Department of Mathematics
Chair and Associate Professor Ford
Assistant Chair and Associate Professor Lay
Professors Egger, R. Hill, Kratz, Lang
Associate Professors Bosworth, Cresswell, Fisher, L. Hill, Huotari, Laquer,
Parker, Stowe, Wolper
Assistant Professors Bernstein, Chang, Kantabutra
The Doctor of Arts program in mathematics is designed to prepare the student for a teaching career in institutions of higher learning. Theprogram emphasizes broad competence in mathematics rather than specialization and makes provision for classroom teaching experience.
Admission to the D.A. program requires the completion of the requirements for a master's degree equivalent to the M.S. in mathematics at Idaho State University with a 3.5 GPA in all graduate work. The aptitude portion of the Graduate Record Examination is required with a minimum score at the 50th percentile. The aptitude percentile is determined by averaging the percentiles of the quantitative, verbal and analytical sections.
Applicants will be selected according to the following criteria:
1. Measure of success in completing the master's program
2. Satisfactory GRE scores
3. Teaching experience
4. Three letters of recommendation
5. Applicant's letter discussing reasons for wishing to pursue this specific program.
Six semester hours beyond the master's degree may be transferred into the program. Two consecutive semesters of full-time study are required in residence.
The student will be advised initially by the departmental graduate committee. This group will be the student's temporary advising committee and will assist in the selection of the student's permanent committee who will supervise the remainder of the student's program.
The program requires coursework, a thesis, teaching internships, and examinations as described below. The program must include a minimum of 48 credits, and at least two 600-level sequences taken in residence. Approval for optional courses is granted by the Mathematics Department Graduate Committee.
A. Coursework
1. Mathematics Component
MATH 625-626 Real Analysis 6 crMATH 627-628 Complex Analysis 6 cr
MATH 631-632 Abstract Algebra 6 cr
MATH 671-672 Topology 6 cr
Twelve additional 600-level Mathematics credits, including one full-year sequence
2. Interdisciplinary and Applied Mathematics Component
MATH 550-551 Mathematical Statistics
Nine additional hours of approved interdisciplinary or applied mathematics coursework
3. Education Component
EDUC 676 College and University Teaching, or an approved related courseMATH 692 Doctor of Arts Seminar
MATH 693 Mathematical Exposition
An approved course in technical or expository writing
B.Doctor of Arts Thesis
The Doctor of Arts Thesis is an expository or research paper in mathematics or mathematics education. Six hours of course credit are given for the completion of the thesis.
C.Teaching Internship
Each candidate must complete teaching internships under the supervision of thedepartmental Graduate Committee. Six hours of course credit must be earned in MATH 700 Supervised Teaching Internship.
D.Examinations
1. DA Written Examination: A written comprehensive examination on undergraduate-level mathematics.
2. Oral Examination: An oral examination on graduate-level mathematics including the four areas of competence described in Section A. above, and the candidate's program of graduate coursework.
3. Final Examination: The candidate will present to the public a lecture on the candidate's dissertation, and will answer any questions that arise. Following the lecture and question period, the candidate will be examined orally by the candidate's dissertation committee on topics related to the dissertation.
The Master of Science degree program is designed to provide a broad and in-depth background and prepare the student for further study at the doctoral level or for an industrial or academic career.
For full admission to the M.S. degree program in mathematics, the applicant must have completed all requirements for a bachelor's degree in mathematics at an accredited institution. The applicant should have a grade point average of at least 3.0 over the last two years of undergraduate work and have taken the Graduate Record Examination, achieving at least the 50th percentile on the quantitative part of the general aptitude test. The student should have completed course work in modern algebra, differential equations, advanced calculus, and introductory analysis. Applicants not fully meeting these requirements may be allowed to make up deficiencies at ISU.
