- UNM Catalog 2022-2023
- >Colleges
- >College of Arts and Sciences
- >Mathematics and Statistics
- >Graduate Program

**Master of Science in Mathematics**(M.S.)

Concentrations: Applied Mathematics; Pure Mathematics.**Master of Science in Statistics**(M.S.)

Concentration: Applied Statistics.**Doctor of Philosophy in Mathematics**(Ph.D.)

Concentrations: Applied Mathematics; Pure Mathematics.**Doctor of Philosophy in Statistics**(Ph.D.)

** Computational Science and Engineering: **The Computational Science and Engineering interdisciplinary graduate certificate program prepares students to effectively use high-performance computing within their disciplines and is open to graduate students in this department. See the

**Nanoscience and Microsystems Engineering: **This department participates in the interdisciplinary Nanoscience and Microsystems Engineering M.S. and Ph.D. programs; for more information, see the *Graduate Interdisciplinary Studies* section of this Catalog.

**Graduate Advisors**

Contact the department for assignment of a faculty graduate advisor.

**Application Deadlines**

Fall semester: | February 15 (with financial aid) |

April 30 (without financial aid) | |

Spring semester: | October 1 |

Master of Science in Mathematics

Concentrations: Applied Mathematics; Pure Mathematics.

The Department of Mathematics and Statistics offers the Master of Science (M.S.) in Mathematics with concentrations in Applied Mathematics and Pure Mathematics. The student planning to study pure mathematics is expected to have taken the courses usually included in an undergraduate mathematics major, that is, linear algebra, abstract algebra and advanced calculus. To pursue the concentration in Applied Mathematics, the student should have taken advanced calculus, linear algebra and have some familiarity with differential equations and scientific computing. Faculty may choose to admit promising students lacking an adequate undergraduate background to the graduate program, but such students are required to remove undergraduate deficiencies.

The M.S. in Mathematics is awarded under either:

**Plan I:** 26 credit hours and 6 credit hours thesis (thesis option), or **Plan II:** 32 credit hours (exam option).

There is no minor requirement. The thesis option is best suited for students seeking jobs in industry or government laboratories. At least 18 credit hours (Plan I) or 24 credit hours (Plan II) of the program must be in the department. Knowledge of a foreign language is not required.

Full-time students are expected to pass their M.S. examinations or finish their M.S. thesis no later than two years after admission.

It is possible to earn a master’s degree on a part-time basis at the Los Alamos Center for Graduate Studies. The training office at the Center should be consulted for details.

**Concentration in Applied Mathematics: **

MATH 504, 512, 513, 514, and 561. The following courses are recommended for students under Plan II: MATH 505, 510, and 583. The remaining courses are electives that are approved by the student’s faculty advisor.

**Concentration in Pure Mathematics:**

MATH 510, 520, 535, and 561. Credit must be earned in at least two of the following courses: MATH 511, 521, 536, or 562. The remaining courses are electives that are approved by the student’s faculty advisor.

**NOTE:** MATH 501 and 502 cannot be counted toward credit hours needed for graduate degrees in Mathematics or Statistics.

Concentrations: Applied Mathematics; Pure Mathematics.

The Department of Mathematics and Statistics offers the Doctor of Philosophy (Ph.D.) in Mathematics with concentrations in Applied Mathematics and Pure Mathematics. Knowledge of one foreign language chosen from French, German or Russian is expected. The Ph.D. requires a minimum of 18 credit hours of work beyond the Master’s degree and those credit hours must be in residence at UNM. No more than 6 of these credit hours may be in reading or special topics courses. An additional 18 credit hours of dissertation are required for the Ph.D.

All full-time students are expected to pass the Ph.D. qualifying examinations before the beginning of their fifth semester in the program.

**NOTE:** MATH 501 and 502 cannot be counted toward credit hours needed for graduate degrees in Mathematics or Statistics.

**Concentration in Applied Mathematics: **MATH 505, 510, 583, 584. The student must have credit for attendance in at least four department seminars or colloquia.

**Concentration in Pure Mathematics:**

The student must complete at least two one-year sequences of advanced MATH courses, for example: 532 and 533; 537 and 538; 563 and 565; 572 and 581. Credit for attendance in four departmental seminars or colloquia is required.

For the graduate minor in Mathematics, the M.S. or Ph.D. student must complete at least 12 credit hours of graduate coursework in mathematics approved by both the student’s major department and the Department of Mathematics and Statistics. For Ph.D. students, this minor may consist of more than 25% of coursework required for the degree. Substitutions may be considered with consultation with the Graduate Committee in the Department of Mathematics and Statistics.

