# Mathematics and Statistics with Interdisciplinary Applications (Ph.D.)

**Overview**

The doctoral program in Mathematics and Statistics with Interdisciplinary Applications (MSIA) is designed to provide a strong mathematics and statistics background to support intense quantitative work in diverse disciplines. The curriculum will prepare scholars to work on problems at the intersection of mathematics, science, engineering, medicine, finance, computer science, and other quantitative disciplines. The program aims to be the most inclusive and broadly interdisciplinary in Texas.

**Program Requirements for Students with a Bachelor’s Degree**

Students admitted with a bachelor’s degree will complete a minimum of 72 hours to earn the PhD in MSIA as follows:

- Required Core Courses – 12 hours
- Prescribed Electives – 15 hours
- Interdisciplinary Courses – 9 hours
- Dissertation and Research – 36 hours

**Program Requirements for Students with Master’s Degree**

Students admitted with a master’s degree will complete a minimum of 57 hours to earn the PhD in MSIA as follows:

- Required Core Courses – 6 hours
- Prescribed Electives – 6 hours
- Interdisciplinary Courses – 9 hours
- Dissertation and Research – 36 hours

**Milestone Requirements**

- Comprehensive Exam – Students will be required to pass the Comprehensive Exam by the end of the second year of graduate study. Through close advising, the first-year coursework will be tailored to a student’s background and similarly, the comprehensive exam will also be tailored to each student’s coursework, background, and research goals. Depending on their background, some students may take the comprehensive exam during their first year while others will take it in the 2nd year. The comprehensive exam will consist of written exams covering topics in each of the eight subjects covered in the core courses. A separate exam in each subject will be offered at the beginning of the fall, spring, and summer semesters. To advance, the student must pass at least three subject exams. An “A” grade in one of the core courses will exempt the student from at most one exam. Students may take each exam up to three times but must pass all the required exams to remain in the program.
- Candidacy Exam – students must pass a candidacy exam to progress into their dissertation.
- Dissertation Defense – students must successfully defend their dissertation.

**Admission Requirements**

Undergraduate students with a degree in a relevant application area do not require an undergraduate degree in mathematics or statistics.

In addition to general requirements of admissions to the UTRGV Graduate College, the doctoral program in Mathematics and Statistics with Interdisciplinary Applications will also require:

- Bachelor's degree in or in a STEM or related field with at least 3 advanced undergraduate courses in mathematics from the following areas: linear algebra, differential equations ,modern algebra I, real analysis I, probability and statistics, complex variables or earned a master's degree in mathematics or a related field from a regionally accredited institution in the United States or a recognized international equivalent in a similar or related field with at least 3 undergraduate classes listed for students entering with a bachelor's degree.
- TOEFL score of 79 or better for international students if the medium of instruction in their bachelors or master’s program was not English.
- Personal Statement.
- Curriculum Vita.
- Three letters of recommendation.

The program will accept part-time students as well as transfer students from other graduate programs. Transfer of graduate credit based on policies set out by the UTRGV Graduate College.

Application for admission must be submitted prior to the published deadline. The application is available at www.utrgv.edu/gradapply.

## Program Requirements for Students Entering with a Bachelor's Degree - 72 Hours

### Core Courses - 12 Hours

Students may choose 12 hours in the core courses upon advisement.

MATH 8330 | Advanced Linear Algebra | 3 |

MATH 8331 | Abstract Algebra | 3 |

MATH 8333 | Advanced Statistical Learning | 3 |

MATH 8352 | Advanced Analysis I | 3 |

MATH 8360 | Advanced Ordinary Differential Equations | 3 |

MATH 8364 | Advanced Statistical Methods | 3 |

MATH 8365 | Advanced Probability & Statistics | 3 |

MATH 8375 | Advanced Numerical Analysis | 3 |

### Prescribed Electives - 15 Hours

This degree plan includes courses that appear in more than one section of the degree plan. Such courses can only be used to fulfill one requirement on the degree plan and credit hours will only applied once.

