Mathematics Graduate Student Handbook
Academic Year 2008-2009

Welcome
Welcome to the Department of Mathematical Sciences at NMSU and thank you for choosing our graduate program. Please, take time to read this handbook carefully and to plan well in advance each step of your graduate education. The Graduate Catalog is an essential document that contains official university rules. You should read this. The Graduate Student Handbook has helpful information about the university and local area. The Handbook for Teaching Assistants has tips about preparing for teaching courses. The NMSU Student Handbook prepared by the Association of Students at NMSU has general university rules and university code of conduct. Finally, the department's Manual for the Staff has policies on using telephones, the copy machine, and teaching. Please, contact us as often as you need. Best wishes to you from the Mathematics Graduate Studies Committee.
Purpose of this Handbook
The purpose of this handbook is to introduce you to the department, to describe in some detail your course of study, to highlight certain items in the Graduate Catalog, and to guide you in preparing for life after NMSU. Read this handbook, the parts of the Graduate Catalog that pertain to your program, and ask if you have questions. The most important principles in this department are fairness and common sense. If you have a good reason for seeking an exception to some policy, contact your advisor or a member of the Graduate Studies Committee.

Advising
Before classes start for your first semester, you will meet with an advisor to form a tentative plan of study. For Master's students, this plan should cover your whole program of study. For Ph.D. students, this plan should cover up to, and including, your comprehensive examinations. The advisor worksheets we use for this purpose are found at the end of this handbook. This plan can be changed at any time, and we expect most students will change their plan. But it is better to have a plan that may change, than have no plan at all.
Your first advising will be done either in conjunction with a member of the Graduate Studies Committee or with the advisor you have been assigned. Thereafter, your advisor will be responsible for helping you with your plan of study. You should meet with your advisor on a regular basis to let them know how things are going (at least once a month). Each semester you and your advisor will update your plan of study. Each incoming student is assigned an advisor. You may select another advisor at any time. You should make sure the advisor you select is someone you feel comfortable with, and who agrees to be your advisor. Forms for changing advisor are available with the graduate secretary in the Math department office.
For Master's student writing a thesis, and Ph.D. students at the research portion of their studies, the advisor should be the faculty member directing the thesis. Choosing an advisor for this role is vital, and it may take several semesters before you can make such a choice. The classes you take, seminars you attend, and conversations you have outside school may all help in this important choice.

TAs and other finances
New TAs are typically asked to assist in the Mathematics Success Center, and more advanced students teach up to two sections of courses. The typical workload for a full TA is 16 hours per week.
TAs are required to enroll and maintain enrollment in at least 9 credits (3 courses) of graduate work per semester, unless prior approval of the Graduate Dean is obtained. Students with TAs from the Math department require approval of the Graduate Studies Committee to take more than 4 credits of coursework outside our department in a given semester. Other rules pertain to maintaining a TA, include keeping a 3.0 average in graduate work. See the Graduate Catalog for more details.
For 2008-2009 the stipends for full-time 9 month TAs are as follows:

Level I $16,600

Level II $16,800

Level III $17,000

Partial summer support is also available.
The Graduate School places limits on the number of years a student may receive state support (http://gradschool.nmsu.edu/publications/GA_Guidelines/). As we do not normally admit student to the Ph.D. program without a Master's degree, these limits are as follows:

MASTERS 2 years, may petition for a 5th semester.

PHD 4 years, may petition for a 5th year.

A student entering here for a Master's, then continuing for a Ph.D. receives 5 years of support and may petition for a 6th. Students entering our Ph.D. program may, under some circumstances, receive a Master's degree as part of their Ph.D. studies, but this does not extend the funding limit.
These funding limits make it imperative that you make a proper plan for the completion of your degree.
Information about other scholarships and fellowships can be found at http://www.gradschool.nmsu.edu and for minority students through Dr. Dave Finston <dfinston@nmsu.edu> in our department.

English Requirements for Graduate Assistants
International graduate assistants need to take the ITA screening upon coming to NMSU. Depending on the screening, they may be required to take COMM 485 and/or SPCD 470. If so, they must take COMM 485 before starting their second year and SPCD 470 before finishing their second year in order to keep their assistantship.

