Course of study
Education purpose

Mathematics with a long history and tradition forms the basis of natural science that combines purity and usefulness Mathematics is the crystallization of intellectual exploration at the height of human logical thought and the language of science, and its usefulness extends beyond the traditional application of mathematics, natural science and engineering, to the whole of learning, including the analysis of social and economic phenomena.

The graduate school of this department teaches a wide range of applications, along with the fundamental disciplines of algebra, interpretation, geometry and topology. The aim of this is to foster flexible thinkers with mathematical basic knowledge that can contribute to the human society, scientific and high-tech development.

Curriculum outline

A. Master/Doctoral Integration Process

This course is for students who aim for a Ph.D..

  1. 1) The following are two procedures for students in the integrated course of master’s and doctorate degrees to qualify for doctoral dissertation.
    1. a ) Must pass the qualification test for doctoral dissertation.
    2. b) Must pass the examination by the professors’ association of mathematics on qualifications for doctoral dissertation..

If a doctoral degree is granted, the doctoral dissertation should be written under the guidance of a professor. You can request review by submitting documents and doctoral dissertations that can prove the fact that you have completed 60 credits (including 33 credits of teaching science) or more for graduation and that some or all of your doctoral dissertations have been published or approved by the graduate school committee, and if the screening is carried out in accordance with the Regulations for Degree Grants in this school Code, you will be awarded a Ph.D

  1. 2) In order for an integrated program student to obtain only a master’s degree and graduate, he or she must submit an application for abandonment of the integrated program to the department and meet the requirements set forth below.
    1. a) 28 credits or more (including 18 credits of the school science department)
    2. b) Submittal of Master’s Degree: Degree earned by enrolling in a subject course must be 18 or higher, and is calculated by including research credits according to the regulations (acquired in the course of master’s and essay studies).

In addition to meeting the minimum requirements, you will receive a master’s degree according to the procedure specified in this school when you are assigned to a professor at the time designated by the Department of Mathematics, and if you complete and submit a thesis for a master’s degree within the designated time limit.

B. The master’s course

The requirements for the acquisition of a degree by a student enrolled in a master’s degree program are the same as in A. 2).

C. Ph.D. program

The minimum required credits for obtaining a degree by a student enrolled in a doctoral program are 32 credits (including 18 credits of a liberal arts college) and the other requirements are the same as for A. Master’s and Doctor’s Integration Course 1).

B. Categorized by family of offering courses

To obtain a master’s or doctorate from freshmen in 2005, you must complete at least one course in three of the following six categories.
There are three levels in the curriculum of mathematics and postgraduate studies in 500, 600, and 700 units. The 500 unit subject is mainly graduate school, the 600 unit subject is advanced, and the 700 unit subject consists of seminar subjects in a particular major. For subjects over 600 units, it is recommended that the professor of thesis guidance take the course after selecting the course. For subjects over 500 units, it is recommended that the professor can choose and take the course of his or her career.

The classes in units of 500 to 600 are divided into six categories as follows: For your convenience, I am attaching the number of students in the subject.

  • Lesson 1 : Algebra, Integer Theory and Algebra related subjects
    (501, 502, 503, 504, 505, 506, 507, 508, 509, 603, 604, 606, 608)
  • Lesson 2 : Subjects related to analytical studies and partial differential equations
    (510, 514, 515, 517,518, 519, 545, 612, 616, 617, 619, 647)
  • Lesson 3 : Topology, Sub-quarter Lectures
    (520, 523, 524,570, 621, 622, 623, 624, 625)
  • Lesson 4 : subject of numerical analysis and applied mathematics
    (541, 542, 551, 641, 645, 647, 651, 652)
  • Lesson 5 : Subjects related to probability theory and mathematical statistics and financial/insurance mathematics (530, 531,532, 533, 537,538)
  • Lesson 6 : Applied Mathematics Subjects Based on Cryptology, Coding Theory, Combination and Algebra and Topology (560, 561, 562, 565, 567, 661, 662)

D. Requirements for completing a seminar (coloquium)
Starting with freshman in the first semester of 2013, the sum of mathematics colquium and applied mathematics colaquium shall be taken for at least 15 hours in a semester as a requirement for obtaining a doctorate. At least three credits must be completed.

Curriculum outline
MATH 501, 502 Algebra Ⅰ,Ⅱ(3-0-3)

Recommended subject : MATH 302 The structure of the army, Nilpotent and the assailants, quartz and short-lived family (Module), Hom and duplex, tensor multiplication, sce and galois theory, finite body, separability and protoplasm.

MATH 503 Commutative Algebra(3-0-3)

Recommended subject : MATH 302 Huan and Neptune eggs, Fountain and Fountain, Semi-Separate, Noetherian, Artinian, Discrete Valuationhwan and Dedekindhwan, Completely arranged.

MATH 504 Commutative Ring Theory(3-0-3)

Recommended subject : MATH 501, 503 Chain conditions, prime ideals, flatness, completion and the Artin-Rees lemma, valuation rings, Krull rings, dimension theory, regular sequences, Cohen-Macaulay rings, Gorenstein rings, regular rings, Derivations, Complete local rings.

MATH 505 Algebraic Number Theory(3-0-3)

Recommended subject : MATH 501 Hydrology in algebraic hydrophilic, Dirichlet singular theorem, ideal class group, decomposition in a few algebraic hydroponics, introduction of galoisceae, class field theory.

MATH 506 Analytic Number Theory(3-0-3)

Recommended subject : MATH 505 Modular form and its arithmetic, elliptical curve theory, Zeta function and L-water supply, analytical proof of hydrology and decimal distribution.

MATH 507 Additive Number Theory(3-0-3)

Learn about the addition structure of the water purifier. The sum of four squares, Polygonal number theorem, Hilbert-Waring problem, The Hardy-Littlewood method, Elementary properties of primes, Vinogradov’s theorem, The linear sieve, Chen’s theorem

MATH 508 Introduction to algebraic geometry(3-0-3)

Competitor subject : MATH 501 The study of algebraic geometry, which deals with the basic concepts and properties associated with this. More specifically, through efficient, projective, quasiprojective variants, coding, regulation field, rational map, barrier and primary maps, blow-up, division, analysis, etc.

MATH 509 Finite Group Theory(3-0-3)

Competitor subject : MATH 301 수학의 제반분야에 응용될 수 있는 군작용, permutation 군론에 대해 배우고, 군의 분류와 관련하여 Solvable and nilpotent groups, Extensions, Wreath product, p-groups, Frattini subgroups, Fitting subgroups, Sylow basis for solvable groups 등에 대해 배웁니다.

MATH 510 Complex Analysis(3-0-3)

Competitor subject : MATH 210 Properties of analytical functions, complex components, singularities, maximal dimensions, interpretation function blanks, runge theorem, interpretative magnification and Riemann curvature, harmonic function theory, Picard theorem.

