### Major in Mathematics

### College Of Natural Sciences Department Of Mathematics

Dept. location | |||
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Phone | 02-2220-0890 | ||

Fax | 02-2281-0019 | ||

/ yhlee825@hanyang.ac.kr | |||

Homepage | * Visit the website for more detail. | ||

SNS |

#### Introduction

Mathematics is the ‘language of science’ necessary to study numerical and computational structures of numbers, the characteristics of functions and the structures of spaces, and to quantify and understand problems occurring in natural phenomena and real life. As civilization and science and technology develop, the role of mathematics has become increasingly recognized as the most effective way of studying various phenomena and complex relationships in natural science, engineering, humanities, and social science. We live in the information-oriented era. Higher level mathematical theories are needed in fields such as information communication, computer, information security, and finance. Also, mathematics commands competitiveness between companies and nations.Mathematics majors will learn about not only differential calculus, linear algebra, numerical analysis, and differential equations that can be learned in Science and Engineering departments but also learn about the total concept of mathematics itself. In addition, students will study statistical and financial mathematics which are used in Business Administration, Economics and Sociology as well as Science and Engineering. They will learn a more fundamental and pure discipline of mathematics used in various fields. Therefore, unlike other mathematics courses taught in other majors, Mathematics majors in the College of Natural Science will focus on more abstract and logical content.

#### Highlights

**Ideal major to converge with other disciplines**

When you study mathematics, you will learn mathematics as well as exceptional logical thinking skills that can be translated to various other fields. It is common to deal with mathematics in a profound sense in order to have a deeper understanding of any study. Therefore, with less pressure on mathematics in studying other majors, students will find this discipline relatively fluid. It is still appealing to study only Mathematics, but it is also attractive to study other majors which use mathematics in practical ways. This will result in amazing synergy.

**Bright Prospects**

It is said that a country's power comes from that nation’s mathematical abilities. It is no wonder then that there has been a growing interest and much investment in mathematics all over the world. Korea also shows much interest in and supports mathematics by hosting events such as the 2014 International Congress of Mathematics (ICM). As we can see, mathematics is developing new fields through disciplinary convergence. The study of mathematics will be increasingly in demand, and the prospects in mathematics will be brighter.

#### Outlook

Academic Society | University professors (mathematics, engineering, and economics), university instructors, public and private school math teachers, academy instructors, researchers, etc. |
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Financial World | Actuary, financial product panners, fund managers, financial analysts, securities and banks, investment company, statistical analysis, etc. |

Computer Communication | Image processing company, artificial intelligence and government information assurance planning division, communication, computer graphicer, etc. |

Kim, Hee Sik / Emeritus Professor | Ho-Jong Jang / Professor |

Cha Kyung Joon / Professor | Song, Jung Hwan / Professor |

Yanghyun Byun / Professor | Youngsik Huh / Professor |

Heo Jaeseong / Professor | Choonkil Park / Professor |

Hyeonmi Lee / Professor | Park Young-Sun / Associate Professor |

CHOI JUNGSOON / Associate Professor | Jae Hong Seo / Associate Professor |

Seunghyeok Kim / Assistant Professor | Jinyeong Park / Assistant Professor |

Shin Kyoil / Adjunct Professor | Woo Suk Roh / Adjunct Professor |

Chin Chung-Un / Adjunct Professor | Suyeon Park / Adjunct Professor |

Young Sik Kim / Research Professor | 김용운 / Emeritus Professor |

장한명 / Emeritus Professor | 이장우 / Emeritus Professor |

Kang Shin Won / Emeritus Professor | 이학래 / Emeritus Professor |

김태동 / Emeritus Professor | Lee, Chang koo / Emeritus Professor |

차형구 / Emeritus Professor | Chong-Man Cho / Emeritus Professor |

Dall Sun Yoon / Emeritus Professor | Byung Hwee Kim / Emeritus Professor |

Chang, Joo Sup / Emeritus Professor | KIM, WAN SE / Emeritus Professor |

Park Jihoon / Post-Doc. | Heewon Chung / Post-Doc. |

Jaehong Jeong / Assistant Professor |

Year | Term | No. | Curriculum | Course | Credits-lecture-experiential learning | |
---|---|---|---|---|---|---|

1 | 1 | CHM1005 | General Chemistry & Experiment 1 | (Compulsory) Requirement in Fundamental Studies | 3-3-2 | |

CHM105 General Chemistry and Lab 1 Aim to understand the structures and the properties of matters in micro- and macroscopic view. Introduction, stoichiometry and the mole concept, the behavior of gases, liquids and solids, thermochemistry, electronic structure of atoms and chemical bonding, descriptive chemistry of selected elements and compounds, chemical equilibrium. Lecture, lab, and discussion. Open to Freshmen. | ||||||

1 | 1 | CUL3011 | General Physics & Experiment 1 | (Compulsory) Requirement in Fundamental Studies | 3-3-2 | |

This course is for the undergraduate students majoring in science- and engineering-fields. This course helps students to understand the basic concepts on mechanics, gravitation, periodic motion and waves, fluid mechanics, thermodynamics and statistical mechanics. It also makes them adept in solving the relevant problems. In each week the course is composed of 3-hour theory lecture and 2-hour lab experiments. Throughout the theory lectures, the students will learn how to understand various phenomena concerning forces and motions based on some fundamental principles and physical laws. The students can broaden their understanding of basic physical concepts by solving homework problems. In the lab experiments, the students get familiar with the scientific analysis methodology by performing the experiments that verify the proposed principles. | ||||||

1 | 1 | GEN2052 | Calculus 1 | (Compulsory) Requirement in Fundamental Studies | 3-3-0 | |

Calculus is an essential knowledge for natural sciences and engineering. This course present the part of calculus which include taking limits, differentiating and integrating functions including a few transcendental ones and also deals with polar coordinate system, sequences and series. The aim of the course is to teach the students the basic concepts of mathematics and to train them so that they may be able to apply these basic concepts to various situations and may get used to scientific thinking. | ||||||

1 | 1 | GEN5029 | Career Development Ⅰ | (Compulsory) Requirement in Fundamental Studies | 1-1-0 | |

The course is aimed to help the freshmen to lay foundation on finding the best ways in which they make adjustment in college and understanding who they are and what vision that they could set for themselves in ever-changing knowledge-information society. Students will be able to do so through various seminars and counselling with their advisors. In so doing, students are expected to come up with Campus Road-map as well as Life Road-map at the end of the semester. Moreover, the course will maximize the efficiency of its offerings to the students with its strategic cooperation with HELP1 and Career Development Ⅰ, thereby it will set and develop the standard model for career development, while the course will help the students to prepare for Career II class offered in their junior year. | ||||||

1 | 1 | GEN6044 | Hanyang Community Service | (Compulsory) Requirement in Fundamental Studies | 1-0-2 | |

His career as a wide range of knowledge and lessons learned in the previous semester plan to explore in depth the process. Employment working in the industry of major interest to seniors invited to hear the information about the industry to prepare for what you need to learn knowhow. In addition, students who already have a job that aim to visit seniors plan their careers and the skills necessary to equip determined to develop a career that any plan. | ||||||

1 | 1 | SYH0001 | HUMAN LEADERSHIP | (Compulsory) Requirement in Fundamental Studies | 2-2-0 | |

Hanyang Leadership(HELP: Hanyang Essential Leadership Plus) is the leadership development program of Hanyang University that "helps" Hanyang students to be CEOs. The first step of this program, Human Leadership(HELP1) is a course offered to freshmen students. It is focused on helping them establish characters and values. By enhancing their humanistic sensitivities and knowledge they learn core values and leadership. Students discover themselves through HELP1 and are able to decide what kind of person they want to be. HELP1 helps students establish their values and prepare them to be balanced leaders who can adjust to new environments. | ||||||

1 | 1 | CUL0011 | Creative Computing | Compulsory General Studies | 3-1-2 | |

For students of no experience in computer programming area, the fundamental concepts and the methods of application of a computer programming language will be studied and learned by going through a developing process of a simple computer game from the bottom using "Python", very easy programming language to start. By inducing students to discuss freely and have question and answer sessions briskly about questions coming to mind during developing computer programs in practice, students will acquire computer programming understandings. Then the purpose of this course is to develop their ability to produce creative ideas in fusion technique for their major area in highly information-oriented society. | ||||||

1 | 1 | CUL3011 | General Physics & Experiment 1 | Basic Major | 3-2-2 | |

This course is for the undergraduate students majoring in science- and engineering-fields. This course helps students to understand the basic concepts on mechanics, gravitation, periodic motion and waves, fluid mechanics, thermodynamics and statistical mechanics. It also makes them adept in solving the relevant problems. In each week the course is composed of 3-hour theory lecture and 2-hour lab experiments. Throughout the theory lectures, the students will learn how to understand various phenomena concerning forces and motions based on some fundamental principles and physical laws. The students can broaden their understanding of basic physical concepts by solving homework problems. In the lab experiments, the students get familiar with the scientific analysis methodology by performing the experiments that verify the proposed principles. | ||||||

1 | 1 | GEN2052 | Calculus 1 | Basic Major | 3-3-0 | |

Calculus is an essential knowledge for natural sciences and engineering. This course present the part of calculus which include taking limits, differentiating and integrating functions including a few transcendental ones and also deals with polar coordinate system, sequences and series. The aim of the course is to teach the students the basic concepts of mathematics and to train them so that they may be able to apply these basic concepts to various situations and may get used to scientific thinking. | ||||||

1 | 1 | GEN5029 | Career Development : Roadmap for Job Searching and Startups | Compulsory General Studies | 1-1-0 | |

The ‘seminar for freshman students’ aims to cover the following aspects: etiquettes of the university life; how to use the university facilities; how to improve oneself and provision of ideal ways to utilize the student period. It aims to broaden the 1st year students’ point of view to their majors as well as the university life in general. The lecture will discuss studying skill including taking notes, taking exams, time management and subject enrollment in order to guide students to achieve an ideal studying pattern and further to set up a career path. It will also deal with basic information about diverse study areas, domestic and international social issues and career development. | ||||||

1 | 1 | ITE1009 | C PROGRAMING | Basic Major | 3-2-2 | |

C language programming to modularize the structure of a function. Module is effective in re-programming. Object-oriented programming algorithm to learn the grammar. Applied Math implementation of modularity may be possible. | ||||||

1 | 1 | SYH0001 | Love in deed and truth1(Hanyang Nanum) | Compulsory General Studies | 2-2-0 | |

