# Outline of Undergraduate Graduation Exams

#### Bachelor’s Degree Comprehensive Examination

Undergraduate thesis paper/comprehensive examination for graduation: students enrolled or double-majored at the Department of Mathematics must submit an undergraduate thesis paper in order to obtain a bachelor’ degree. However, the thesis may be replaced by the comprehensive examinations for graduation.

**Bachelor’s Thesis**

For a student who wants to write an undergraduate thesis paper, he/she must submit the Undergraduate Thesis Review Request to the Department of Mathematics after consultation with the academic advisor. Then the student must write the thesis under the guidance of the academic advisor and submit the result of the thesis review to the Department of Mathematics followed by the deliberation of the thesis review committee.

**Comprehensive Examination for Graduation**

The comprehensive examination takes place once every semester (May and November) to verify students’ basic knowledge of mathematics including those gained from basic and major required courses. Any student who wishes to take the exam must submit the application for the comprehensive examination by the specified period.

The student who wants to take the exam must register for a common course (MATH110: Calculus) and 4 out of 8 elective courses. (However, if the student is absent without notice after the exam registration, he/she will not be allowed to take the exam in the next semester.)

- Common Course
- ο MATH110 Calculus

- Electives (8subjects)
- ο MATH120 Applied Linear Algebra
- ο MATH210 Applied Complex Variables
- ο MATH230 Probability and Statistics
- ο MATH261 Discrete Mathematics
- ο MATH301 Modern AlgebraⅠ
- ο MATH311 Analysis I
- ο MATH351 Introduction to Numerical Analysis
- ο MATH426 Introduction to Differential Geometry

The Comprehensive Examination is to verify whether the students have fully learned the basic knowledge of mathematics including basic and major required courses during their 4 years of college. The exam is one of the graduation requirements.

#### Exam Preparation

The exam covers the basic required course (MATH110: Calculus) and 4 out of 8 major required courses. The exam is given once each semester and the student must register for the exam at the beginning of each semester if he/she wants to take the exam. 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 equations