University of Nevada, Las Vegas  
 

Department of Mathematical Sciences
Graduate Student Handbook
Ph.D. Program

printable version (.doc)

The doctoral program in Mathematical Sciences at the University of Nevada Las Vegas has four areas of concentration:

    1. Applied Mathematics
    2. Computational Mathematics
    3. Pure Mathematics
    4. Statistics

This handbook is meant to assist both prospective and in-house students in understanding the procedures and requirements of the program. It contains the following sections:

  1. Admission Requirements
  2. Admission Procedure
  3. Requirements for the Doctoral Program
  4. Advising Procedure
  5. Representative Course of Study
  6. Synopsis of Faculty Interests

Whereas every effort is made to keep this handbook reasonably complete and current, it must be understood that specific details and issues regarding the program are determined as needed by the Department of Mathematical Sciences.

1. Admission Requirements

In addition to departmental requirements, applicants must satisfy the admission requirements of the Graduate College; please refer here.

The requirements of the Department of Mathematical Sciences for admission to the doctoral program are summarized as follows. Applicants must have a minimum grade point average of 3.00 for all undergraduate work or a minimum 3.25 grade point average for the last two years of undergraduate work. In addition, applicants seeking direct admission to the doctoral program without a previously earned Master of Science degree must have a minimum GPA of 3.00 for all undergraduate work or an overall 3.25 GPA for the last two years of mathematics undergraduate work. Applicants with a master's degree must have an overall 3.00 GPA in their master's program and at least 15 credit hours of graduate level course work in Mathematical Sciences with a grade of B or better. Applicants must also submit official scores from the GRE General Test; successful applicants to the program are expected to have GRE scores among the upper 50th percentile of examinees taking the General GRE Test.

2. Admission Procedure

To apply for admission to the Ph.D. Program prospective students must submit application material to both the Graduate College and the Department of Mathematical Sciences.

Part 1. For details regarding application material for the Graduate College refer to:

Applicants are encouraged to apply on-line here.

An alternative is to submit via regular mail the following material

    1. A completed application form.
    2. Official transcripts from all colleges and universities you have attended.
    3. Official score from the GRE General Test.
    4. If interested: A completed application for a Graduate Assistantship.

to the following address

Graduate College
University of Nevada Las Vegas
4505 Maryland Parkway
Box 451017
Las Vegas, NV 89154-1017

Application forms can be downloaded from the online site of the Graduate College. International students must additionally submit a completed financial statement and show competency in English (a TOEFL score of 550 or comparable evidence).

Part 2. Please submit the following material

    1. Copies of all transcripts sent to the Graduate College.
    2. Three letters of recommendation from persons familiar with the applicant's academic record and potential for doctoral study in the mathematical sciences.
    3. A statement of purpose. Please state your purpose in applying for doctoral study, your desired area of specialization within the mathematical sciences (if known), and any additional information that may aid the selection committee in evaluating your preparation and your aptitude for graduate study at UNLV.
    4. Copy of the GRE General Test score.

to the following address

Graduate Coordinator, Department of Mathematical Sciences
University of Nevada Las Vegas
4505 Maryland Parkway
Box 454020
Las Vegas, NV 89154-4020

Deadlines. Due to programmatic reasons, admission to the doctoral program in mathematical sciences is usually restricted to the Fall semester. The Graduate College and the Department of Mathematical Sciences must receive all application materials from applicants by February 1.

3. Requirements of the Doctoral Program

1. Proficiency. After admission to the doctoral program, each student must demonstrate proficiency in the subject matter of the following three courses:

    1. MAT 657: Introduction to Real Analysis
    2. MAT 663: Advanced Matrix Theory and Application
    3. STA 667: Introduction to Mathematical Statistics

Each of the three parts of this requirement can be satisfied by earning a B or better grade in the course or by passing a proficiency exam on the course. The Department's Graduate Studies Committee in consultation with the Chair of the Department will rule on whether equivalent courses taken at another institution can count toward this entrance requirement. For students who take one or more of these courses, or who have taken equivalent courses at another institution, a maximum of 3 credits for students with a master's degree or a maximum of 6 credits for students with a baccalaureate can be counted toward the 60 credits total required for completion of the program.

2. Credit requirement. Doctoral students are required to complete a minimum of 60-credit hours beyond the baccalaureate, at least 36 of which must be in courses at the 700-level. For students entering the program with an M.S. degree, at least 30 credit hours must be completed at UNLV and at least 18 credit hours must be at the 700-level. Each doctoral student must complete a dissertation embodying the results of original research which is acceptable to the student's dissertation committee. Normally, a student will enroll in a minimum of 24 hours and a maximum of 36 hours of Dissertation/Research.

3. Qualifying Examination. The purpose of the Qualifying Examination is to measure the student's knowledge of basic graduate level coursework in selected areas and to make sure that the student is prepared to proceed to more advanced studies. The student will take a Qualifying Examination, usually within the second year, based on specified core courses in the student's concentration. For each concentration, these core courses are:

Applied Mathematics

Computational Mathematics

Pure Mathematics

Statistics

Students who fail the Qualifying Examination on the first attempt must complete a second examination within the next twelve months. Students who entered the program with a baccalaureate degree and who fail the second examination may be allowed to complete a Master of Science in Mathematical Sciences with the consent of the Graduate Studies Committee. To be eligible for the Master of Science the students must fulfill the requirements of the Master of Science degree as stipulated in the Graduate Catalog. Such students will not be permitted to seek readmission to the Doctoral Program in Mathematical Sciences at UNLV. Students who fail the examination a second time and who entered the doctoral program with a master's or other graduate degree will be separated from the program. The current procedure for carrying out the Qualifying Examination is described in Appendix A.

