Choi, Suhyoung - Department of Mathematics, Korea Advanced Institute of Science and Technology

• Algebraic Topology I: Midterm Exam: Brief Answers Justify your answers fully.
• Marden's conjecture for hyperbolic 3-manifolds and
• 1 Introduction Geometries
• 1 Introduction 1 2 Arguments 2
• 1 Discrete groups 2 1.1 Theory of discrete groups . . . . . . . . . . . . . . . . . . . . . . . . 2
• 1 Introduction About this lecture
• 6.4. Invariant subspaces Decomposing linear maps into
• Recall lines and planes x+y=4, x-5y=1. Solve this system.
• Ch. 5 Determinants Determinant functions
• 1 Introduction Section 3: Topology of 2-orbifolds
• October 29, 2009 13:37 World Scientific Book -9in x 6in mjsbook Publishers' page
• 7.4. Computations of Invariant Let A be nxn matrix with entries in F[x].
• 8_6 Singular value decomposition Diagonalizations
• Matrix notation, operations, row and column vectors, product AB(important), transpose
• 1 Introduction Preliminary
• 1 Introduction Definition of geometric structures on 2-orbifolds
• THE PL-METHODS FOR HYPERBOLIC 3-MANIFOLDS TO PROVE SUHYOUNG CHOI
• Publication list: 1. Real projective surfaces, Ph.D. Thesis, Princeton University, June 7, 1988.
• Chapter 2: Vector spaces Vector spaces, subspaces, basis,
• 6.8. The primary decomposition theorem
• 1 Introduction Preliminary
• 1 Discrete group actions Discrete groups and discrete group actions
• 1 Introduction Section 3: Topology of 2-orbifolds: Compact group actions
• 1 Introduction Topological operations on 2-orbifolds: constructions and decompositions
• Summer 2008 The informations are all in math.kaist.ac.kr/
• Length, norm, magnitude of a vector v=(v1,...,vn) is ||v||= (v1
• The purpose is to understand linear transformations , see various examples, kernel
• 1 Introduction The definition of the Teichmller space of 2-orbifolds
• The purpose is to understand linear transformations , see various examples, kernel range, compositions and
• 1 Introduction Section 3: Topology of 2-orbifolds
• Click to edit Master subtitle style 2.1. Introduction to Systems of
• 1 Introduction Lie groups
• Chapter 1. Linear equations Review of matrix theory
• Linear transformations Linear transformations, Algebra of
• 1 Introduction About this course
• 8_6 Singular value decomposition Diagonalizations
• Matrix notation, operations, row and column vectors, product AB(important), transpose
• Length, norm, magnitude of a vector v=(v1,...,vn) is ||v||= (v1
• 7.2. Cyclic decomposition and rational forms
• Linear Algebra Fall 2008 Teaching, grading policies, homeworks, and
• A survey of projectively flat structures on 2-and 3-manifolds.
• Deformation spaces of real projective structures on Coxeter 3-orbifolds
• A survey of structures on
• Summer 2010 The informations are all in
• 1 Introduction The deformation space of (X, G)-structures on an orbifold.
• 1 Introduction About this lecture
• 6. Elementary Canonical How to characterize a
• Linear Algebra: Final Exam (2007 Spring) Justify your answers fully.
• 7.3. Jordan form Canonical form for matrices and
• 1 Introduction About this lecture
• 6.3. Annihilating polynomials Cayley-Hamilton theorem
• 8.4. Quadratic Forms Quadratic forms generalize norm, lengths, inner-products,..
• Rank+nullity=dimension The dimension theorem for
• A method to find A-1 Elementary operations
• Logic and the set theory Lecture 2: Arguments
• Geometric structures on 2-orbifolds
• 3.6. Matrices with special3.6. Matrices with special Diagonal matrix, triangular matrix, symmetric and
• Ch 4: Polynomials Polynomials
• THE CONVEX REAL PROJECTIVE MANIFOLDS AND ORBIFOLDS WITH RADIAL ENDS: THE OPENNESS OF
• GPS, Network Analysis, Electric Circuits, Balancing Chemical equations, polynomial interpolations
• 7.7. The projection theorem and its
• 7_3 The fundamental spaces of a matrix.
• Section 3: Topology of Introduction
• QR-DECOMPOSITION HOUSEHOLDER TRANSFORMATIONS
• Linear Algebra: Final Exam (2006 Spring) Justify your answers fully.
• 1 Introduction About this lecture
• Chapter 4 Determinants Determinants are useful because it gives us
• LU decomposition L: lower triangular
• 1 Introduction About this lecture
• Geometry of linear operators Orthogonal opertors
• 7_5. The rank theorem Column rank = row rank.
• Logic and the set theory Lecture 1: Introduction
• Chapter 4 Determinants Determinants are useful because it gives us
• Logic and the set theory Lecture 3: Propositional Logic
• 1 Introduction About this lecture
• 1 Introduction About this lecture
• Topology of Introduction
• The SO(3)-character space and spherical triangles Spherical triangles and the two
• 8.5. Applica+on of Quadra+c forms to op+miza+on
• In many cases, such as finding eigenvalues, it is difficult to obtain an exact values.