MATH 514, 515 Real Analysis Ⅰ,Ⅱ(3-0-3)

Competitor subject : MATH 311 Lebesgue measures and basic theorem of Lebesgue integral, differential theory, classical Banach space, maximum function, general theory, expression theorem, function analysis.

MATH 517 Partial Differential Equations(3-0-3)

Competitor subject : MATH 313 Cauchy problem, Laplace equation, the method of Hilbert spatial theory, Sobolev space, Potential method, Heat equation, wave equation.

MATH518 Ergodic Theory(3-0-3)

Competitor subject : MATH 514 It deals with the basic concepts of the ergonomic theory and its application."It's a matter of fact that we're talking about our relationship with each other.

MATH 519 Functional Analysis(3-0-3)

Competitor subject : MATH 311 phase vector space, Banach space, Hahn-Banach theorem, operator theory, Fredholm theory, Hilbert spatial theory, super function theory and Fourier transformation and its application, Banach exchange.

MATH 520 Differentiable Manifolds(3-0-3)

Competitor subject : MATH 321, 422 Differential and partial diversity, Tangent, Vector Chapter, Frobenius theorem, tensor theory, differential form, Lie differential, Lie algebra, Exponential Maps, matrix, clump theory, multidisciplinary integral theory.

MATH 523 Introduction to Differential Topology(3-0-3)

Competitor subject : MATH 321 Immersion, Submersion, Transversality, Topological invariants

MATH 524 Algebraic Topology I(3-0-3)

Competitor subject : MATH 321 complex, homology, eilenberg-steenrod axiom, cohomology, universal factor theorem, cohomology multiplication, poincare binary

MATH 530 Mathematical Statistics(3-0-3)

Competitor subject : MATH 430 Decision problem, Neyman-Pearson's auxiliary theorem, Wudobi test, Ilyang's strongest test, Irregularity test, Axis test, Nonparametric test, Bayesian method.

MATH 531 Probability Theory(3-0-3)

Competitor subject : MATH 311, 431 Probability theory, probabilistic process theory, Brownian motion, Markov property, drug convergence, infinitely separable distribution, martingale, probability differential equation, probability approximation.

MATH532 Applications of Mathematics and Big Data(3-0-3)

Competitor subject : MATH 230 In this course, we understand the basic concepts of data analysis and machine learning using mathematical methodology. Based on this, we will implement the Machine Learning algorithm and further analyze the latest trends.

MATH 533 Regression Analysis(3-1-3)

Competitor subject : MATH 333, 430 Typical least self-assessment in regression analysis, including Gauss-Markov theorem and probabilism, experimental data analysis, variance analysis in regression analysis, robust estimation and planning.

MATH 537 Stochastic Calculus & Financial Mathematics(3-0-3)

Competitor subject : MATH 230, 311 The basic mathematical theory required for valuation of financial assets, financial risk analysis, and optimal investment decision are studied, and the probability differential equation describing financial theory is induced by using the probability process theory based on analysis, and the year is studied.

MATH538/EVSE579 Enviromential Statistics(3-0-3)

Learn how to acquire the basic principles and concepts of various statistical techniques frequently used in environmental science/engineering and global environment, analyze actual environmental data using statistical software and interpret the results. In addition, through presentation classes, the characteristics of the data in the environment are comprehensively understood and appropriate statistical techniques are selected, utilized and analyzed.

MATH 541 Methods of Applied Mathematics Ⅰ(3-0-3)

Competitor subject : MATH 412 The shape of the mucus muscle in the differential equation, calculation of integral mucus value, regular and Singular perturbation method, boundary layer method, WKB method, function of green.

MATH 542 Methods of Applied Mathematics Ⅱ(3-0-3)

Competitor subject : MATH 413 integral equation, Volterra equation, Fredholm equation, Hilbert-Schmidt theorem, Wiener- Hopf method, PDE, hyper-function theory.

MATH 545 Calculus of Variations(3-0-3)

Competitor subject : MATH 311 fractionation method of mathematical physics, Euler equation, Hamilton-Jacobi equation, auxiliary condition, quasi-convex function, existence theorem, differential probability.

MATH 551 Numerical Analysis(3-1-3)

Competitor subject : MATH 451 Numerical solutions of the equation of a coalition, direct and iterative solutions, inverse rows, conditional numbers, end-treatment errors, numerical calculations of a polynomial root, numerical solutions of a coalition nonlinear equation, eigenvalue and eigenvector calculation.

MATH 560 Applied Geometry for Computer Graphics and Vision(3-0-3)

Competitor subject : MATH 120, 261 Of the geometric methods of computer graphics and vision, the subgrade of curves and curves, the phase mathematics of polyhedron, algebraic curvature and curvature of images. Select from Pattern recognition by Morphology, Fractal geometry, signal compression by Wavelet, etc.

MATH 561 Combinatorics Ⅰ(3-0-3)

Voltage graph, cluster action on graph, Cayley graph, embedding on graph, Map Colors, Genus of army, graph and matrix theory, algorithm.

MATH 561 Combinatorics Ⅱ(3-0-3)

Combination coefficients, Polya theorem and application, Interconnection network, graph design, Block design, finite geometry, algorithm.

MATH 562 Combinatorics Ⅱ(3-0-3)

Combination coefficients, Polya theorem and application, Interconnection network, graph design, Block design, finite geometry, algorithm.

MATH 565 Coding Theory(3-0-3)

Study the error correction developed in communication theory and the mathematical research subjects associated with it. Linear Codes, Nonlinear Codes, Hadamard matrices, The Golay codes, Finite fields, Dual Codes and their right distribution, Codes and designations, Perfect codes, BCHodes, Cull-Codes, Modes, Modes, Modes, Modes, Modes, Modes, Modes, Modes, Modes, Modes, Modes, Modes, Modes, C

MATH 567 Algebraic Cryptology(3-0-3)

Competitor subject : MATH 302 Leveraging the concepts and results of modern algebra and hydrone, Discrete log protocol RSA, eliptic curve cryptosystem.MATH 570/CSED508 Discreate and Computer Geometry ··········(3-0-3) learn about the basic concepts of geometry problems such as convexity, encidence probabilities, main properties of convex polytopes, arrangements of geometric objects, lower levels, crossing numbers, etc. and learn how to design optimal geometry algorithms by using techniques from these combinations and algorithms.

MATH 570/CSED508 Discreate and Computational Geometry(3-0-3)

learn about the basic concepts of geometry problems such as convexity, encidence probabilities, main properties of convex polytopes, arrangements of geometric objects, lower levels, crossing numbers, etc. and learn how to design optimal geometry algorithms by using techniques from these combinations and algorithms.