4. Comprehensive Examination. The purpose of the Comprehensive Examination is to measure the student's knowledge of the advanced level graduate work that will be required as the student begins to do original research in his or her area of concentration. After passing the Qualifying Examination, the student will engage in approved course work specified by the Doctoral Advising Committee and submit to the latter a dissertation proposal. Usually a year after the Qualifying Examination, the student will complete a Comprehensive Examination, designed and administered by the Doctoral Advising Committee, based on the student's course work with focus on his/her ability to perform research on the dissertation proposal. Students who fail to pass the Comprehensive Examination on the first attempt must complete a second examination within the next semester. Students who fail the examination a second time will be separated from the program. A student who has successfully passed the Comprehensive Examination will be admitted to candidacy for the Ph.D. degree and thereby be allowed to proceed with the approved dissertation proposal.

5. Dissertation. In addition to the 60 credits total listed earlier, each doctoral candidate must complete a minimum of 24 hours and a maximum of 36 hours of Dissertation/Research.

6. Additional Requirements. Skills in foreign languages, computer programming or interdisciplinary areas, dependent on the concentration of the student's program, will be determined by the Doctoral Advising Committee and the Graduate Study Committee in consultation with the Department Chair.

7. Dissertation Defense. The candidate, having submitted to the Doctoral Advising Committee a dissertation draft, previously approved by the Dissertation Advisor, will orally defend the dissertation before said Committee and any other graduate faculty members who wish to attend. The Doctoral Advising Committee will recommend to the Department Chair whether the dissertation and defense are both satisfactory.

The listing of graduate courses is constantly under review by the Department. Graduate students will automatically receive new listings. Since some courses are taught on an 'on demand' basis, course prerequisites for each of the four concentrations are considered guidelines with courses roughly equivalent accepted as prerequisites, subject to approval of the Graduate Studies Committee and the student's Doctoral Advising Committee.

A student will be placed on academic probation if a minimum 3.00 grade point average is not maintained in all work taken in the degree program. A grade of C or less in one graduate-level course will cause a student to be placed on academic probation and will elicit a critical review of the student's program by the Graduate Studies Committee.

The Graduate College requires two years of full-time residency on the campuses of UCCSN and at least one continuous academic year of residence must be at UNLV.

Note: The Ph.D. in Mathematical Sciences at UNLV requires both a Qualifying Examination and a Comprehensive Examination. The Qualifying Examination is a test of the student's readiness to enter into advanced coursework. The Comprehensive Examination measures the student's readiness to enter into independent and original research toward the dissertation.

4. Advising Procedure

  1. The Graduate Studies Committee will appoint an interim advisor to each student. The interim advisor will introduce the student to the personnel and resources Entrance interviews will be held by the Graduate Studies Committee for all new students in the week prior to the start of classes. The goal of these interviews is to review for each student the courses taken and to determine how program requirements can best be met.
  2. available in the Department, will assist in designing an initial curriculum, engage in discussions about possible research directions, and assist the student in choosing a dissertation advisor.
  3. Usually within a semester after satisfying the MAT 657 - MAT 663 - STA 667 proficiency requirement, the student will have a Dissertation Advisor approved by the Graduate Studies Committee and the Department Chair. The dissertation advisor must be a tenured Associate Professor or Professor with graduate faculty status and successful research record. A tenured graduate faculty with a developing research record may become a co-dissertation advisor jointly with a qualified senior faculty.
  4. The dissertation advisor will form and chair a Doctoral Advising Committee, consisting of two additional members from the graduate faculty of the Department in the area of research interest, one outside committee member with expertise in the student's field of research, and a graduate faculty representative appointed by the Graduate College.
  5. The student's Doctoral Advising Committee will establish an approved program of studies and annually review the student's progress.

5. Representative Course of Study

For each of the four concentrations, sample courses to be taken prior to taking the qualifying examinations are listed below. New courses, as needed, will be added later.

Applied Mathematics

Computational Mathematics

Pure Mathematics

Statistics

Year 1:
STA 667
MAT 707
MAT 709
MAT 729
MAT 771
Elective

Year 1:
STA 667
MAT 707
MAT 709
MAT 729
MAT 771
Elective

Year 1:
STA 667
MAT 663
MAT 703
MAT 707
MAT 704
MAT 708

Year 1:
MAT 657
MAT 663
STA 767
STA 763
STA 715
STA 765

Year 2:
MAT 708
MAT 710
MAT 772
Elective
Elective
Elective

Year 2:
MAT 765
MAT 766
MAT 772
Elective
Elective
Elective

Year 2:
MAT 709
MAT 789
MAT 701
MAT 702
Elective
Elective

Year 2:
STA 713
STA 751
STA 789
STA 769
STA 764
Elective

The Qualifying Examination for each concentration is based on the core courses listed below.

