^{Washington State University}

_{Factsheets}

# Doctor of Philosophy in Mathematics

- Fall January 10
- Spring August 10

- Pullman: Yes

- 600 TOEFL Minimum score
- 100 TOEFLI Minimum score
- 7 IELTS Minimum score

## Degree Description:

PhD in Mathematics

This degree is awarded in recognition of distinctive scholarship and original contributions to knowledge in Mathematics. The PhD program is especially designed to prepare the student for teaching at the graduate level and doing mathematical research in academic, industrial and business settings. Students studying various fields within the realm of pure mathematics would be included in this PhD program.

PhD in Mathematics (Applied Mathematics Option)

The specialization of modern academic disciplines provides both a challenge to those who wish to do research at the interface of mathematics and its areas of application and many opportunities to make valuable contributions. The Applied Mathematics Option allows students from a range of backgrounds to pursue a traditional applied mathematics program, while retaining the option to thoroughly learn an area of application. Entering students may not necessarily have a bachelor’s degree in Mathematics. However, they will be required to demonstrate a grasp of the core areas of advanced calculus and linear algebra at the level of a bachelor’s degree in Mathematics. They will then be given great latitude to take specialized courses in Mathematics and their area of application.

PhD in Mathematics with Education Emphasis

The degree of PhD in Mathematics with Education Emphasis is awarded in recognition of scholarship and original contributions to the teaching and learning of mathematics. The main difference from the other PhD choices is in the research focus. The requirements for this PhD include competence in core mathematics, as well as study in the research methodologies applicable to research in mathematics education.

The PhD in Mathematics with Statistics Option has been replaced with a new degree program, the PhD in Statistical Science. Please visit https://gradschool.wsu.edu/degrees/factsheet/doctor-philosophy-statistical-science/ for more information.

## Admission Requirements:

Students should have taken upper-level analysis and linear algebra courses before applying, and have the equivalent of an undergraduate degree in mathematics, statistics, or a related field. Additional upper-level courses like abstract algebra, functional or complex analysis, optimization, applied mathematics, topology, etc. will be taken into account.

For international students, either a TOEFL or IETLS score is required; recommended TOEFL score of 100 and IELTS of 7. Exceptions can be found here: https://gradschool.wsu.edu/international-requirements/

Students applying to the PhD Mathematics program will be automatically considered for an assistantship position.

The application will require:

- Unofficial transcripts from all previous institutions.
- GPA above a 3.0 on a 4.0 scale.
- Resume/cv.
- Email contact information for 3 references.
- Personal statement. The personal statement is your chance to highlight relevant experiences and discuss your future research interests.
- GRE scores are not required but encouraged.

## Student Learning Outcomes:

All graduates will be able to:

- Critical Thinking: Students will be able to think critically and creatively.
- Knowledge and Scholarship: Students will be able to identify and conduct original research and scholarship. Ethical and Responsible Research: Students will be able to conduct research in an ethical and responsible manner.
- Effective Communication: Students will be able to effectively communicate research work in written and oral form.

## Career Opportunities:

Academia (tenure-track positions at universities and colleges worldwide), Bio-statistics (health and pharmaceutical companies), Risk analysis (financial and insurance companies, investment management), Research (state or federal government, software development), Mathematics education (publishing, consulting and developing of educational software).

## Career Placements:

Graduates from the Mathematics PhD program begin careers in both academia and government or industry. A few examples of career placements in academia from the past few years include:

- Postdoc, USDA Northwest Climate Hub and WSU Center for Sustaining Agriculture
- Assistant Professor, Central Washington University
- Assistant Professor, Marian University (WI)

A few examples of career placements in government and industry from the past few years include:

- Regulatory Data Scientist, Office of Regulatory Innovation and Assistance, Washington State Government
- Quantitative Model Validation Analyst, First Tech Federal Credit Union (OR)
- Data Scientist, Emsi Labor Market Analytics (ID)

## Faculty Members:

### Asaki, Thomas James, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Applied optimization, image and data analysis

### Chen, Xiongzhi, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Simultaneous inference (including variable/model selection and multiple comparison) with applications in biology and pharmaceutical science