MATH 603 Algebraic Geometry(3-0-3)

Competitor subject : MATH 503, 524, 612 complex algebraic variety, extinction theorem, Riemann curve and algebraic curve, glass and herd curvature, Residues, Quadric Line Complex.

MATH 604 Elliptic Curves(3-0-3)

Competitor subject : MATH 505 algebraic variety, algebraic curve, geometry of elliptic curve, finite-body elliptic curve, local-body elliptic curve, band-body elliptic curve

MATH 606 Automorphic forms(3-0-3)

Modular form, Siegel modular form, Jacobi form, Quadratic form, L-function.

MATH 608 Homological Algebra(3-0-3)

Competitor subject : MATH 301 Learning about the basic concept of Hom, tenor, and Tom, the Derived function of Hom, Tent, and Thor, the Derived function of Tensor, and using them to demonstrate the theorem of Quillen-Suslin, a famous problem in algebra history, and Auslander-Buchbaum.

MATH 612 Several Complex Variables(3-0-3)

Competitor subject : MATH 510 Bergman kernel and integral formula, Plurisubharmonic function, Pseudoconvexity, Domain of Holomorphy, Levi problem, Hardy space, Kosiriman equation.

MATH 616 Fourier Fourier Analysis(3-0-3)

Competitor subject : MATH 311 The basic properties of Fourier water supply, mean convergence, convergence and emission at points, coefficients, maximum functions of Hardy- Littlewood, and Fourier transformation in Lebesgue space.

MATH 617 Harmonic Analysis(3-0-3)

Competitor subject : MATH 514 We study basic theories such as Fourier transformations and vibration integral operators, and then we study the theory of modern harmonic analysis on Fourier transform-specific operators, Bockner-less operators, and the kakeya maximal functions, and the association with the dimensional problems of the Vesicovich set.

MATH 619 Theory of Banach spaces(3-0-3)

Competitor subject : MATH 519 Basic sequence, Dvoresky-Rogers theorem, traditional Banach space, Choquet integral representation theorem, Grothendike inequality.

MATH 621 Riemannian Geometry(3-0-3)

Competitor subject : MATH 520 theory of connection, n-dimensional Riemann manifold, curvature, Ricci curvature-tensor and Scala curvature, Jacobi field, geometrical invariance, Gauge transformation, curvature and phase

MATH 622 Complex Manifolds(3-0-3)

Competitor subject : MATH 520 Geometry of Sheaves, Coomology, Infinitesimal Formations, Hermitian and Kaehler Diversity

MATH 623 Differential Topology(3-0-3)

Competitor subject : MATH 520 Embedding, Sard theorem, Transversality, Vector in theory, Euler number, Hopf Degree, Morse theory, Cobordism theory of diversity.

MATH 624 Algebraic Topology Ⅱ(3-0-3)

Competitor subject : MATH 524 homotopy county, fibrations, cobblations, whitehead theorem, hurewicz theorem, freudenthal theorem, interference theory, spectral sequence

MATH 625 Lie Groups and their Representations(3-0-3)

Competitor subject : MATH 520 Exponential Maps, Clifford and Spinor counties, semi-simple order and expression theory, Presentation Ring, Lie algebra's expression theory, Peter-Weyl theorem, Dynkin Diagram.

MATH 641 Eigenvalue and Boundary Value Problems(3-0-3)

General boundary layer method, effective balance approximation method, coordinate transformation method, average method, Krylov method, eigenvalue problem, variable time scale.

MATH 645 Mathematical Fluid Dynamics(3-0-3)

Competitor subject : MATH 413 Navier-Stokes equation, Weak & Strong Solution, Euler equation, Kato, Ponce and Yudovich results, Vortex Dynamics, Measure-validated Solutions, Singular Solutions of 3-D Euler Equations, Conferences.

MATH 647 Nonlinear Partial Differential Equations(3-0-3)

Competitor subject : MATH 517 Schauder theory, Fixed Point theory, Harnack inequality, and the existence and uniqueness of the year of nonlinear equations used in repair physics, such as fluidity or gas conditioning.

MATH 651 Advanced Numerical Analysis(3-0-3)

Competitor subject : MATH 551 interpolation, orthogonal polynomial, FFT, spline, numerical integral, differential integral Extrapolation differential equation, differential equation, and integral equation.

MATH 652 Numerical Analysis of PDE(3-0-3)

Competitor subject : MATH 413, 651 Ritz Gallerkin method, pre-point method, mixing method, secondary and three-dimensional element, accuracy, convergence, stability, static and dynamic problem, finite differential method, and homogeneity of finite element method and finite difference method.

MATH 661 Algebric Graph Theory(3-0-3)

Competitor subject : MATH 464 Symmetric graph, Strongly regular graph and special regular graph, Distance Transient graph, Distance Regular graph, Properties of Primitive and Imprimitive, Association Scheme and Bose-Mesner Algebra, Design theory or Coding theory.

MATH 662 Topological Graph Theory(3-0-3)

Competitor subject : MATH 301, 421 It's an area where you study the nature of the graph in relation to its store on the curved surface. Through this course, you will learn about the store and store distribution of graphs, the regular and irregular coatings of graphs, the relationship between the cluster's activities and distributed coatings, and the elevation of the graph stores, the graph and map color problems on curves, the genus of graphs, the Cayley graph, and the genus of the county.

MATH 699 Master Thesis Research(가변학점)

By studying the latest papers and results of a student's research field under the guidance of a professor of thesis guidance, the students develop their own learning and research skills by publishing their understanding. Repeatable training is possible

MATH 709-789 TopicsⅠ,Ⅱ,Ⅲ (Topics)(1-0-1,2-0-2,3-0-3)

In addition to the courses offered in graduate school, we give special lectures on research areas that need to be opened or that have recently gained attention in the academic world. The time, title, lecture, and player subject of the special lecture are decided by the professor in charge and repeatable classes are available.

MATH 709 Algebra class(Topics in Algebra)

MATH 711 Essential theory class(Topics in Number Theory Algebra)

MATH 719 Analytical studies class(Topics in Analysis)

MATH 729 Geometry(Topics in Geometry)

MATH 739 Statistics(Topics in Statistics)

MATH 749 Mathematics(Topics in Applied Mathematics)

MATH 759 Computational Mathematics(Topics in Computational Mathematics)

MATH 761 Combinatiorics(Topics in Combinatiorics)

MATH 762 Graph Theory(Topics in Graph Theory)

MATH 768 Coding Theory(Topics in Coding Theory)

MATH 769 Cryptography(Topics in Cryptography)

MATH 779 Numerical Analysis(Topics in Numerical Analysis)

MATH 789 Topology(Topics in Topology)

MATH 789 Topology(Topics in Topology)

MATH 798 Seminar(1-0-1)

Faculty speakers from both inside and outside the school who demonstrate the applicability of mathematical theory help graduate students better understand the application of mathematics.