Applied Mathematics

Computational Mathematics

Pure Mathematics

Statistics

After the Qualifying Examination, the student will take an additional 24 credits of course work, dependent on the concentration, with approval of the Doctoral Advising Committee, the Graduate Study Committee, and the Chair of the Department, in order to meet the program requirements specified in Section IX-C below. Lists of courses that may be used for that purpose in each concentration are listed below in this section. Due to the interdisciplinary nature of their curricula, students in the Applied Mathematics, Computational Mathematics, and Statistics concentrations are required to take approved courses in other departments. These courses are also listed below.

About a year after the Qualifying Examination, the student is expected to take a Comprehensive Examination, designed and administered by the Doctoral Advising Committee, aimed at determining the student's readiness to do research on the dissertation topic. After course work, consisting of a minimum of 60 credits beyond the baccalaureate, each doctoral candidate must in addition complete a minimum of 24 and a maximum of 36 credits for a dissertation.

For completeness, we list below the current pool of courses that may be taken by students in each concentration. Due to overlap in disciplines, several courses are available in two or more concentrations. For ease of reading, we repeat these entries under each of the concentration headings.

Applied Mathematics:

Internal 700-level courses include:

External 700-level courses include:

Internal 600-level courses include:

External 600-level courses include:

Computational Mathematics:

Internal 700-level courses include:

External 700-level courses include:

Internal 600-level courses include:

External 600-level courses include:

Pure Mathematics:

Internal 700-level courses include:

Internal 600-level courses include:

Statistics:

Internal 700-level courses include:

External 700-level courses include:

Internal 600-level courses include:

6. Synopsis of Faculty Interests

The Department of Mathematical Sciences currently comprises over 30 regular and visiting faculty members with specialties that range from Number Theory, Graph Theory, Combinatorics, Set Theory, Partial Differential Equations (PDEs) and Critical Point Theory to Control Theory, Numerical PDEs, Scattering Theory, Waves Propagation, Lightning Radiative Transfer, Mathematical Statistics, Statistical Decision Theory, Statistical Inference, Reliability Theory, Spatial Statistics, Stochastic Processes, and Environmental Statistics. The following table summarizes the general areas of faculty specialization.

Name

Rank

Year Ph.D.

Research Area

Paul Aizley

Prof.

1969

Pure Math

Malwane Ananda

Prof./Assoc. Chair

1989

Applied Stat

Carryn Bellomo

Assistant Prof.

1998

Applied Math / Math Ed

Gennady Bachman

Prof.

1991

Pure Math

Arthur Baragar

Associate Prof.

1991

Pure Math

Satish Bhatnagar

Prof.

1974

Applied Math / Math Ed

Douglas Burke

Associate Prof.

1991

Pure Math

Sandra Catlin

Associate Prof.

1997

Applied Stat

Hokwon Cho

Assistant Prof.

1997

Applied Stat

David Costa

Prof.

1973

Pure/Applied Math

Rohan Dalpatadu

Associate Prof.

1986

Applied Math

Zhonghai Ding

Associate Prof.

1994

Pure/Applied Math

Derek Dubose

Associate Prof.

1987

Pure Math

Chih-Hsiang Ho

Prof.

1986

Applied Stat

Daniel Kern

Assistant Prof.

1999

Applied Math

Jichun Li

Assistant Prof.

1998

Computational Math

Xin Li

Associate Prof.

1991

Computational Math

Michael Marcozzi

Associate Prof.

1994

Computational Math

George Miel

Prof.

1976

Computational Math

Angel Muleshkov

Associate Prof.

1988

Applied Math

Dieudonne Phanord

Prof.

1988

Applied Math / Space Sciences

Farrokh Saba

Assistant Prof.

1992

Graph Theory / Math Ed

Ebrahim Salehi

Associate Prof.

1985

Pure Math

Michelle Schultz

Associate Prof.

1996

Pure Math

Peter Shiue

Prof.

1971

Pure Math

Hossein Tehrani

Associate Prof.

1994

Pure / Applied Math

Sadanand Verma

Prof.

1958

Pure Math

Corran Webster

Assistant Prof.

1997

Pure Math

William Wells

Prof.

1968

Engineering / Applied Math

A synopsis of the teaching and research records of the Department's faculty is given below.

Malwane Ananda

Research area -- Dr. Ananda's primary research interests are in basic and applied research in statistics, statistical inference, Bayesian methods, reliability estimation, and environmental statistics. Courses developed and taught - Dr. Ananda has taught a wide variety of undergraduate and graduate courses in Mathematics and Statistics (24 different courses). He has developed several upper level statistics courses (STA 767, STA 463/663). He also contributed to creating and revising several other graduate level statistics courses and the Applied Statistics concentration for the MS in Mathematical Sciences. Creative accomplishments -- Dr. Ananda has published over 30 articles in refereed journals and several other conference proceedings and book chapters. He is a leading expert in the area of generalized p-values and related issues, an area that has grown in recent years. Some of his work in this area, namely testing two-way ANOVA models and nested design models under unequal error variances, are already incorporated in several standard statistical packages which are commercially available through out the world. At UNLV he mentored several M.S. students and currently 5 MS graduate students are working on their thesis under him. Several of his students' MS thesis resulted in journal publications and currently two such articles are under review for publication. Dr. Ananda will be able to mentor doctoral students in the area of Statistics.

