### Bachelor's Course Graduation Comprehensive Exam

The Comprehensive Examination is to check achievement of basic knowledge including basic required and major required courses, which has been studied in the department of Mathematics for four years

It covers the basic required course Calculus and the self-selected 4 subjects out of 8 major required courses and is given once each semester.

The followings are the main topics of each course for the examination.

Calculus | Series solutions, Convergence of sequence and series, Taylor Theorem, Gradient, Directional derivatives, Maximum & Minimum, Lagrange multipliers, Green's Theorem, Stokes Theorem, Divergence Theorem |

Probability and Statistics | Conditional probability, Probability distributions, Central limit theorem, Moment generating function, Estimation (MLE). |

Discrete Mathematics | Relation with Sets, Algorithm & Analysis, Graph Theory, Boolean Algebra |

Applied Linear Algebra | Gaussian Elimination, Projection onto subspaces, Eigenvalues and eigenvectors, Determinants. |

Modern Algebra I | Definition of Group & Examples, Lagrange Theorem, Basic Theorems of Homomorphisms. |

Applied Complex Variables | Cauchy-Riemann equations, Cauchy integral formula, Residues, Maximum modulus principle |

Analysis I | Properties of Continuous Function, Compact Sets, Convergence of Sequence |

Introduction to Differential Geometry | Curvature on Curves and Surfaces and its basic theorems. |

Introduction to Numerical Analysis | Interpolation, integration, System of linear eguations. |