**Graduate Advisors**Contact the department for assignment of a faculty graduate advisor.

**Application Deadlines**

Fall semester: | February 15 (with financial aid) |

April 30 (without financial aid) | |

Spring semester: | October 1 |

General requirements for both the M.S. and Ph.D. degrees are given in the *Graduate Program* section of this Catalog. Lists of required courses, the number of credit hours that must be taken in courses labeled STAT and various concentrations can be found in the *Statistics Graduate Handbook* obtained from the Department Web site.

Concentration: Applied Statistics.

The Department of Mathematics and Statistics offers the Master of Science (M.S.) in Statistics with a concentration in Applied Statistics. The M.S. in Statistics student should have taken introductory statistics, linear algebra and a calculus sequence including multivariable calculus. Promising students lacking an adequate undergraduate background may be admitted to the graduate program but are required to remove undergraduate deficiencies.

The M.S. in Statistics is awarded under either:

**Plan I:** 26 credit hours and 6 credit hours of thesis (thesis option), or **Plan II:** 32 credit hours (exam option).

There is no minor requirement. At least 18 credit hours (Plan I) or 24 credit hours (Plan II) of the program must be in the department. Knowledge of a foreign language is not required. Students must take a minimum of 14 elective credit hours for Plan I or 20 elective credit hours for Plan II. These courses are approved by the student’s faculty advisor. Students planning to pursue a Ph.D. should elect Plan II and are encouraged to include MATH 510, 563; and STAT 546 in their program.

Full-time students are expected to pass their M.S. examinations or finish their M.S. thesis no later than two years after admission.

**Required Coursework**

STAT 561, 540, 545, 553.

**NOTE:** MATH 501 and 502 cannot be counted toward credit hours needed for graduate degrees in Mathematics or Statistics.

The Department of Mathematics and Statistics offers the Doctor of Philosophy (Ph.D.) in Statistics. Knowledge of a computer language is required, but knowledge of a foreign language is not. General requirements for the Ph.D. include 18 credit hours of coursework above the Master’s level. No more than 6 of these credit hours may be taken in reading or special topics. 18 credit hours of dissertation is required for the Ph.D. in Statistics.

All full-time students are expected to pass the Ph.D. qualifying examinations before the beginning of their fifth semester in the program.

**Required Coursework**

STAT 546, 547, 556, 557, 577.

**NOTE:** MATH 501 and 502 cannot be counted toward credit hours needed for graduate degrees in Mathematics or Statistics.

For the graduate minor in Statistics, the M.S. or Ph.D. student must complete at least 12 credit hours of graduate coursework in statistics approved by both the student’s major department and the Department of Mathematics and Statistics. For the Ph.D. degree, this minor may consist of more than 25% of the coursework required for the degree. Substitutions may be considered with consultation with the Graduate Committee in the Department of Mathematics and Statistics.

**Undergraduate courses in Mathematics (MATH) may be categorized as Introductory Course, or as Courses for Teachers and Education Students. Courses in these categories are identified in parenthesis at the end of the course description according to the following legend:**