Carryn Bellomo

Research area -- Dr. Bellomo's research interests are: Efficient grid generation for numerical solution of PDEs, mathematical modeling in biology, and scientific computing. Courses taught.-- Dr. Bellomo has taught a variety of undergraduate and graduate Applied Mathematics and Mathematics Education courses, both at UNLV and Texas A & M University, Corpus Christi. Creative accomplishments -- She was the recipient of the following research award: Math Early Intervention Project, 'Instrumentation for Recruiting and Teaching Underrepresented Students.' USDA grant number 2002-38422-12160. 9/1/2002 through 9/1/2003 (Co-PI).

Gennady Bachman

Research area -- Dr. Bachman's primary research interest is Number Theory. His most recent research efforts are directed toward the understanding of coefficients of cyclotomic polynomials of order three. Courses taught -- Dr. Bachman has taught a variety of courses, ranging from Calculus to advance courses in pure and applied mathematics. Creative accomplishments -- Dr. Bachman has solved several difficult and long-standing problems in Number Theory. Most recently, for example, he established the existence of a certain long-anticipated class of cyclotomic polynomials, which went undetected for over one hundred years.

Arthur Baragar

Research area -- Dr. Baragar conducts research in Number Theory and Algebraic Geometry. Courses taught -- Dr. Baragar has taught a variety of courses, ranging from Calculus to advance courses in Geometry. Creative accomplishments - Dr. Baragar published papers in Compositio Mathematica and the American Mathematical Monthly. Had papers accepted in the Canadian Mathematics Bulletin, the Mathematics of Computation, and the Rocky Mountain Journal of Mathematics. Submitted one more paper. Supervised one MS thesis to completion and submitted a co-authored paper with that student. He is now supervising another MS student. Coached the 2002 Canadian IMO team to its best showing ever.

Douglas Burke

Research area - Dr. Burke's research interests are in foundations of mathematics and set theory. His work, and the work of the foundations research in the Department, has brought national and international recognition to UNLV. Course taught and awards - Dr. Burke has taught a wide variety of courses, from pre-calculus to graduate level courses. He also served for three years as graduate coordinator, helping to strengthen the masters program in the Department. Creative Accomplishments -- Dr. Burke has published papers in internationally recognized refereed journals. Jointly with Dr. Dubose he was awarded a very completive three year NSF grant. He has mentored two graduate students at UNLV. One went on to a Ph.D. program in mathematics; the other is in medical school.

Sandra Catlin

Research area - Dr. Catlin's research interests are primarily in applied stochastic processes. She is currently working with scientists at several other institutions on two projects modeling biological phenomena, and tumor growth. She is also continuing her work in statistical inference for partially observed spatial stochastic processes. In addition, she is also interested in more general applications of space-time methodology in both the health and social sciences. Courses developed and taught - She has taught a variety of undergraduate and graduate courses in Mathematics and Statistics. Creative accomplishments - Dr. Catlin has spent considerable time on a project joint with the School of Social Work at UNLV funded by a Title IV-E federal grant entitled, 'The impact of welfare reform on foster care/pregnancy planning'. This state-wide project is the first of its kind in Nevada, and is of particular national significance due to Nevada's unique laws requiring a 'sit-out' period of one year after two years of continuous welfare receipt. This project has provided funding for two students.

Hokwon Cho

Research area -- Dr. Cho has a wide variety of interests in research. His main research areas are in both development of methodologies and applications of statistical decision theory, sequential methods, linear models, and sampling. In addition, he is also expanding his interests to Biostatistics and Boundary Value problems in Applied Mathematics. Courses taught -- Dr. Cho has taught a variety of undergraduate and graduate courses in Statistics. Creative accomplishments -- Recently Dr. Cho has published three papers in internationally renowned journals and co-authored (the book is now being printed by Wessex Institute of Technology, Southampton, England) a book entitled Introduction to Regression analysis. Currently he has one article accepted (about clinical trials) and one other submitted for publication. He did supervise one MS Thesis and is planning to write an additional monograph on his specialized topic, Dirichlet Integrals and application in Statistics.

D.G. Costa

Research area -- Dr. Costa's research interests are directed towards Partial Differential Equations (PDEs) and applications of Variational and Topological Methods to differential equations. Together with his research group in the Department and through his work on various theoretical and computational aspects of elliptic and wave type equations, he has helped to bring recognition of UNLV in the mathematical community, both nationally and internationally. This is evidenced by the many invitations received by the group to present talks in specialized meetings and to visit reputed institutions. Courses taught and awards -- Dr. Costa has taught a variety of undergraduate and graduate courses both at UNLV and at his former university in Brazil. At UNLV he also designed a split-level course in PDEs (MAT 487/687) and helped with the management and development of the M.Sc. program in the Department, especially during his term as Graduate Coordinator. Creative accomplishments -- Dr. Costa has published over 50 articles in refereed journals of international circulation and 7 expository articles/books. Currently he has two articles accepted and two other submitted. Before coming to UNLV, in his native country of Brazil, he was the recipient of many research grants and mentored 1 Ph.D. student and several M.Sc. students. At UNLV he mentored 3 M.Sc. students, two of which went on to pursue Ph.D. degrees at other institutions.