Becoming a New Mexico Resident
This may seem like a silly thing to mention near the beginning of the handbook for mathematics graduate students, but it is actually very important for the purpose of deciding who may pay resident tuition and who will have to pay nonresident tuition.
For all the details on becoming eligible for resident tuition inquire at the Registrar's office in the Educational Services Building immediately upon your arrival in Las Cruces. The website, http://www.gradschool.nmsu.edu/publications/GA_Guidelines/ is also very helpful. Promptness in attention to the relevant matters is important, as the rule-of-thumb is that a domestic student becomes a New Mexico resident after having lived in the state for twelve months. Among the actions one takes to establish oneself in New Mexico are transferring motor vehicle registrations to New Mexico, obtaining a New Mexico driver's license, and registering to vote in the City Clerk's Office. The City Clerk and the Department of Motor Vehicles provide receipts, which should be kept. Don't forget to hold onto your rent receipts, too. Students younger than 23 years of age should also make sure that their parents no longer declare them as dependents on income tax forms. It goes without saying that new students will file income tax returns with the State of New Mexico as part-year residents.

Facilities
The department is housed in two adjacent buildings, Science Hall (SH), built in 1988, and Walden Hall (WH), built in 1966 and renovated in 1987. All graduate teaching assistants have offices in Walden Hall.
The science and mathematics library collections are housed in Branson Library, across the street from Science Hall. In addition, a mathematics reading room is located in SH 226, where the recent mathematics publications as well as a collection of mathematics texts are housed.
During the departmental orientation you will have your picture taken for our Rogue Gallery. You will also complete the paperwork to obtain an account on the department's computers. The computer labs are SH 118, 221, and 222. Depending on availability, computers are also provided in TA's offices. If you have questions about your computer account, please see Maria Sanchez in SH 236, or talk to our Computer Operations Manager, Mark Leisher, SH 174.
The department buildings have classrooms, a colloquium room (SH 107), seminar rooms, and a lounge area (SH 234) with a small kitchen.
If you are interested in coffee, ask Maria Sanchez about joining the coffee club.
Refreshments are served in SH 234 at 3:30 pm, before every colloquium talk. Don't miss them!

Minor in Mathematics
- Master's students
  According to the Graduate Catalog, any candidate for a Master's degree may declare up to two minors in addition to the major area of study. All minors must be approved by the minor department head and the dean of the Graduate School and normally consist of a minimum of eight credits. Upon request of the student, advisor, minor department head, and graduate dean, a minor may be recorded by the registrar on the permanent record of the student.
  Course requirements for a minor in Mathematics. A student should take at least three mathematics or statistics courses numbered 501 or higher which are approved for mathematics graduate students, at least one of which should be numbered 525 or above. A Master's degree student interested in a minor in mathematics should obtain an advisor in the Department of Mathematical Sciences before the Application for Candidacy papers are filed and at least two semesters before the student plans to obtain the degree. This faculty member will work with the advisor in the major department to arrange an appropriate program of mathematics and/or statistics courses and who will represent the Department of Mathematical Sciences at the final examination. The mathematics advisor will prepare a written explanation of the student's mathematics courses and forward it to the Head of the Department of Mathematical Sciences for approval.
- Ph.D. students.
  According to the Graduate Catalog, “any doctoral candidate may declare up to two minors in addition to the major area of study. All minors must be approved by the minor department head and the dean of the Graduate school and normally consist of twelve credits. Demonstration of competency in the minor area will be required at both comprehensive and final examinations.”
  Course requirements for a minor in Mathematics. A student should take at least four mathematics or statistics courses numbered 501 or higher which are approved for mathematics graduate students, at least two of which should be numbered 525 or above. A Ph.D. student interested in a minor in mathematics should obtain an advisor in the Department of Mathematical Sciences at least one semester prior to taking the oral comprehensive examination. This faculty member will work with the major advisor to arrange an appropriate program of mathematics and/or statistics courses and who will represent the Department of Mathematical Sciences at the comprehensive and final examinations. The student and the student's major and mathematics advisors should agree on a program of mathematics and statistics courses, and submit a copy of the program to the Head of the Department of Mathematical Sciences for approval.