Hanyang Leadership(HELP: Hanyang Essential Leadership Plus) is the leadership development program of Hanyang University that "helps" Hanyang students to be CEOs. The first step of this program, Hanyang Leadership(HELP1) is the core course for freshmen. This course is composed of 3 parts, "pride in Hanyang", "core values in global society" and "life planning". In "pride in Hanyang" students will review the history, values and vision of Hanyang University. In "core values in global society" students will study 6 core values and case study on the core values of global companys. In "life planning" students will reflect on their history and present and develop the vision and mission statement. | ||||||

1 | 1 | CUL0011 | Creative Computing | Compulsory General Studies | 3-1-2 | |

For students of no experience in computer programming area, the fundamental concepts and the methods of application of a computer programming language will be studied and learned by going through a developing process of a simple computer game from the bottom using "Python", very easy programming language to start. By inducing students to discuss freely and have question and answer sessions briskly about questions coming to mind during developing computer programs in practice, students will acquire computer programming understandings. Then the purpose of this course is to develop their ability to produce creative ideas in fusion technique for their major area in highly information-oriented society. | ||||||

1 | 1 | CUL3011 | General Physics & Experiment 1 | Basic Major | 3-2-2 | |

This course is for the undergraduate students majoring in science- and engineering-fields. This course helps students to understand the basic concepts on mechanics, gravitation, periodic motion and waves, fluid mechanics, thermodynamics and statistical mechanics. It also makes them adept in solving the relevant problems. In each week the course is composed of 3-hour theory lecture and 2-hour lab experiments. Throughout the theory lectures, the students will learn how to understand various phenomena concerning forces and motions based on some fundamental principles and physical laws. The students can broaden their understanding of basic physical concepts by solving homework problems. In the lab experiments, the students get familiar with the scientific analysis methodology by performing the experiments that verify the proposed principles. | ||||||

1 | 1 | GEN2052 | Calculus 1 | Basic Major | 3-3-0 | |

Calculus is an essential knowledge for natural sciences and engineering. This course present the part of calculus which include taking limits, differentiating and integrating functions including a few transcendental ones and also deals with polar coordinate system, sequences and series. The aim of the course is to teach the students the basic concepts of mathematics and to train them so that they may be able to apply these basic concepts to various situations and may get used to scientific thinking. | ||||||

1 | 1 | GEN5029 | Career Development : Roadmap for Job Searching and Startups | Compulsory General Studies | 1-1-0 | |

The ‘seminar for freshman students’ aims to cover the following aspects: etiquettes of the university life; how to use the university facilities; how to improve oneself and provision of ideal ways to utilize the student period. It aims to broaden the 1st year students’ point of view to their majors as well as the university life in general. The lecture will discuss studying skill including taking notes, taking exams, time management and subject enrollment in order to guide students to achieve an ideal studying pattern and further to set up a career path. It will also deal with basic information about diverse study areas, domestic and international social issues and career development. | ||||||

1 | 1 | ITE1009 | C PROGRAMING | Basic Major | 3-2-2 | |

C language programming to modularize the structure of a function. Module is effective in re-programming. Object-oriented programming algorithm to learn the grammar. Applied Math implementation of modularity may be possible. | ||||||

1 | 1 | SYH0001 | Love in deed and truth1(Hanyang Nanum) | Compulsory General Studies | 2-2-0 | |

Hanyang Leadership(HELP: Hanyang Essential Leadership Plus) is the leadership development program of Hanyang University that "helps" Hanyang students to be CEOs. The first step of this program, Hanyang Leadership(HELP1) is the core course for freshmen. This course is composed of 3 parts, "pride in Hanyang", "core values in global society" and "life planning". In "pride in Hanyang" students will review the history, values and vision of Hanyang University. In "core values in global society" students will study 6 core values and case study on the core values of global companys. In "life planning" students will reflect on their history and present and develop the vision and mission statement. | ||||||

1 | 2 | CUL0005 | Korean Speaking and Writing | (Compulsory) Requirement in Fundamental Studies | 3-3-0 | |

This course is to understand about the culture of the moderns, can be represented in the speaking and writing skills and a free imagination, and creative and critical reason for celebration. In addition, students can participate in lectures and presentations, a discussion of the end of class for free and a variety of writing and the correct writing of the progress and lessons will be conducted. Subjective reason ability and come in a variety of situations, each student through this class so that you can be a true and accurate communication, speaking and writing skills will be able to exert. | ||||||

1 | 2 | CUL3012 | General Physics & Experiment 2 | (Compulsory) Requirement in Fundamental Studies | 3-3-2 | |

The goal of this course is to make you familiar, at the conceptual and basic problem-solving level, with the physics of electricity, magnetism, heat, and waves, optics and modern physics. The basic philosophy of CUL3012 can be summarized as follows: The approaches used to achieve these goals involve 1) lectures to interactively discuss and demonstrate the principles, 2) laboratory experiments allowing you to actively explore these principles, and 3) interaction with instructors in discussion sections to provide one-on-one help with concepts and problem solving. | ||||||

1 | 2 | GEN2053 | Calculus 2 | (Compulsory) Requirement in Fundamental Studies | 3-3-0 | |

This course is a continuation of CALCULUS1, which aims at preparing the students for their study in their respective major subjects in natural sciences or engineering by equipping them with the knowledge of calculus and some basics of analytic geometry so that they may have the necessary mathematical background and the ability to take logical approaches when they confront the various problems in their study. The course presents the part of calculus and analytic geometry which include linear algebra, matrices and systems of linear equations, functions of several variables, partial differentiation, double integration and vector calculus, which are more advanced subjects then those of CALCULUS1. | ||||||

1 | 2 | GEN4091 | Philosophical Understanding of Science and Technology | (Compulsory) Requirement in Fundamental Studies | 3-3-0 | |

This course aims to survey some important theoretical results recently obtained in science and technology studies. We will carefully examine a number of concrete case studies studied by scholars from philosophy of science and technology, sociology of science and technology, and history of science and technology. The students taking the course shall learn various aspects of modern science and technology in the context of modern society. They shall appreciate how modern science and technology from the nineteenth century has come to manifest a number of its unique features, which can be clearly distinguished from the science and technology of even, the eighteenth century. We will discuss in the class the significance of differences for proper understanding of science and technology of our time. The course will also encourage more interactions between humanities and natural sciences so that we can make well-informed and reasonable decisions concerning complicated issues which are so common in our multi-layered society. The target audience of the course is students studying natural sciences and/or engineering. The contents of the course will be stylized each term, considering the student';s needs and backgrounds. | ||||||

1 | 2 | ITE1009 | C PROGRAMING | (Compulsory) Requirement in Fundamental Studies | 3-2-2 | |

C language programming to modularize the structure of a function. Module is effective in re-programming. Object-oriented programming algorithm to learn the grammar. Applied Math implementation of modularity may be possible. | ||||||

1 | 2 | CUL0005 | Korean Speaking and Writing | Compulsory General Studies | 3-3-0 | |

Through kiscussion this course ask the following questions: (1) What is free associaton?; (2) How do you compose and make a text? How do you talk about a certain issue?; (3) What is rational and logical thought?; (4) How do you enhance originality and rationlity? The course help students acquire an understanding of text and composition. | ||||||

1 | 2 | CUL3012 | General Physics & Experiment 2 | Basic Major | 3-2-2 | |

The goal of this course is to make you familiar, at the conceptual and basic problem-solving level, with the physics of electricity, magnetism, heat, and waves, optics and modern physics. The basic philosophy of CUL312 can be summarized as follows: The approaches used to achieve these goals involve 1) lectures to interactively discuss and demonstrate the principles, 2) laboratory experiments allowing you to actively explore these principles, and 3) interaction with instructors in discussion sections to provide one-on-one help with concepts and problem solving. | ||||||

1 | 2 | GEN2053 | Calculus 2 | Basic Major | 3-3-0 | |

This course is a continuation of CALCULUS1, which aims at preparing the students for their study in their respective major subjects in natural sciences or engineering by equipping them with the knowledge of calculus and some basics of analytic geometry so that they may have the necessary mathematical background and the ability to take logical approaches when they confront the various problems in their study. The course presents the part of calculus and analytic geometry which include linear algebra, matrices and systems of linear equations, functions of several variables, partial differentiation, double integration and vector calculus, which are more advanced subjects then those of CALCULUS1. | ||||||

1 | 2 | GEN4091 | Philosophical Understanding of Science and Technology | Compulsory General Studies | 3-3-0 | |

This course aims to cultivate among students the comprehensive understanding of science and technology in modern society, employing philosophical methods and concepts. To do this, the course offers a survey of some important theoretical results recently obtained in science and technology studies. We will carefully examime a number of concrete case-studies, ranging from the electrification of America, quantum revolution to the introduction of western science to traditional Korea. We will then discuss the intrinsic nature of modern science and technology as well as its socio-cultural aspects in the context of modern society. Students who take the course shall appreciate how modern science and technology from the nineteenth century has come to manifest a number of unique characteristics, which can be clearly distinguished from the science and technology of even, the eighteenth century. We will discuss in the class the significance of this difference. The course will also highlights the importance of dialogue between experts with different background and encourage more interactions between humanities and natural sciences, so that we can make well-informed and reasonable decisions concerning complicated issues which are so common in our multi-layered society. | ||||||

1 | 2 | MAT4072 | SETS AND LOGIC | Basic Major | 3-3-0 | |

For modern mathematics, set theory is the underlying grammar for all subjects. In fact, all the mathematical objects are built from the underlying set by imposing various structures, which are also given within set theory. This course offers basic concepts of set theory, such as the definition of a set, various operations between sets, function between sets, cardinality, and ordering. Also various systems of axioms such as those of set theory and classical geometry will be dealt. | ||||||

1 | 2 | CUL0005 | Korean Speaking and Writing | Compulsory General Studies | 3-3-0 | |

Through kiscussion this course ask the following questions: (1) What is free associaton?; (2) How do you compose and make a text? How do you talk about a certain issue?; (3) What is rational and logical thought?; (4) How do you enhance originality and rationlity? The course help students acquire an understanding of text and composition. | ||||||

1 | 2 | CUL3012 | General Physics & Experiment 2 | Basic Major | 3-2-2 | |

The goal of this course is to make you familiar, at the conceptual and basic problem-solving level, with the physics of electricity, magnetism, heat, and waves, optics and modern physics. The basic philosophy of CUL312 can be summarized as follows: The approaches used to achieve these goals involve 1) lectures to interactively discuss and demonstrate the principles, 2) laboratory experiments allowing you to actively explore these principles, and 3) interaction with instructors in discussion sections to provide one-on-one help with concepts and problem solving. | ||||||