Rohan Dalpatadu

Research area - Dr. Dalpatadu's research interests are in numerical methods applied to problems in actuarial science and estimation. Courses taught and awards - Dr. Dalpatadu has taught almost all the undergraduate mathematics and statistics courses offered at UNLV and a wide array of graduate courses including MAT 775 (designed by him) and MAT 767. He has designed several undergraduate mathematics courses including MAT 429 and MAT 430 and the entire actuarial science sequence. Furthermore, Dr. Dalpatadu was instrumental in the creation of all three concentrations in the M.S. program and the four concentrations in the B.S. program. Dr. Dalpatadu has supervised two Masters students in Applied Mathematics and was the advisor of four other Masters students in Applied Mathematics. He was on numerous M.S. committees within and outside the Department. He has also supervised five undergraduate research projects in Statistics. Creative accomplishments - Dr. Dalpatadu is the author of 14 publications and currently has two papers under review. He has made numerous presentations at regional, national, and international conferences. Dr. Dalpatadu's research interests are in numerical methods applied to problems in actuarial science and estimation.

Zhonghai Ding

Research area: Dr. Ding's research interests are control theory, partial differential equations, and numerical computation. In particular, he has been working on modeling, analysis, control and numerical computation of structural dynamical systems of smart materials and smart actuators such as shape memory alloy actuators, oxidation of metal matrix composites, thin elastic plates of polygonal domains, suspension bridges, and Josephson -junctions of superconductivity. Part of his research has been supported by the NSF. Courses taught and awards: Dr. Ding has taught a variety of undergraduate and graduate courses at UNLV. He designed and offered the new graduate courses 'Introduction of Mathematical Control Theory'. He has received the Outstanding Faculty Award from UCCSN in 2001; the Barrick Scholar Award from UNLV in 2000; the Proposal Bonus Award from UNLV in 1996; and the Outstanding Dissertation Award with Ph.D thesis ``Topics on potential theory on Lipschitz domains and boundary control problems'' from AMS Central Section in 1994. He has also received the NSF Grant award on the project entitled ``Computation, optimization, singularity and vibration analysis of polygonal elastic thin plates'', NSF DMS-9622910, $44,258, June 1996-May, 2000, and the Proposal Development Grant award, NSF Nevada EPSCoR, $5,000, 1997. Creative accomplishments: Dr. Ding has published twenty eight peer-reviewed papers in top pure and applied mathematical journals, and has been invited to present his research work in many prestigious universities and international conferences. He has served as an invited Reviewer for the Mathematical Reviews, and has organized and chaired many special sessions in the prestigious national and international conferences. He was nominated as the distinguished member of the National Society of Collegiate Scholars in 2003. He has supervised one M.S. thesis and several graduate students, who are pursuing Ph.D degree in mathematics in other institutions because there is no Ph.D program in mathematics at UNLV. Dr. Ding will be able to mentor doctoral students in the concentration of applied mathematics and computational mathematics.

Derrick DuBose

Research area -- Dr. DuBose conducts research in Foundations. Courses taught -- Dr. DuBose has taught a variety of courses, ranging from calculus to advance courses in algebra and analysis. Creative accomplishments - Dr. DuBose's long-term project is to obtain level by level correspondences of determinacy within determinacy with large cardinal properties. Determinacy is a standard field within set theory and refers the existence of winning strategies usually for two-person games of perfect information.

Chih-Hsiang Ho

Research area - Statistical modeling and analysis for interdisciplinary research Courses taught - Dr. Ho has taught a wide range of undergraduate and graduate courses in Statistics. Creative accomplishments and goals - Dr. Ho's research interests continue to be: Statistical modeling and analysis for interdisciplinary research which concerns with human and social betterment. He has been able to incorporate both undergraduate and graduate students into research projects that used statistics to solve real problems - one of many goals of the Department of Mathematical Sciences at UNLV. He is the Principal investigator for the Yucca Mountain Probabilistic Volcanic Hazard and Risk Analysis Project, funded by the Nuclear Waste Project Office, State of Nevada (October 1989 - December 1996 and January 2002 - present). He was an invited speaker at the meeting (November 9 - 10, 1993) of the National Academy of Sciences' Committee on the Technical Bases for Yucca Mountain Standards

Daniel L. Kern

Research area -- Dr. Kern's research interests are in the areas of optimal control and systems of partial differential equations(PDEs), taking approach best described under the more general description of applied analysis. Applications range from the ecological to the biomedical to groundwater, most of which can be described as being part of either biomathematics or environmental mathematics. He has current and past collaborators throughout the United States on a variety of topics, such as a compartmental model of cancer, nonlinear parabolic systems of PDEs, and stochastic optimal control of groundwater remediation. He was recently invited to give a talk at a special session on natural resource modeling at a national mathematical conference. Courses taught -- Dr. Kern has taught a wide range of courses through out is mathematical career, ranging from the remedial level through a senior undergraduate/beginning graduate course. His experience includes integrating a wide range of technologies and teaching techniques into various course structures. Creative accomplishments and goals -- Dr. Kern has published in refereed journals starting at the end of his graduate work. He has given talks at a number of conferences, as well as at numerous seminars. While at UNLV only since August, he has made contact with several people in Mathematical Sciences (such as those interested in PDEs) and Biological Sciences hold promise for future collaborations.