Master of Science Degree
A student's program of study for the Master's degree should be a coordinated program that emphasizes one area of study or that prepares a student for further graduate work. Possible areas of study in the department are pure mathematics, applied mathematics, statistics, and mathematics education. The program takes approximately two years to complete.

Mathematics Requirements for the Master's Degree
- Required courses
  Math 525, 527, 528, 581. These must be completed or transferred.
- Additional courses
  The Graduate School requires at least 30 credits of graduate coursework. At least 24 of these credits must be in Mathematics or Statistics, with at least 15 credits being above the 529 level. At most, 6 credits of individual study courses such as Math 540 or Stat 540 may be used. Math 459 may not be used for these requirements.
- Master's final oral examination.
Students may petition the Graduate Studies Committee to replace as core courses either Math 525 or 581 with Math 582, and to replace one or both of Math 527, 528 with Math 593, 594.

Master's Thesis
A Master's thesis may be written as part of a Master's degree, but is not required. If the thesis option is chosen, the student takes 6 credits of Math 599, the course for Master's level research. These 6 credits may be applied toward the course requirements for the Master's degree.
There are many opinions about the role of a Master's thesis for a mathematics student. For a student planning to enter a non-academic job after their Master's, a thesis in a work related topic and conference presentation help fill out a resume, but require substantial effort and may limit the variety of courses taken. For a student planning to continue for a Ph.D., a Master's thesis is excellent preparation for a Ph.D. thesis, but may delay preparation for Ph.D. comprehensive exams.
A Master's thesis can be original research, a survey of the literature of a topic, or a historical development of a mathematical idea. It does not have to be a publishable result, but should be suitable for a conference presentation.
If you are interested in the thesis option, you should discuss with your potential thesis advisor whether it is a good choice for you.
Advancement to Candidacy for Master's Degree
Graduate school regulations call for the student to file advancement to candidacy papers (“the program of study”) for the Master's degree before completion of 12 credits of work in the department. If a thesis is to be written, a tentative title is to be given at this time.

The Master's Final Exam
The final Master's examination is an oral examination administered by the student's committee. The committee should consist of at least four faculty, three members from the mathematics department and one member from a related field of study (Dean's representative), which the student or advisor must find (Graduate School no longer appoints the Dean's representatives effective Spring 2007). If the student has a minor area of study, then either the Dean's representative or an additional member must come from the minor department. The examination committee is approved by the Graduate Studies Committee, by the head of the department, and by the Dean of the Graduate School. The examination is restricted to course work presented in the student's program of studies. You will be evaluated on your knowledge of the core courses for the Master's as well as your ability to construct and write mathematical definitions and arguments. When a Master's thesis has been written, the Master's final exam will be in part an oral defense of the thesis and in part a general examination of the candidate's course work.
The Master's final examination must be completed at least 10 days prior to the end of the semester in which the candidate wishes to receive the degree. It is prudent to start organizing an examination committee early in the semester, as it takes time to round up faculty and find a time (allow about two hours for the exam) when everybody can meet and more time for the Dean's office to handle the paperwork. Students should note that the Master's oral may serve as the Ph.D. qualifying examination for Master's students continuing with the Ph.D. program in our department. See the Graduate Catalog for more information.
The comments given later in this handbook on the oral comprehensive examination taken by Ph.D. students will give you tips on how to make a Master's oral exam go smoothly.