**Introductory Courses (I), Courses for Teachers and Education Students (T).**

**MATH 107. Problems in College Algebra. (1)**

**MATH 110. Problems in Elements of Calculus. (1)**

**MATH 1118. Mathematics for Elementary and Middle School Teachers I. (3)**

**MATH 1130. Survey of Mathematics. (3)**

**MATH 116. Topics in Pre-Calculus Mathematics. (1-6 to a maximum of 12 Δ)**

**MATH 1215X. Intermediate Algebra IA. (1)**

**MATH 1215Y. Intermediate Algebra IB. (1)**

**MATH 1215Z. Intermediate Algebra IC. (1)**

**MATH 1220. College Algebra. (3)**

**MATH 1230. Trigonometry. (3)**

**MATH 1240. Pre-Calculus. (3)**

**MATH 1250. Trigonometry and Pre-Calculus. (5)**

**MATH 1300. Statistical Literacy. (3)**

**MATH 1350. Introduction to Statistics. (3)**

**MATH 1430. Applications of Calculus I. (3)**

**MATH 1440. Applications of Calculus II. (3)**

**MATH 1512. Calculus I. (4)**

**MATH 1522. Calculus II. (4)**

**MATH 1996. Topics. (1-6, no limit Δ)**

**MATH 2115. Math for Middle School Teachers. (3)**

**MATH 2118. Mathematics for Elementary and Middle School Teachers III. (3)**

**MATH 2531. Calculus III. (4)**

**MATH 2996. Topics. (1-6, no limit Δ)**

**MATH 305 / 507. Mathematics from a Historical Perspective. (3)**

**MATH 306. College Geometry. (3)**

**MATH 311. Vector Analysis. (3)**

**MATH **312. Partial Differential Equations for Engineering. (3)**

**MATH **313. Complex Variables. (3)**

**MATH **314. Linear Algebra with Applications. (3)**

**MATH **316. Applied Ordinary Differential Equations. (3)**

**MATH **317. Elementary Combinatorics. (3)**

**MATH **319. Theory of Numbers. (3)**

**MATH **321. Linear Algebra. (3)**

**MATH 322. Modern Algebra I. (3)**

**MATH **327. Introduction to Mathematical Thinking and Discrete Structures. (3)**

**MATH 338. Mathematics for Secondary Teachers. (3)**

**MATH **356. Symbolic Logic. (4)**

**MATH **375. Introduction to Numerical Computing. (3)**

**MATH 391. Advanced Undergraduate Honors Seminar. (1-3 to a maximum of 8 Δ)**

**MATH 393. Topics in Mathematics. (3, no limit Δ)**

**MATH 401 / 501. Advanced Calculus I. (4)**

**MATH 402 / 502. Advanced Calculus II. (3)**

**MATH **412. Nonlinear Dynamics and Chaos. (3)**

**MATH **415. History and Philosophy of Mathematics. (3)**

**MATH *421. Modern Algebra II. (3)**

**MATH *431. Introduction to Topology. (3)**

**MATH **439. Topics in Mathematics. (1-3, no limit Δ)**

**MATH 441. Probability. (3)**

**MATH 462 / 512. Introduction to Ordinary Differential Equations. (3)**

**MATH 463 / 513. Introduction to Partial Differential Equations. (3)**

**MATH 464 / 514. Applied Matrix Theory. (3)**

**MATH *471. Introduction to Scientific Computing. (3)**

**MATH 472 / 572. Fourier Analysis and Wavelets. (3)**

**MATH 499. Individual Study. (1-3 to a maximum of 6 Δ)**

**MATH 501 / 401. Advanced Calculus I. (4)**

**MATH 502 / 402. Advanced Calculus II. (3)**

**MATH 504. Introductory Numerical Analysis: Numerical Linear Algebra. (3)**

**MATH 505. Introductory Numerical Analysis: Approximation and Differential Equations. (3)**

**MATH 507 / 305. Mathematics from a Historical Perspective. (3)**

**MATH 510. Introduction to Analysis I. (3)**

**MATH 511. Introduction to Analysis II. (3)**

**MATH 512 / 462. Introduction to Ordinary Differential Equations. (3)**

**MATH 513 / 463. Introduction to Partial Differential Equations. (3)**

**MATH 514 / 464. Applied Matrix Theory. (3)**

**MATH 519. Selected Topics in Algebra and Number Theory. (3, no limit Δ)**

**MATH 520. Abstract Algebra I. (3)**

**MATH 521. Abstract Algebra II. (3)**

**MATH 530. Commutative Algebra. (3)**

**MATH 531. Algebraic Geometry. (3)**

**MATH 532. Algebraic Topology I. (3)**

**MATH 533. Algebraic Topology II. (3)**

**MATH 535. Foundations of Topology. (3)**

**MATH 536. Introduction to Differentiable Manifolds. (3)**

**MATH 537. Riemannian Geometry I. (3)**

**MATH 538. Riemannian Geometry II. (3)**

**MATH 539. Selected Topics in Geometry and Topology. (3, no limit Δ)**

**MATH 540. Stochastic Processes with Applications. (3)**

**MATH 549. Selected Topics in Probability Theory. (3, no limit Δ)**

**MATH 551. Problems. (1-3, no