Jichun Li

Research area - Dr. Li's research interests are in Numerical Analysis, Mathematical Modeling, and Scientific Computing. He is currently working on groundwater contaminant modeling using meshless method, parallel computing of environmental transport by finite element method, and numerical analysis and computer simulation for image processing. Course taught and awards - Dr. Li has taught many undergraduate courses (MAT124, MAT181, and MAT 182) at UNLV. He also taught a graduate course MAT777/MEG777 in Spring 2002. Creative accomplishments - Dr. Li has authored 20 peer-reviewed articles, and has several papers submitted for possible publication in journals. He has presented a paper in the AMS Western Sectional Meeting held in Las Vegas during April 21 (in which he organized a special section), and he was an invited speaker at the 2001 AMS-IMS-SIAM Summer Research Conference on Fluid Flow and Transport in Porous Media held in Mount Holyoke College, South Hadley, Massachusetts during June 17-21. He also presented a paper at the International Conference on Computational Engineering & Science held in Puerto Vallarta, Mexico, during August 19-25, 2001.

Xin Li

Research area - Dr. Xin Li's research interests are in applied analysis. He is currently collaborating with other researchers on neural networks and numerical solutions of partial differential equations. Courses taught and awards - Dr. Xin Li has ever taught various math courses, including entry level courses like Mat 127 (Precalculus), senior engineering courses such as Mat 429, and graduate courses such as Mat 709/710. He served 5 graduate committees for their thesis defense. Currently he works with a graduate student in directing his master thesis. Creative accomplishments - Dr. Li has authored or co-authored 21 research articles, and 1 paper is in press. He currently has 3 papers under review. He has presented 16 talks at national and international conferences.

Michael Marccozzi

Research Area - Dr. Marcozzi's research interests are in mathematical finance. In particular, this involves the areas of finance, stochastic processes, functional analysis, partial differential equations, and numerical methods. Dr. Marcozzi is currently working on a portfolio selection problem; that is, how one should distribute one's assets between treasury bonds and stocks, given that there is a fee for transferring assets between securities. A second problem Dr. Marcozzi is investigating involves the valuation of so-called Barrier options. Such securities are ubiquitous in the financial services industry, but lack a mathematically relevant pricing model. Finally, Dr. Marcozzi is developing a model for credit risk, or the valuation of a bond issued by a corporation. This problem is arguably the most pressing problem facing the financial services industry. Course taught and awards - Dr. Marcozzi has taught courses in ordinary and partial differential equations, numerical analysis, engineering mathematics, finite mathematics, and college mathematics. Creative accomplishments - Dr. Marcozzi is the author of 14 peer reviewed publications and currently has five papers under review. He has presented 14 abstracts at national/international meetings. Dr. Marcozzi has received an award from the National Partnership for the Advancement of Computational Infrastructure (NSF) and a SITE award the UNLV Research Council for the development of numerical methods for option pricing models.

George J. Miel

Research area - His areas of research have been theoretical and applied numerical analysis; approximate solution of operator equations in function spaces; signal processing on dedicated parallel computers; aerospace system engineering; algorithms for parallel micro-architecture computers, especially systolic and cellular array processors; modeling on supercomputers of water infiltration in soils and related problems in environmental engineering; and on the method of paired comparisons in statistics. He is currently working in the area of computational linear algebra. Course taught and awards - He has taught a wide variety of undergraduate and graduate courses. He formalized a now standard course sequence in numerical analysis, MAT 465-466, right after first coming to UNLV in 1978. After returning to UNLV in 1991, at the request of the Department of Computer Science, he created and designed our undergraduate course MAT 365 on computational Linear Algebra. He also co-created and co-designed the graduate courses MAT 771-772, 765-767, and 777 (also co-listed as MEG 777), which form an integral part of the course work for the proposed Ph.D. program described in this document. He supervised thirteen Masters students, served on doctoral committees of nine Ph.D. students in applied mathematics (outside of UNLV) and in computational mechanical engineering , and served on quite a few Masters committees in foreign languages. He was awarded the Bausch-Lomb Science Award and the Chauvenet Prize in 1986 from the Mathematical Association of America. In 1990, He served as Chairman of the national Committee on Computational Science of the Aerospace Industries Association, and in 1991-1992, as Vice Chair of the national Technical Committee on Software Systems of the American Institute of Aeronautics and Astronautics. Creative accomplishments - His resume has over 50 articles in refereed publications, over 50 papers in conferences and symposia, and over 25 technical reports for diverse organizations. During the period 1985-1991, as a member of teams at the Aerospace Corp. and later at Hughes Research Laboratories, he received research grants from DARPA, NSF, USAF, and NASA in order to conduct research on dedicated parallel processing and in aerospace signal processing. At UNLV, during 1993-1994, he was awarded from DOE about $250,000 in a cooperative grant agreement with Reynolds Electrical and Engineering Co. (a former caretaker of the Nevada Test Site) and NSCEE on campus, to conduct research on supercomputer modeling of water infiltration in desert soils. For the year 2000, Drs. Marcozzi and Miel received an award from the National Partnership for the Advancement of Computational Infrastructure (NPACI) from NSF, for access to the resources of the San Diego Supercomputer Center toward the development of numerical methods in option pricing models.