1 | 2 | GEN2053 | Calculus 2 | Basic Major | 3-3-0 | |

This course is a continuation of CALCULUS1, which aims at preparing the students for their study in their respective major subjects in natural sciences or engineering by equipping them with the knowledge of calculus and some basics of analytic geometry so that they may have the necessary mathematical background and the ability to take logical approaches when they confront the various problems in their study. The course presents the part of calculus and analytic geometry which include linear algebra, matrices and systems of linear equations, functions of several variables, partial differentiation, double integration and vector calculus, which are more advanced subjects then those of CALCULUS1. | ||||||

1 | 2 | GEN4091 | Philosophical Understanding of Science and Technology | Compulsory General Studies | 3-3-0 | |

This course aims to cultivate among students the comprehensive understanding of science and technology in modern society, employing philosophical methods and concepts. To do this, the course offers a survey of some important theoretical results recently obtained in science and technology studies. We will carefully examime a number of concrete case-studies, ranging from the electrification of America, quantum revolution to the introduction of western science to traditional Korea. We will then discuss the intrinsic nature of modern science and technology as well as its socio-cultural aspects in the context of modern society. Students who take the course shall appreciate how modern science and technology from the nineteenth century has come to manifest a number of unique characteristics, which can be clearly distinguished from the science and technology of even, the eighteenth century. We will discuss in the class the significance of this difference. The course will also highlights the importance of dialogue between experts with different background and encourage more interactions between humanities and natural sciences, so that we can make well-informed and reasonable decisions concerning complicated issues which are so common in our multi-layered society. | ||||||

1 | 2 | MAT4072 | SETS AND LOGIC | Basic Major | 3-3-0 | |

For modern mathematics, set theory is the underlying grammar for all subjects. In fact, all the mathematical objects are built from the underlying set by imposing various structures, which are also given within set theory. This course offers basic concepts of set theory, such as the definition of a set, various operations between sets, function between sets, cardinality, and ordering. Also various systems of axioms such as those of set theory and classical geometry will be dealt. | ||||||

2 | 1 | MAT2001 | Differential Equation 1 | Core Major | 3-3-0 | |

Introductiontodifferentialequations,first-orderdifferentialequations,higher-orderlineardifferentialequations,initial-valueandboundary-valueproblems,seriessolutionsoflineardifferentialequations,Laplacetrandformandapplication. | ||||||

2 | 1 | MAT2015 | Advanced Calculus 1 | Core Major | 3-3-0 | |

Thiscoursecoversthefollowingmaterials:Realnumbersystem,limitsandcontinuityoffunctionsofonevariables,convergenceofsequencesandseries.Seriesexpansionsoffunctions,R^nspaces,DerivativesonR^n,Directionalderivative,Meanvaluetheorem,Inverfunctiontheorem,Implicitfunctiontheorem. | ||||||

2 | 1 | MAT2022 | Principles of Statistics | Core Major | 3-3-0 | |

It is designed to introduce principles of statistics. This course in necessary to take advanced statistics courses such as statistical computing and mathematical statistics. This course covers probability and conditional probability, random variable and random sample, sampling distribution, interval estimation, testing hypotheses, simple linear regression and categorical data analysis. | ||||||

2 | 1 | MAT2023 | Linear Algebra 1 | Core Major | 3-3-0 | |

Westudythefundamentalconceptsofvectors,basesandfinitdimensionalvectorspaces,lineartransformations,matrcesandlineartransformations,thefundamentalconceptsofmatrices,andsystemoflinearequations. | ||||||

2 | 1 | MAT4070 | NUMBER THEORY1 | Core Major | 3-3-0 | |

1. COURSE DESCRIPTION The basic concepts of classical number theory, as well as to impart some of the historical background in which the subject evolved, are treated carefully and rigorously. Topics covered include primes, divisibility and congruences with applications, Fermat theorem, number theoretic functions, Euler's theorem, and primitive roots and indices. 2. COURSE OBJECTIVES Number theory is a pure mathematics, however The aim of this subject is of developing the problem solving ability and creative concepts of students for numerical problems appeared in science areas. For this aim, we emphasize mainly to students Objective 1 : understanding the fundamental properties of the number theoretic aspects Objective 2 : Finding some patterns of the number theoretic structures of integers Objective 3 : Developing the ability to solve applied problems related to the above facts 3. CONTENTS Chapter 1. Some preliminary Consideration 1.1 Mathematical Induction 1.2 The Binomial Theorem Chapter 2. Divisibility Theory 2.1 Early Number Theory 2.2 The Division Algorithm 2.3 The Greatest Common Divisor 2.4 The Euclidean Algorithm 2.5 The Diophantine Equation Chapter 3. Primes and Their Distribution 3.1 The Fundamental Theorem of Arithmetic 3.2 The Sieve of Eratosthenes 3.3 The Goldbach Conjecture Chapter 4. The Theory of Congruences 4.1 Karl Friedriech Gauss 4.2 Special Divisibility of Tests 4.3 Binary and Decimal Representations of Integers 4.4 Linear Congruences and the Chinese Remainder Theorem Chapter 5. Fermat's Theorem 5.1 Fermat 5.2 Fermat's Little Theorem and Pseudoprimes 5.3 Wilson's Theorem 5.4 The Fermat-Kraitchik Factorization Theorem Chapter 6. Number Theoretic Functions 6.1 The Sum and Number of Divisors 6.2 the Moebius Inversion Formula 6.3 The Greatest Integer Functions 6.4 An Application to the Calender Chapter 7. Euller's Theorem 7.1 Euler 7.2 Euler's Phi-Function 7.3 Euler's Theorem 7.4 some Properties of the Phi-Function Chapter 8. Primitive Roots and Indices 8.1 The Order of an Integer Modulo n 8.2 Primitive Roots for Primes 8.3 Composite Numbers Having Primitive Roots 8.4 The Theory of Indices 4. THE EXPECTED EFFICIENCIES The number theory is a fundamental and main subject in mathematics area, as well as natural science and engineering. It provides the students some creative ideas to get through the numerical problems appeared in science area through the use of inducing various theoretical principles and treating many applied problems in number theory. | ||||||

2 | 1 | MAT4072 | SETS AND LOGIC | Core Major | 3-3-0 | |

For modern mathematics, set theory is the underlying grammar for all subjects. In fact, all the mathematical objects are built from the underlying set by imposing various structures, which are also given within set theory. This course offers basic concepts of set theory, such as the definition of a set, various operations between sets, function between sets, cardinality, and ordering. Also various systems of axioms such as those of set theory and classical geometry will be dealt. | ||||||

2 | 1 | MAT2006 | Number Theory | Basic Major | 3-3-0 | |

The basic concepts of classical number theory, as well as to impart some of the historical background in which the subject evolved, are treated carefully and rigorously. Topics covered include primes, divisibility and congruences with applications, Fermat theorem, number theoretic functions, Euler's theorem, and primitive roots and indices. 2. COURSE OBJECTIVES Number theory is a pure mathematics, however The aim of this subject is of developing the problem solving ability and creative concepts of students for numerical problems appeared in science areas. For this aim, we emphasize mainly to students Objective 1 : understanding the fundamental properties of the number theoretic aspects Objective 2 : Finding some patterns of the number theoretic structures of integers Objective 3 : Developing the ability to solve applied problems related to the above facts 3. CONTENTS Chapter 1. Some preliminary Consideration 1.1 Mathematical Induction 1.2 The Binomial Theorem Chapter 2. Divisibility Theory 2.1 Early Number Theory 2.2 The Division Algorithm 2.3 The Greatest Common Divisor 2.4 The Euclidean Algorithm 2.5 The Diophantine Equation Chapter 3. Primes and Their Distribution 3.1 The Fundamental Theorem of Arithmetic 3.2 The Sieve of Eratosthenes 3.3 The Goldbach Conjecture Chapter 4. The Theory of Congruences 4.1 Karl Friedriech Gauss 4.2 Special Divisibility of Tests 4.3 Binary and Decimal Representations of Integers 4.4 Linear Congruences and the Chinese Remainder Theorem Chapter 5. Fermat's Theorem 5.1 Fermat 5.2 Fermat's Little Theorem and Pseudoprimes 5.3 Wilson's Theorem 5.4 The Fermat-Kraitchik Factorization Theorem Chapter 6. Number Theoretic Functions 6.1 The Sum and Number of Divisors 6.2 the Moebius Inversion Formula 6.3 The Greatest Integer Functions 6.4 An Application to the Calender Chapter 7. Euller's Theorem 7.1 Euler 7.2 Euler's Phi-Function 7.3 Euler's Theorem 7.4 some Properties of the Phi-Function Chapter 8. Primitive Roots and Indices 8.1 The Order of a | ||||||

2 | 1 | MAT2009 | Differential Equations | Core Major | 3-3-0 | |

n this lecture, we introduce and study differential equations, first-order differential equations, higher-order linear differential equations, initial-value and boundary-value problems, series solutions of linear differential equations, Laplace transform and applications. | ||||||

2 | 1 | MAT2015 | Advanced Calculus 1 | Basic Major | 3-3-0 | |

Thiscoursecoversthefollowingmaterials:Realnumbersystem,limitsandcontinuityoffunctionsofonevariables,convergenceofsequencesandseries.Seriesexpansionsoffunctions,R^nspaces,DerivativesonR^n,Directionalderivative,Meanvaluetheorem,Inverfunctiontheorem,Implicitfunctiontheorem. | ||||||

2 | 1 | MAT2022 | Principles of Statistics | Core Major | 3-3-0 | |

It is designed to introduce principles of statistics. This course in necessary to take advanced statistics courses such as statistical computing and mathematical statistics. This course covers probability and conditional probability, random variable and random sample, sampling distribution, interval estimation, testing hypotheses, simple linear regression and categorical data analysis. | ||||||

2 | 1 | MAT2023 | Linear Algebra 1 | Basic Major | 3-3-0 | |

Westudythefundamentalconceptsofvectors,basesandfinitdimensionalvectorspaces,lineartransformations,matrcesandlineartransformations,thefundamentalconceptsofmatrices,andsystemoflinearequations. | ||||||