MATH 799 Seminar(1-0-1)

The lectures by invited speakers from inside and outside the school help graduate students broaden their understanding of various fields of mathematics and enhance their academic sophistication.

MATH 899 Doctoral Dissertation Research(Variable grade)

Under the guidance of professor of thesis guidance, we study the latest papers and results of a student's research field and announce our understanding to develop our own learning and research skills. Repeat training is possible.

Graduate Degree by Admission
Entrance after the 2010 school year
Process Subject credit Research credit Graduation credit
Integration process 33 27 60
Ph.D. program 18 14 32
The master’s course 18 10 28
Admission to the 2006-2009 school year
Process Subject credit Research credit Graduation credit
Integration process 24 36 60
Ph.D. program 9 23 32
The master’s course 15 13 28
The selection of teaching professorship
QE Meeting with Hopeful Professor after Acceptance
  • Students in the integrated course are assigned temporary living guidance professors until they pass the QE Higher Course. After passing the QE General Course, each student passes the QE Higher Course Exam, which the professor takes through individual interviews with the professor who wishes to receive the thesis guidance, and thus confirms the teaching
  • It is recommended that you select in your mind two to three mentors who want to be assigned when you plan your course, request a meeting in advance, gather the necessary information, and plan carefully.
Decision of the Faculty of Advocacy for the Abandoned in the Integration Process
  • Students who wish to give up mathematics and obtain a master’s degree must have a separate meeting with a professor who wishes to be coached within one year of admission.
a change in the teaching professor of a dissertation.
  • If you need to change the professor, you can change it through a meeting with the dean of the Graduate School. If you want to change the professor, you can submit an application for change of the professor’s thesis guidance to the department office.
Regulations for Postgraduate Degree Grants
재정 1989. 10. 01 Revision 2002. 01. 01 Revision 2007. 08. 22 Revision 2012. 03. 01
Revision 1995. 05. 15 Revision 2003. 05. 01 Revision 2009. 07. 01 Revision 2014. 01. 01
Revision 1998. 03. 01 Revision 2003. 12. 22 Revision 2010. 10. 18 Revision 2014. 03. 01
Revision 1999. 06. 16 Revision 2004. 09. 01 Revision 2010. 12. 09
Revision 1999. 08. 02 Revision 2004. 12. 01 Revision 2011. 09. 01
Revision 2001. 06. 01 Revision 2006. 11. 18 Revision 2012. 01. 01
Article 1 (Objective)

The purpose of this regulation is to prescribe matters concerning the degree conferred by this graduate school pursuant to Article 3 of the Graduate School Regulations of Pohang University of Science and Technology (hereinafter referred to as the “University Rules”).

Article 2 (Type of degree)

Under the program called ESTA (Excellent Student Teaching Assistant), the undergraduate education assistant is a system designed to provide excellent senior students with opportunities to build their education experience and knowledge through teaching experiences, and to show low-grade students a role model.
Education assistant students are provided with a fixed monthly allowance.

Qualifying for Graduate School QE (Qualifying Exam)

The types of degrees conferred by this graduate school are as follows(Amendment: 2012.1.1)

  1. Mathematics, Physics, Chemistry, and Bioscience
  2. New Material Engineering, Mechanical Engineering, Industrial Engineering, Electronics and Electrical Engineering, Computer Engineering, Chemical Engineering, Creative IT Convergence Engineering: Master of Engineering and Doctor of Engineering.
  3. Faculty of Interdisciplinary Collaboration, Advanced Materials Science, Convergence Biotechnology, Information and Electronic Convergence Engineering, and Advanced Nuclear Engineering: Bachelor of Science and Doctor of Engineering

Article 2 Master’s and Ph.D.’s degrees may be awarded jointly with foreign universities and the details shall be set aside.(New building : 2010.10.18)

Article 3 (requirements for receiving degrees)

according to school regulations

  1. You have completed each course in this graduate school.
  2. as a passer-by on the comprehensive examination
  3. In principle, one or more papers will be published as the first author in the international academic journal recognized by the department concerned, but the academic characteristics and exceptions must be approved by the graduate school committee. (Revision: 2007.8.22)
  4. Those who pass the dissertation examination will be awarded a certain degree according to the classification of Article 2.

However, the requirements of paragraph 2 above are limited to the Ph.D. and integration process.

Article 4 (Second foreign language test)

A second foreign language test may be included in the Ph.D. degree acceptance requirements as required by department.

Article 5 (Comprehensive Test)

The comprehensive test shall be carried out separately as follows.

  1. Ph.D. qualification test
  2. oral examination of a major
  3. An oral examination on paper.
Article 6 (Doctor Qualification Test)
  1. The Ph.D. qualification test shall be conducted in accordance with the Ph.D. qualification test guidelines for each department.
  2. A master’s degree student can take the Ph.D. qualification exam while he is in school. Those who pass the Ph.D. qualification exam by the 4th semester of the M.A. can apply for the integrated program. (Revision: 2004.12.1)
  3. If a student with a master’s degree from this university or another university intends to enter a Ph.D. program, the Ph.D. qualification test can be carried out simultaneously in the Ph.D. program entrance exam, depending on the department, and this is reflected in the admission process.
  4. Students who have only taken the prescribed doctoral program entrance exam must pass the Ph.D. qualification exam within the fourth semester of their admission. If they fail the program twice, they shall be expelled. However, failed twice in the process of integration can be, you can switch to Master’s course. (Revision: 2011.9.1)
Article 8 (Phone oral examination)

The content of the thesis for a degree shall be executed in parallel with the review of the thesis for a degree, and the judgment shall be passed or rejected.