Angel S. Muleshkov

Research area - Dr. Muleshkov's research interest are: Analytical and Numerical Methods for Ordinary and Partial Differential Equations; Applied Complex Analysis and Special Functions; Boundary Element Method. Dr. Muleshkov is currently working with Drs. Goldberg and Chen on two papers developing analytical and Boundary Element Method solutions for various cases of the Helmholtz PDE. Course taught and awards - Dr. Muleshkov has taught various applied mathematics courses including the graduate MAT 709, MAT 710, and MAT 723. Creative accomplishments - Dr. Muleshkov authored or coauthored 23 peer-reviewed papers. Dr. Muleshkov presented several papers at conferences. Dr. Muleshkov received the following rewards lately: 1994 Finalist for the 1993 Teaching Award of the CoSM, UNLV; 1994 Honored as "Professor worthy of recognition" from the Department of Mathematical Sciences for 1993 by UNLV Alumni Association on the Recognition Luncheon of April 12, 1994; 1987 Boeing Fellowship in Applied Mathematics.

Dieudonne D. Phanord

Research area - Dr. Phanord's research interests are directed towards Multiple Scattering Theory (MST), Wave Propagations, Space Sciences, Lightening Radiative Transfer (LRAT), and Cloud Dynamics and Modeling. Course taught and awards - Dr. Phanord has taught many advanced courses in PDE, Mathematical Physics, Lightening Radiative Transfer at University of Alabama - Huntsville and University of Wisconsin - Whitewater (UW-W). During the last 10 years, Dr. Phanord was the recipient of several awards and certificates of recognition. Creative accomplishments - In addition to publishing articles, Dr. Phanord has submitted over 100 grant proposals in the last 10 years. Many of these proposals have been funded. With his NASA partner, Dr. William Koshak, he is in the process of designing, developing, and testing a ground based lightning detector (ODF). The prototype of the ODF is now deployed at UW-W.

Farrokh Saba

Research area - Dr. Saba's research interests are Graph Theory and Combinatorics, both theoretical and applied. He has a number of contributions that are building bridges with other disciplines including but not limited to Computer Science, and Software Engineering. Moreover, his specific interests are interdisciplinary applications of Graph Theory in other fields of sciences such as Chemistry and biology including DNA detection. Courses taught and awards - Dr. Saba has taught a variety of graduate and undergraduate mathematics, computer science, and mathematics education courses for twenty eight years, including mathematics for mathematics majors as well as mathematics for non-mathematics majors. He received the Charles H. Butler Award in recognition of excellence in the teaching of mathematics from Western Michigan University, April 1981. Creative accomplishment - Dr. Saba is the coauthor of nearly 28 published papers and a reviewer for Mathematical Reviews since 1983. He has been an Assistant Director for several International Conferences including the Second International Conference in Graph Theory, Combinatorics, Algorithms and Applications at San Francisco State University, July 24-28, 1989 and several International Conferences on the Theory and Applications of Graphs at Western Michigan University.

Ebrahim Salehi

Research area - Dr. Salehi's research interests are directed towards different branches of Mathematics including: Graph Theory and its applications, Topological Dynamics, Real and Complex Analysis. Together with his research collaborators and presentations, he has helped to bring recognition of UNLV in the mathematical community, both nationally and internationally. Courses taught and awards - Dr. Salehi has taught variety of undergraduate and graduate courses at UNLV. He has the reputation of being one of the best mathematics teachers, for which he has received the Distinguished Teaching Award of the College of Sciences and being recognized by the UNLV Alumni Association. Creative accomplishments - Dr. Salehi has recently published over nine articles in refereed journals of international circulation. Currently he has three articles accepted and two other submitted. In view of his recently increased scholarly activities and his excellent teaching, Dr. Salehi will be able to prepare and mentor doctoral students in the concentrations of Applied and Pure Mathematics.

Michelle Schultz

Research area - Dr. Schultz specializes in graph theory. Her work includes the study of degrees in graphs, graph decompositions, distance in graphs, Hamiltonian graphs, domination in graphs, oriented graphs, and graph embeddings. Currently her attention is primarily with distance in graphs and graph embeddings. The work on distance is varied, covering the study of ordinary distance in graphs by means of eccentric vertices to the study of new distances defined on classes of graphs or on a collection of objects associated with a given graph such as subgraphs or maximum matchings, while the work on graph embeddings is mainly concerned with the study of a natural genus parameter for a special class of Cayley graph embeddings known as Cayley maps and the study of the likelihood that certain Cayley maps are symmetrical. Courses taught and awards - Dr. Schultz is an accomplished teacher (teaching courses in topics ranging from the training of future elementary education teachers and Precalculus to graduate level graph theory) who has received considerable recognition from her students and from the administration of the University of Nevada, Las Vegas. The Theta of Michigan Chapter at Western Michigan University elected her for membership into Phi Beta Kappa as an Alumna Member in 2003 for her devotion to intellectual pursuits and to the objectives of a liberal education. She is a National Councilor for Pi Mu Epsilon, the National Honorary Mathematics Society and the faculty advisor of the Nevada Beta Chapter of Pi Mu Epsilon at the University of Nevada, Las Vegas. Creative accomplishments - Dr. Schultz has published twenty-six articles in major refereed journals. In addition, she currently has an article accepted and two others in preparation for submission. Dr. Schultz has mentored four master's theses in graph theory and two of her students have publications from their work. She has also presented her research at fourteen mathematics conferences and with her mentorship three students have presented their work at national conferences. For the last three years, Dr. Schultz has co-organized the Midwest Conference on Combinatorics, Cryptography, and Computing, helping to bring international recognition to the University of Nevada, Las Vegas as the conference was held here for two of the three years.