Latent variable models for high-dimensional data with applications in genomics and signal processing

Analysis of non-Euclidean data (such as networks, shapes, images and tensors)

Spectra of random matrices (including those of sample auto-correlation/auto-covariance matrices) with applications to inference on high-dimensional data

Statistical inference on stochastic differential equations (including those driven by fractional Brownian motions) with applications in finance, biology and geology

### Cooper, Kevin Dale, Ph.D.

Serves as: co-chair or member of graduate committee

### Dasgupta, Nairanjana, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Non-parametric Statistics, Multiple Comparisons, Comparison to Control, Logistic Distribution, Optimal Designs, Design of Experiments, Innovative Methods of Teaching Statistics, The history of statistics.

### Dillon, Robert, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Mathematical modeling, mathematical biology, numerical partial differential equations, computational biofluids.

### Dimitrov, Alexander, Ph.D.

**Location:**Vancouver

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Information-theoretic and probabilistic approaches to neural computing and cognitive processes, non-linear neuronal models, chaotic dynamical systems, non-linear signal processing and prediction, systems identification, neural-based intelligent agents. Bioinspired engineering.

### Hall, William, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Mathematics Education: the teaching and learning of calculus; professional identity of preservice and in-service secondary mathematics teachers

### Hudelson, Matthew G, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Combinatorics and Discrete Geometry, Random Algorithms

### Jandhyala, Venkata Krishna, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Change-point problems for statistical models and their applications, Quality control, Environmental monitoring, Econometrics.

### Johnson, Dean, Ph.D.

Serves as: co-chair or member of graduate committee

#### Research Interests

Educational statistics.

Teaching of statistics.

Statistical consulting.

Item response theory.

### Kaul, Abhishek, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

High dimensional change point regression models; computational statistics and statistical learning

### Khapalov, Alexander, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Applied Analysis; Mathematical Control Theory for Linear and Nonlinear Partial Differential Equations; Modeling, Wellposedness and Motion Capabilities for Swimming Phenomenon; Systems Theory: Controllability, Stabilization, Observability and Unique Continuation; Control of Power Systems.

### Krishnamoorthy, Bala, Ph.D.

**Location:**Vancouver

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Applied algebraic topology, computational geometry, geometric measure theory, discrete optimization, data science; applications in computational chemistry, life sciences, and biomedicine.

### Lapin, Sergey, Ph.D.

Serves as: co-chair or member of graduate committee

#### Research Interests

Numerical modeling in many applied fields including (but not limited to) diagnosing and monitoring systemic disease, channel routing for flood forecasting, dynamic granular matter formation process, infectious disease epidemics, and simulation of fluid flow.

### Li, Haijun, Ph.D.

**Location:**Everett

Serves as: chair or member of graduate committee

#### Research Interests

Probability, Stochastic Processes, Risk Analysis.

Current Research: multivariate regular/rapid variation, cooperative games, copulas with graph structure

### Liu, Sheng-Chi, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Number theory, automorphic forms and representation theory.

### Manoranjan, Valipuram S, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Mathematical and computer modeling of nonlinear phenomena that arise in engineering and life sciences.

Problems of particular interest: Contaminant transport in groundwater, transdermal drug delivery, models in developmental biology, nonlinear waves (solitons); iterative methods with large convergence regions.

### McDonald, Judi, Ph.D.

**Location:**Pullman

Serves as: chair of graduate committee

#### Research Interests

Matrix Analysis and Linear Algebra

### Moore, Charles, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Analysis, Harmonic analysis, Partial Differential Equations, Probability Theory

### New, Leslie, Ph.D.

**Location:**Vancouver

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

The use of hierarchical Bayesian state-space models to study species interactions with the environment and other species, including ecological modeling to investigate how changes in individual behavior, either anthropogenic or natural, can affect population dynamics.

Current research: estimating the impact of wind facilities on eagles in the US and the effectiveness of Marine Protected Areas in reducing the impacts of noise in whale habitat.

### Panchenko, Alexander, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Data Science: feature extraction from networks, learning network dynamics from limited time-series, statistical inference on networks. Application areas to plant biology and neuroscience.