Article 9 (Professor of Journalism)
  1. The principal professor of each department shall select each student’s thesis guidance professor (hereinafter referred to as the “guide professor”) within one year of admission and report the results to the graduate school president. However, for students in the integrated course of master’s and doctorate, the thesis guidance professor can be selected within two years of admission.(Revision: 2009.7.1)
  2. Co-Advisor may be selected after review by the respective department and the results shall be reported to the graduate school president.(New building: 2006.11.18.)(Revision: 2014.3.1)
  3. (Delete: 2009.7.6)
Article 10 (Select of the thesis judges)
  1. The evaluation committee for the thesis on master’s degree shall be composed of three professors, including the guidance professor, and shall be selected by the professor and approved by the principal professor of the department.
  2. The doctoral dissertation’s review committee consists of five professors, including the mentors, and is selected by the guidance professor and approved by the dean of the graduate.
  3. At least one out of every five judges of the doctoral dissertation must be selected from private tutoring, and at least half of the professors of this university must be appointed.
Article 11 (Editorial Writer)
  1. The chairman of the review committee of the dissertation will be a professor of guidance.
Article 12 (Submission and examination of the research plan for the dissertation of a degree)
  1. Students who enter the Ph.D. and integration courses must complete a thesis research plan for graduation and undergo review by the examiner.(Revision: 2006.11.18)
Article 13 (Degree thesis review)
  1. The chair of the dissertation review committee shall convene an audit committee to examine the submitted dissertation research plan (doctoral course only), major oral examination, and thesis oral examination, and report the results to the graduate school president.
  2. The judgment of the dissertation review shall be made by passing or failing
  3. The passage of the dissertation shall be decided by a collective agreement.
  4. If a student in the integration course fails to meet sufficient requirements for obtaining a Ph.D. degree, he or she can receive a Master’s degree after completing the graduation procedure necessary for obtaining a master’s degree.
  5. Article14 (Delegation of Degree Grants) The paper passed by the review committee shall be finalized by the graduate committee with the approval of two-thirds or more of its members and approved by the president.
Article 14 2(Academic crisis)

The commencement of this graduate school is conducted by means of a separate form 1 and 2.(Revision: 2009.7.1)

Article 15 (Article of Writing)

All student papers shall be prepared in accordance with the graduate paper preparation guidelines set out separately.

Article 16 (Degree of Master's Degree)
  1. Honorary Ph.D.s can be awarded to those who contribute greatly to the development of the academic and cultural development of our country and the enhancement of human culture, and the degree period by Annex 2 and 2.(Revision: 2009.7.1)
  2. The honorary doctorate degree is awarded by the president after the voting procedure of the graduate school committee.(Revision: 2006.11.18)
Article 17 (Cancelation of Degree Grants)
  1. In case a degree is obtained in a false or dishonest manner, the President may cancel the degree acceptance after review by the Graduate Council.
a supplementary rule
  1. These Regulations shall go into effect on 1 October 1989.
  2. These Regulations shall be amended and enforced from 15 May 1995.Any amendments made before this Regulation shall be deemed to have been made under this Regulation.
  3. These Regulations are amended and enforced as of 1 March 1998.
  4. These Regulations shall be amended and enforced from 16 June 1999.
  5. Revision to August 2, 1999, this Regulation should enter into force.
  6. These Regulations shall be amended and enforced from 1 June 2001.
  7. These Regulations shall be amended and enforced from 1 January 2002.
  8. These Regulations shall be amended and enforced from 1 May 2003.
  9. These Regulations shall be amended and enforced from 22 December 2003.
  10. These Regulations shall be amended and enforced on September 1, 2004.
  11. The regulations shall be amended as of Dec. 1, 2004, but the effective date of Article 6 paragraph 2 shall be from Jan. 1, 2005.
  12. From November 18, 2006 revision, this Regulation should enter into force.
  13. The Regulations were amended as of August 22, 2007 and implemented as of March 1, 2008.These Regulations shall apply to freshmen in 2008.
  14. These Regulations shall be amended and enforced from 1 July 2009.Article 14 2 and Article 16 which stipulate honorary doctorate degrees, which stipulate graduate degrees, shall apply from August 2008 onwards.
  15. These Regulations shall be amended and enforced from 18 October 2010.
  16. The regulations will be revised and implemented from 9 December 2010.
  17. These Regulations shall be amended and implemented from September 1, 2011.
  18. (Enforcement date) These Regulations are amended and enforced from 1 January 2012.The revision of Article 2 (type of degree) shall take effect as of September 1, 2011.
  19. The regulations will be revised and implemented from March 1, 2012.
  20. These Regulations will be revised and implemented from 1 January 2014.
  21. These Regulations will be revised and implemented starting March 1, 2014.
Guide book
Korean language
English language
GUIDELINES FOR PREPARATION OF A postgraduate dissertation
1. writing a dissertation
A. writing a dissertation

Degree papers are divided into essay writing and submission papers, and their preparation and submission dates are as follows.

B. Tips for writing a paper for seam use
  1. It is written in English and does not limit the volume of the text.
  2. Write as a word processor.
  3. Use white paper and size of 4×6 backing plate (182mm×257mm).
  4. Write the thesis book (Abstract) in English with less than 1,000 words, and if the text is a foreign language, a summary of the Korean language (Reference 9) shall be written and attached in about 10 200-character manuscripts.
  5. The prepared paper submits three parts for master’s and five parts for doctorate courses to the relevant dissertation review committee.
C. Submission period

up to 15 days before the thesis review

D. a paper for submission

When a thesis for degree is passed by the dissertation review committee, the paper submits (transmits) four hard cover pages and EM days according to the instructions for writing electronic document forms to the Cheongam Academic Information Center within the submission period by printing and binding the following tips:

E. How to Write a Submission
  1. The front cover of the paper is printed in English, the name of the submitter is written in Korean in the following ( ) in English, and bound in black hard bound. (However, in the case of foreigners, mark it in English and national language)
  2. On the next page of the paper’s front cover, insert a quick sign (reference 2) with the thesis subject in Korean and English.
  3. The specifications of the paper are 4×6 x 6 x 255 mm. Geology is in white swan, top 20, bottom 15, head horse 15, tail 15, left 25 and right 25
  4. The writing style is the same as that of the Ming dynasty, the New Ming dynasty, the background, the rollers, and the Arial or Times New Roman in the case of English letters, and the handwriting color is black.(More data available)
  5. Page numbers are placed at the bottom of the middle, and the text is Roman capital letters and the text is Arabic numerals. Body page numbers shall be hyphenated to the right or left of the number.
  6. Content :
    – 11pt letter size, 170 or more line spacing, Changpyeong 100, Zagan 0
    – Footnote: letter size 9 to 10pt
  7. Photographs should be offset printed so that the original color is maintained.
  8. When printing is completed, the paper is reviewed with a seal (Reference 4) and bound together.
  9. Other guidelines for preparation of labels and texts shall be in accordance with the general principles of paper preparation, but the standards shall be unified by referring to examples of paper preparation (reference 1 to reference 13).
    ※ Paper margins, line spacing, and font can be adjusted considering legibility.
  10. The contents of this dissertation should be stated at the end of the paper (example: all rights to be used for academic and educational purposes are delegated to Pohang University of Science and Technology).
F. Submission period

The period of submission is as shown in the table below.

Sortation February graduation scheduled graduation scheduled for Aug.
Process (Dr. Stone and Ph.D) until January 6th of the previous year until July 6th of the year

* Date can be adjusted according to school schedule.

G. suspension of one's degree

“F. Submission period”Students who fail to submit their dissertations within the time limit set in , regardless of whether or not they pass the thesis review, will be suspended from accepting their degrees in the same semester, and will automatically be deemed to be eligible for graduation in the next semester.