Two 600-level sequences are required. The department routinely offers the following sequences:
MATH 625-626 Real Analysis 6 cr
MATH 627-628 Complex Analysis 6 cr
MATH 631-632 Abstract Algebra 6 cr
MATH 641-642 Numerical Analysis 6 cr
MATH 662-663 Differential Equations 6 cr
MATH 671-672 Topology 6 cr
Of the remaining 18 credits at least 12 must be taken in graduate mathematics and at most 6 may, subject to departmental approval, be chosen from graduate courses in other disciplines. The student must complete a written examination in one of the two required sequences, and must pass a final oral examination which is intended to verify satisfactory understanding of the major field. Each student's program must be approved by the departmental graduate committee.
The degree of Master of Natural Science with a major in mathematics is designed specifically for people who hold a standard secondary school teaching certificate for the teaching of mathematics. The objective of the program is to enhance the mathematical training of secondary teachers and to equip such teachers with a broad and modern background in mathematics.
For full admission to the M.N.S. program in mathematics the applicant must hold a bachelor's degree and a standard secondary school teaching certificate. The applicant must have a GPA of at least 2.75 for the last two years of undergraduate work and must have taken the Graduate Record Examination (GRE), achieving at least the 50th percentile on the quantitative part of the general aptitude test. Applicants should have completed undergraduate work in both analytic geometry and calculus, a first course in both linear algebra and modern algebra, and at least one other mathematics course at the upper-division level.
Candidates for the Master of Natural Science in Mathematics degree must meet the following criteria:
1. Possession of a standard secondary teaching certificate or the equivalent.
2. Completion of a program of study approved by the graduate committee of the Mathematics Department and the Dean of the Graduate School.
3. A minimum of 30 credits beyond the bachelor's degree in courses numbered 300 or above. At least 22 credits must be in residence.
4. Satisfactory performance on final written and oral examinations.
Required coursework will depend upon the student's background in mathematics.
MATH g326 Elementary Analysis 3 credits. Rigorous calculus on the real line. Completeness, compactness, connectedness. Continuity, imagesof compact and connected sets. Series, uniform convergence. Differentiability, inverse functions, chain rule. Integration, fundamental theorem, improper integrals. PREREQ: MATH 223 AND MATH287.
MATH g327 Vector Analysis 3 credits. Calculus of vector functions of several variables. Derivative matrix. Chain rule. Inverse function theorem. Multiple integration. Change of variables. Integrals over curves and surfaces. Green's, Stokes' and divergence theorems. Applications to physics. PREREQ: MATH 223.
MATH g330 Linear Algebra 3 credits. Fields, vector spaces, linear transformations and matrices, triangular and Jordan forms, eigenvalues, dual spaces and tensor products, bilinear forms, inner product spaces. PREREQ: MATH 222 AND MATH 230.
MATH g331-g332 Modern Algebra 3 credits each. Rings, fields, groups, algebras, and selected topics in abstract algebra. PREREQ: MATH 287 AND MATH 330.
MATH g343 Modern Geometry 3 credits. Projective, Euclidean, and non-Euclidean geometries from an axiomatic point of view. PREREQ: MATH 230 OR PERMISSION OF INSTRUCTOR.
MATH g352 General Statistics 3 credits.Probability, random variables, discrete and continuous distributions such as the Binomial, Poisson, Geometric, Hypergeometric, Normal, and Gamma, sampling distribution, point and interval estimation, hypothesis testing. PREREQ: MATH 120 OR MATH 222.
MATH g355 Operations Research I 3 credits. Deterministic problems in operations research oriented towards business. Includes linear programming, transportation problems, network analysis, PERT, dynamic programming, and elementary game theory. PREREQ: MATH 230, 250 OR PERMISSION OF INSTRUCTOR.
MATH g356 Operations Research II 3 credits. Probabilistic models oriented towards business.Selections from stochastic processes, Markov chains, queuing theory, inventory theory, reliability, decision analysis, and simulation. PREREQ: MATH 355.
MATH g360 Differential Equations 3 credits. Theory and applications of ordinary differential equations. PREREQ: MATH 222 AND MATH 230 OR PERMISSION OF INSTRUCTOR.
MATH g421 Advanced Engineering Mathematics I 3 credits. Cross-listed as ENGR g421. Analysis of complex linear and non-linear engineering systems using advanced techniques, including Laplace transforms, Fourier series and classical partial differential equations. PREREQ: MATH 360, ENGR 264.