Dynamics of active particle systems and active materials: mathematics of robot swarms involving the analysis and simulation of self-organizing particle systems possessing some means of self-propulsion and decision-making capability.

Continuum theories of large particle systems: production of a continuum description of a large system of atoms or molecules (like a fluid) starting from the atomistic equations of motion for the particles (Sixth Hilbert Problem)

### Pascual, Francis, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Engineering Reliability, Failure-Time Models and Data Analysis, Robust Designs in Accelerated Life Tests.

### Schreyer, Lynn, Graduate Studies Committee Chair

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Graduate Studies Committee Chair

Broad Interests: Deterministic Modeling, PDEs, Continuum Mechanics.

Currently: Mathematically modeling porous media – any material consisting of a solid and one or more other phases, including swelling porous materials. Examples include clays (expansive soils), polymers (such as drug-delivery polymers and bio-polymers), and cell membranes.

### Schumaker, Mark F, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Models of respiratory and photosynthetic electron transport

### Schwartz, Elissa, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

– Experimental and theoretical techniques to investigate mechanisms in virology, immunology, and infectious disease epidemiology

– Control of lentiviral infection, including human immunodeficiency virus (HIV) and equine infectious anemia virus (EIAV).

– Mathematical and computational models of viral dynamics with clinical and experimental data to elucidate the determinants of virus control and escape.

### Slavit, David, Ph.D.

**Location:**Vancouver

Serves as: chair or member of graduate committee

#### Research Interests

Teacher development, particularly in collaborative professional contexts, teacher understanding and instruction STEM schools, the ways in which K-12 students develop understandings of algebraic ideas, particularly mathematical functions, and educational technology.

### Sottile, Matthew, Ph.D.

Serves as: member only of graduate committee

#### Research Interests

Agent-based models

Image processing

Complex systems

Graph algorithms

Scientific computing

Programming languages

### Strigul, Nicholas, Ph.D.

**Location:**Vancouver

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Broadly: environmental problems and research in mathematical biology, as well as a variety of modeling, experimental and field studies in different areas such as ecotoxicology, soil, microbial and avian ecology.

Current primary research:

1) Forest modeling – One of the major directions of this project is to investigate effects of environmental stressors and different land-use practices on forest dynamics. Forested ecological systems can be considered as complex adaptive systems, which result from self-organization on multiple levels.

2) Ecotoxicology, in particular tungsten ecotoxiology, in order to provide a scientific basis for pollution regulation and environmental risk-assessment.

### Tsatsomeros, Michael, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Matrix theory, linear algebra and its applications

### Vincent, Kimberly McGinley, Ph.D.

Serves as: co-chair or member of graduate committee

#### Research Interests

Collegiate and pre-service mathematics education.

### Vixie, Kevin, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Geometric analysis and geometric measure theory, geometry and analysis in high dimensions, and data science. Examples include data driven advances in geometric measure theory, image analysis, regularity of minimizers, geometric analysis in metric measure spaces and graphs

### Voulgarakis, Nikolaos, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Nanoscale modeling and simulation of soft biological systems and complex fluids. Applications areas: a) gene and drug delivery, b) cell membrane dynamics, and c) energy transfer in biomolecules.

### Wang, Xueying, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Mathematical Biology: the mathematical analysis of deterministic and stochastic dynamics.

Current applications include synaptic noise, channel noise of a single neuron and coupled neurons, clustering and plasticity of neural networks, transmission dynamics of infectious diseases such as cholera and Ebola, and TrojanY-Chromosome eradication strategy of an invasive species.

### Wang, Yuan, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Statistical learning of complex data objects including tree, curves and images

Bayesian variable selection

Adaptive clinical trial design

Compressive sensing and system design

### Yin, Hong-Ming, Ph.D.

Serves as: chair, co-chair, or member of graduate committee

#### Research Interests

Financial Engineering and Portfolio Management; Applied Mathematics; Partial Differential Equations, Inverse and Ill-posed problems; Electromagnetic Fields and Semiconductor/Superconductor modeling.