※ See also

The thesis items of the examination results report and the thesis titles for submission shall be consistent.

2. the examination of a dissertation
A. Request for review of doctoral dissertation
  1. The research paper is submitted to all judges by 15 days before the review.
  2. The thesis review request is submitted to the dean of the graduate school after the student enters it in the POVIS and prints it out for verification by the professor of guidance (inputs the international academic journal into the POVIS and attaches the relevant supporting documents to the principal professor of the department).– Submission documents: Request for review of doctoral dissertations (form 1)
B. Report on the results of the review of the dissertation between master and doctorate degree

The Chairperson of each dissertation review committee shall submit the thesis review by the student concerned to the Bachelor’s Management Team within the following submission deadline.

  1. The dissertation review result report is submitted to the department after the student enters and outputs it in the POVIS, obtains the professor’s confirmation and the judge’s signature.
    (In case of Ph.D.: When submitting a thesis review request and the changed contents can be modified and supplemented by POVIS)
  2. The dissertation review result report (professor/doctor) is submitted to the academic management team by 12.31 (reference: 6.30) upon approval by the principal professor of the department.
    ① Submission documents
    – Journal of dissertation review and comprehensive examination results report for master’s and doctorate degrees (form 2)
    – The Essay on the Review of theses for Master’s and Doctor’s Degree Part 1 (Form 3)
    ② Submission period
Sortation February graduation scheduled graduation scheduled for Aug.
Process (Dr. Stone and Ph.D) until January 6th of the previous year until July 6th of the year

* Date can be adjusted according to school schedule.

C. order of writing a dissertation

D. order of writing a dissertation

The order of dissertation writing is as follows.

  1. See front cover : 1.
  3. Certificate for submission of dissertation (written in English) : Reference 3
  4. Examination of dissertation completion (missing date): See 4
  5. Abstract: Reference 5 to 6
  6. White-billed in White
  7. Example : 7 a list of contents
  8. Body Text Example: Reference 8
    – Introduction
    – Nomenclature and abbreviation
    – Theoretical & Mathematical Development
    – Experimental methods and materials (Experimental Method & Materials)
    – Results
    – Discussion
  9. Summary of Korean Language:To create text if it is a foreign language:Refer to 9
  10. References:Refer to 10
  11. Acknowledgements:Note 11
  12. Curriculum Vitae:Refer to 12
  13. White-billed in White
  14. The back cover

Note) The content contained in the text (the introduction to the conclusion) may vary depending on the author, but other information cannot be changed.

D. Method of paper file preparation

The following is the method for writing the paper file.

    1. Possible paper file format
      – Document : HWP, DOC, GUL, PPT, XLS, and TXT recommend Latex and convert to PDF.
    2. Other types of files are uploaded by converting to PS (Post Script) files or PDF files.
    3. Composition of dissertation file
      – It should be the same file as the published paper.
      – The entire paper should be uploaded to one file from the cover page to the green and the picture file.

The paper file is uploaded after checking for virus infection.

  • When saving a file, it is not compressed.


E. procedure for online registration of dissertation

The procedure for online registration of electronic type dissertations is as follows.

  1. Login: Log in to the thesis submission page (the Cheongam Academic Information Center website/ Library service/Degree thesis issue page) and select the thesis submission menu.
  2. Select collection: Select the appropriate collection (year) to check the notice and submission method, then click the “Submit dissertation materials” button.
  3. Submitter Information: Check and modify the submitter’s basic information and click the next step.
  4. Metadata entry: Paste green, table of contents, etc. as a step to enter surge information for a paper.
  5. Copyright Agreement: Choose whether to accept the copyright of the submission paper. If agreed, it will be converted into a PDF file and serviced to the general user. If you do not agree, write the reason.
  6. Original text registration: In case of large capacity (more than 100MB) it can be submitted separately, it, Microsoft Word, Excel, PowerPoint, PDF, etc. and submit it separately.
  7. Submission confirmation: Make sure that the submitted paper information is properly registered and select the “Final submission” button when the modification is completed.
  8. Submission details inquiry: The details of the submitted paper can be checked and the situation handled by the manager can be checked.
  9. Personal notice confirmation: If returned due to a problem with the paper, a return notice will be sent, and an approval notice will be sent if the administrator finally approves it. On the detailed screen of the approval notice, the” Copyright Agreement” and” Submission Confirmation” may be printed.
E. the process of submitting a dissertation
  1. POVIS application for graduation settlement
  2. Degree thesis online text registration: “ma” above. See the online registration procedure for dissertations.
  3. Paper brochure and public consent submission: After completion of the paper conversion, the public consent form can be printed out and submitted to the Cheongam Academic Information Center along with the four copies of the paper “Hard cover.
Ph.D. qualification test
Second semester 2017 Ph.D. qualification exam (QE)

2017Year of school 2Semester Since the entering freshmen Ph.D. qualification test(QE)


These rules below will apply for entering first-year doctoral candidates starting from the second semester of the 2017 academic year.

* Existing rules are applied to matters not mentioned below.


Details on the QE Course

The QE consists of two kinds of examinations – general and advanced courses. Students must pass both examinations within four semesters of study.

General QE Courses

Ÿ Students must pass written examinations of the following two courses: Algebra and Analysis. The department shall write a syllabus for each course and announce it. If a student signed up for general QE and does not show up (except for unavoidable circumstances such as the student’s illness, death of a family member, etc.), the student will not be allowed to take any QE for one year.

Ÿ The evaluation committee for each course deals with exam questions and grading.


Forming and Operating an Evaluation Committee

ŸThe Evaluation Committee consists of 3 members per course, and the members’ term is 3 years. One of the members changes each year and the Head Professor of the Department appoints the new member. The first committee members’ term is 1 year, 2 years, and 3 years.

ŸThe first Evaluation Committee since execution of the policy makes a syllabus of the QE.


QE Schedule

Ÿ In principle, the QE is on the last Thursday and Friday of every January and July.

Ÿ The Evaluation Committee decides the length of the exam ranging from 3 hours to 5 hours.


Grading and Pass/Fail

Ÿ The student’s name must not be visible when grading.

Ÿ In principle, the same person must grade the same questions.

Ÿ An Evaluation Committee composed of the Head Professor of the Department, Chair of the Graduate Studies Committee, and Chair of Examinations Committee holistically decides pass/fail based on the results. (There is no pass/fail per course.)


▣ Advanced QE Courses

Ÿ Each professor announces the major’s advanced QE’s range.

Ÿ Students who passed general QE must choose their tentative academic advisor.

ŸTentative academic advisor establishes a committee composed of 3 professors and should be the Chair of the Committee. The tentative academic advisor develops the plan for advanced QE, submits it to the department, and notifies the student.


