KOREA UNIVERSITY Department of Mathematics | Undergraduate

Elective Courses

Major-Related General Education

Major-Related General Education
Course No.	Course Name	Credit(Hour)	Description
MATH161	CALCULUS WITH LAB I	3(4)	Derivatives and Integrals of First Derivative, Application of Integration, Polar Coordinate System, Sequences and Series, Vector and Vector Fields
MATH162	CALCULUS WITH LAB II	3(4)	Derivatives of Multivariable Functions, Multiple Integration, Line Integral, Surface Integral, Divergence Theorem
MATH163	ELEMENTARY MATHEMATICS AND CALCULUS WITH LAB	3(5)	Mathematics in Third grade in high school(Based on Korea), Derivatives and Integrals of First Derivative, Application of Integration, Polar Coordinate System, Sequences and Series, Vector and Vector Fields, Derivatives and Integrals of Vector Functions
MATH164	CALCULUS WITH LAB FOR LIFE SCIENCE	3(4)	Derivatives and Integrals of First Derivative, Application of Integration, Polar Coordinate System, Sequences and Series, Derivatives and Integrals of Vector Functions, Derivatives of Multivariable Functions, Multiple Integration

Quantitative Research

Quantitative Research
Course No.	Course Name	Credit(Hour)	Description
GEQR011	METHODOLOGY OF MATHEMATICAL SCIENCE	3(3)	We understand the noncontradictional and perfect structure of the mathematical science and research results of modern mathematics, then we study the methodological character of mathematical research and an application of methodology to the humanitic and social science.
GEQR012	LANGUAGE OF MATHEMATICS AND SCIENCE OF PATTERNS	3(3)	In this course, we investigate mathematics as a science of patterns. Patterns of counting, Patterns of reasoning, Patterns of motion, Patterns of shape, Patterns of position, and Patterns of shape of universe will be discussed.
GEQR013	MATHEMATICS FOR HUMANITIES AND SOCIAL SCIENCES	3(3)	Mathematical methods needed in social studies and related fields. We study a variety of mathematical notions one encounters when he tries to convey his subjective concepts to others. Also we study modeling practical problems and choices of specific methods needed in dealing them. The topics include min-max problem of linear functions, getting information out of data, voting and decision problem, games, modeling with graphics, interests and probabilities, etc.
GEQR034	CALCULUS IN CONTEX	3(4)	This course deals with practical applications and basic concepts of Calculus.
GEQR042	HISTORY OF KOREAN MATHEMATICS AND MODERN MATHEMATICS	3(3)	In this course, we will study the history of Korean mathematics and compare it with western mathematics. Through this we try to understand various aspects of mathematics and the nature in it. We survey the history of Korean mathematics, read original Korean mathematics books, understand the forms and the contents in it, and compare them with the related western concepts. This will tell us about the developmental process of mathematics which suits the needs of the contemporary society and, through comparisons with modern mathematics, this will show us the status of mathematics.