limit Δ)**

**MATH 557. Selected Topics in Numerical Analysis. (3, no limit Δ)**

**MATH 561. Functions of a Complex Variable I. (3)**

**MATH 562. Functions of a Complex Variable II. (3)**

**MATH 563. Analysis III. (3)**

**MATH 565. Analysis IV. (3)**

**MATH 569. Selected Topics in Analysis. (3, no limit Δ)**

**MATH 570. Singular Perturbations. (3)**

**MATH 572 / 472. Fourier Analysis and Wavelets. (3)**

**MATH 576. Numerical Linear Algebra. (3)**

**MATH 577. Numerical Ordinary Differential Equations. (3)**

**MATH 578. Numerical Partial Differential Equations. (3)**

**MATH 579. Selected Topics in Applied Mathematics. (3, no limit Δ)**

**MATH 581. Functional Analysis I. (3)**

**MATH 583. Methods of Applied Mathematics I. (3)**

**MATH 584. Methods of Applied Mathematics II. (3)**

**MATH 598. Practicum. (1-6 to a maximum of 6 Δ)**

**MATH 599. Master's Thesis. (1-6, no limit Δ)**

**MATH 605. Graduate Colloquium. (1, may be repeated three times Δ)**

**MATH 639. Seminar in Algebra and Geometry. (1-3, no limit Δ)**

**MATH 649. Seminar in Probability and Statistics. (1-3, no limit Δ)**

**MATH 650. Reading and Research. (1-6 to a maximum of 12 Δ)**

**MATH 669. Seminar in Analysis. (1-3, no limit Δ)**

**MATH 679. Seminar in Applied Mathematics. (1-3, no limit Δ)**

**MATH 699. Dissertation. (3-12, no limit Δ)**

**STAT 279. Topics in Introductory Statistics. (1-3 to a maximum of 3 Δ)**

**STAT **345. Elements of Mathematical Statistics and Probability Theory. (3)**

**STAT 427 / 527. Advanced Data Analysis I. (3)**

**STAT 428 / 528. Advanced Data Analysis II. (3)**

**STAT 434 / 534. Contingency Tables and Dependence Structures. (3)**

**STAT 440 / 540. Regression Analysis. (3)**

**STAT 445 / 545. Analysis of Variance and Experimental Design. (3)**

**STAT 453 / 553. Statistical Inference with Applications. (3)**

**STAT 461 / 561. Probability. (3)**

**STAT 470 / 570. Industrial Statistics. (3)**

**STAT 472 / 572. Sampling Theory and Practice. (3)**

**STAT 474 / 574. Biostatistical Methods: Survival Analysis and Logistic Regression. (3)**

**STAT 476 / 576. Multivariate Analysis. (3)**

**STAT 477 / 577. Introduction to Bayesian Modeling. (3)**

**STAT 479. Topics in Statistics. (3, no limit Δ)**

**STAT 481 / 581. Introduction to Time Series Analysis. (3)**

**STAT 495. Individual Study. (1-3 to a maximum of 6 Δ)**

**STAT 520. Topics in Interdisciplinary Biological and Biomedical Sciences. (3, no limit Δ)**

**STAT 527 / 427. Advanced Data Analysis I. (3)**

**STAT 528 / 428. Advanced Data Analysis II. (3)**

**STAT 534 / 434. Contingency Tables and Dependence Structures. (3)**

**STAT 540 / 440. Regression Analysis. (3)**

**STAT 545 / 445. Analysis of Variance and Experimental Design. (3)**

**STAT 546. Theory of Linear Models. (3)**

**STAT 547. Multivariate Analysis and Advanced Linear Models. (3)**

**STAT 553 / 453. Statistical Inference with Applications. (3)**

**STAT 556. Advanced Statistical Inference I. (3)**

**STAT 557. Advanced Statistical Inference II. (3)**

**STAT 561 / 461. Probability. (3)**

**STAT 565. Stochastic Processes with Applications. (3)**

**STAT 569. Selected Topics in Probability Theory. (3, no limit Δ)**

**STAT 570 / 470. Industrial Statistics. (3)**

**STAT 572 / 472. Sampling Theory and Practice. (3)**

**STAT 574 / 474. Biostatistical Methods: Survival Analysis and Logistic Regression. (3)**

**STAT 576 / 476. Multivariate Analysis. (3)**

**STAT 577 / 477. Introduction to Bayesian Modeling. (3)**

**STAT 579. Selected Topics in Statistics. (3, no limit Δ)**

**STAT 581 / 481. Introduction to Time Series Analysis. (3)**

**STAT 586. Nonparametric Curve Estimation and Image Reconstruction. (3)**

**STAT 590. Statistical Computing. (3)**

**STAT 595. Problems. (1-3, no limit Δ)**

**STAT 599. Master's Thesis. (1-6, no limit Δ)**

**STAT 605. Graduate Colloquium. (1, may be repeated three times Δ)**

**STAT 649. Seminar in Probability and Statistics. (1-3, no limit Δ)**

**STAT 650. Reading and Research. (1-6 to a maximum of 12 Δ)**

**STAT 699. Dissertation. (3-12, no limit Δ)**

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