2 | 1 | MAT2006 | Number Theory | Core Major | 3-3-0 | |

The basic concepts of classical number theory, as well as to impart some of the historical background in which the subject evolved, are treated carefully and rigorously. Topics covered include primes, divisibility and congruences with applications, Fermat theorem, number theoretic functions, Euler's theorem, and primitive roots and indices. 2. COURSE OBJECTIVES Number theory is a pure mathematics, however The aim of this subject is of developing the problem solving ability and creative concepts of students for numerical problems appeared in science areas. For this aim, we emphasize mainly to students Objective 1 : understanding the fundamental properties of the number theoretic aspects Objective 2 : Finding some patterns of the number theoretic structures of integers Objective 3 : Developing the ability to solve applied problems related to the above facts 3. CONTENTS Chapter 1. Some preliminary Consideration 1.1 Mathematical Induction 1.2 The Binomial Theorem Chapter 2. Divisibility Theory 2.1 Early Number Theory 2.2 The Division Algorithm 2.3 The Greatest Common Divisor 2.4 The Euclidean Algorithm 2.5 The Diophantine Equation Chapter 3. Primes and Their Distribution 3.1 The Fundamental Theorem of Arithmetic 3.2 The Sieve of Eratosthenes 3.3 The Goldbach Conjecture Chapter 4. The Theory of Congruences 4.1 Karl Friedriech Gauss 4.2 Special Divisibility of Tests 4.3 Binary and Decimal Representations of Integers 4.4 Linear Congruences and the Chinese Remainder Theorem Chapter 5. Fermat's Theorem 5.1 Fermat 5.2 Fermat's Little Theorem and Pseudoprimes 5.3 Wilson's Theorem 5.4 The Fermat-Kraitchik Factorization Theorem Chapter 6. Number Theoretic Functions 6.1 The Sum and Number of Divisors 6.2 the Moebius Inversion Formula 6.3 The Greatest Integer Functions 6.4 An Application to the Calender Chapter 7. Euller's Theorem 7.1 Euler 7.2 Euler's Phi-Function 7.3 Euler's Theorem 7.4 some Properties of the Phi-Function Chapter 8. Primitive Roots and Indices 8.1 The Order of a | ||||||

2 | 1 | MAT2009 | Differential Equations | Core Major | 3-3-0 | |

n this lecture, we introduce and study differential equations, first-order differential equations, higher-order linear differential equations, initial-value and boundary-value problems, series solutions of linear differential equations, Laplace transform and applications. | ||||||

2 | 1 | MAT2015 | Advanced Calculus 1 | Basic Major | 3-3-0 | |

Thiscoursecoversthefollowingmaterials:Realnumbersystem,limitsandcontinuityoffunctionsofonevariables,convergenceofsequencesandseries.Seriesexpansionsoffunctions,R^nspaces,DerivativesonR^n,Directionalderivative,Meanvaluetheorem,Inverfunctiontheorem,Implicitfunctiontheorem. | ||||||

2 | 1 | MAT2022 | Principles of Statistics | Core Major | 3-3-0 | |

It is designed to introduce principles of statistics. This course in necessary to take advanced statistics courses such as statistical computing and mathematical statistics. This course covers probability and conditional probability, random variable and random sample, sampling distribution, interval estimation, testing hypotheses, simple linear regression and categorical data analysis. | ||||||

2 | 1 | MAT2023 | Linear Algebra 1 | Basic Major | 3-3-0 | |

Westudythefundamentalconceptsofvectors,basesandfinitdimensionalvectorspaces,lineartransformations,matrcesandlineartransformations,thefundamentalconceptsofmatrices,andsystemoflinearequations. | ||||||

2 | 2 | CSE2008 | Computer Mathematics | Core Major | 3-3-0 | |

This course is designed to meet the needs of students wishing to gain knowledge in the basic computer mathematics using the computer, including a study of computer arithmetic, boolean algebra, vectors, matrices, linear equations and elementary graph theory with practical numerical examples. The laboratory work for mathematics software MATLAB is mandatory. | ||||||

2 | 2 | GEN6032 | PROFESSIONAL ACADEMIC ENGLISH | (Compulsory) Requirement in Fundamental Studies | 3-3-0 | |

The Professional Academic English for students at Hanyang University focuses on the development of the oral and written communication skills, which are required in the globalized world community. The course aims to help students develop the competencies that are required in their future studies and career: professional knowledge, interpersonal and communicative competences. The course requires the students to develop creative problem solving skills. For this, the students perform various tasks by investigating and analyzing engineering topics as well as developing solutions. The students’ communication and negotiation skills are systematically supported by language skill development such as learning academic forms and structures of the language that are used in formal oral presentations and essays. The expected course outcome is that students are able to write academic reports, participate in discussions and make oral presentations in English on their major topics. Throughout the course, the students are encouraged to explore various major-related topics, to conduct systematic problem analyses, and to collaborate for creative problem solutions. Classroom activities mainly focus on the oral presentation and writing skills, and the preparatory activities of the essay writing. The course requires the students to make three oral presentations and write three essays in English on their major-related topics. Students are required to make a portfolio of their work, to be submitted and assessed. This will be discussed in class. Professional Academic English (PAE) is a required course for all HYU students that develops students’ academic presentation and writing skills using major-related content. Instruction will focus on the concepts and strategies needed in order to both organize and deliver a presentation, along with informal and formal opportunities to practice them. Students will also learn to improve their academic writing through assignments that require the dem | ||||||

2 | 2 | MAT2002 | Differential Equation 2 | Extended Major | 3-3-0 | |

Systemoflinearfirst-orderdifferentialequations,automoussystemsandstability,orthogonalfunctionsandFourierseries,partialdifferentialequationsandboundary-valueproblems,integraltransformmethod. | ||||||

2 | 2 | MAT2016 | Advanced Calculus 2 | Core Major | 3-3-0 | |

This course is the continuation of MAT 216. The course covers Fourier series, Riemann integral of functions of one variable, limits and continuity of functions on R^n, Integration on R^n, Iterated integral, Change of variables, Line integral, Surface integral, Green's theorem, Gauss's theorem, Stokes's theorem. | ||||||

2 | 2 | MAT2021 | Statistical Computing | Core Major | 3-3-0 | |

Weintroducealgorithmstocomputestatisticalmethods.Inordertodothis,weusethelanguagecalledR(orS-Plus)thatiswidelyusedforstatistics.Thiscoursecoverssolutionsforlinearandnon-linearequation,integrals(trapezoidalrule,Simpson'srule),randomnumbergeneration,percentile,MonteCarlointegration,etc. | ||||||

2 | 2 | MAT2024 | Linear Algebra 2 | Extended Major | 3-3-0 | |

Scalarproducts,orthogonalbases,bilinearmapsandmatrices,symmetric,Hermiteandunitaryoperator,eigenvaluesandeigenvectors,characteristicpolynomial,diagonalization,polynomialsandmatrices,triangulationofmatricesandlinearmaps. | ||||||

2 | 2 | MAT4071 | NUMBER THEORY2 | Core Major | 3-3-0 | |

1. COURSE DESCRIPTION The advanced concepts of classical number theory, as well as to impart some of the historical background in which the subject evolved, are treated carefully and rigorously. Topics covered include quadratic reciprocity law, basic cryptography, Mersenne primes and Fermat numbers, Fermat's last theorem, sums of squares, Fibobacci numbers, continued fractions, and prime number theorem and zeta functon 2. COURSE OBJECTIVES Number theory is a pure mathematics, however The aim of this subject is of developing the problem solving ability and creative concepts of students for numerical problems appeared in science areas. For this aim, we emphasize mainly to students Objective 1 : understanding the fundamental properties of the number theoretic aspects Objective 2 : Finding some patterns of the number theoretic structures of integers Objective 3 : Developing the ability to solve applied problems related to the above facts 3. CONTENTS Chapter 9. The Quadratic Reciprocity law 9.1 Euler's Criterion 9.2 The Legendra Symbol and Its Properties 9.3 Quadratic Reciprocity 9.4 Quadratic Congruences with Composite Moduli Chapter 10. Introduction to Cryptography 10.1 From Caesar Cyper to Public Key Cryptography 10.2 The Knapsack Cryptosystem 10.3 An Application of Primitive Roots to Cryptography Chapter 11. Numbers of Special Form 11.1 Mersenne 11.2 Perfect Numbers 11.3 Mersenne primes and Amicable Numbers 11.4 Fermat Numbers Chapter 12. Certain Nonlinear Diophantine Equations 12.1 The Equation 12.2 Fermat's Last Theorem Chapter 13. Representation of Integers as Sums of Squares 13.1 lagrange 13.2 Sums of Squares 13.3 Sums of More Than Two Squares Chapter 14. Fibonacci Numbers 14.1 Fibonacci 14.2 The Fibonacci Sequences 14.3 Certain Identities Involving Fibonacci Numbers Chapter 15. Continued Fractions 15.1 Ramanujan 15.2 Finite Continued Fractions 15.3 Infinite Continued Fractions 15.4 pell's Equation Chapter 16. Some Twentieth-Century Developements 16.1 Hardy, Dickson, and Erdos 16.2 Primality Testing and Factorization 16.3 An Application to Factoring: Remote Coin Flipping 16.4 The Prime Number Theorem and Zeta Function 4. THE EXPECTED EFFICIENCIES The number theory is a fundamental and main subject in mathematics area, as well as natural science and engineering. It provides the students some creative ideas to get through the numerical problems appeared in science area through the use of inducing various theoretical principles and treating many applied problems in number theory. | ||||||

2 | 2 | SYH0002 | GLOBAL LEADERSHIP | (Compulsory) Requirement in Fundamental Studies | 2-2-0 | |

Hanyang Leadership(HELP: Hanyang Essential Leadership Plus) is the leadership development program of Hanyang University that "helps" Hanyang students to be CEOs. The second step of this program, Global Leadership(HELP2) is the core course for sophomores. In the 21st century, we are moving into a global society where all countries are interconnected. Everything is changing at the speed of light. Competition is increasing. Digital convergence is occurring. Global leaders are the key to success for all organizations. In the global society, you can prepare for your future through HELP2. The purpose of HELP is to prepare students to be global leaders for the next generation. HELP2 teaches students: Global Leadership, Global Paradigm, Global Literacy, Global Manners and Global Mindset. Hanyang University students will be global leaders through HELP2. | ||||||

2 | 2 | CSE2008 | Computer Mathematics | Core Major | 3-3-0 | |

This course is designed to meet the needs of students wishing to gain knowledge in the basic computer mathematics using the computer, including a study of computer arithmetic, boolean algebra, vectors, matrices, linear equations and elementary graph theory with practical numerical examples. The laboratory work for mathematics software MATLAB is mandatory. | ||||||

2 | 2 | GEN6032 | PROFESSIONAL ACADEMIC ENGLISH | Compulsory General Studies | 3-3-0 | |