Ph.D. Degree
The Ph.D. program has two phases, one consisting of coursework and exams, the second primarily of research for the dissertation (although some courses are taken then as well). It is important to progress to the research phase of the Ph.D. in a timely manner to produce a high quality dissertation.
Requirements for the Ph.D.:
- Qualifying examination — an oral examination on current coursework taken toward the end of the first semester.
  Every student admitted to the Ph.D. program must complete a Ph.D. oral qualifying examination. Students who complete their mathematics Master's degree at NMSU may request at the time of applying for their Master's oral final examination that the Master's examination also fulfill the Ph.D. qualifying examination requirement. In all other cases, towards the end of the student's first semester in the Ph.D. program, the student and his/her advisor will convene an oral examination with three examiners, the examiners being the advisor and some of the student's current or past instructors. As a result of the qualifying examination, the department will take one of the following actions: (1) admit the student to further work toward the Ph.D.; (2) recommend that the student's program be limited to the Master's degree; (3) recommend a reevaluation of the student's progress after the lapse of one semester; or (4) recommend a discontinuation of the student's graduate program in mathematics.
- Written Comprehensive examinations — 3 examinations in different areas of mathematics subject to the conditions below.
- Course Requirements — At least 12 Math or Stat courses above the 529 level subject to the requirements below. Some of this coursework may be done before your comprehensive exams, some may be done after.
  A Ph.D. student must take 12 courses numbered above Math/Stat 529, not counting the reading and research courses numbered Math/Stat 540, Math/Stat 598, Math 599, Math 600, and Math 700. Among these 12 courses must be at least four of the sequences leading to written comprehensive exams, including at least three of the sequences in algebra (Math 581-2), complex analysis (Math 591-2) real analysis (Math 593-4), and topology (Math 541-2). For a Master's degree student who continues to the Ph.D. program, the student must take at least 4 of the 12 required courses after enrolling as a Ph.D. student.
  It is expected that the candidate will take a considerable number of courses with the goal of obtaining familiarity with the basics of several areas of mathematics. We now discuss some reasons for this.
  Familiarity with broad areas of mathematics is vital for your future career. Research areas grow and change often incorporating results and methods from different fields. Professors must teach a variety of courses and guide students with varied interests. You should try to take at least one non-thesis math course each semester, even if the required courses are completed.
- Foreign Language Exam
  The department requires that each Ph.D. student pass a basic mathematical reading knowledge exam in a language, other than English, relevant to the student's research interests. This exam is coordinated by the student's advisor and consists of the open-dictionary written translation into English of a mathematical text of interest to the student. Fulfillment of this requirement is needed in order to be admitted to the oral part of the Ph.D. comprehensive examination.
- Oral Comprehensive examination.
- Write Thesis.
- Final Oral Thesis examination.