MATH g422 Advanced Engineering Mathematics II 3 credits. Cross-listed as ENGR g422. Analysis of complex linear and non-linear engineering systems using advanced techniques, including probability and statistics, advanced numerical methods and variational calculus. PREREQ: ENGR 421 OR MATH 421.
MATH g423-g424 Introduction to Real Analysis 3 credits each. The real number system, limits, sequences, series, and convergence; metric spaces; completeness; and selected topics on measure and integration theory. PREREQ: MATH 287, MATH 326, MATH 330, AND MATH 360.
MATH g435 Elementary Number Theory
3 credits. Diophantine equations, prime numbertheorems, residue systems, theorems
of Fermat andWilson, and continued fractions. PREREQ: MATH331.
MATH g441 Introduction to Numerical Analysis 3 credits. Designed to offer students in any applied science a reasonably broad introduction to standard numerical techniques for solving problems dealing with non-linear equations, systems of linear equations, differential equations, as well as techniques of interpolation, numerical integration, and differentiation. PREREQ: MATH 326 AND MATH 360 OR PERMISSION OF INSTRUCTOR.
MATH g442 Introduction to Numerical Analysis 3 credits. Extension of MATH 441 for students who wish to pursue more advanced techniques with emphasis on analysis. Typical topics covered include numerical methods applied to partial differentialequations, integral equations, and in-depth treatmentof topics covered in MATH 441. PREREQ: MATH441.
MATH g450-g451 Mathematical Statistics 3 credits each. Probability, random variables, discrete and continuous distributions, order statistics, limit theorems, point and interval estimation, uniformly most powerful tests, likelihood ratio tests, chi-square and F tests, nonparametric tests. PREREQ: MATH 326.
MATH g462 Introduction to Complex Variables 3 credits. Introduction to the study of functions of a complex variable including analytic functions, power series, integral theorems, and applications. PREREQ: MATH 360 AND EITHER MATH 326 OR MATH 421.
MATH g465 Partial Differential Equations 3 credits. Equations of the first and second orders, methods of solution, Laplace's Equation, heat equation, and the wave equation. Emphasis on applications to problems in the physical sciences and engineering. PREREQ: MATH 360 AND EITHER MATH 326 OR MATH 421.
MATH g473 Introduction to Topology 3 credits. Metric spaces; convergence; notions of continuity; connected, separable and compact spaces. PREREQ: PERMISSION OF INSTRUCTOR.
MATH g481 Special Problems 1-3 credits. Reading and conference in an area not usually covered by a regular offering. Individual work under the supervision and guidance of a professor whose specialty includes the chosen area. Open to seniors and graduate students in good standing and with the consent of the instructor. May be repeated until 6 credits are earned.
MATH g491 Mathematics Seminar 1-3 credits. Advanced reading and discussion on selected topics in mathematics. May be taken for credit more than once. PREREQ: SENIOR STANDING OR EQUIVALENT.
MATH 597 Professional Education Development Topics. Variable credit. May be repeated. A course for practicing professionals aimed at the development and improvement of skills. May not be applied to graduate degrees. May be graded S/U.
MATH 625-626 Real Analysis 3 credits each. Structure of the Real number system, measures and measurable functions, the Lebesgue integral, other integrals, Lp spaces, differentiable functions, the Radon-Nikodym Theorem, Fubini's Theorem. PREREQ: MATH 424.
MATH 627-628 Complex Analysis 3 credits each. Classical theorems of Cauchy, Goursat, Mittag-Leffler, Weierstrass, Riemann, and Picard involving analytic functions, representation theorems, conformal mappings, entire and meromorphic functions, analytic continuation, and other topics. PREREQ: PERMISSION OF INSTRUCTOR.
MATH 631-632 Abstract Algebra 3 credits each. Categories, groups, rings and ideals, polynomials, and fields through Galois Theory, modules, lattices, advanced linear and multilinear algebra. PREREQ: MATH 332 AND 330 OR PERMISSION OF INSTRUCTOR.