The Professional Academic English for students at Hanyang University focuses on the development of the oral and written communication skills, which are required in the globalized world community. The course aims to help students develop the competencies that are required in their future studies and career: professional knowledge, interpersonal and communicative competences. The course requires the students to develop creative problem solving skills. For this, the students perform various tasks by investigating and analyzing engineering topics as well as developing solutions. The students’ communication and negotiation skills are systematically supported by language skill development such as learning academic forms and structures of the language that are used in formal oral presentations and essays. The expected course outcome is that students are able to write academic reports, participate in discussions and make oral presentations in English on their major topics. Throughout the course, the students are encouraged to explore various major-related topics, to conduct systematic problem analyses, and to collaborate for creative problem solutions. Classroom activities mainly focus on the oral presentation and writing skills, and the preparatory activities of the essay writing. The course requires the students to make three oral presentations and write three essays in English on their major-related topics. Students are required to make a portfolio of their work, to be submitted and assessed. This will be discussed in class. | ||||||

2 | 2 | MAT2016 | Advanced Calculus 2 | Core Major | 3-3-0 | |

This course is the continuation of MAT 216. The course covers Fourier series, Riemann integral of functions of one variable, limits and continuity of functions on R^n, Integration on R^n, Iterated integral, Change of variables, Line integral, Surface integral, Green's theorem, Gauss's theorem, Stokes's theorem. | ||||||

2 | 2 | MAT2021 | Statistical Computing | Core Major | 3-3-0 | |

Weintroducealgorithmstocomputestatisticalmethods.Inordertodothis,weusethelanguagecalledR(orS-Plus)thatiswidelyusedforstatistics.Thiscoursecoverssolutionsforlinearandnon-linearequation,integrals(trapezoidalrule,Simpson'srule),randomnumbergeneration,percentile,MonteCarlointegration,etc. | ||||||

2 | 2 | MAT2024 | Linear Algebra 2 | Core Major | 3-3-0 | |

Scalarproducts,orthogonalbases,bilinearmapsandmatrices,symmetric,Hermiteandunitaryoperator,eigenvaluesandeigenvectors,characteristicpolynomial,diagonalization,polynomialsandmatrices,triangulationofmatricesandlinearmaps. | ||||||

2 | 2 | SYH0002 | GLOBAL LEADERSHIP | Compulsory General Studies | 2-2-0 | |

Hanyang Leadership(HELP: Hanyang Essential Leadership Plus) is the leadership development program of Hanyang University that "helps" Hanyang students to be CEOs. The second step of this program, Hanyang Leadership(HELP2) is the core course for Sophomores. In the 21st century, we are moving into a global soceity where all countries are interconnected. Everything is changing at the speed of light. Competition is increasing. Digital Convergence is occurring. Global leaders are the key to success for all organizations. In a global soceity, you can prepare for your future through HELP2. The purpose of HELP is to prepare students to be global leaders for the next generation. HELP2 teaches students: Global Leadership, Global Paradigm, Global Literacy, Global Manners, and Global Mindset. Hanyang university students will be global leaders through HELP2. | ||||||

2 | 2 | CSE2008 | Computer Mathematics | Core Major | 3-3-0 | |

This course is designed to meet the needs of students wishing to gain knowledge in the basic computer mathematics using the computer, including a study of computer arithmetic, boolean algebra, vectors, matrices, linear equations and elementary graph theory with practical numerical examples. The laboratory work for mathematics software MATLAB is mandatory. | ||||||

2 | 2 | GEN6032 | PROFESSIONAL ACADEMIC ENGLISH | Compulsory General Studies | 3-3-0 | |

The Professional Academic English for students at Hanyang University focuses on the development of the oral and written communication skills, which are required in the globalized world community. The course aims to help students develop the competencies that are required in their future studies and career: professional knowledge, interpersonal and communicative competences. The course requires the students to develop creative problem solving skills. For this, the students perform various tasks by investigating and analyzing engineering topics as well as developing solutions. The students’ communication and negotiation skills are systematically supported by language skill development such as learning academic forms and structures of the language that are used in formal oral presentations and essays. The expected course outcome is that students are able to write academic reports, participate in discussions and make oral presentations in English on their major topics. Throughout the course, the students are encouraged to explore various major-related topics, to conduct systematic problem analyses, and to collaborate for creative problem solutions. Classroom activities mainly focus on the oral presentation and writing skills, and the preparatory activities of the essay writing. The course requires the students to make three oral presentations and write three essays in English on their major-related topics. Students are required to make a portfolio of their work, to be submitted and assessed. This will be discussed in class. | ||||||

2 | 2 | MAT2016 | Advanced Calculus 2 | Core Major | 3-3-0 | |

This course is the continuation of MAT 216. The course covers Fourier series, Riemann integral of functions of one variable, limits and continuity of functions on R^n, Integration on R^n, Iterated integral, Change of variables, Line integral, Surface integral, Green's theorem, Gauss's theorem, Stokes's theorem. | ||||||

2 | 2 | MAT2021 | Statistical Computing | Core Major | 3-3-0 | |

Weintroducealgorithmstocomputestatisticalmethods.Inordertodothis,weusethelanguagecalledR(orS-Plus)thatiswidelyusedforstatistics.Thiscoursecoverssolutionsforlinearandnon-linearequation,integrals(trapezoidalrule,Simpson'srule),randomnumbergeneration,percentile,MonteCarlointegration,etc. | ||||||

2 | 2 | MAT2024 | Linear Algebra 2 | Basic Major | 3-3-0 | |

Scalarproducts,orthogonalbases,bilinearmapsandmatrices,symmetric,Hermiteandunitaryoperator,eigenvaluesandeigenvectors,characteristicpolynomial,diagonalization,polynomialsandmatrices,triangulationofmatricesandlinearmaps. | ||||||

2 | 2 | SYH0002 | Love in deed and truth2(Smart Communication) | Compulsory General Studies | 2-2-0 | |

Hanyang Leadership(HELP: Hanyang Essential Leadership Plus) is the leadership development program of Hanyang University that "helps" Hanyang students to be CEOs. The second step of this program, Hanyang Leadership(HELP2) is the core course for Sophomores. In the 21st century, we are moving into a global soceity where all countries are interconnected. Everything is changing at the speed of light. Competition is increasing. Digital Convergence is occurring. Global leaders are the key to success for all organizations. In a global soceity, you can prepare for your future through HELP2. The purpose of HELP is to prepare students to be global leaders for the next generation. HELP2 teaches students: Global Leadership, Global Paradigm, Global Literacy, Global Manners, and Global Mindset. Hanyang university students will be global leaders through HELP2. | ||||||

3 | 1 | GEN6094 | Fieldwork 1 | Extended Major | 3-0-3 | |

Mathematics Placement1 is a internship or work placement course to provide students with opportunity of undertaking a period of practical, working related experience. Students will work at industry or research institute, this is, at an organization external to the university during the semester or vacation. Students are expected to get opportunity for career exploration and aptitude understanding by experiencing practical application of their knowledge learned in the university class. | ||||||

3 | 1 | MAT2066 | Analysis 1 | Core Major | 3-3-0 | |

In this course, we first treat the real and complex number system, and the basic topology under the background of advanced calculus. And then, we treat the numberical sequences and series. Finally, we treat the important properties of functions, that is, continuity and differentiability, and the Remann-Stieltjes integrability. The purpose of this course is to make the foundation of analysis. | ||||||

3 | 1 | MAT3001 | Modern Algebra 1 | Core Major | 3-3-0 | |

General theory with emphasis on fundamentals of ring theory. : integral domains, ring of polynomials, and factor rings and ideals; unique factorization domains, euclidean domains, and Gaussian integers and norms. | ||||||

3 | 1 | MAT3004 | Topology 1 | Core Major | 3-3-0 | |

The course starts from metric spaces moving quickly toward general topological spaces. Some basic properties of topological spaces in connection with continuous maps are studied. Among them are connectedness, compactness and some separation axioms such as the Hausdorff property, regularity and normality. | ||||||

3 | 1 | MAT3022 | Mathematical Statistics 1 | Core Major | 3-3-0 | |

Mathematical statistics is a foundation of statistics itself because it provides basic ideas of what statistics are. Valuable for students who are majoring in sciences such as natural sciences and engineering. It covers probabillity, random variables, discreate and continuous distribution functions and sampling distribution as well as estimation and testing. Will provide a strong background for theoretical statistics that would be used for applied statistics. | ||||||

3 | 1 | MAT3027 | Complex Analysis 1 | Core Major | 3-3-0 | |

This is an introductary course of theory of complex functions and treats following materials : The algebraic and geometric structures of complex number systems, Limits and continuity of complex functions, differentiality, Cauchy-Remann equation, harmonic functions, various elementary functions, Contour integral, Cauchy integral formula, Liouville theorem. | ||||||

3 | 1 | MAT3051 | Numerical Analysis 1 | Core Major | 3-3-0 | |

Theory and practice of computational procedures including approximation of functions by interpolating polynomials, numerical differentiation and integration, and solution of ordinary differential equations including both initial value and boundary value problems. Computer applications and techniques. | ||||||

3 | 1 | TEA5009 | Mathematics Educational Theories on Subject | --Major for Teacher Certifica-- | 3-3-0 | |

This course is an introduction to the scholarly discipline of mathematics education. The overall goal of this course is to make students acquainted with the scholarly discipline of mathematics education, including central themes and concepts of theories in mathematics education in relation to mathematical practices. | ||||||

3 | 1 | MAT3001 | Modern Algebra 1 | Core Major | 3-3-0 | |

General theory with emphasis on fundamentals of ring theory. : integral domains, ring of polynomials, and factor rings and ideals; unique factorization domains, euclidean domains, and Gaussian integers and norms. | ||||||

3 | 1 | MAT3004 | Topology 1 | Core Major | 3-3-0 | |

The course starts from metric spaces moving quickly toward general topological spaces. Some basic properties of topological spaces in connection with continuous maps are studied. Among them are connectedness, compactness and some separation axioms such as the Hausdorff property, regularity and normality. | ||||||

3 | 1 | MAT3022 | Mathematical Statistics 1 | Core Major | 3-3-0 | |

Mathematical statistics is a foundation of statistics itself because it provides basic ideas of what statistics are. Valuable for students who are majoring in sciences such as natural sciences and engineering. It covers probabillity, random variables, discreate and continuous distribution functions and sampling distribution as well as estimation and testing. Will provide a strong background for theoretical statistics that would be used for applied statistics. | ||||||

3 | 1 | MAT3027 | Complex Analysis 1 | Core Major | 3-3-0 | |

This is an introductary course of theory of complex functions and treats following materials : The algebraic and geometric structures of complex number systems, Limits and continuity of complex functions, differentiality, Cauchy-Remann equation, harmonic functions, various elementary functions, Contour integral, Cauchy integral formula, Liouville theorem. | ||||||

