Graduate Program

Mathematics Graduate Program

See separate listings under Statistics for additional degree concentrations.

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:   November 1
 

Mathematics Degrees Offered

M.S. in Mathematics

Concentrations: Pure Mathematics, Applied Mathematics.

The Master of Science in Mathematics degree is offered by the Department of Mathematics and Statistics in the concentration of pure mathematics and applied 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 program 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 Master of Science in Mathematics degree is awarded under either:

Plan I: 26 credit  hours and 6 credit hours thesis (thesis option), or
Plan II: 32 credit hours (non-thesis 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. Courses required for a concentration in Pure Mathematics include: 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. Courses required for a concentration in Applied Mathematics  are: 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.

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.

Ph.D. in Mathematics

Concentrations: Pure Mathematics, Applied Mathematics.

The Doctor of Philosophy in Mathematics degree is offered by the department with concentrations in the areas of pure mathematics and applied mathematics. Knowledge of one foreign language chosen from French, German or Russian is expected. Students must pass the Ph.D. qualifying examinations no later than one year after admission. 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. The concentration program of study in Pure Mathematics must complete at least two one-year sequences of advanced courses, for example: MATH 563 and 581;MATH 530 and 531; MATH 532 and 533; MATH 536 and 537; MATH 572 and 565; and/or MATH 519 and 539. Credit for attendance in four departmental seminars or colloquia is required for the concentration in Pure Mathematics, The program of study for the concentration of Applied Mathematics must complete: MATH 505, MATH 510, MATH 583, MATH 584, and student must have credit for attendance in at least four department seminars or colloquia.

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

Nanoscience and Microsystems Engineering M.S. & Ph.D. Degree Program

This department participates in the interdisciplinary Nanoscience and Microsystems Engineering program; for more information, see the Graduate Interdisciplinary Studies section of this catalog.

Minor Study

Graduate Minor in Mathematics (M.S.)

For a graduate minor at least 9 credit hours of work in mathematics or statistics approved by both the student’s major department and the Department of Mathematics and Statistics are required. A student may receive a Master of Arts in Education with supporting courses in mathematics or statistics.

Students desiring to take a course who do not have the indicated prerequisite should consult with the course instructor.

Graduate Minor in Applied Mathematics (Ph.D.)

For a graduate minor for the Ph.D. student at least 9 credit hours of work in mathematics to include Math 512 and 513 and an elective at the Math 500 level or above, to exclude colloquia or seminars and approved by both the student’s major department and the Department of Mathematics and Statistics are required. This minor may not be more than 25% of course work required for the Ph.D. degree. The minor form must be submitted to OGS with the Program of Studies.

Students desiring to take a course who do not have the indicated prerequisite should consult with the course instructor.

Graduate Minor in Pure Mathematics (Ph.D.)

For a graduate minor for the Ph.D. student at least 9 credit hours of work in mathematics to include Math 510 and 511 and an elective at the Math 500 level or above, to exclude colloquia or seminars and approved by both the students major department and the Department of Mathematics and Statistics are required. This minor may not be more than 25% of course work required for the Ph.D. degree. The minor form must be submitted to OGS with the Program of Studies.


Statistics Graduate Program

See separate listings under Mathematics for additional degree concentrations.


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:     November 1

  
Statistics Degrees Offered

M.S. in Statistics

Concentration: Applied Statistics.

The Master of Science degree 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 Master of Science in Statistics degree is awarded under either:

Plan I: 26 credit  hours and 6 credit hours of thesis (thesis option), or
Plan II: 32 credit hours (non-thesis 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. The following courses are required for all students: STAT 561, 540, 545, and 553. 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.

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

Ph.D. in Statistics

The Doctor of Philosophy in Statistics degree is offered by the Statistics Program. 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 course work 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. Students who enter the Ph.D. program with a Master’s degree are expected to take the Ph.D. qualifying examination as soon as possible and no later than one year after admission. The following courses are required for the Ph.D. students: STAT 546, 556, 557, and 567.

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

General requirements for both the M.S. and Ph.D. degrees are given in the earlier pages of the 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 Handbook for Statistics Graduate Students obtained from the Statistics Web page.

Minor Study

Graduate Minor in Statistics (M.A.)

For a graduate minor at least 9 credit hours of work in statistics approved by both the student’s major department and the Statistics Program faculty are required (for a Masters using Plan II, 12 credit hours are required). Students desiring to take a course who do not have the indicated prerequisites should consult with the course instructor.

NOTE: STAT 538 and 539 cannot be counted toward the credit  hours needed for graduate degrees in Mathematics and Statistics.