Syllabi for Written Comprehensive Examinations
As mentioned in the overview of the comprehensive examination, the department uses the written examinations to ensure that Ph.D. recipients are acquainted with the terminology and methods of a broad section of mathematics. Exam questions reflect fundamental aspects of each subject, as listed in the syllabi below.
- Algebra
  - Groups: definition, permutations, Lagrange's theorem, homomorphisms, quotient groups, group actions, fundamental theorem of finite abelian groups, Sylow theorems, solvable groups.
  - Commutative Rings: polynomial rings, homomorphisms, principal ideal domains, quotient rings, non-commutative rings, prime and maximal ideals, Noetherian rings, unique factorization domains.
  - Modules: free, projective, injective, tensor products, Hom, localization.
  - Fields: field extensions, splitting fields, Galois theory, separable polynomials, finite fields, solvability of polynomials, ruler and compass constructions.
  - Linear Algebra: vector spaces, determinants, eigenvalues and eigenvectors, Jordan and rational canonical forms, Cayley-Hamilton theorem.
  - Basic Courses: 525, 581, 582.
  - References:
    - “Introduction to Abstract Algebra” by E. A. Walker
    - “Topics in Algebra” by I. Herstein
    - “Algebra” by T. Hungerford
    - “Field and Galois Theory” by P. Morandi
    - “Introduction to Commutative Algebra” by M.F. Atiyah and I.G. Macdonald
    - “Advanced modern algebra” by J. Rotman
    - “Linear Algebra” by K. Hoffman and R. Kunze
    - “A first course in abstract algebra” by J. Fraleigh
- Complex Analysis
  - Complex Differentiation and Integration: derivatives, antiderivatives, Cauchy-Goursat Theorem, Morera's theorem, isolated singularities and residues, Cauchy's integral formula, Rouché's theorem.
  - Properties of Analytic Functions: identity theorem, maximum modulus principle Liouville's theorem, mapping properties of analytic functions.
  - Sequences of Analytic Functions: preservation of properties under normal convergence.
  - Series and Product Representations: Taylor and Laurent expansions, classification of singularities, Blaschke and Weierstrass products, Mittag-Leffler's theorem.
  - Mapping in the Extended Plane: conformality, the Riemannian sphere, Möbius transformations, chordal and hyperbolic metrics, Riemann mapping theorem.
  - Analytic Continuation: connectivity and multiple-valued functions, continuation by rearrangement of series, singularities.
  - Basic Courses: 517, 591, 592.
  - References:
    - “Complex Analysis” by T. W. Gamelin
    - “Complex Analysis” by L. V. Ahlfors
    - “Functions of One Complex Variable” by J. B. Conway
    - “Theory of Functions of a Complex Variable” by I. A. Markushevich
    - “Real and Complex Analysis” by W. Rudin
    - “Complex Analysis” by Sansone and Gerretson
    - “Classical Complex Analysis” by Liang-Shin Hahn and Bernard Epstein
    - “Complex Analysis” by R. Nevanlinna and V. Paatero
    - “Analytic Function Theory” by E. Hille
- Differential Equations
  - Linear Systems Eigenvalues and eigenvectors, primary decomposition, Jordan form, matrix exponentials and their computations, qualitiative theory of linear equations.
  - Fundamental theory for ordinary differential equations: Existence and uniqueness of solutions using the Picard method, smooth dependence on initial conditions and parameters, maximal intervals of definition, flows.
  - Dynamical systems: Equilibria and their stability. Stable and unstable manifold theorem. Applications of the center manifold theorem. Basic bifurcations: saddle-node, pitchfork and Hopf.
  - Basic notions for partial differential equations: Separation of variables, Fourier series solutions, characteristic forms, characteristic manifolds, the Cauchy problem, the Cauchy- Kovalevski theorem.
  - Elliptic partial differential equations: Laplace's equation, harmonic functions, Green's functions, Poisson's equation, Newtonian potentials, Dirichlet and Neumann problems.
  - Parabolic differential equations: Heat equation, existence, uniqueness and regularity of solutions, heat kernels, energy estimates, the maximum principle, initial boundary problems.
  - Hyperbolic differential equations: Wave equation; D'Alembert's formula; domains of dependence, influence and propagation; method of spherical means; method of descent.
  - Basic Courses: Math 472, Math 531, Math 532.
  - References:
    - “Differential Equations and Dynamical Systems” by Lawrence Perko
    - “Differential Equations and Dynamical Systems” by Lawrence Perko
    - “Dynamical Systems and Linear Algebra” by M. Hirsch and S. Smale (Academic Press 1974)
    - “Applications of center manifold theory” by J. Carr (Springer-Verlag, 1981)
    - “Methods of bifurcation theory” by S. N. Chow and J. Hale (Springer-Verlag, 1982)
    - “Partial Differential Equations” by F. John
    - “Partial Differential Equations” by L.C. Evans
    - “Introduction to Partial Differential Equations” by G.B. Folland
- Logic and Foundations
  - Lattices: closure systems, Galois connections, Boolean algebras, distributive lattices, Heyting algebras, modular lattices.
  - Logic: classical, intuitionistic, and modal propositional logics. Predicate calculus; the completeness and compactness theorems, Lowenheim-Skolem theorems, elementary equivalence, ultraproducts.
