry; it deals with sets having a structure called the "topology" on the set, which permits the definition of continuity for functions and a concept of closedness of points and sets. The goal of topology is to determine the nature of topological spaces by means of properties which are invariant under homeomorphisms. This subject deals with the required concepts of set theory, the usual topology on the Euclidean spaces, basic properties of topological, metric and normed spaces. INTRODUCTION TO GEOMETRY This course introduces the basic ideas of Euclidean geometry and non-Euclidean geometry. The main purpose of this course is not studying deep theory of geometry but understanding basic concepts of geometry by using basic undergraduate courses such as calculus (I), (II) and linear algebra. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS This one semester course is an introductory course of Differential geometry and its applications. Goal of this course is to build up their mathematical application abilities related to engineering. Preceding subjects are Euclid Geometry, Linear Algebra, Numerical Analysis, and C Language, Calculus. Guide jobs, Give chances to enter graduate schools in the area of IT. GENERAL TOPOLOGY Topology is an abstraction of geometry. The goal of topology is to determine the nature of topological spaces by means of properties which are invariant under homeomorphisms. As a continuation of Introduction to Topology, this subject deals with the separation axioms, countability, the product topology, connectedness, complete metric spaces, and function spaces. INTRODUCTION TO APPLIED ANALYSIS The definition and properties of Riemann-Stieltjes integral will be treated in comparison with Riemann integrals. The definition and properties of outer measure on real number system will be studied and Lebesgue integrals and Fourier series also are briefly introduced. MATHEMATICS CAPSTONE DESIGN(1) This course is oriented to develop and increase the research capacity of the students in mathematics major. In this course students are subjected to design and carry out a research project, by applying some basic theories and experimental methods. An intimate relationship between the students and the advising professor will be held on analyzing experimental data performing further experiments. MATHEMATICS FIELD WORK(1) The objective of this course is designed for the students in the major of mathematics to achieve both the practical knowledge and the experience in the related job fields. PEDAGOGY FOR TEACHING SECONDARY SCHOOL MATHEMATICS This course develops various teaching methods and instructional strategies of secondary school mathematics for effective teaching on the basis of contemporary learning psychology. This course also provide teaching practicum for utilizing such pedagogical knowledge in mathematics. DISCRETE MATHEMATICS AND ALGORITHMS This course provides some foundations for the course of Data Structure and Algorithm, Switching and Logic Theory, Formal Languages, Artificial Intelligence, which are following topics; logic, set, relation, graph, function, algebra and Boolean algebra, program correctness, and complexity of programs. MODERN ALGEBRA This course provides more advanced theory of groups and rings which contains; Sylow's theorem, structure of finite groups, UFD, Dedekind domain and basic concepts of non commutative rings.
• 4-1,2
4- 1 GRAPH THEORY Graph Theory is the study of objects called graphs. In this course, we will study the fundamental concepts in the graph theory such as graph coloring, graph connectivity, planarity, matching, network flow, graph spectra, graph symmetry and so on. We also explore some of their interesting applications. MATHEMATICS CAPSTONE DESIGN(2) This course is oriented to develop and increase the research capacity of the students in mathematics major. In this course students are subjected to design and carry out a research project, by applying some basic theories and experimental methods. An intimate relationship between the students and the advising professor will be held on analyzing experimental data performing further experiments. MATHEMATICS FIELD WORK(2) The objective of this course is designed for the students in the major of mathematics to achieve both the practical knowledge and the experience in the related job fields. MATHEMATICS SEMINAR Ⅰ This course introduces how to study the overall mathematical fields covered throughout the undergraduate courses. Students are encouraged to participate in the discussions so that the systematic and logical ways of thinking are cultivated. MODERN ALGEBRA WITH APPLICATIONS Modern Algebra with Applications This course provides the basic concepts of abstract algebra for undergraduate students. We also study solvability of equations by radicals, geometric construction and error correcting codes. THEORY OF TEACHING SCHOOL MATHEMATICS This course provides the foundational knowledge of mathematics education by studying the nature and historical development of mathematics, psychology of learning mathematics, various instructional strategics, assessment and evaluation, techniques, and technology for school mathematics for the prospective teachers. TOPICS IN APPLIED MATHMATICS I Recent trend of research in applied mathematics is the main topic of the course. ACTUARIAL MATHEMATICS Ⅱ It deals with mathematical modeling of actuarial problems for the risk, premium, reserve, solvency, annuities etc. COMPLEX ANALYSIS This course presents a solid foundation for an introductory complex analysis including exponents of complex numbers, limits, continuity and differentiations of complex foundations and harmonic functions, contour integrals and residue theorem. MATHEMATICAL PROGRAMMING This course introduces simplex algorithms, dual problems and duality principles for linear programming problems, and also deals with various optimization problems arising in natural and social sciences. MATHEMATICS SEMINAR Ⅱ This course is a continuation of Mathematics Seminar(1) and introduces how to study the mathematical fields in a deeper level. Students are encouraged to participate in the discussion and suggest the potential improvements to each other so that the systematic and logical ways of thinking are cultivated. PARTIAL DIFFERENTIAL EQUATIONS This course introduces basic properties(characteristic curves, maximum principles etc.) of linear partial differential equations, classification of second order linear partial differential equations into parabolic(diffusion) type, hyperbolic(wave) type and elliptic(Laplace's) type, and method of separations of variables for constant coefficient second order linear partial differential equations. TOPICS IN APPLIED MATHMATICS II Recent trend of research in applied mathematics is the main topic of the course.