Grading and Pass/Fail

Ÿ Students take exams for the courses designated by their advisor and take QE with all members of Advanced QE Committee present.

Ÿ Advanced QE Committee decides the results (pass vs. fail) in 3 to 6 months after the approval by the department.


Management of Academic Records after Passing the QE

Ÿ Once the student passed the QE, he/she will not be under any obligation to take exams. However, the Department of Mathematics will evaluate graduate students’ academic achievements once or twice a year in a faculty meeting and notify the results to students.

Ÿ A student will receive a warning letter if his/her performance seems to be poor. If a student receives the warning letter twice, he/she will not be able to earn a doctoral degree from the Department of Mathematics at POSTECH.

Ph.D. Qualification Examination Subjects and Scope of Testing

algebraic QE range

◆ Group Theory

  • Basic definitions and examples
  • Dihedral and symmetric groups
  • The quotient group
  • Homomorphisms and isomorphisms
  • Group actions
  • Subgroups and normal subgroups
  • Subgroups generated by subsets of a group
  • Lagrange theorem
  • The isomorphism theorems
  • Cayley’s theorem and the class equation
  • Automorphisms
  • Sylow’s theorems
  • The simplicity of  
  • Direct and semi-direct product
  • The fundamental theorem of finitely generated abelian groups

◆ Ring Theory

  • Basic definitions and examples
  • Ring homomorphisms and quotient rings
  • Properties of ideals
  • Ring of fractions
  • Chinese remainder theorem
  • Euclidean domains
  • Principal ideal domains
  • Unique factorization domains
  • Polynomial rings over UFDs
  • Eisenstein criterion

◆ Modules and vector spaces

  • Basic definitions and examples of modules
  • Quotient Modules and module homomorphisms
  • Direct sums and free modules
  • Exact sequences of modules
  • Projective, injective and flat modules
  • Basic definitions and examples of vector spaces
  • The matrix of a linear transformations
  • Determinants
  • Modules of PIDs
  • Characteristic and minimal polynomials
  • eigenvalues and eigenvectors
  • Rational canonical forms
  • Jordan canonical forms

◆ Field Theory

  • Basic theory of field extensions
  • Finite and algebraic extensions
  • Splitting field and algebraic closures
  • Cyclotomic polynomials and extensions
  • Fundamental theorem of Galois theory
  • Finite fields
  • Simple extensions
  • Galois groups of polynomials
  • Cyclotomic extensions
  • Solvable and radical extensions
  • Insolvability of the quintic

※ Note: Details of the qualification exam can be found in Chapters 1 through 5, 7 through 9, 10 through 12, 13 through 14 in the section “David S. Dummit and Richard M. Foote, Abstract Algebra (3rd edition).

Analytical QE Scope

  1. Contents of Analytical I and II in the Faculty of Education
  2. Basic properties in the Lebesgue integral
  3. Undergraduate curriculum complex analysis.
  4. Ordinary Differential Equations (ODE)the harm and application of

Specifically, what is going to be covered are as follows :
(Analysis of the undergraduate curriculum I, the contents of the ii).

    1. Basic Topology on a Metric Space: Limit Point, Interior Point, Open Set, Closed Set, Compact Space (Finite Intersection Property, Heine-Borel Theorem, Sequentially Compact, Countably Compact, Lebesgue Number), Separable Space, Second Countable Space, Connected Space, Perfect Set
    2. Countable Set, Uncountable Set, Cantor Set
    3. Sequence & Series: Convergent Sequence, Cauchy Sequence, Monotone Real Sequence, Limsup & Liminf, Complete Metric Space, Baire Category Theorem,
      Convergent Series, Comparison Test, Integral Test, Ratio Test, Root Test, Absolute Convergence, Conditional Convergence, Radius of Convergence
    4. Continuity: Continuous Function, Uniformly Continuous Function, Intermediate Value Theorem, Discontinuity, Properties of a continuous function on a compact(connected) set, Convex Function, Extension of a Uniformly Continuous Function
    5. Differentiability: Differentiable Function, Critical Point, Mean Value Theorem, L’Hospital’s Rule, Taylor Theorem
    6. Riemann-Stieltjes Integral: Integrable Function, Properties of the Integral, Fundamental Theorem of Calculus
    7. Sequence of Functions: Pointwise versus Uniform Convergence, Uniform Convergence and Continuity, Uniform Convergence and Differentiability, Uniform Convergence and Integration, Stone-Weierstrass Theorem, Ascoli-Arzela Theorem, Continuous but Nowhere Differentiable Function
    8. Analytic Function, Gamma Function, Trigonometric Polynomial, Convergence of Fourier Series in L_2
    9. Functions of Several Variable: Inverse Function Theorem, Implicit Function Theorem
    10. Integration of Differential Forms: Green Theorem, Stokes‘ Theorem, Closed Form, Exact Form(Lebesgue 적분에서 기본 성질)
    11. Lebesgue Integral: Lebesgue Measure, Measurable Function, Comparison with the Riemann Integral, Monotone Convergence Theorem, Lebesgue Dominated Convergence Theorem, L_2 Space(학부 교육과정의 Complex Analysis)
    12. Properties of Holomorphic Functions: Cauchy-Riemann Equation, Elementary Functions, Branches of Log z, Power Series, Taylor Series, Uniqueness Theorem
    13. Complex Integration: Cauchy-Goursat Theorem, Cauchy Integral Formula, Calculus of Residue, Cauchy’s Residue Theorem, Contour Integration, Evaluation of
      Definite Integrals
    14. Applications of Complex Integration: Morera’s Theorem, Liouville’s Theorem, Analytic Continuation, Schwarz Reflection Principle, Maximum Modulus Principle,
    15. Meromorphic function: Zeros and Isolated Singularities, Laurent Series, Casorati-Weierstrass Theorem, Argument Principle, Rouche’s Theorem, Open
      Mapping Theorem
    16. Conformal mapping: Mapping by Elementary Functions, Fractional Linear Transformation, Schwarz Lemma, Riemann Mapping Theorem(Ordinary Differential Equations (ODE)the harm and application of)
    17. First Order ODE, Second Order ODE, Higher Order ODE, Systems of ODE, Applications
Ph.D. qualification exam up to freshman year 2017 (QE)
a general outline

The minimum criteria for passing the qualification examination shall be at least 60 out of 100 and shall be determined by the graduate school committee.

