교과목해설

This course includes learning the nature of mathematics education, the necessity and purpose of learning mathematics, the history of math education, and the philosophy of math education. More specifically, students also learn math problem solving theory, psychology of learning math, mathematizing teaching-and-learning theory, van Hiele levels, and didactic transposition of mathematical knowledge. This course focuses on the instructional strategies of teaching secondary math, and the process-oriented assessment, both of which are emphasized on the national secondary math curriculum document.

In this course, students study the contents of secondary math textbook, and design classroom instruction by learning related education theories and practices. Students will study the nature of math and math education, analyze secondary math curriculum and textbook, develop lesson plans, and acquire various instructional strategies. This course prepares students for their teaching practicum in the following academic year.

Students learn how to think logically and write essays on the issues relevant to mathematics education and contents of mathematics subject. Especially, they practice thinking critically and argue logically the contents of the secondary mathematics by employing the theories of mathematics education to improve their abilities in writing.

This course covers series, parametric equations and polar coordinates and vectors and the geometry of space.

This course covers partial derivativies, multiple integrals, vector calculus.

The main teaching contents are as follows: Real number system and its axioms, limits in real sequences, limits and continuity in real functions, mean value theorem; inverse function theorem and so on.

Deals with basic logic, functions, relations, equivalence relations, finite set, infinite set, denumerable set, nondenumerable set, cardinal numbers, axiom of choice.

The existencetheorem of solution of the differential equations, particular or general solutions of various type of the first order differential equations, lineardifferentialequations,linearequationwithconstantcoefficients, differentialoperators,linearsystemsofdifferential equations, an introduction of nonlinear differential equations arecoveredinthiscourse.

Analytic geometry is probably the most old mathematical subjects. It was well launched after Descartes had laid the foundations of coordinate geometry. Many results concerning straight lines, and quadratic curves and quadratic surfaces in 3-space were obtained by Kepler and Newton in the first half of the seventeenth century. In this subject of study, first of all we develops the coordinate system, the straight linea and the circles. Next we investigate the conis, that is, the parabola, the ellipse, the hyperbolas. Finally we study the quadratic surfaces in 3-space, that is, the ellipsoid, the hyperbolic paraboloid, the hyperboloid of one and two sheet, the conical surfaces etc.

Students investigate their future jobs based on their hope and aptitude. So they find their course beforehand and can find curriculum related to their future course. Also by investigating jobs which can be obtained students understand their major and gain confidence. Furthermore, as a future teacher, students will learn about character building education, understanding multiculture, protection of youth human rights.

The main teaching contents are as follows: Riemann integral, improper integral, convergence and divergence of real series, sequences and series of real functions, pointwise and uniform convergences, power series, Taylor series and so on.

Students learn about divisor, multiple, prime numbers, greatest common divisors, least common multipies, diophantine equations, congruence on module, order, primitive roots, index, the quadratic reciprocity rule.

We study in the field of mathematics basic underlying computer science combination mathematical logic, set, function of relationship, binary relations, graph theory, trees, Boolean algebra, and permutations, such as language and finite state machine.

We discussed about the following things; Normal distribution, Sampling method of population, Analysis of experiment data, Nonparametric test, Rare and correlation analysis, Probability variable, Distribution function, Law of large number, Central limit theorem, Stochastic processes, Theory of sampling, Multivariate distribution function, Theory of estimation, Hypothesis geomjeungron and etc.

The eigenvalue problem, vector space and linear transformations, determinants, eigenvalues and applications, numerical methods in linear algebra. complex linear spaces, complex inner product spaces.

Deal with the definition of group, basic theorems of groups, normal subgroups, quotient groups, properties of homomorphisms between groups, Sylow theorems.

We study topology based on set theory. Deal with definition of a topological space, base, subbase, relative topology, subspaces, continuous functions on topological spaces, metirc spaces.

The main teaching contents are as follows: Complex number system; Analytic functions; Elementary complex functions and logarithm function; Contour integrals; Cauchy-Goursat theorem; Cauchy integral formula; Liouville theorem; Maximum modulus theorem and so on.

Vector function, -curve whose parameters are regular curve function, analysis functions, regular curve, the steep, the length of the arc, normal plane unit tangent vector, tangent and curvature, the unit normal vector, seed normal vector, spherical curve , I deal Frenet system, Involure, Evolute, to the contact surface.

We study integral domain, field, ideal, properties of homomorphisms between rings, ring of polynomials, Euclidean domains, principal ideal domains and unique factorization domains.

Deal with countability, separable axiom, compact spaces, connected spaces, disconnected spaces, path connected spaces, complete spaces.

The main teaching contents are as follows: Convergence of complex sequences and series; Taylor series; Laurent series; Residues; Classification of isolated singular points; Cauchy's residue theorem; Applications of residues; Mapping by elementary functions and so on.

The main teaching contents are as follows: Fundamentals of real analysis; General topology and function spaces; The theory of measure; The Lebesgue integral; Normed spaces and -spaces and so on.

To study courses(numbercial analysis, differentional equation, linear algebra) related to computer we deals with basic computer ability and its applications.

Students learn the curriculum of secondary mathematics and the method and tools of the educational evaluation as well as its purpose and concept.

In this course we focus on the methods of combining differential geometry, analytic geometry and topology with mathematics education in middle and high school.

The main objective of this course is to cultivate students’professional teaching skills to combining number theory, linear algebra and modern algebra with mathematics education in middle and high school.

The main objective of this course is to cultivate students' capability and make students themselves find their own ways to relate the courses in university such as calculus, differential equations, analysis, complex analysis with mathematics education in middle and high schools.