• 4.3. Cramer's Rules and applications of determinant C_ij cofactor of A_ij
• 1 Introduction About this lecture
• 7_5. The rank theorem Column rank = row rank.
• A composition of functions: f:X->Y,g:Y->Z, we obtain gf:X->Z.
• This should be at least 10 pages long with 12 pt font and double spaced. Due by Monday 4:00 pm February 16th 2009.
• Logic and the set theory Lecture 4: Refutation trees
• 8.2 Similarity and8.2 Similarity and diagonalizabilitydiagonalizability
• Topology: Midterm Exam (Spring 2006) Justify your answers fully.
• 1 Introduction About this lecture
• Kernel of a linear transformation
• 7.6 The pivot theorem Basis problem
• 1 Introduction About this lecture
• 6.6 Direct sum decompositions
• 3.6. Double dual Dual of a dual space
• 7.6 The pivot theorem Basis problem
• Section 1: Rational Forms 7.1. Rational forms
• Each basis gives you are coordinate system and conversely.
• 7.8 Best approxima0on and least We wish to find the best
• 7.7. The projection theorem and its
• 5.4. Additional properties Cofactor, Adjoint matrix,
• A subspace is a set one can do scalar multiplication and addition and not leave the
• Rank+nullity=dimension The dimension theorem for
• Solutions for inhomogeneous systems. Consistency
• February 14, 2011 18:11 WSPC/INSTRUCTION FILE so3v42ijm International Journal of Mathematics
• diagonalizability Symmetric matrices can be diagonalized by an
• 1 Introduction About this lecture
• Matrix of a linear operator with respect to a One can use different representation of a
• Diagonal matrix, triangular matrix, symmetric and skew-symmetric matrices,AAT, Fixed points, inverting
• 7.2. Cyclic decomposition and rational forms
• Polynomial Ideals Euclidean algorithm
• A method to find A-1 Elementary operations
• Ax=x. (I-A)x=0. If I-A is invertible, then there are only trivial
• For 2x2 matrix det(A)=det(AT). In general we have
• 1 Introduction About this lecture
• A subspace is a set one can do scalar multiplication and addition and not leave the set.
• Geometric structures on 2-orbifolds Section 1: Manifolds and differentiable structures
• Introduction Topology of orbifolds II
• QR-DECOMPOSITION HOUSEHOLDER TRANSFORMATIONS
• The convex real projective manifolds and orbifolds with radial ends The convex real projective manifolds and orbifolds with
• Di erentiable Manifolds Exam: Midterm (May 2000) 1. Rotate the circle (x 2) 2 + z 2 = 1 on the xz-plane about the z-axis to obtain a surface in
• Differentiable Manifolds Exam: Midterm (April 1999) 1. Let f : R 2 ! R 2 be the map given by f(x; y) = (xy; y 2 ). Let X be a vector field on R 2 given
• Geometry of linear operators Orthogonal opertors
• Representation by matrices Representation.
• 7.9. Orthonormal basis and the Gram-Schmidt
• Linear Algebra: Midterm Exam (2006 Spring) Justify your answers fully.
• 1 Introduction About this lecture
• Deforming convex RP3-structures on 3-orbifolds Deforming convex RP3-structures on 3-orbifolds
• 7.11. Coordinates with7.11. Coordinates with respect to a basisrespect to a basis
• For 2x2 matrix det(A)=det(AT). In general we have
• 7_3 The fundamental spaces of a matrix.
• diagonalizability Symmetric matrices can be diagonalized by an
• LU decomposition L: lower triangular
• 6.4 Composition and invertibility of linear transformations
• Bases for subspaces Consider V=Span{v_1,v_2,...,v_l}.
• Logic and the set theory Lecture 7, 8: Predicate Logic
• Logic and the set theory Lecture 18: Mathematical Inductions in How to Prove It.
• Logic and the set theory Lecture 15: Relations in How to Prove It.
• Logic and the set theory Lecture 5: Propositional Calculus: part 1
• ERRATA IN "GEOMETRIC STRUCTURES ON LOW-DIMENSIONAL MANIFOLDS"
• Logic and the set theory Lecture 16: Relations in How to Prove It.
• Logic and the set theory Lecture 19: The set theory
• Logic and the set theory Lecture 13: Proofs in How to Prove It.
• Logic and the set theory Lecture 17: Functions in How to Prove It.
• Logic and the set theory Lecture 14: Proofs in How to Prove It.
• Logic and the set theory Lecture 9: Predicate Calculus
• October 1, 2011 20:11 World Scientific Book -9in x 6in mjsbook Publishers' page
• Logic and the set theory Lecture 21: The set theory: Review Sections 12-25
• Logic and the set theory Lecture 20: The set theory (NS)
• Logic and the set theory Lecture 11,12: Quantifiers (The set theory) in How to Prove It.
• Logic and the set theory Lecture 6: Propositional Calculus: part 2
• THE SO(3)-REPRESENTATION SPACES OF THE FUNDAMENTAL GROUP OF A SURFACE OF GENUS 2