  - Universal Algebra: isomorphism theorems, subdirect products, varieties, free algebras, Birkhoff theorems, Jónsson's lemma.
  - Set Theory: axioms of ZF set theory, ordinals, cardinals, transfinite induction and recursion, axiom of choice.
  - Basic Courses: 504, 506, 557, 585.
  - References:
    - “A course in Universal Algebra” by S. Burris and H. P. Sankappanavar
    - “Mathematical Logic” by H. D. Ebbinghaus
    - “Mathematical Logic” by H. D. Ebbinghaus
    - “Mathematical Logic” by J. Shoenfield
    - “Algebraic Theory of Lattices” by P. Crawley and R. P. Dilworth
    - “Lattice Theory” by G. Gratzer
    - “Introduction to Set Theory” by K. Hrbacek and T. Jech
    - “Set Theory: An Introduction to Independence Proofs” by K. Kunen.
- Probability and Statistics
  - Probability: probability spaces, conditional expectations, random variables/vectors and
  - Limit Theorems: law of large numbers, central limit theorem, law of iterated logarithm, weak convergence of probability measures.
  - Statistics: multivariate normal distributions, samples from the multivariate normal distributions, Wishart and multivariate Beta distributions.
  - Estimations and Hypothesis Testing: Estimation in multivariate normal distributions, generalized T2-statistic, distribution of sample covariance matrix and sample generalized variance, testing the general hypotheses.
  - Basic Courses: Stat 562 and Stat 571.
  - References:
    - “A first course in Probability and Statistics” by H. Nguyen and T. Wang
    - “Probability: Theory and Examples” by Richard Durrett
    - “Fundamentals of Probability” by Saeed Ghahramani
    - “An Introduction to Multivariate Statistical Analysis” by T. W. Anderson
    - “Aspects of Multivariate Statistical Theory” by Robb J. Muirhead
- Real Analysis
  - Measure Theory: outer measures and extensions, measurable sets, and measurable functions, Hahn and Jordan decomposition theorems.
  - Abstract Lebesgue Integral: major convergence theorems such as the dominated convergence theorem, Fubini's theorem.
  - Differentiation: absolutely continuous functions and measures, Radon-Nikodym theorem.
  - Functional Analysis: Hahn-Banach theorem, uniform boundedness principle, elements of the theory of Banach spaces and Hilbert spaces.
  - Function Spaces: Lp spaces and their duals, Riesz-Fischer theorem, Stone-Weierstrass theorem, Riesz representation theorem for positive and continuous linear functionals.
  - Basic Courses: 527, 528, 593, 594.
  - References:
    - “Introduction to Real Analysis” by J. DePree and C. Swartz
    - “Principles of Mathematical Analysis” by W. Rudin
    - “Real Analysis” by H. L. Royden
    - “Real and Abstract Analysis” by E. Hewitt and K. Stromberg
    - “Principles of Real Analysis” by C. Aliprantis and J. Burkinshaw
    - “Lebesgue Integration on Euclidean Space” by F. Jones
    - “General Theory of Functions and Integration” by A. E. Taylor
    - “Real and Complex Analysis” by W. Rudin and Measure and Integration by R. Wheeden and A. Zygmund
    - “Real and Complex Analysis” by W. Rudin and Measure and Integration by R. Wheeden and A. Zygmund
    - “Integration and Function Spaces” by C. Swartz
- Topology
  - Topological Spaces: separation, covering, and countability axioms; connectedness, compactness, Tychonoff's theorem, Tietze extension theorem, embedding and metrization theorems, function spaces, topological groups.
  - Homotopy Theory: homotopy equivalence, fundamental group, Seifert-van Kampen theorem, covering spaces, higher homotopy groups.
  - Homology Theory: singular homology groups, Brouwer's fixed point theorem, invariance of domain, Jordan-Brouwer separation theorem, homology of cell complexes.
  - Manifolds: classification of surfaces, real and complex projective spaces, lens spaces, matrix groups.
  - Basic Courses: 541, 542.
  - References:
    - “Topology” by J. Dugundji
    - “Topology” by J. Munkres
    - “A Basic Course in Algebraic Topology” by W. S. Massey
    - “Homology Theory” by J. Vick
    - “Topology” by H. Schubert
    - “Topology and Geometry” by G. Bredon
    - “A First Course in Algebraic Topology” by C. Kosniowski
    - “Introduction to topology and real analysis” by G. Simmons
Most of the references are available either in the Branson Library or in the mathematics reading room, SH 226. Copies of written exams given in previous years, are filed in the main office; you may borrow the notebook of old exams and photocopy the ones in which you are interested. You will see that large parts of the exams are based on applications of theorems proved and discussed in the basic courses, and are therefore similar to homework problems. So the first requirement for success on the exams is to master the material of the basic courses. Because of the time limit, there is an implicit second requirement that you develop a clear and concise style of explanation, the style being somewhat dependent on the subject area. For the sake of the second requirement we recommend the formation of study groups in which you can compare approaches to sample problems and have your peers give you editorial feedback. Also members of the faculty will be willing to provide a “courtesy critique.”

