Chairperson and Associate Professor Ford
Assistant Chair and Professor Egger
Professors R. Hill, Kratz
Associate Professors Cresswell, Fisher, L. Hill, Huotari, Lang, Lay, Parker, Stowe
Assistant Professors Bernstein, Bosworth, Chang, Driessel, Laquer, Wolper
Doctor of Arts in Mathematics
The Doctor of Arts program in mathematics is designed to prepare the student for a teaching career in institutions of higher learning. The program 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:
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.
Committees and Advising
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 a minimum of 48 semester hours distributed among a subject-matter component, an education component, an interdisciplinary component, and a teaching internship as follows:
a. Mathematics Component: Competence in six sequences is required:
MATH 541-542 Numerical Analysis 6 cr MATH 550-551 Probability and Statistics 6 cr MATH 625-626 Real Analysis 6 cr MATH 627-628 Complex Analysis 6 cr MATH 631-632 Abstract Algebra 6 cr MATH 671-672 Topology 6 cr
These requirements may be met in several ways. Since most students entering the program will have previously taken several of these sequences, the departmental graduate committee may determine that previously taken courses meet the ISU requirements. Up to four sequences may be satisfied by this method. If it is the opinion of the advisory group that more work would be beneficial, they may stipulate that the candidate satisfy the requirement either by completing the course with a grade of B or better, or by sitting for and passing a two-hour exam administered at the semester break.
The two or more sequences not satisfied as outlined above must be taken as part of the candidate's program along with 12 additional mathematics credits at the 600 level.
b. Education Component: 3 credits from the College of Education and 3 credits from the Mathematics Department.
c. Interdisciplinary Component: 6 credits of approved courses in related academic fields.
d. Thesis: 6 credits.
e. Teaching Internship: 6-9 credits. Each student is required to serve a teaching internship. By the end of the first year of residence, a proposal should be submitted to the graduate committee outlining the details of the internship. From this proposal a mutually acceptable plan for the internship will be worked out.
Internships at other colleges are possible. Other possibilities for internship are work in the computer center, work with curriculum, work on individual education projects, or coordination of departmental functions.
The thesis consists of an expository or research paper in mathematics or mathematics education. Six hours' credit is given for completion of the thesis.
Ordinarily, full-time study consists of 9-12 hours of graduate credits per semester.
In addition to demonstrations of competence in the six basic areas, the student must pass two comprehensive examinations. Early in a student's program, she/he must pass a written examination on undergraduate mathematics, administered by the departmental graduate committee. The second, an oral examination administered by the candidate's permanent committee, tests knowledge of the six required areas of competence and the student's program of study. In the event of unsatisfactory performance on either or both exams, they may be attempted again after a semester's wait. A second failure eliminates a candidate from the program.
Mathematical Topic Exposition
After successfully completing the Undergraduate Mathematics Examination and before entering into investigation leading to the Thesis, the D.A. candidate will complete a Mathematical Topic Exposition. The purpose of the Exposition is to present the candidate with the experience of investigating, organizing, and reporting to the Department on a mathematical subject not otherwise included in his/her program of study. This is conducted as follows:
In consultation with the candidate's advisory committee, the Graduate Committee will select a topic complementary to the candidate's approved program. Within 11 days of the assignment of the topic, the candidate will present a 50-minute lecture at a departmental colloquium and will deliver a written report to the Graduate Committee. The candidate's oral and written work will be evaluated according to both their breadth and their depth. Two failures at the Exposition will eliminate a candidate from the D.A. Program.
Upon completion of the required course work, the teaching internship, exams, and the thesis, the candidate must present him/herself for a final oral examination which is a thesis defense. The final examination is open to all persons invited by the major advisor, the department chairperson, or the Dean of the Graduate School.
Master of Science in Mathematics
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 industrial or academic careers.
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. 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 655-656 Combinatories 3 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.
No thesis is required; the emphasis is on course work. No language study is required. Each student's program must be approved by the departmental graduate committee.
Master of Natural Science in Mathematics
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).
Applicants should have completed undergraduate work in analytic geometry and calculus, a first course in 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:
MATH g326 Elementary Analysis 3 credits. Rigorous calculus on real line. Completeness, compactness and connectedness. Continuity, images of compact and connected sets. Series, uniform convergence. Differentiability, inverse functions, chain rule. Integration, fundamental theorem, improper integrals. PREREQ: MATH 223 AND MATH 287.
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. Reviews some essential material from a first course in applied statistics and proceeds to additional statistical techniques; estimation, testing hypotheses, regression and correlation, analysis of variance, and non-parametric statistics. Oriented toward the behavioral, social, and managerial sciences. PREREQ: MATH 250, 252 OR EQUIVALENT.
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 are treated. 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 number theorems, residue systems, theorems of Fermat and Wilson, and continued fractions. PREREQ: MATH 331.
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 differential equations, integral equations, and in-depth treatment of topics covered in MATH 441. PREREQ: MATH 441.
MATH g450-g451 Probability and Statistics 3 credits each. MATH 450 includes discrete and continuous random variables, central limit theorem and some special distributions. Other topics may include Markov chains, branching processes, and random walks. MATH 451 includes interval and point estimation with emphasis on sufficient statistics, testing hypotheses, including uniformly most powerful tests, sequential probability ratio tests, Chi square tests, analysis of variance, regression analysis, tests for independence, and non-parametric methods. Applications to the physical, social, and biological sciences will be stressed. PREREQ FOR MATH 450: MATH 223.
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. Continuity, convergence, measurable sets and functions, the Lebesgue integral, measure spaces, integration, normed linear spaces. Hilbert and Banach spaces; extension and representation theorems. PREREQ: PERMISSION OF INSTRUCTOR.
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 Theory 3 credits. Modern aspects of matrix theory. Perron-Frobenius-Wielandt theory of nonnegative matrices, M-matrices, theory of doubly stochastic matrices, inertia theorems, canonical forms, elementary divisor theory. PREREQ: MATH 330 OR PERMISSION OF INSTRUCTOR.
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. Poisson processes, renewal processes, branching processes, continuous and discrete time Markov chains and queuing theory. Applications of the theory and methods of model building are stressed. PREREQ: MATH 327 AND 450.
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. Topics selected from the theory of existence, uniqueness, extension, stability and behavior of solutions of differential equations. Numerical techniques, transform theory, expansions of solutions, and related areas may be studied. PREREQ: MATH 360.
MATH 667 Introduction to Functional Analysis 3 credits. Metric spaces and their completion, convergence, Banach and Hilbert spaces, linear operators and related topics. PREREQ: MATH 423 OR 625 OR PERMISSION OF INSTRUCTOR.
MATH 668 Topics in Functional Analysis 3 credits. Major results of functional analysis, such as the Hahn-Banach, uniform boundedness, open mapping, and fixed point theorems and their applications to other areas of mathematics. PREREQ: MATH 667.
MATH 671-672 Topology 3 credits each. Fundamental theorems of point-set topology. Metric spaces, compact spaces, topological spaces, and applications. PREREQ: PERMISSION OF INSTRUCTOR.
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 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.