3 | 1 | MAT3051 | Numerical Analysis 1 | Core Major | 3-3-0 | |

Theory and practice of computational procedures including approximation of functions by interpolating polynomials, numerical differentiation and integration, and solution of ordinary differential equations including both initial value and boundary value problems. Computer applications and techniques. | ||||||

3 | 1 | TEA5009 | Mathematics Educational Theories on Subject | --Major for Teacher Certifica-- | 3-3-0 | |

This course is an introduction to the scholarly discipline of mathematics education. The overall goal of this course is to make students acquainted with the scholarly discipline of mathematics education, including central themes and concepts of theories in mathematics education in relation to mathematical practices. | ||||||

3 | 1 | MAT3001 | Modern Algebra 1 | Core Major | 3-3-0 | |

General theory with emphasis on fundamentals of ring theory. : integral domains, ring of polynomials, and factor rings and ideals; unique factorization domains, euclidean domains, and Gaussian integers and norms. | ||||||

3 | 1 | MAT3004 | Topology 1 | Core Major | 3-3-0 | |

The course starts from metric spaces moving quickly toward general topological spaces. Some basic properties of topological spaces in connection with continuous maps are studied. Among them are connectedness, compactness and some separation axioms such as the Hausdorff property, regularity and normality. | ||||||

3 | 1 | MAT3022 | Mathematical Statistics 1 | Core Major | 3-3-0 | |

Mathematical statistics is a foundation of statistics itself because it provides basic ideas of what statistics are. Valuable for students who are majoring in sciences such as natural sciences and engineering. It covers probabillity, random variables, discreate and continuous distribution functions and sampling distribution as well as estimation and testing. Will provide a strong background for theoretical statistics that would be used for applied statistics. | ||||||

3 | 1 | MAT3027 | Complex Analysis 1 | Core Major | 3-3-0 | |

This is an introductary course of theory of complex functions and treats following materials : The algebraic and geometric structures of complex number systems, Limits and continuity of complex functions, differentiality, Cauchy-Remann equation, harmonic functions, various elementary functions, Contour integral, Cauchy integral formula, Liouville theorem. | ||||||

3 | 1 | MAT3051 | Numerical Analysis 1 | Core Major | 3-3-0 | |

Theory and practice of computational procedures including approximation of functions by interpolating polynomials, numerical differentiation and integration, and solution of ordinary differential equations including both initial value and boundary value problems. Computer applications and techniques. | ||||||

3 | 1 | TEA5009 | Mathematics Educational Theories on Subject | --Major for Teacher Certifica-- | 3-3-0 | |

This course is an introduction to the scholarly discipline of mathematics education. The overall goal of this course is to make students acquainted with the scholarly discipline of mathematics education, including central themes and concepts of theories in mathematics education in relation to mathematical practices. | ||||||

3 | 2 | GEN5100 | Career Development II (Portfolio and Business model Creation) | (Compulsory) Requirement in Fundamental Studies | 1-1-0 | |

This course is opened to the juniors. It will help students to evaluate the road-maps that students designed in Career I class, determine their competency in terms of making a career-decision, and set a concrete direction on how to prepare for jobs when they graduate. Students who are enrolled in the class will have to submit an individual portfolio at the end of the semester. The portfolio will have to be based on students’ counseling with their advisors and what they learn in class. Additionally, the course will maximize the efficiency of its offerings to the students with its strategic cooperation with HELP 3 (an on-line required course) and Career Development II, thereby it will set and develop the standard model for career development, while the course will feature as an advanced course for Career Development I offered for freshmen. | ||||||

3 | 2 | GEN6095 | Fieldwork 2 | Extended Major | 3-0-3 | |

Mathematics Placement2 is a internship or work placement course to provide students with opportunity of undertaking a period of practical, working related experience. Students will work at industry or research institute, this is, at an organization external to the university during the semester or vacation. Students are expected to get opportunity for career exploration and aptitude understanding by experiencing practical application of their knowledge learned in the university class. | ||||||

3 | 2 | MAT2067 | Analysis 2 | Extended Major | 3-3-0 | |

In this course, we first treat the Riemann-Stieltjes integral which is a generalization of the Riemann integral. And them, we treat the sequences and series of functions. Furthermore, we treat the some special functions, that is, the gamma and beta functions, and the transcendental function, and we also treat the functions of several variables. The purpose of this coures is to make a foundation of analysis. | ||||||

3 | 2 | MAT3002 | Modern Algebra 2 | Extended Major | 3-3-0 | |

3 | 2 | MAT3018 | Mathematical Programming | Core Major | 3-3-0 | |

Basic concepts including : a unified development of linear systems and linear programming, simplex and dual simplex method, relationship between primal and dual linear programs, an introduction to quadratic programming and the linear complementarity problem, convex sets and functions, an introduction to integer linear programming and an introduction to nonlinear programming with development of optimality criteria. | ||||||

3 | 2 | MAT3023 | Mathematical Statistics 2 | Extended Major | 3-3-0 | |

Basic concept of statistical estimation and Testing Statistical Hypotheses; T-test, F-test, and Chi-squared test in Regression Analysis, Analysis of variance, and Analysis of contingency Tables; Practice using MINITAB | ||||||

3 | 2 | MAT3028 | Complex Analysis 2 | Extended Major | 3-3-0 | |

This course is a continuation of complex analysis 1. The meterials covered by this course includes the followings: Sequence and series of complex numbers, Taylor series, Laurent series, functions defined by power series, residue theorem and its application, zeros and singularities of analytic functions, mapping by linear fractional transformation and so on. | ||||||

3 | 2 | MAT3052 | Numerical Analysis 2 | Extended Major | 3-3-0 | |

Computational procedures including direct and iterative solution of linear and nonlinear equations, matrices and eigenvalue calculations, function approximation by least squares, smoothing functions, and minimax approximations. | ||||||

3 | 2 | MAT4004 | Topology 2 | Extended Major | 3-3-0 | |

The course deals with surfaces from topological view point. The notion of orientation is illustrated by introducing the Mobius band and the Klein bottle. The Euler number is introduced and used as a window to the modern landscape of topology and geometry. Fundamental group is presented with the mathematical rigor intact while homology groups are explained in a more areal manner with some applications such as generalized Jordan curve theorem. | ||||||

3 | 2 | MAT4005 | Differential Geometry | Core Major | 3-3-0 | |

The course is recommended to the students who have taken the two courses in advanced calculus the department offers. Curves and surfaces in Euclidean 3-space are the main topics. Regarding the curves, vector field and its derivative along the curve, Frenet formula together with curvature and torsion are taught. Concerning surfaces, the normal and the Gaussian curvatures are dealt with together with the Gauss-Bonnet theorem. | ||||||

3 | 2 | SYH0003 | ENTREPRENEURSHIP AND BUSINESS LEADERSHIP | (Compulsory) Requirement in Fundamental Studies | 2-2-0 | |

Businesss Leadership (HELP 3) program is a course for juniors, which aims to help students 1) understand principles of capitalism and market economy and learn common sense in relation to economy and finance, 2) learn principles and nature of corporations and how to develop a critical view toward them, and 3) acquire an administrative mind through self-management. | ||||||

3 | 2 | TEA3029 | MATHEMATICS LOGIC AND ESSAY WRITING | --Major for Teacher Certifica-- | 2-2-0 | |

This course is designed as writing workshop for preservice teachers of mathematics education. Class activity intends to strengthen students' ability to writing with a proper style and to foster their reflection on issues in mathematics education. In this workshop, students' writing will be reviewed to evaluate whether their writing is well shaped and whether their arguments are reasonable. | ||||||

3 | 2 | GEN5100 | Career Development II (Portfolio and Business model Creation) | Compulsory General Studies | 1-1-0 | |

His career as a wide range of knowledge and lessons learned in the previous semester plan to explore in depth the process. Employment working in the industry of major interest to seniors invited to hear the information about the industry to prepare for what you need to learn knowhow. In addition, students who already have a job that aim to visit seniors plan their careers and the skills necessary to equip determined to develop a career that any plan. | ||||||

3 | 2 | MAT3002 | Modern Algebra 2 | Extended Major | 3-3-0 | |

3 | 2 | MAT3018 | Mathematical Programming | Extended Major | 3-3-0 | |

Basic concepts including : a unified development of linear systems and linear programming, simplex and dual simplex method, relationship between primal and dual linear programs, an introduction to quadratic programming and the linear complementarity problem, convex sets and functions, an introduction to integer linear programming and an introduction to nonlinear programming with development of optimality criteria. | ||||||

3 | 2 | MAT3023 | Mathematical Statistics 2 | Extended Major | 3-3-0 | |

Basic concept of statistical estimation and Testing Statistical Hypotheses; T-test, F-test, and Chi-squared test in Regression Analysis, Analysis of variance, and Analysis of contingency Tables; Practice using MINITAB | ||||||

3 | 2 | MAT3028 | Complex Analysis 2 | Extended Major | 3-3-0 | |

This course is a continuation of complex analysis 1. The meterials covered by this course includes the followings:Sequence and series of complex numbers, Taylor series, Laurent series, functions defined by power series, residue theorem and its application, zeros and singularities of analytic functions, mapping by linear fractional transformation and so on. | ||||||

3 | 2 | MAT3052 | Numerical Analysis 2 | Extended Major | 3-3-0 | |

Computational procedures including direct and iterative solution of linear and nonlinear equations, matrices and eigenvalue calculations, function approximation by least squares, smoothing functions, and minimax approximations. | ||||||

3 | 2 | MAT3066 | Vector Calculus | Extended Major | 3-3-0 | |

This course is concerned with calculus of several variables. The discussion of differentiation of a vector function of a vector variable has been modernized by essentially defining the derivative to be the Jacobian matrix. The general form of the chain rule is given, as in the general form of the implicit transformation theorem. We deal with triple products, bases, vector analytic geometry, vector functions, curves, rectifiable curves, arc length, differentiable curves, vector functions of a vector, limits and continuity, matrices and linear transformation, partial derivatives, differentiability, total differentials, gradient, del operator, directional derivatives, chain rule, mean value theorem, Taylor’s Theorem for several variables, divergence and curl of a vector field, line integral, potential, Green’s Theorem, Surface area, Surface Integral, Divergence Theorem, Stokes’ Theorem, Change of variable in multiple integrals, transformation and inverse transformation, inverse theorem, implicit functions, and global inverse. | ||||||