MATH 8323 | Representation Theory | 3 |

MATH 8329 | Analytic Number Theory | 3 |

MATH 8332 | Commutative Algebra | 3 |

MATH 8334 | Machine Learning | 3 |

MATH 8335 | Deep Learning | 3 |

MATH 8336 | Advanced Data Science | 3 |

MATH 8337 | Information Theory | 3 |

MATH 8338 | Mathematical Foundations of Statistical and Quantum Mechanics | 3 |

MATH 8339 | Advanced Complex Analysis | 3 |

MATH 8343 | Linear Models | 3 |

MATH 8344 | Function Space Methods in System Theory | 3 |

MATH 8346 | Hydrodynamic Stability | 3 |

MATH 8347 | Turbulence | 3 |

MATH 8348 | Survival Analysis | 3 |

MATH 8349 | Loss Models | 3 |

MATH 8350 | Actuarial Risk Theory | 3 |

MATH 8351 | Nonlinear hyperbolic PDEs | 3 |

MATH 8353 | Measure Theory | 3 |

MATH 8361 | Advanced Partial Differential Equations | 3 |

MATH 8362 | Advanced Fourier Analysis | 3 |

MATH 8363 | Solitons and Integrable Models | 3 |

MATH 8366 | Advanced Microlocal Analysis | 3 |

MATH 8367 | Advanced Functional Analysis | 3 |

MATH 8369 | Mathematical Methods in Applied Sciences | 3 |

MATH 8371 | Differentiable Manifolds | 3 |

MATH 8374 | Applications of Differential Geometry | 3 |

MATH 8376 | Numerical Methods for Differential Equations | 3 |

MATH 8377 | Advanced Fluid Mechanics | 3 |

MATH 8378 | Advanced Inverse Problems and Image Reconstruction | 3 |

MATH 8379 | Advanced Stochastic Processes | 3 |

MATH 8381 | Advanced Mathematical Statistics | 3 |

MATH 8382 | Advanced Statistical Computing | 3 |

MATH 8384 | Advanced Biostatistics | 3 |

MATH 8385 | Advanced Cryptology & Codes | 3 |

MATH 8387 | Advanced Mathematical Modeling | 3 |

MATH 8388 | Advanced Discrete Mathematics and Combinatorics | 3 |

MATH 8398 | Interdisciplinary Research | 3 |

MATH 8399 | Advanced Topics in Mathematics and Statistics | 3 |

### Interdisciplinary Courses - 9 Hours

This degree plan includes courses that appear in more than one section of the degree plan. Such courses can only be used to fulfill one requirement on the degree plan and credit hours will only applied once.

#### Computational Mathematics and Computer/Electrical Engineering

MATH 8343 | Linear Models | 3 |

MATH 8344 | Function Space Methods in System Theory | 3 |

MATH 8362 | Advanced Fourier Analysis | 3 |

MATH 8378 | Advanced Inverse Problems and Image Reconstruction | 3 |

MATH 8385 | Advanced Cryptology & Codes | 3 |

MATH 8388 | Advanced Discrete Mathematics and Combinatorics | 3 |

MATH 8399 | Advanced Topics in Mathematics and Statistics | 3 |

#### Mathematical Physics

MATH 8323 | Representation Theory | 3 |

MATH 8338 | Mathematical Foundations of Statistical and Quantum Mechanics | 3 |

MATH 8351 | Nonlinear hyperbolic PDEs | 3 |

MATH 8361 | Advanced Partial Differential Equations | 3 |

MATH 8363 | Solitons and Integrable Models | 3 |

MATH 8371 | Differentiable Manifolds | 3 |

MATH 8374 | Applications of Differential Geometry | 3 |

MATH 8399 | Advanced Topics in Mathematics and Statistics | 3 |

#### Statistics with Data Analytics and Medical Applications

MATH 8334 | Machine Learning | 3 |

MATH 8335 | Deep Learning | 3 |

MATH 8336 | Advanced Data Science | 3 |

MATH 8337 | Information Theory | 3 |

MATH 8348 | Survival Analysis | 3 |

MATH 8349 | Loss Models | 3 |

MATH 8350 | Actuarial Risk Theory | 3 |

MATH 8382 | Advanced Statistical Computing | 3 |

MATH 8384 | Advanced Biostatistics | 3 |

MATH 8399 | Advanced Topics in Mathematics and Statistics | 3 |

#### Mathematical Biology and Nonlinear Mechanics

MATH 8346 | Hydrodynamic Stability | 3 |

MATH 8347 | Turbulence | 3 |

MATH 8369 | Mathematical Methods in Applied Sciences | 3 |

MATH 8377 | Advanced Fluid Mechanics | 3 |

MATH 8379 | Advanced Stochastic Processes | 3 |

MATH 8387 | Advanced Mathematical Modeling | 3 |

MATH 8399 | Advanced Topics in Mathematics and Statistics | 3 |

### Dissertation and Research - 36 Hours

#### Research - 6 Hours

MATH 8398 | Interdisciplinary Research | 3 |

Or | ||

MATH 8698 | Interdisciplinary Research | 6 |

#### Dissertation - 30 Hours

MATH 9301 | Dissertation | 3 |

MATH 9601 | Dissertation | 6 |

MATH 9901 | Dissertation | 9 |

## Program Requirements for Students with Master’s Degree - 57 Hours

### Core Courses - 6 Hours

Students may choose 6 hours in the core courses upon advisement.

MATH 8330 | Advanced Linear Algebra | 3 |

MATH 8331 | Abstract Algebra | 3 |

MATH 8333 | Advanced Statistical Learning | 3 |

MATH 8352 | Advanced Analysis I | 3 |

MATH 8360 | Advanced Ordinary Differential Equations | 3 |

MATH 8364 | Advanced Statistical Methods | 3 |

MATH 8365 | Advanced Probability & Statistics | 3 |

MATH 8375 | Advanced Numerical Analysis | 3 |

### Prescribed Electives - 6 Hours

This degree plan includes courses that appear in more than one section of the degree plan. Such courses can only be used to fulfill one requirement on the degree plan and credit hours will only applied once.