MATH 633 Matrix Analysis 3 credits. Eigenvalues, special matrices, normal forms, matrix polynomials, matrix functions, matrix norms, Kronecker products, stability, matrix equations, generalized inverses, nonnegative matrices. PREREQ: MATH 330 AND MATH 424.
MATH 641-642 Numerical Analysis 3 credits each. Topics selected from approximation theory, optimization, numerical linear algebra, differential and integral equations, spline analysis, computer algorithms, and other areas of current research in numerical analysis. PREREQ: MATH 423 AND MATH 441.
MATH 650 Thesis (D.A.) 1-6 credits.
MATH 652 Stochastic Processes 3 credits. Topics from conditional probability and expectation, martingales, Kolmogorov's Theorem, Markov processes, random walks, Brownian motion, diffusions, dynamic programming, stochastic differential equations. Applications to modeling physical and/or social dynamical systems. PREREQ: MATH 450.
MATH 653 Advanced Topics in Probability and Statistics 3 credits. Topics such as experimental design, regression analysis, multivariate statistical analysis. PREREQ: MATH 352 AND MATH 230, OR PERMISSION OF INSTRUCTOR.
MATH 655-656 Combinatorics 3 credits each. Theory and applications of: choice and enumeration techniques, generating functions, partitions, designs and configurations, graph theory including digraphs, algebraic graph theory and extremal problems. PREREQ: PERMISSION OF INSTRUCTOR.
MATH 662-663 Differential Equations 3 credits each. Existence, uniqueness, and dependence of solutions upon initial conditions; linear equations; autonomous equations; dynamical systems and stability; partial differential equations of first and second order, with applications. PREREQ: MATH 326, MATH 327, AND MATH 360.
MATH 664-665 Applied Mathematics 3 credits each. Differential operators, variational formulations, transform theory, spectral theory, Green's functions, bifurcations, stability, integrability, perturbation methods, applications to physical problems stressing construction and analysis of ODE and PDE models. PREREQ: MATH 330 AND MATH 465.
MATH 667-668 Functional Analysis 3 credits each. Major results of functional analysis, such as the Hahn-Banach, open mapping, and closed graph theorems; study of Hilbert and Banach spaces; spectral analysis. PREREQ: MATH 423 OR MATH 625 OR PERMISSION OF INSTRUCTOR.
MATH 671-672 Topology 3 credits each. Fundamental theorems and examples from point-set topology; emphasis on general and metric topologies and continuous mappings; introduction to topology of manifolds, covering spaces, homotopy, homology, and cohomology. PREREQ: MATH 473 OR PERMISSION OF INSTRUCTOR.
MATH 681-682 Differential Geometry 3 credits each. Differentiable manifolds and mappings; bundles, connections, geodesics, and curvature; Lie groups; topics from Riemannian, Hermitian, or symplectic geometry. PREREQ: MATH 327 AND MATH 330.
MATH 691 Seminar 1-3 credits. Advanced readings, problems, and discussion on selected topics in mathematics. May be taken for credit more than once on distinct topics.
MATH 692 Doctor of Arts Seminar 2 credits. Topics include the nature and practice of mathematical research, grants, public speaking, professionally and classroom related software, information media, issues in mathematical pedagogy, standards, and curricula, university organization, history of mathematics. Graded S/U.
MATH 693 Mathematical Exposition 1 credit. Presentation of mathematics in a seminar setting. Small group practice in and critique of mathematical exposition. Requirements include presentation of a departmental colloquium on an assigned topic. Graded S/U.
MATH 699 Special Topics in Mathematics 1-3 credits. Each offering will deal with a topic selected from such fields of mathematics as algebra, analysis, geometry, number theory, topology, applied analysis, probability, and mathematical logic. May be taken for credit more then once. PREREQ: PERMISSION OF INSTRUCTOR.
MATH 700 Supervised Teaching Internship. Credit variable up to 9 credits. Graded S/U.
Idaho State University Academic Information
Revised: May 1, 1996
URL http://www.isu.edu/academic-info/prev-isu-cat/grad96/artsci/mathdept.html