* Vector Calculus
Students learn about differentiation of a function with
several variables, method of Lagrange's multiplier, integral
calculus, Green¡¯s theorem, divergence theorem, and Stokes¡¯
theorem.
* Linear Algebra (1), (2)
Deals with space vector, basis, dimension, matrix, determinant,
linear change, eigenvalue, matrix diagonalization and the
Jordan form of matrix.
* Set Theory
Deals with numbers and sets, relations, functions, semi-ordered
sets, axiom of choice, supplementary theorem, well-ordering
theorem, the finite set of natural numbers, infinite sets,
cardinal numbers, ordinal numbers and the transfinite cyclic
method.
* Introduction to Mathematical Analysis (1)
Students learn about the strict definitions of the limit
of sequences, infinite series, and continuity of function,
based on which they learn various characteristics related
to continuity of function and series.
* Introduction to Mathematical Analysis (2)
Students learn about the definitions and characteristics
of derivatives of function and integral function; as well
as the limits of series of function.
* Introduction to Mathematical Analysis (3) (Planned
to be closed down in 2010)
This course covers series, infinite series, limit of a
function, continuous, differentiation, series of functions,
series, and integrals of Riemann-Stieltjes.
* Metric Space
Based on the set theory, the course focuses on metric space
in the dimension of phase space.
* Number Theory
Deals with denominators and prime numbers, greatest common
denominators, least common multiples, congruence on module,
polynomial and primitive elements, residue formula, the
quadratic reciprocal rule and the continued fraction.
* Multivariable Calculus
Deals with implicit function theorem, factorization theorem,
Jacodians Simplexes and Stokes¡¯ theorem.
* Theory of Differential Equations
Based on the basic theories of linear algebra and analysis,
the course systematically studies solutions to differential
equations that determine the various mathematical models
in natural science and engineering.
* Topology (1), (2)
Main topics include metric space, topological space, continuous
mapping, relative topology, completeness, separated
space, connectivity, relativity and Tychonoff¡¯s theorem.
* Computer & Mathematics
Focuses on programming using Mathematica or Matlab.
* Modern Algebra (1), (2)
This course covers groups, quotient groups, Sylow theorem,
rings, quotient rings, polynomial rings, and isomorphism.
* Differential Geometry (1), (2)
Deals with curvature of curves, torsion, geometry on surface
and differentiable manifold.
* Complex Analysis
Deals with complex number fields, analytic functions, power
series, line integral, Cauchy¡¯s Theorem, Laurent series
and series and residue integrals.
* Applied Analysis
Covers calculus, linear algebra, and differential equations
using computer software such as Mathematica.
* Topics in Algebra
In the course, topics include Sylow Subgroups, free commutative
groups, automorphism, meronts, separable extension, and
the Galois theory.
* Mathematical Finance
Measures the value of derivatives through mathematics.
Main topics include futures, options, hedging, strategy,
Black-Scholes analysis and numerical procedures. Futures,
Options, Hedging strategy, Black-Scholes Analysis, Numerical
Procedures.
* Actuarial Mathematics
Main topics include survival distributions and table, life
insurance, life annuities, amortization schedules, yield
rates and bonds.
* History of Mathematics
Covers mathematics of Babylonia and Egypt, Pythagorean
mathematics, the three construction problems, Euclidean
principles, Greek, Chinese, Arabic mathematics, European
mathematics from the 6th to the 16th century, mathematics
in Germany, Great Britain and France, 18th century calculus,
the initial developments in geometry and algebra, 19th
century mathematics and 20th century abstracts.
* Real Analysis
Deals with the general features of measure. Based on this,
the course will cover Lebesque integral.
Seoul Campus 107, Imun-ro, Dongdaemun-gu, Seoul, 130-791,
Korea Tel +82-2-2173-2063 Fax +82-2-2173-3387
Global Campus 81, Oedae-ro, Mohyeon-myeon, Cheoin-gu,Yongin-si,
Gyeonggi-do, 449-791, Korea Tel +82-31-330-4114
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