MATH 8323 | Representation Theory | 3 |

MATH 8329 | Analytic Number Theory | 3 |

MATH 8332 | Commutative Algebra | 3 |

MATH 8334 | Machine Learning | 3 |

MATH 8335 | Deep Learning | 3 |

MATH 8336 | Advanced Data Science | 3 |

MATH 8337 | Information Theory | 3 |

MATH 8338 | Mathematical Foundations of Statistical and Quantum Mechanics | 3 |

MATH 8339 | Advanced Complex Analysis | 3 |

MATH 8343 | Linear Models | 3 |

MATH 8344 | Function Space Methods in System Theory | 3 |

MATH 8346 | Hydrodynamic Stability | 3 |

MATH 8347 | Turbulence | 3 |

MATH 8348 | Survival Analysis | 3 |

MATH 8350 | Actuarial Risk Theory | 3 |

MATH 8351 | Nonlinear hyperbolic PDEs | 3 |

MATH 8353 | Measure Theory | 3 |

MATH 8361 | Advanced Partial Differential Equations | 3 |

MATH 8362 | Advanced Fourier Analysis | 3 |

MATH 8363 | Solitons and Integrable Models | 3 |

MATH 8366 | Advanced Microlocal Analysis | 3 |

MATH 8367 | Advanced Functional Analysis | 3 |

MATH 8369 | Mathematical Methods in Applied Sciences | 3 |

MATH 8371 | Differentiable Manifolds | 3 |

MATH 8374 | Applications of Differential Geometry | 3 |

MATH 8376 | Numerical Methods for Differential Equations | 3 |

MATH 8377 | Advanced Fluid Mechanics | 3 |

MATH 8378 | Advanced Inverse Problems and Image Reconstruction | 3 |

MATH 8379 | Advanced Stochastic Processes | 3 |

MATH 8381 | Advanced Mathematical Statistics | 3 |

MATH 8382 | Advanced Statistical Computing | 3 |

MATH 8384 | Advanced Biostatistics | 3 |

MATH 8387 | Advanced Mathematical Modeling | 3 |

MATH 8385 | Advanced Cryptology & Codes | 3 |

MATH 8388 | Advanced Discrete Mathematics and Combinatorics | 3 |

MATH 8398 | Interdisciplinary Research | 3 |

MATH 8399 | Advanced Topics in Mathematics and Statistics | 3 |

### Interdisciplinary Courses - 9 Hours

#### Computational Mathematics and Computer/Electrical Engineering

MATH 8343 | Linear Models | 3 |

MATH 8344 | Function Space Methods in System Theory | 3 |

MATH 8362 | Advanced Fourier Analysis | 3 |

MATH 8378 | Advanced Inverse Problems and Image Reconstruction | 3 |

MATH 8385 | Advanced Cryptology & Codes | 3 |

MATH 8388 | Advanced Discrete Mathematics and Combinatorics | 3 |

MATH 8399 | Advanced Topics in Mathematics and Statistics | 3 |

#### Mathematical Physics

MATH 8323 | Representation Theory | 3 |

MATH 8338 | Mathematical Foundations of Statistical and Quantum Mechanics | 3 |

MATH 8351 | Nonlinear hyperbolic PDEs | 3 |

MATH 8361 | Advanced Partial Differential Equations | 3 |

MATH 8363 | Solitons and Integrable Models | 3 |

MATH 8371 | Differentiable Manifolds | 3 |

MATH 8374 | Applications of Differential Geometry | 3 |

MATH 8399 | Advanced Topics in Mathematics and Statistics | 3 |

#### Statistics with Data Analytics and Medical Applications

MATH 8334 | Machine Learning | 3 |

MATH 8335 | Deep Learning | 3 |

MATH 8336 | Advanced Data Science | 3 |

MATH 8337 | Information Theory | 3 |

MATH 8348 | Survival Analysis | 3 |

MATH 8349 | Loss Models | 3 |

MATH 8350 | Actuarial Risk Theory | 3 |

MATH 8382 | Advanced Statistical Computing | 3 |

MATH 8384 | Advanced Biostatistics | 3 |

MATH 8399 | Advanced Topics in Mathematics and Statistics | 3 |

#### Mathematical Biology and Nonlinear Mechanics

MATH 8346 | Hydrodynamic Stability | 3 |

MATH 8347 | Turbulence | 3 |

MATH 8369 | Mathematical Methods in Applied Sciences | 3 |

MATH 8377 | Advanced Fluid Mechanics | 3 |

MATH 8379 | Advanced Stochastic Processes | 3 |

MATH 8387 | Advanced Mathematical Modeling | 3 |

MATH 8399 | Advanced Topics in Mathematics and Statistics | 3 |

### Dissertation and Research – 36 Hours

#### Research - 6 Hours

MATH 8398 | Interdisciplinary Research | 3 |

Or | ||

MATH 8698 | Interdisciplinary Research | 6 |

#### Dissertation - 30 Hours

MATH 9301 | Dissertation | 3 |

MATH 9601 | Dissertation | 6 |

MATH 9901 | Dissertation | 9 |