Major Subject

Major Subject
Course No.	Course Name	Credit(Hour)	Remarks	Description
MATH003	TOPIC COURSE	3(3)	Major Elective	The topic of this course is determined each semester.
MATH201	SET THEORY	3(3)	Major Elective	Axiom System, Algebraic Structure, The Foundations of Geometry, The Foundations of Continuity.
MATH203	DISCRETE MATHEMATICS	3(3)	Major Elective	Basic Topology on Euclidean Space. Continuity, Convergence, Uniform Convergence, Series, Convergence Tests. Differentiation, Inverse and Implicit Function Theorems.
MATH211	ANALYSISⅡ WITH LAB	3(3)	Major Elective	Riemann-Stieltjes Integrals, Sequences and series of functions, Uniform convergence, Fourier series, Functions of Several Variables, Integration of Differential Forms, Stokes’ Theorem.
MATH 221	LINEAR ALGEBRAⅠ WITH LAB	3(3)	Major Elective	Vector Spaces & Systems of Linear Equations, Linear Transformations & Matrices, Vector Spaces with an Inner Product, Determinants.
MATH 222	LINEAR ALGEBRAⅡ WITH LAB	3(3)	Major Elective	The Theory of Single Linear Transformation, Dual Vector Spaces & Multilinear Algebra, Orthogonal & Unitary Transformations.
MATH 223	NUMBER THEORY	3(3)	Major Elective	Divisibility, Primes, Congruences, Quadratic Reciprocity, Farey Sequences, Euler Phi-Function, Fermat’s Last Theorem.
MATH 232	INTRODUCTION TO GEOMETRY	3(3)	Major Elective	We study modern methods of mathematics through the various theories of classical geometry. Non-euclidean geometry shows the concepts of duality, projectivity, hyperbolicity and also shows the role of group structures and metric structures in geometry. The study of these concepts also reveals how mathematics is applied to other sciences and solving practical problems.
MATH 240	DIFFERENTIAL EQUATIONS WITH LAB	3(3)	Major Elective	First order differential equations, Second order linear differential equations, Series solution of second order linear Equations, Higher order linear differential equations, The Laplace transform.
MATH 282	ADVANCED DIFFERENTIAL EQUATIONS	3(3)	Major Elective	Boundary value problem, Sturm-Liouville theory, Linear Systems theory, Oscillation theory, Stability theory.
MATH 315	COMPLEX ANALYSIS I	3(3)	Major Elective	Complex Line Integral, Holomorphic Functions, Cauchy’s Theorem, Power Series Representation, Zeros of Holomorphic functions, Maximum Modulus Theorem, Singularities, Residue Calculus.
MATH 321	ALGEBRAⅠ	3(3)	Major Elective	Groups, Subgroups, Cosets, Homomorphism Theorems, Sylow Theorems, Ring, Ideal, Field of Quotients, Ring of Polynomials, Principal Ideal Domain, Euclidean Rings.
MATH 331	DIFFERENTIAL GEOMETRYⅠ	3(3)	Major Elective	Tangent vectors and differential forms in euclidean spaces, Elementary vector calculus, Curves and Frenet formula, Visualization of curves, Examples of surfaces, Visualization of surfaces, Gauss curvature and mean curvature, Computation of curvatures, Geodesics.
MATH 333	TOPOLOGYⅠ	3(3)	Major Elective	This is an introduction to topology with an emphasis on the set-theoretical aspect of the subjects. The topics covered are topological and metric spaces, continuous functions, homeomorphisms, compactness, connectness and separation axioms.
MATH 342	NUMERICAL ANALYSIS AND COMPUTER	3(3)	Major Elective	Root finding for nonlinear equations, interpolation theory, approximation theory, numerical integration, numerical solutions of system of linear equations.
MATH 343	PROBABILITY AND STATISTICS WITH LAB	3(3)	Major Elective	We introduce basic concepts in probability such as random variable, distribution function, expectation, conditional expectation and limit theorems. Basic theory of mathematical statistics including estimation and testing hypotheses is developed.
MATH 344	STOCHASTIC PROCESSES	3(3)	Major Elective	This course is intended to introduce stochastic processes by using elementary probability theory. We present basic important topics such as Poisson processes, Markov processes, and Brownian motion as well as their applications.
MATH 358	COMPLEX ANALYSISⅡ	3(3)	Major Elective	Mapping properties of holomorphic functions, Riemann mapping theorem, Harmonic functions, Maximum principle, Mean value property, Poisson integral formula, Analytic continuation, Infinite products, Special functions.
