# Qualifying Examination: typical syllabi and past exams

Please refer to Ph.D. in Applied Mathematics for the current catalog description of the qualifying examination.

## Course Syllabi:

- MATH 8120 Probability Theory I (2024 August)
- MATH 8143 Real Analysis I (
**2024 August**) - MATH 8144 Real Analysis II (
**2024 August**) - MATH 5128 Applied Probability I (2024 August)
- MATH 5129 Applied Probability II
**(**2018 August**)** - MATH 5161 Number Theory
- MATH 5163 Modern Algebra (
**2024 August**) - MATH 5164 Abstract Linear Algebra (
**2024 August**) - MATH 5165 Numerical Linear Algebra (2020 August)
- MATH 5172 The Finite Element Method (2021 August)
- MATH 5173 Ordinary Differential Equations (
**2024 August**) - MATH 5174 Partial Differential Equations (
**2024 August**) - MATH 5176 Numerical Methods for PDEs (2021 August)
- MATH 5181 Introduction to Topology (2024 August)
- MATH 6203 Stochastic Calculus for Finance I (2019 August)
- MATH 6206 Stochastic Calculus for Finance II (2022 August)
- MATH 8070 Topics in Numerical Analysis in Inverse Problems (2021 August)
- MATH 8172 Partial Differential Equations (2019 August)
- MATH 8181 Topology I (2018 August)
- MATH 8182 Topology II (2018 August)
- MATH 8275 Dynamical Systems I (
**2023 August**) - MATH 8276 Dynamical Systems II (
**2023 August**) - STAT 5126 Theory of Statistics I (
**2024 August)** - STAT 5127 Theory of Statistics II (
**2024 August**)

## Past MATH 8120/8143/8144 Exams:

**Disclaimer:** These sample exams are provided for the benefit of students. However, there is no guarantee regarding the “types” of questions that will appear on any future exam. In other words, even if a particular type of question appears in all of these sample past exams, it does not imply that a similar problem will also appear in a future exam. Conversely, if a certain type of question has never appeared in any of these sample past exams, it does not imply that a problem of this type will never appear in a future exam.

**Note:** In a typical MATH 8120/8143/8144 exam, there are four questions, and each question is given equal weight. Your total score will be the sum of your scores on your **best three **questions.