Oral Comprehensive Examination
Students will be admitted to this examination after passing the three written comprehensive examination and the foreign language requirement. This oral exam is normally scheduled within a month of completion of the written examinations. The mathematics covered is at the same level as the written examinations, but it is not restricted to the three areas in which the student has passed the written examinations. For example, a student planning to write a Ph.D. thesis in applied mathematics may be examined in this area at this time, for instance by presenting and being questioned on a relevant paper. The exam committee will have at least four members. Three of them must be from the mathematics department and one member is appointed by the Graduate School. If a minor is declared, at least one but not more than two members of the committee must be from the minor area. All members of the committee will attend the comprehensive oral and the final defense for the dissertation. No change in membership of the doctoral committee may be made without prior approval of the Dean of the Graduate School. The examination committee is approved by the Graduate Studies Committee, by the head of the department and by the Dean of the Graduate School. The student must notify the Graduate School of the choice of committee and of the exam date and time at least two weeks prior to the examination. The Graduate School selects someone to represent the Dean's office and sends back the paperwork pertinent to administering the exam.
What should the student be doing in the meantime? Preparing, obviously, but how? First of all, the student should clarify with members of the examining committee what particular areas interest them. For instance, an examiner may betray an interest in knowing why a certain problem on a certain written examination went unanswered. Second, the student should try to rehearse taking an oral exam. In a written exam one may sit quietly for several minutes collecting one's ideas before one puts pen to paper; in an oral exam examiners are generally interested in exactly this process of thought collection, so standing there silently for several minutes before starting to write on the blackboard doesn't provide examiners with what they want to observe. This game of thinking on one's feet is not what one does regularly; one may take an enormous amount of time to do research and to write it up later, and even the process of fielding questions coming from students in classes one teaches does not correspond to taking an oral examination, for one's students tend to bear in the direction of what one was explaining the day before yesterday until they are satisfied, but faculty in an oral exam may want to switch from the topic you reviewed yesterday to one you reviewed last month as soon as they can see the outcome of a particular line of questioning. In order to rehearse taking an oral exam, one may put the old study group together and practice fielding their questions. One may also ask a member of the examining committee for a practice session; most of the faculty would be willing to invest a little time in coaching a candidate, so that the stress level of the examination remains low and the visitor from outside the department leaves impressed by the poise and preparedness of our students. The weekly seminar in your area of interest can also provide a friendly audience.

