Assessment Plan Template

Assessment Plan Template Program Ph.D. in Mathematical Sciences Assessment Coordinator for the program Farrokh Saba Department(s) or Interdisciplinary Council Responsible for the Program Mathematical Sciences Five-Year Implementation Dates______(2004-2005 to 2009-2010)_

Is this program accredited by an external organization? No X Yes, and the organization is Northwest Commission on Colleges and Universities. NOTE: The program may submit the most recent self study assessment documents/information in substitution for this plan.

1. Student Learning Outcomes for the program. List the Student Learning Outcomes for the program. Upon completion of the Ph.D degree in mathematical sciences, students would be able to demonstrate:

1. A solid foundation in mathematics and, conduct independent research in their selected area of specialization (Applied Mathematics, Computational Mathematics, Pure Mathematics, and Statistics). 2. Demonstrate the ability to conduct original research in his or her area of concentration.

MAT 703 & 704 Abstract Algebra: Detailed study of the following algebraic structures: groups, rings, and ideals, fields, modules, and Galois theory.

MAT 707 & 708 Real Analysis: Measure theory, differentiation and integration, Banach spaces, Hilbert spaces, and continuous functions.

MAT 709 & 710 Complex Function Theory: Analytic functions, conformal mappings, Cauchy’s theorem, and power series, Riemann mapping theorem, harmonic functions, and analytic continuation.

MAT 765 & 766 Advanced Numerical Analysis: Numerical solution of ordinary and partial differential equations. Topics selected by instructor.

1 MAT 771 & 772 Applied Analysis: Functional analysis, Banach spaces, Hilbert spaces, computational applications, linear functionals and operators, operators, fixed point theorems, iterative methods, elementary spectral theory, and applications.

STA 715 Multivariate Statistical Methods. Multivariate techniques with emphasis on application. Topics include multivariate analysis of variance, discriminant analysis, canonical correlation and independence, principal component analysis, factor analysis, cluster analysis and analysis of repeated measurements.

STA 763 & 764 Regression and Multivariate Analysis. Fitting a straight line, matrix theory, examining residuals, selecting the “best” fit, multiple regression, non-lineal regressions.

STA 765 Statistical Decision Theory. Introduction to decision theory, decision rules, loss functions, risk functions, decision principles, utility theory, Bayesian estimators, Bayesian sequential analysis.

STA 767 Mathematical Statistics I. Basic probability theory, conditional probability, independence, random variables, probability distribution functions, principles of data reduction.

2 2. Curriculum Alignment of Student Learning Outcomes. Where is the information introduced, enriched, and/or reinforced in the courses required in the program? Required Courses Program Minimum of 60 Applied Math Computational Pure Math Statistics Outcome Goals credit hours Concentration Math Concentration Concentration beyond the Concentration baccalaureate, at least 36 of MAT 707 MAT 707 MAT 703 STA 715 which must be at the 700 level. MAT 709 MAT 709 MAT 707 STA 763 At least 30 MAT 771 and MAT 765 MAT 709 STA 765 credit hours 2 Electives. MAT 766 2 Electives STA 767 must be 1 Elective 1 Elective completed at UNLV and at 24 Credits 24 Credits 24 Credits (Max. 36) 24 Credits (Max. least 18 credits (Max. 36) for (Max. 36) for for dissertation. 36) for hours of which dissertation. dissertation. dissertation. must be at 700 level.

Demonstrate I I, E I I, E I strongly knowledge of mathematics and Concentration Analyze I I, E I I, E I strongly mathematics concepts and Concentration Do master I I, E I I, E I problem- solving in mathematics and Concentration I = Introduced E = Enhanced R = Reintroduced

3 Required Courses Program MAT 707 MAT 709 MAT 771 MAT 765 MAT 766 Outcome Goals Demonstrate I, E I, E I, E I, E strongly knowledge of mathematics and Concentration Analyze I, E I, E I, E I, E strongly mathematics concepts and Concentration Do master I, E I, E I, E I, E problem- solving in mathematics and Concentration

I = Introduced E = Enhanced R = Reintroduced

4 Required Courses Program MAT 703 STA 715 STA 763 STA 765 STA 767 Outcome Goals Demonstrate I, E I, E I, E I, E strongly knowledge of mathematics and Concentration Analyze I, E I, E I, E I, E strongly mathematics concepts and Concentration Do master I, E I, E I, E I, E problem- solving in mathematics and Concentration

I = Introduced E = Enhanced R = Reintroduced

5 3. Methods, Instruments and Analysis. What instruments will be used in each of the five years? When and where will they be administered in each of the five years? Which Student Learning Outcomes will be assessed during each of the 5 years? How will results be reported (e.g. percentages, ranks, state or national comparisons) for each of the 5 years?

Learning Assessment Person Instrument When and Person Expected Benchmark Outcome Questions responsible for where will responsible for Measures instrument data be data analysis (mean & A student at development/ collected and report standard Grade of A- completion of Who will deviation), or better the degree will administer component be able to instruments analysis, demonstrate and collect percentage completing in: data Farrokh Saba of Did students End of Assessment agreement master? semester and Coordinator or strongly In class agree, percentage who meet of exceed benchmark

Abstract Did students Instructor/ MAT 703 & End of Assessment Grade of B Grade of A- Algebra: master Instructor 704 semester and Coordinator or better or better Detailed study Detailed study Exams In class of the of the following following algebraic algebraic structures: structures: groups, rings, groups, rings, and ideals, and ideals, fields, fields, modules, and modules, and Galois theory. Galois theory?