Graduate Minor in Statistics (Ph.D.)

For a graduate minor for the Ph.D. student at least 9 credit hours of work in statistics courses including STAT 540 and 545 and one elective at the 500 level or above, to exclude colloquia or seminars and approved by both the student’s major department and the Department of Mathematics and Statistics are required. This minor may not be more than 25% of course work required for the Ph.D. degree. The minor form must be submitted to OGS with Program of Studies.


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).


Courses

MATH 101. Intermediate Algebra Part 1. (1)



MATH 102. Intermediate Algebra Part 2. (1)



MATH 103. Intermediate Algebra Part 3. (1)



MATH 106. Problems in Intermediate Algebra. (1)



MATH 107. Problems in College Algebra. (1)



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



MATH 111. Mathematics for Elementary and Middle School Teachers I. (3)



MATH 112. Mathematics for Elementary and Middle School Teachers II. (3)



MATH 116. Topics in Pre-calculus Mathematics. (3)



MATH 121. College Algebra. (3)



MATH 123. Trigonometry. (3)



MATH 129. A Survey of Mathematics. (3)



MATH 150. Pre-Calculus Mathematics. (3)



MATH 162. Calculus I. (4)



MATH 163. Calculus II. (4)



MATH 180. Elements of Calculus I. (3)



MATH 181. Elements of Calculus II. (3)



MATH 215. Mathematics for Elementary and Middle School Teachers III. (3)



MATH 264. Calculus III. (4)



MATH 275. Honors Calculus. (3)



MATH 301 / 503. Calculus for Teachers. (3)



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



MATH 306 / 506. 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 **318. Graph Theory. (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 / 542. Mathematics for Secondary Teachers. (3)



MATH 339 / 543. Topics in Mathematics for Elementary and Middle School Teachers. (1-3, no limit ?)



MATH 350 / 550. Topics in Mathematics for Secondary Teachers. (1-3, no limit ?)



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 ?)



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



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 **422. Modern Algebra for Engineers. (3)



MATH *431 / 535. Introduction to Topology. (3)



MATH 434 / 534. Introduction to Differential Geometry. (3)



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



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 *466. Mathematical Methods in Science and Engineering. (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 ?)



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



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



MATH 503 / 301. Calculus for Teachers. (3)



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



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



MATH 506 / 306. College Geometry. (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 Number Theory. (3, no limit ?)



MATH 520. Abstract Algebra I. (3)



MATH 521. Abstract Algebra II. (3)



MATH 530. Algebraic Geometry I. (3)



MATH 531. Algebraic Geometry II. (3)



MATH 532. Algebraic Topology I. (3)



MATH 533. Algebraic Topology II. (3)



MATH 534 / 434. Introduction to Differential Geometry. (3)



MATH 535 / 431. 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 ?)



MATH 540. Stochastic Processes with Applications. (3)



MATH 541. Advanced Probability. (3)



MATH 542 / 338. Mathematics for Secondary Teachers. (3)



MATH 543 / 339. Topics in Mathematics for Elementary and Middle School Teachers. (1-3, no limit ?)



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



MATH 350 / 550. Topics in Mathematics for Secondary Teachers. (1-3, no limit ?)



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



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



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



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



MATH 563. Measure Theory. (3)



MATH 565. Harmonic Analysis. (3)



MATH 568. Stochastic Differential Equations. (3)



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



MATH 570. Singular Perturbations. (3)



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



MATH 573. Partial Differential Equations. (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 ?)



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 ?)



MATH 599. Master?s Thesis. (1-6, no limit ?)



MATH 605. Graduate Colloquium. (1 to a maximum of 4 ?)



MATH 639. Seminar in Geometry and Topology. (1-3, no limit ?)



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



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



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



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



MATH 689. Seminar in Functional Analysis. (1-3)



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



STAT 145. Introduction to Statistics. (3)



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



STAT 425 / 525. SAS? Programming. (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 ?)



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



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



STAT 520. Topics in Interdisciplinary Biological and Biomedical Sciences. (3, unlimited ?)



STAT 524. Collaborative Interdiciplinary Teaching. (3)



STAT 525 / 425. SAS? Programming. (3)



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 567. Advanced Probability. (3)



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



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 ?)



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



STAT 585. Nonparametric and Robust Methods. (3)



STAT 586. Nonparametric and Robust Methods. (3)



STAT 590. Statistical Computing. (3)



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



STAT 599. Master?s Thesis. (1-6, no limit ?)



STAT 605. Graduate Colloquium. (1 to a maximum of 4 ?)



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



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



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



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