3 | 2 | MAT3069 | Math Lab Internship 3 | Extended Major | 1-0-1 | |

3 | 2 | MAT4004 | Topology 2 | Extended Major | 3-3-0 | |

The course deals with surfaces from topological view point. The notion of orientation is illustrated by introducing the Mobius band and the Klein bottle. The Euler number is introduced and used as a window to the modern landscape of topology and geometry. Fundamental group is presented with the mathematical rigor intact while homology groups are explained in a more areal manner with some applications such as generalized Jordan curve theorem. | ||||||

3 | 2 | SYH0003 | ENTREPRENEURSHIP AND BUSINESS LEADERSHIP | Compulsory General Studies | 2-2-0 | |

Businesss Leadership (HELP 3) program is a course for juniors, which aims to help students 1) understand principles of capitalism and market economy and learn common sense in relation to economy and finance, 2) learn principles and nature of corporations and how to develop a critical view toward them, and 3) acquire an administrative mind through self-management. | ||||||

3 | 2 | TEA3029 | MATHEMATICS LOGIC AND ESSAY WRITING | --Major for Teacher Certifica-- | 2-2-0 | |

This course is designed as writing workshop for preservice teachers of mathematics education. Class activity intends to strengthen students' ability to writing with a proper style and to foster their reflection on issues in mathematics education. In this workshop, students' writing will be reviewed to evaluate whether their writing is well shaped and whether their arguments are reasonable. | ||||||

3 | 2 | GEN5100 | Career Development II (Portfolio and Business model Creation) | Compulsory General Studies | 1-1-0 | |

His career as a wide range of knowledge and lessons learned in the previous semester plan to explore in depth the process. Employment working in the industry of major interest to seniors invited to hear the information about the industry to prepare for what you need to learn knowhow. In addition, students who already have a job that aim to visit seniors plan their careers and the skills necessary to equip determined to develop a career that any plan. | ||||||

3 | 2 | MAT3002 | Modern Algebra 2 | Extended Major | 3-3-0 | |

3 | 2 | MAT3018 | Mathematical Programming | Extended Major | 3-3-0 | |

Basic concepts including : a unified development of linear systems and linear programming, simplex and dual simplex method, relationship between primal and dual linear programs, an introduction to quadratic programming and the linear complementarity problem, convex sets and functions, an introduction to integer linear programming and an introduction to nonlinear programming with development of optimality criteria. | ||||||

3 | 2 | MAT3023 | Mathematical Statistics 2 | Extended Major | 3-3-0 | |

Basic concept of statistical estimation and Testing Statistical Hypotheses; T-test, F-test, and Chi-squared test in Regression Analysis, Analysis of variance, and Analysis of contingency Tables; Practice using MINITAB | ||||||

3 | 2 | MAT3028 | Complex Analysis 2 | Extended Major | 3-3-0 | |

This course is a continuation of complex analysis 1. The meterials covered by this course includes the followings:Sequence and series of complex numbers, Taylor series, Laurent series, functions defined by power series, residue theorem and its application, zeros and singularities of analytic functions, mapping by linear fractional transformation and so on. | ||||||

3 | 2 | MAT3052 | Numerical Analysis 2 | Extended Major | 3-3-0 | |

Computational procedures including direct and iterative solution of linear and nonlinear equations, matrices and eigenvalue calculations, function approximation by least squares, smoothing functions, and minimax approximations. | ||||||

3 | 2 | MAT3066 | Vector Calculus | Extended Major | 3-3-0 | |

This course is concerned with calculus of several variables. The discussion of differentiation of a vector function of a vector variable has been modernized by essentially defining the derivative to be the Jacobian matrix. The general form of the chain rule is given, as in the general form of the implicit transformation theorem. We deal with triple products, bases, vector analytic geometry, vector functions, curves, rectifiable curves, arc length, differentiable curves, vector functions of a vector, limits and continuity, matrices and linear transformation, partial derivatives, differentiability, total differentials, gradient, del operator, directional derivatives, chain rule, mean value theorem, Taylor’s Theorem for several variables, divergence and curl of a vector field, line integral, potential, Green’s Theorem, Surface area, Surface Integral, Divergence Theorem, Stokes’ Theorem, Change of variable in multiple integrals, transformation and inverse transformation, inverse theorem, implicit functions, and global inverse. | ||||||

3 | 2 | MAT3069 | Math Lab Internship 3 | Extended Major | 1-0-1 | |

3 | 2 | MAT4004 | Topology 2 | Extended Major | 3-3-0 | |

The course deals with surfaces from topological view point. The notion of orientation is illustrated by introducing the Mobius band and the Klein bottle. The Euler number is introduced and used as a window to the modern landscape of topology and geometry. Fundamental group is presented with the mathematical rigor intact while homology groups are explained in a more areal manner with some applications such as generalized Jordan curve theorem. | ||||||

3 | 2 | SYH0003 | Love in deed and truth3(Entrepreneurship) | Compulsory General Studies | 2-2-0 | |

Businesss Leadership (HELP 3) program is a course for juniors, which aims to help students 1) understand principles of capitalism and market economy and learn common sense in relation to economy and finance, 2) learn principles and nature of corporations and how to develop a critical view toward them, and 3) acquire an administrative mind through self-management. | ||||||

3 | 2 | TEA3029 | MATHEMATICS LOGIC AND ESSAY WRITING | --Major for Teacher Certifica-- | 2-2-0 | |

This course is designed as writing workshop for preservice teachers of mathematics education. Class activity intends to strengthen students' ability to writing with a proper style and to foster their reflection on issues in mathematics education. In this workshop, students' writing will be reviewed to evaluate whether their writing is well shaped and whether their arguments are reasonable. | ||||||

4 | 0 | PBL4012 | Math Capstone PBL | Extended Major | 3-2-2 | |

4 | 0 | PBL4012 | Math Capstone PBL | Extended Major | 3-2-2 | |

4 | 1 | MAT3011 | Geometry | Extended Major | 3-3-0 | |

The course is intended to help the students understand the basics of Riemannian geometry. Specifically, after Euclidean geometry and non-Euclidean geometry are introduced with focus on the parallel postulate, both geometries are dealt from the viewpoint of Riemannian geometry. A special emphasis is put on the independence of parallel postulate to introduce the students a basic tool of mathematical logic, which consists the second main purpose of the course. | ||||||

4 | 1 | MAT4008 | Abstract Algebra | Core Major | 3-3-0 | |

Advanced group theory: group actions, isomorphism theorems, and Sylow theorems with applications, and free groups. Introduction to extensions fields and vector spaces, including algebraic extensions, and finite fields. | ||||||

4 | 1 | MAT4009 | Graph Theory | Extended Major | 3-3-0 | |

Basic concepts including : definitions of graphs and digraphs, relationship between matrices and graphs, trees and the Prufer sequence, algorithm for finding an optimal spanning tree, dual and planar graphs, Euler and Hamilton graphs, enumeration theorems for graphs, and matching problems. The method and results of graph theory will be applied in such areas as electrical networks, flow problems, computer sciences. | ||||||

4 | 1 | MAT4023 | Mathematical Modeling | Extended Major | 3-3-0 | |

Introduction to high performance computing and numerical modeling. Matrix models and boundary value problems with an emphasis on heat and mass transfer. Assessments of all approximations in the computational engineering and science process. | ||||||

4 | 1 | MAT4031 | PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS | Extended Major | 3-3-0 | |

We introduce basic theories of partial differential equations. First order quasilinear PDE, local existence, uniqueness, Cauchy-Kovalevsky theorem, Laplace equation, maximum principle, Harnack's inequality, Hilbert space methods, variational principle are discussed. Furthermore, we will study some applications in physics. | ||||||

4 | 1 | MAT4033 | INTRODUCTION TO REAL ANALYSIS | Extended Major | 3-3-0 | |

Lebesgue integral and measure on the real line, absolutely continuous functions, functions of bounded variations, space of integrable functions, product of measures and Fubini theorem are discussed. | ||||||

4 | 1 | MAT4075 | Research In Mathmatics 1 | Extended Major | 1-0-2 | |

Mathematics Research 1 aims at combining the knowledges learned in the basic courses including advanced calculus, linear algebra, set theory, differential equation and complex analysis and in the major courses including mathematical statistics, numerical analysis, topology, geometry, introduction to real analysis and probability theory and applying them to applied mathematics research thereby increasing the ability to practice the learned knowledges in reality. Under the supervision of professors, students carry out the selection of a research subject, making the research plan, practicing the research, writing a paper, and the presentation. Each student is assigned to a laboratory suitable for his research subject to increase the ability to do actual research and participates in the seminar and discussion to raise the ability to communicate and to cooperate. To allow enough time for the long-term research, the course is covered in two semesters. | ||||||

4 | 1 | MAT4084 | STATISTICAL METHODS IN FINANCE | Core Major | 3-3-0 | |

A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include probability distributions for financial models (Portfolio, Asset pricing models), statistical methods (descriptive statistics, statistical inference, estimation, and test etc) in tests of Portfolio Efficiency. Regression analysis, time series and applications to the capital asset pricing model, and value at risk (VaR). Hands-on experience/ Statistical Package (SAS) with financial data. | ||||||

4 | 1 | SYH0004 | SELF-LEADERSHIP | (Compulsory) Requirement in Fundamental Studies | 2-2-0 | |

SELP Leadership(HELP4) program will give students chances to look back on themselves before they enter society and to analyze their advantages and weak points to complete the road map for leadership development. This class trains prepared leaders based on analysis of personal strengths and weaknesses and helps them to complete the Leadership Road Map. | ||||||

4 | 1 | TEA6009 | Mathematics Research and Guidance in Subject Matters | --Major for Teacher Certifica-- | 3-3-0 | |

This course marks a turning point in your transformation from a student of mathematics to a teacher of mathematics. Our goals for this course are to continue working on the transition from learner to teacher, to think deeply about the mathematics content you will teach, and to consider what it means to successfully teach that content to all students, including those from diverse backgrounds and cultures. | ||||||

4 | 1 | MAT4005 | Differential Geometry | Extended Major | 3-3-0 | |

The course is recommended to the students who have taken the two courses in advanced calculus the department offers. Curves and surfaces in Euclidean 3-space are the main topics. Regarding the curves, vector field and its derivative along the curve, Frenet formula together with curvature and torsion are taught. Concerning surfaces, the normal and the Gaussian curvatures are dealt with together with the Gauss-Bonnet theorem. | ||||||

