Mathematics - Doctor of Philosophy
Candidates for the Ph.D. degree in the Department of Mathematical Sciences must pass
- a qualifying examination,
- a basic comprehensive written examination,
- an advanced comprehensive examination with written and oral components, and
- a final oral doctoral thesis examination.
These are briefly described below. For more information, see the Graduate School requirements in this catalog.
Course Requirements
| Prefix | Title | Credits |
|---|---|---|
| Core Requirements | ||
| MATH 5450 | Abstract Algebra II: Fields, Rings and Modules | 3 |
| MATH 5460 | Measure and Integration | 3 |
| MATH 5463 | Real Analysis | 3 |
| MATH 5465 | Introduction to Functional Analysis | 3 |
In addition to the core requirements, each student must complete one of the following two options.
| Prefix | Title | Credits |
|---|---|---|
| Option 1 | ||
Choose three course sequences from Group A, as described below. | ||
| Option 2 | ||
Choose two course sequences from Group B and one from Group A, as described below. | ||
Course Sequences
Group A
| Prefix | Title | Credits |
|---|---|---|
| Algebra: Choose two of the following. | ||
| Module Theory and Homological Algebra | 3 | |
| Introduction to Commutative Algebra and Algebraic Geometry | 3 | |
| Topics in Algebra | 3 | |
| Foundations: Choose two of the following. | ||
| Mathematical Structures in Logic | 3 | |
| Universal Algebra and Model Theory | 3 | |
| Topics in Foundations | 3 | |
| Topology: Choose two of the following. | ||
| Topology I | 3 | |
| Topology II | 3 | |
| Topics in Topology | 3 | |
Group B
| Prefix | Title | Credits |
|---|---|---|
| Differential Equations: Choose two of the following. | ||
| Partial Differential Equations I | 3 | |
| Partial Differential Equations I | 3 | |
| Topics in Analysis | 3 | |
| Probability: Choose two from the following. | ||
| Foundations of Probability | 3 | |
| Advanced Topics in Stochastic Processes | 3 | |
| Topics in Probability and Statistics | 3 | |
| Statistics: Choose two of the following. | ||
| Continuous Multivariate Analysis | 3 | |
| Linear Models | 3 | |
| Advanced Theory of Statistics I | 3 | |
| Advanced Theory of Statistics II | 3 | |
| Topics in Probability and Statistics | 3 | |
Additional Course Requirements
A full time graduate student is required to register each semester for at least two Math/Stat graduate courses. With the exception of the final semester, of these two, only one may be MATH 6991 Doctoral Research or MATH 7000 Doctoral Dissertation. Moreover, these two courses must not include:
| Prefix | Title | Credits |
|---|---|---|
| MATH 5210 | Complex Variables | 3 |
| MATH 5220 | Fourier Series and Boundary Value Problems | 3 |
| MATH 5997 | Directed Reading | 1-6 |
| MATH 5120 | History and Theories of Mathematics Education | 3 |
| MATH 5130 | Algebra with Connections | 3 |
| MATH 5140 | From Number to Algebra | 3 |
| MATH 5150 | Data Analysis with Applications | 3 |
| MATH 5160 | From Measurement to Geometry | 3 |
| MATH 5170 | Using Number Throughout the Curriculum | 3 |
| MATH 5180 | Geometry with Connections | 3 |
| MATH 5999 | Master's Thesis | 1-15 |
Qualifying Examination
Every student admitted to the Ph.D. program must pass a written qualifying examination. Students who complete their mathematics Master's degree at NMSU may request that the Master's written examination also fulfill the Ph.D. qualifying examination requirement. In all other cases, the student takes a written Ph.D. qualifying exam. This exam is identical to the Master's written exam (based on the courses 5350/5360) and is administered and graded at the same time, but a higher passing score is required than for a Master's student. Ph.D. candidates need to pass the exam within their first year.
Basic Comprehensive Examinations
Every Ph.D. student must pass a Basic Comprehensive Exam, either in Algebra or in Analysis. The Algebra exam is based on the courses MATH 5340 Abstract Algebra I: Groups and Rings and MATH 5450 Abstract Algebra II: Fields, Rings and Modules and the Analysis exam is based on the courses MATH 5365 Introduction to Real Analysis II and MATH 5460 Measure and Integration.
These exams are offered every August and January. A student choosing to take the exam in Algebra must pass the exam within fourteen months of completing Math 581; similarly, a student taking the exam in Analysis must pass the exam within fourteen months of completing MATH 5460. Students failing to pass the exams within this period of time may be removed from the program. Students will normally not be given more than two attempts at any one exam.
Advanced Comprehensive Examinations
Candidates for the Ph.D. must pass an advanced comprehensive examination in their chosen research area. The examination has a written and an oral component. The written exam, which is written and administered by the student’s committee, is based on two of the student’s courses, normally among those listed in Options 1-2, chosen by the student in consultation with his/her committee and approved by the Graduate Studies Committee. Full-time students should complete the written component of the Advanced Comprehensive Exam after passing the Basic Comprehensive Exam and in the first two years. Those who have not made substantial progress towards completion of their written exams at the start of the fifth semester may be removed from the program. Students who have not completed the written exams by the start of the sixth semester will normally have any departmental funding revoked. The student must take the oral part of the exam at the end of the semester after completing the advanced written comprehensive exam. For the oral exam, the student should present a proposed direction for thesis work.
Final Oral Exam
This is an exam over the student's thesis. It is administered by the student's thesis committee.