Dissertation
The dissertation must be an original work in a significant branch of mathematics, as judged by contemporary standards and the NMSU faculty.
The form and style of the dissertation must comply with the regulations given in the Guidelines for Preparing a Thesis or Dissertation which may be obtained from the Graduate School website. For optimal stress management, this publication ought to be consulted soon after the material of the dissertation becomes clear, or at least well before writing of a final version starts. The other technicalities of finishing up are described in the Graduate Catalog.
Not later than seven working days before the final oral examination the student must personally deliver a final copy of the dissertation to each member of the examining committee.

Final Oral Examination
This examination is primarily over the student's dissertation and is administered and scheduled by the Graduate School. See the Graduate Catalog for details.

Special Courses
There are certain courses offered at all times, other courses offered every year, and a number of courses which are only offered occasionally. We also attempt to offer special topics courses each year. As mentioned before, there are many reasons why we would like for you to have the opportunity to take courses in as many areas of mathematics as you can. Because certain courses are only offered occasionally, this takes a little bit of planning. A list of courses that are offered regularly or occasionally can be found in the Graduate Catalog. In addition, we hope to offer special topics courses each semester. Students should register early to prevent the cancellation of a course, due to low enrollment.

Preparing for Employment
Students should keep teaching evaluations and materials from the courses they teach if they are seeking a job that could involve teaching.
Conference presentations and/or publications are going to be very helpful in making a resume that is attractive to a future employer. A Master's student probably won't have a publication, but may have a conference presentation. A PhD student really should have a conference presentation or two based on results in their thesis, and hopefully will have at least one or two papers submitted. This would apply whether the student was looking for an academic job, or a job in industry. Obviously students looking for a job in industry will have a better chance if their research topic matches their intended career.
Students should visit the NMSU Career Services webpage: http://www.nmsu.edu/~pment/ and contact them at Garcia Annex 224, (575) 646-1631, to take advantage of the many services that they offer.
You can check the Mathematical Sciences Career Information at http://www.ams.org/careers. The booklet “The Academic Job Search in Mathematics” is available at http://www.ams.org/employment/. All issues of The Notices of the AMS contains academic job advertisements and can be found in the Branson library. The website of the American Mathematical Society (http://www.ams.org) maintains a section on employment opportunities as well. Another good source of job information is at http://chronicle.com/jobs. Also, our department receives many job postings. You can find them in one of the display racks in the lounge (SH 234).
Generally, it is advisable to attend the National Joint Meetings of the American Mathematical Society/Mathematical Association of America in January of the year in which you hope to graduate. There you may participate in a large organized job fair called Mathematical Sciences Employment Center. Many departments also arrange informal interviews during the National Joint Meetings. For information on how this Employment Center works, see the September 1999 issue of the Notices of the AMS, p. 1013. See the article “A Student Guide to the National Meetings” in the November 1998 issue of Math Horizons, which is posted at http://www.maa.org.

Highlights of Department History
Early in 1888 a group of Las Cruces citizens established Las Cruces College and installed Hiram Hadley (Hadley Hall) as the College's first president and first professor of mathematics. The next year Las Cruces College was reorganized as a land-grant institution and renamed the New Mexico College of Agriculture and Mechanic Arts. At the beginning the department was primarily a service department, teaching among other courses one called “Descriptive Geometry.” In 1925 this course went to the Department of Civil Engineering and the department added a course called “Philosophy of Mathematics.” In 1927 John W. Branson (Branson Library) came to head the department, serving the College as President (several times!) and as first Dean of the College of Arts and Sciences before he retired from the presidency in 1955. In 1947 Earl Walden (Walden Hall) became head of the department, after which the department began to grow into the form it has today. Under the leadership of Branson and Walden the university and the department moved away from the early emphasis on vocational training toward an emphasis on liberal studies, unifying existing undergraduate degree programs and sowing the seeds of a vital graduate program. Crowning the development of the post-war period, in 1960 the name of College was changed to New Mexico State University, and Allan B. Gray, Jr., received the Ph.D. in mathematics, the very first Ph.D. degree granted by the university. In 1965 the department won an NSF Departmental Development Grant, which funded further growth of the department and the construction of Walden Hall. Science Hall was opened for business in 1988.

Conclusion
All this advice may sound quite overwhelming right now. Take it steadily in small doses and you will see that the end product is an enjoyable graduate experience that will help you to attain a fulfilling career.
Work hard and have fun!

Graduate Studies Committee
Name	Office	Phone	Email
Ernie Barany	SH 236	575-646-3901	ebarany@math.nmsu.edu
Louiza Fouli	WH 214	575-646-2201	lfouli@math.nmsu.edu
John Harding	SH 247	575-646-4315	jharding@math.nmsu.edu
Susana Salamanca	SH 260	575-646-2305	ssalaman@math.nmsu.edu
Robert Smits	SH 232	575-646-4218	rsmits@math.nmsu.edu
Tonghui Wang	SH 254	575-646-2507	twang@math.nmsu.edu

		MASTERS	2 years, may petition for a 5th semester.
		PHD	4 years, may petition for a 5th year.

		Level I	$16,600
		Level II	$16,800
		Level III	$17,000

Mathematics Graduate Student Handbook Academic Year 2008-2009

TABLE OF CONTENTS

Mathematics Graduate Student Handbook
Academic Year 2008-2009