4 | 1 | MAT4009 | Graph Theory | Extended Major | 3-3-0 | |

Basic concepts including : definitions of graphs and digraphs, relationship between matrices and graphs, trees and the Prufer sequence, algorithm for finding an optimal spanning tree, dual and planar graphs, Euler and Hamilton graphs, enumeration theorems for graphs, and matching problems. The method and results of graph theory will be applied in such areas as electrical networks, flow problems, computer sciences. | ||||||

4 | 1 | MAT4023 | Mathematical Modeling | Extended Major | 3-3-0 | |

Introduction to high performance computing and numerical modeling. Matrix models and boundary value problems with an emphasis on heat and mass transfer. Assessments of all approximations in the computational engineering and science process. | ||||||

4 | 1 | MAT4033 | INTRODUCTION TO REAL ANALYSIS | Extended Major | 3-3-0 | |

Lebesgue integral and measure on the real line, absolutely continuous functions, functions of bounded variations, space of integrable functions, product of measures and Fubini theorem are discussed. | ||||||

4 | 1 | MAT4075 | Research In Mathmatics 1 | Extended Major | 1-0-2 | |

Mathematics Research 1 aims at combining the knowledges learned in the basic courses including advanced calculus, linear algebra, set theory, differential equation and complex analysis and in the major courses including mathematical statistics, numerical analysis, topology, geometry, introduction to real analysis and probability theory and applying them to applied mathematics research thereby increasing the ability to practice the learned knowledges in reality. Under the supervision of professors, students carry out the selection of a research subject, making the research plan, practicing the research, writing a paper, and the presentation. Each student is assigned to a laboratory suitable for his research subject to increase the ability to do actual research and participates in the seminar and discussion to raise the ability to communicate and to cooperate. To allow enough time for the long-term research, the course is covered in two semesters. | ||||||

4 | 1 | SYH0004 | SELF-LEADERSHIP | Compulsory General Studies | 2-2-0 | |

HELP(Hanyang Essential Leadership Plus) is a key program of Hanyang University for educating students who want to be future CEOs. Self Leadership(HELP4) is a leadership development online program for seniors. This program aims to foster leaders based on an analysis of an individual's strengths and weaknesses and complete the Leadership Road Map. Learning contents of Self Leardership(HELP4) incluse Self-Assessment, Self-Management and Skills to apply in Social Practices. Learning objectives of each module are as follows; Self-Assessment: Grade value of the work to do and decide priority, understand importance and meaning of manners and improve manners in social life, and understand attitudes associated with success and put them into practice. Skills to Apply in Social Practice: Define followership, understand the principles of imagination and creativity. This 16 week length course had been developed by the high-tech teaching system and online course development methods. | ||||||

4 | 1 | TEA6009 | Mathematics Research and Guidance in Subject Matters | --Major for Teacher Certifica-- | 3-3-0 | |

This course marks a turning point in your transformation from a student of mathematics to a teacher of mathematics. Our goals for this course are to continue working on the transition from learner to teacher, to think deeply about the mathematics content you will teach, and to consider what it means to successfully teach that content to all students, including those from diverse backgrounds and cultures. | ||||||

4 | 1 | MAT4005 | Differential Geometry | Extended Major | 3-3-0 | |

The course is recommended to the students who have taken the two courses in advanced calculus the department offers. Curves and surfaces in Euclidean 3-space are the main topics. Regarding the curves, vector field and its derivative along the curve, Frenet formula together with curvature and torsion are taught. Concerning surfaces, the normal and the Gaussian curvatures are dealt with together with the Gauss-Bonnet theorem. | ||||||

4 | 1 | MAT4009 | Graph Theory | Extended Major | 3-3-0 | |

Basic concepts including : definitions of graphs and digraphs, relationship between matrices and graphs, trees and the Prufer sequence, algorithm for finding an optimal spanning tree, dual and planar graphs, Euler and Hamilton graphs, enumeration theorems for graphs, and matching problems. The method and results of graph theory will be applied in such areas as electrical networks, flow problems, computer sciences. | ||||||

4 | 1 | MAT4023 | Mathematical Modeling | Extended Major | 3-3-0 | |

Introduction to high performance computing and numerical modeling. Matrix models and boundary value problems with an emphasis on heat and mass transfer. Assessments of all approximations in the computational engineering and science process. | ||||||

4 | 1 | MAT4033 | INTRODUCTION TO REAL ANALYSIS | Extended Major | 3-3-0 | |

Lebesgue integral and measure on the real line, absolutely continuous functions, functions of bounded variations, space of integrable functions, product of measures and Fubini theorem are discussed. | ||||||

4 | 1 | MAT4092 | Cryptography PBL | Extended Major | 3-3-0 | |

4 | 1 | SYH0004 | SELF-LEADERSHIP | Compulsory General Studies | 2-2-0 | |

HELP(Hanyang Essential Leadership Plus) is a key program of Hanyang University for educating students who want to be future CEOs. Self Leadership(HELP4) is a leadership development online program for seniors. This program aims to foster leaders based on an analysis of an individual's strengths and weaknesses and complete the Leadership Road Map. Learning contents of Self Leardership(HELP4) incluse Self-Assessment, Self-Management and Skills to apply in Social Practices. Learning objectives of each module are as follows; Self-Assessment: Grade value of the work to do and decide priority, understand importance and meaning of manners and improve manners in social life, and understand attitudes associated with success and put them into practice. Skills to Apply in Social Practice: Define followership, understand the principles of imagination and creativity. This 16 week length course had been developed by the high-tech teaching system and online course development methods. | ||||||

4 | 1 | TEA6009 | Mathematics Research and Guidance in Subject Matters | --Major for Teacher Certifica-- | 3-3-0 | |

This course marks a turning point in your transformation from a student of mathematics to a teacher of mathematics. Our goals for this course are to continue working on the transition from learner to teacher, to think deeply about the mathematics content you will teach, and to consider what it means to successfully teach that content to all students, including those from diverse backgrounds and cultures. | ||||||

4 | 2 | MAT4032 | FOURIER ANALYSIS AND ITS APPLICATION | Extended Major | 3-3-0 | |

This course is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. We will provide notions of convergence and summability of Fourier series and will deal with the Fourier transform and its applications to classical partial differential equations. These range from numerical analysis, control theory and and electrical engineering. | ||||||

4 | 2 | MAT4073 | PROBABILITY THEORY | Extended Major | 3-3-0 | |

In this course we develop the basics of measure theory from a probability perspective, for example, this course includes basic concepts of probability, conditional probability and the central limit theorem. In particular, we will deal with probability spaces, independence of random variables and algebraic laws of independent identically distributed random variables. | ||||||

4 | 2 | MAT4076 | Research In Mathmatics 2 | Extended Major | 1-0-2 | |

Mathematics Research 2 aims at combining the knowledges learned in the basic courses including advanced calculus, linear algebra, set theory, differential equation and complex analysis and in the major courses including mathematical statistics, numerical analysis, topology, geometry, introduction to real analysis and probability theory and applying them to applied mathematics research thereby increasing the ability to practice the learned knowledges in reality. Under the supervision of professors, students carry out the selection of a research subject, making the research plan, practicing the research, writing a paper, and the presentation. Each student is assigned to a laboratory suitable for his research subject to increase the ability to do actual research and participates in the seminar and discussion to raise the ability to communicate and to cooperate. | ||||||

4 | 2 | MAT4085 | TOPICS IN GEOMETRY AND TOPOLOGY | Extended Major | 3-3-0 | |

This course is designed for the undergraduate students in high level who are supposed to be familiar with the point-set topology or elementary differential geometry. The topics to be covered in this course will be selected among Riemannian Geometry and Manifold theory from the viewpoint of geometric topology. | ||||||

4 | 2 | MAT3011 | Geometry | Extended Major | 3-3-0 | |

The course is intended to help the students understand the basics of Riemannian geometry. Specifically, after Euclidean geometry and non-Euclidean geometry are introduced with focus on the parallel postulate, both geometries are dealt from the viewpoint of Riemannian geometry. A special emphasis is put on the independence of parallel postulate to introduce the students a basic tool of mathematical logic, which consists the second main purpose of the course. | ||||||

4 | 2 | MAT4031 | PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS | Extended Major | 3-3-0 | |

We introduce basic theories of partial differential equations. First order quasilinear PDE, local existence, uniqueness, Cauchy-Kovalevsky theorem, Laplace equation, maximum principle, Harnack's inequality, Hilbert space methods, variational principle are discussed. Furthermore, we will study some applications in physics. | ||||||

4 | 2 | MAT4073 | PROBABILITY THEORY | Extended Major | 3-3-0 | |

In this course we develop the basics of measure theory from a probability perspective, for example, this course includes basic concepts of probability, conditional probability and the central limit theorem. In particular, we will deal with probability spaces, independence of random variables and algebraic laws of independent identically distributed random variables. | ||||||

4 | 2 | MAT4076 | Research In Mathmatics 2 | Extended Major | 1-0-2 | |

Mathematics Research 2 aims at combining the knowledges learned in the basic courses including advanced calculus, linear algebra, set theory, differential equation and complex analysis and in the major courses including mathematical statistics, numerical analysis, topology, geometry, introduction to real analysis and probability theory and applying them to applied mathematics research thereby increasing the ability to practice the learned knowledges in reality. Under the supervision of professors, students carry out the selection of a research subject, making the research plan, practicing the research, writing a paper, and the presentation. Each student is assigned to a laboratory suitable for his research subject to increase the ability to do actual research and participates in the seminar and discussion to raise the ability to communicate and to cooperate. | ||||||

4 | 2 | MAT3011 | Geometry | Extended Major | 3-3-0 | |

The course is intended to help the students understand the basics of Riemannian geometry. Specifically, after Euclidean geometry and non-Euclidean geometry are introduced with focus on the parallel postulate, both geometries are dealt from the viewpoint of Riemannian geometry. A special emphasis is put on the independence of parallel postulate to introduce the students a basic tool of mathematical logic, which consists the second main purpose of the course. | ||||||

4 | 2 | MAT4031 | PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS | Extended Major | 3-3-0 | |

We introduce basic theories of partial differential equations. First order quasilinear PDE, local existence, uniqueness, Cauchy-Kovalevsky theorem, Laplace equation, maximum principle, Harnack's inequality, Hilbert space methods, variational principle are discussed. Furthermore, we will study some applications in physics. | ||||||

4 | 2 | MAT4073 | PROBABILITY THEORY | Extended Major | 3-3-0 | |

In this course we develop the basics of measure theory from a probability perspective, for example, this course includes basic concepts of probability, conditional probability and the central limit theorem. In particular, we will deal with probability spaces, independence of random variables and algebraic laws of independent identically distributed random variables. |