Peter J. S. Shiue

Research area - Number Theory and Combinatorial Theory are two of Dr. Shiue's research expertise. Polynomials in Finite Fields, Elementary Number Theory and Enumerative Combinatorial Theory, Quasi-Monte Carlo Methods and Cryptography are his major focus of investigations. His extensive record of research publications and various other mathematics activities have given him a considerable external, both national and international, reputation. Throughout his career as a mathematician he has given approximately 100 invited talks at universities and professional meetings in United States, Canada, Europe and Asia. Many mathematicians have come to UNLV to cooperate with him in the past several years because of his research reputation. Courses taught and awards - Dr. Shiue has more than 30 years of teaching experience in UNLV, Michigan, Illinois, North Carolina and Taiwan. He has taught courses ranging from service courses below Calculus to graduate level courses. Dr. Shiue is the recipient of the Distinguished Teaching Award of the College of Sciences in 1989 and one of the finalists in 2002. He is also a recipient of several research awards: Research Fellow of the Italian National Research Council of Italy; The Alexander Von Humboldt Foundation of Germany; The Barrick Distinguished Scholar Award of UNLV and the Distinguished Researcher Award, College of Sciences, UNLV. In addition, Dr. Shiue has also received grants from National Science Foundation, National Security Agency, UNLV Research Council and Applied Research Initiative, UCCSN. Creative accomplishments - Dr. Shiue has published over 90 research papers so far with several latest works already accepted/submitted at present. With the exception of a few rookie papers, all of his works appeared in first rated refereed academic journals/proceedings of international reputation. Dr. Shiue, over the years, has served as a referee for numerous journals, Math Reviews and grant proposals. He has co-authored four conference proceedings, serving as an editor of 3 international journals. Moreover, he has mentored 2 Ph.D. students and more than 40 Master students.

Hossein Tehrani

Research area - Dr Tehrani's research area is the study of Nonlinear Partial Differential equations mainly through application of and topological and variational methods. These techniques are particularly helpful in the study of quasilinear Partial Differential equations which have diverse applications in different areas of sciences such as physics, astronomy , chemistry and such. Dr. Tehrani has organized as well as participated in a number of national and international conferences on Partial Differential Equations bringing positive exposure to UNLV. Courses taught and awards - Dr. Tehrani has taught a variety of undergraduate and graduate courses both at UNLV and UBC where he spent three years as a postdoctoral fellow before coming to UNLV. He has also been involved with creating the Teaching Mathematics concentration of the Department. Creative accomplishments - Dr. Tehrani has published 15 research articles in top journals in Partial Differential Equations and Mathematical Analysis with two more submitted for publication at this time. In addition Dr. Tehrani has refereed a number of papers for reputable journals in the area of PDEs. Based on this experience, Dr. Tehrani together with his colleagues in his research group, will be able to mentor doctoral students in the concentrations of Applied Mathematics and Pure.

Corran Webster

Research area - Real Analysis and Functional Analysis. Courses taught and awards - As the only functional analyst in the Department, he would also be contributing by teaching core courses in real analysis, topology and algebra at the 600 and 700 levels, as well as potential topics courses in functional analysis. Creative accomplishments - His most recent work has contributed to the understanding of certain metrics on the state spaces of C*-algebras. These metrics arise from consideration of the "non-commutative transport problem," a quantized version of the classical problem of how to most efficiently change from one distribution of objects on a metric space to another distribution. The problems he has most recently solved involve the so-called metric boundary of Cayley graphs of finitely generated groups.

William R. Wells

Research area - Dr. Wells' research interests are in the mathematical analysis of engineering systems, in particular, the control and identification of nonlinear dynamical control systems. This involves the application of such mathematical disciplines as nonlinear differential equations, partial differential equations, perturbation methods and estimation and filtering theory, to name a few. Courses taught and awards - Dr. Wells has taught courses in ordinary and partial differential equations, linear systems theory, perturbation methods, flight control systems, space dynamics, optimal control theory, and college mathematics. Creative accomplishments - Dr. Wells is the author of more than 140 journal articles, reviewed conference publications and research reports in the areas of applied mathematics and engineering. He currently serves on the international organizing committee of three international mathematics and engineering conferences and serves as Chair, International Conference of Systems Engineering. He is an Associate Fellow of the American Institute of Aeronautics and Astronautics and is a Director of the International Council of Systems Engineering. He serves as a technical reviewer for several technical journals, the National Science Foundation and the Department of Education.