  • Ph.D. Qualification Details
  • The Ph.D. qualification exam consists of two levels (general course exam, higher course exam), and the student must successfully pass all two levels within four semesters of admission.
    • QE General subject: You must pass the written test by selecting four of the eight subjects below.
      AlgebraicⅠAlgebraic Ⅱventral analysistheory of real variable functionⅠDifferential Diversity and LieAn Introduction to AlgebraMathematical statisticsNumerical analysis
      ο The test is conducted once every semester and you can take up to four.
      ο You will be disqualified from QE for one year without cancellation after taking the exam, except in cases where you are absent without permission (such as your illness and family’s death).
    • QE (General Subject) Test
    • ο Out of the eight general QE exams, you must pass all four courses within the four semesters after admission.
      ο  In order to prevent reckless QE applications, the department operates a token system and can apply to one token once Students who fail to pass a QE course at the time of admission are given nine tokens and eight tokens to other students.
      (For example, if you take 2 subjects once, you can take only 6 subjects after that. If you retake the same course, you will get 2 subjects.)
      ο  The exam will be held every semester (January 1st semester, July 2nd semester: mid-January of next year), and the entrance will be accepted by each subject, so there is no need to pass four subjects simultaneously.
    • QE advanced subject: An academic adviser and to select his first offer are just an exam, you can.
    • Higher subject (QE) test
      ο  Submit the high-level QE results report to the department office by the end of August in the first semester and the end of February in the second semester.Caution: 500 units of subject are not always available, so it is necessary for each student to design a course for the early stages of admission.
      ο  The scope of the higher subjects test shall be determined through a meeting with individual professors (future thesis guidance professors). Higher course test results are also confirmed after review by the graduate school committee.
      ο  If you complete at least 15 credits of mathematics and science in 500 units for two years after entering the school, the average score of 500 units is 3.5 or higher, and pass all four of the QE general subjects, you will be eligible for the test.
    • Management of Bachelor’s Degree after passing QE
      ο After passing QE, there is no longer any obligation for the test, but for continued academic management, the mathematics department will conduct a graduate student’s scholastic performance assessment once or twice a year at a faculty meeting to inform each student of the evaluation results.
      ο An official warning letter will be sent to students who are assessed to be insufficient. If you receive two warnings, you will not be able to obtain a Ph.D. in the mathematics department of this school because of the reason for disqualification in the review of dissertation of doctoral degree.
Ph.D. Qualification Examination Subjects and Scope of Testing
MATH502 AlgebraII
  • The contents of the book by T.W. Hungerford, Algebra ch.5~ch.8.
MATH501 AlgebraI
  • The contents of the book by T.W. Hungerford, Algebra ch.1~ch.4.
MATH510 ventral analysis
  • Cauchy-Riemann equations, Harmonic functions and conjugates, Elementary analytic mappings, Complex line integrals: Cauchy’s theorems, Maximum modulus principle, Open mapping theorem, unique analytic continuation.Singularities, Residues, Argument principle, Schwarz’s lemma and conformal mappings, Normal families, Riemann mapping theorem, Infinite product and Weierstrass factorization, Runge’s theorem, Subharmonic functions, Dirichlet problem. [See L. Ahlfors, “Complex Analysis”, Ch 1-6.]
MATH520 Differential Diversity and Lie
  • Manifolds, Differentiable structures, immersions, submersions, diffeomorphisms, tangent and cotangent bundles, vector fields and differential forms, Orientation, Lie derivatives, Distributions and integrability (Frobenius theorem), Exact and closed forms, integration on manifolds, Lie group
  • Textbook: M. Spivak, “A Comprehensive Introduction to Differential Geometry”, Volume I (except Riemannian geometry contents)
  • F. Warner : Foundations of Differentiable Manifolds and Lie Group.
  • Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry
MATH514 Real variable function theoryI
  • Lebesgue measure, Fatou Lemma, Convergence theorems, Fubini’s Theorem, Approximation of the Identity and kernels, Functions of bounded variation, Absolutely Continuous Functions, Hlder and Minkowski Inequalities, L^p Spaces, Fourier Series, Riesz Representation Theorem, Radon-Nikodym Theorem
  • Textbook: G. Folland, “Real Analysis”, Wiley: Ch 1-7.
  • References: H.L. Royden, “Real Analysis” ; W. Rudin, “Real and Complex Analysis” ;
  • Wheeden and Zygmund “Real Analysis
MATH524 An Introduction to Algebra
  • Topics:
    • ο Singular homology
    • ο Cellular and simplicial homology
    • ο Excision and Mayer-Vietoris sequences
    • ο Eilenberg-Steenrod axioms and universal coefficient theorems
    • ο Applications of homology theory
  • Textbook: A. Hatcher, Algebraic topology, Cambridge University Press, 2002, p.97-184.
  • Other references:
    • ο J.W. Vick, Homology theory, Academic Press, 1973.
    • ο M. J. Greenberg and J. R. Harper,  Alegbraic topology: a first course, Benjamin-Cummings, 1981.
    • ο J. R. Munkres, Elements of algebraic topology, Addison-Wesley, 1984.
MATH530 Mathematical statistics

* Choose one between(7-1) Math530 and(7-2) Math531. (These courses are offered in alternating years.) Text Book: “Mathematical Statistics: Basic Ideas and Selected Topics” by Bickel and Doksum, Holden-Day.

  • Chapter 1 Statistical Models: Sufficiency, Exponential family
  • Chapter 2 Estimation: Estimating equations, Maximum like lihood
  • Chapter 3 Measure of Performance: Bayes, Minimax, Unbiased estimation
  • Chapter 4 Testing and Confidence Regions: NP lemma, Uniformly most powerful tests, Duality, Likelihood ratio test
  • Chapter 5 Asysmptotic Approximation: Consistency, First- and higher-order asymptotics, Asymptotic normality and efficiency
MATH531 Probability theory

Text Book: “Probability” by Breiman, Addison-Wesley.

  • Chapter 2 Mathematical Framework: Random variable, Expectation, Convergence
  • Chapter 3 Independence:
  • Chapter 4 Conditional Expectation:
  • Chapter 5 Martingales: Optimal sampling theorem, Martingale convergence theorem, Stopping times
  • Chapter 8 Convergence in Distribution: Characteristic function, Continuity theorem
MATH551 Numerical analysis

Textbook: “Introduction to Numerical Analysis” by Stoer and Bulirsch, 3rd Edition, Springer

  • Chapter 1 Error Analysis: machine number, condition Number.
  • Chapter 2 Interpolation: polynomial interpolation, interpolation Error, trigonometric interpolation, spline function
  • Chapter 3 Topics in Integration: numerical integration, numerical differentiation, Peano’s representation, Romberg integration, Gaussian quadrature.
  • Chapter 4 Systems of Linear Equations: LU-decomposition, error bounds, Householder matrix, least-squares problem, pseudo inverse, iterative methods for linear system.
  • Chapter 6 Eigenvalue problems: Jordan Normal Form, Shur Normal Form, LR and QR methods, Estimation of Eigenvalues The Gershgorin theorem).
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