MATH 362	ALGEBRAⅡ	3(3)	Major Elective	We study the topics of fields, extension fields, algebraic elements, transcendental elements, finite fields, function fields, Galois theory and algebraic solutions of polynomial equations.
MATH 372	DIFFERENTIAL GEOMETRYⅡ	3(3)	Major Elective	Calculus of variations and geodesics, Completeness, Isometries, Parallel translation and geodesic curvatures, Riemann curvature tensor, Gauss-Bonnet theorem, Geodesic coordinates. Also some topics chosen from the followings: Minimal surfaces and surfaces of constant mean curvature(CMC), Visualization of minimal and CMC surfaces, Calculus of variations and applications to physics, Geometry of manifolds, Geometry of metric spaces.
MATH 374	TOPOLOGYⅡ	3(3)	Major Elective	Beginning with the classification of surfaces, this course introduces Euler characteristic, fundamental groups and its applications to 2 and 3 manifolds.
MATH 453	REAL ANALYSIS	3(3)	Major Elective	Lebesgue measure, Lebesgue integrals, Lpspaces, Hilbertspaces, Duality
MATH 458	TOPICS IN ANALYSIS	3(3)	Major Elective	Topics will be selected from various advanced subjects of functions of complex or real variables. For functions of complex variables, topics include conformal mappings, analytic continuation, properties of analytic functions, harmonic functions, infinite products. For functions of real variables, Topics include complex measures, Hilbert spaces, Dual spaces and normed linear spaces.
MATH 462	APPLIED NUMBER THEORY	3(3)	Major Elective	The theory of finite fields, the theory of polynomial rings, the theory of elliptic curves, RSA system, ECC system, XTR system, NTRU system, coding theory.
MATH 464	COMBINATORICS	3(3)	Major Elective	Permutations and combinations, generating functions, recurrence relations, inclusion and exclusion, Polya’s enumerations.
MATH 469	TOPICS IN ALGEBRA	3(3)	Major Elective	We study the topics of representations of groups, mathematical cryptology, computational algebra, algebraic geometry.
MATH 476	TOPICS IN GEOMETRY	3(3)	Major Elective	Topics will be chosen from the subjects of recent interests related to geometry. Topics vary accordingly and may include one of may the followings : Metric geometry, Minimal surfaces, Combinational geometry, Geometric analysis, Complex geometry, CAGD(Computer Aided Geometric Design), Mathematical mechanics, etc.
MATH 477	TOPICS IN TOPOLOGY	3(3)	Major Elective	In this course, we are going to discuss the Knot theory which is applied to physics and biology. Moreover we will explore other related areas of mathematics such as group theory, differential geometry and algebraic topology.
MATH 481	PARTIAL DIFFERENTIAL EQUATIONS AND COMPUTER EXPERIMENT	3(3)	Major Elective	Fourier series, Wave equations, Heat equations, Laplace equations, Special functions, Existence and Uniqueness theorem.
MATH 483	MATHEMATICAL FINANCE	3(3)	Major Elective	We study the important problems in finance such as derivatives, interest rate models, and risk managements based on probability theory, PDE, and numerical computations.
MATH 484	ACTUARIAL MATHEMATICS	3(3)	Major Elective	Probability theory, Statistical Inference, Risk model, Loss distribution, Risk premium, Experience rating, Life insurance, Annuities, Population theory.
MATH 485	TELECOMMUNICATION MATHEMATICS	3(3)	Major Elective	Basic queueing theory and its applications to telecommunication systems are covered: Introduction to queueing theory and telecommunication systems, M/M/C queue, M/G/1 queue, modeling of various traffics such as voice and video, delay and loss probability of networks, performance analysis of various transmission schemes.
MATH 487	TOPICS IN APPLIED MATHEMATICS	3(3)	Major Elective	We study mathematical theories and methods which are used to analyze the physical and industrial problems.
MATH 488	TOPICS IN PROBABILITY THEORY	3(3)	Major Elective	Special topics are chosen from recent developments of research in probability theory. Topics covered vary from year to year.

* Basic Major include Major Required 24 credits and 36 credits from Department of Mathematics Major courses.
* Advanced Major should complete 24 credits or more. However, Major Acknowledged courses can be recognized up to 6 credits.