6 Real Analysis: Did students Instructor/ MAT 707 & End of Assessment Grade of B Grade of A- Measure master Instructor 708 semester and Coordinator or better or better theory, Measure Exams In class differentiation theory, and integration, differentiation Banach spaces, and integration, Hilbert spaces, Banach spaces, and continuous Hilbert spaces, functions. and continuous functions.?

Complex Did students Instructor/ MAT 709 & End of Assessment Grade of B Grade of A- Function master Instructor 710 semester and Coordinator or better or better Theory: Analytic Exams In class Analytic functions, functions, conformal conformal mappings, mappings, Cauchy’s Cauchy’s theorem, and theorem, and power series, power series, Riemann Riemann mapping mapping theorem, theorem, harmonic harmonic functions, and functions, and analytic analytic continuation.? continuation.

7 Advanced Did students Instructor/ MAT 765 & End of Assessment Grade of B Grade of A- Numerical master Instructor 766 semester and Coordinator or better or better Analysis: Numerical Exams In class Numerical solution of solution of ordinary and ordinary and partial partial differential differential equations. equations. Topics selected Topics selected by instructor? by instructor. Applied Did students Instructor/ MAT 771 & End of Assessment Grade of B Grade of A- Analysis: master Banach Instructor 772 semester and Coordinator or better or better Functional spaces, Hilbert Exams In class analysis, spaces, Banach spaces, computational Hilbert spaces, applications, computational linear applications, functionals and linear operators, functionals and operators, fixed operators, point theorems, operators, fixed iterative point theorems, methods, iterative elementary methods, spectral theory, elementary and spectral theory, applications? and applications.

8 Multivariate Did students Instructor/ STA 715 End of Assessment Grade of B Grade of A- Statistical master Instructor semester and Coordinator or better or better Methods. Multivariate In class Multivariate techniques Exams techniques with emphasis with emphasis on application. on application. Topics include Topics include multivariate multivariate analysis of analysis of variance, variance, discriminant discriminant analysis, analysis, canonical canonical correlation and correlation and independence, independence, principal principal component component analysis, factor analysis, factor analysis, analysis, cluster analysis cluster analysis and analysis of and analysis of repeated repeated measurements? measurements.

9 Regression and Did students Instructor/ STA 763 & End of Assessment Grade of B Grade of A- Multivariate master Instructor 764 semester and Coordinator or better or better Analysis. Fitting a Exams In class Fitting a straight line, straight line, matrix theory, matrix theory, examining examining residuals, residuals, selecting the selecting the “best” fit, “best” fit, multiple? multiple regression, regression, non-lineal non-lineal regressions? regressions. Statistical Did students Instructor/ STA 765 End of Assessment Grade of B Grade of A- Decision master Instructor Exams semester and Coordinator or better or better Theory. Introduction to In class Introduction to decision decision theory, theory, decision rules, decision rules, loss functions, loss functions, risk functions, risk functions, decision decision principles, principles, utility theory, utility theory, Bayesian Bayesian estimators, estimators, Bayesian Bayesian sequential sequential analysis? analysis.

10 Mathematical Did students Instructor/ STA 767 End of Assessment Grade of B Grade of A- Statistics I. master Instructor semester and Coordinator or better or better Basic Basic In class probability probability theory, theory, conditional conditional probability, probability, independence, independence, random random variables, variables, probability probability distribution distribution functions, functions, principles of principles of data reduction. data reduction?

Or Or Instructor/ MAT 765 End of Assessment Grade of B Grade of A- Advanced Did students Instructor Exams semester and Coordinator or better or better Numerical master In class Analysis: Numerical Numerical solution of solution of ordinary and ordinary and partial partial differential differential equations? equations.

Topics in Did students Instructor/ MAT 767 End of Assessment Grade of B Grade of A- Numerical master Topics Instructor Exams semester and Coordinator or better or better Analysis. in Numerical In class Analysis?

11 Analysis & Did students Instructor/ 6 Credit: End of Assessment Grade of B Grade of A- Applied math master Instructor Analysis & semester and Coordinator or better or better at 700 level. Analysis & Applied math In class Applied math at 700 level. at 700 level? Exams Demonstrate Did students Instructor/ 6 Credit: End of Assessment Grade of B Grade of A- the ability to demonstrate Instructor Thesis or 6 semester and Coordinator or better or better search the ability to credit MAT or In class scientific search STA at 700 literature and scientific level. work on a literature and specific work on a problem. specific problem?

Demonstrate Did students Instructor/ Thesis End of Assessment Pass/Fail Pass the ability to demonstrate Instructor Defense: semester and Coordinator successfully the ability to Demonstrate In class present results successfully the ability to in both oral present results successfully and written in both oral present results formats. and written in both oral formats? and written formats. Demonstrate Did students Instructor/ Written End of Assessment Pass/Fail Pass Written Demonstrate Instructor Comprehensive semester and Coordinator Comprehensive Written Examination: In class Examination: Comprehensive Based on Based on Examination: degree degree Based on requirements. requirements. degree requirements?

12 4. Process for Program Improvement and Dissemination. When, where, and how will results be disseminated to stakeholders? Every semester the results will be disseminated to stakeholders.

Identify person(s) responsible for reviewing results and making How will assessment results be disseminated to stakeholders? recommendations Chair of the Department of Mathematical Sciences University website for Provost

updated 6 July 2008