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Mathematics
Department of Mathematical Sciences
(406) 994-3601
The Department of Mathematical Sciences enforces prerequisites. By University policy, in order for any course to serve as the prerequisite you must earn a "C-" or better. In addition to the specific prerequisite courses listed, students in 100 level math courses and STAT 216 may also meet the prerequisite with the appropriate Math ACT, Math SAT, or Math Placement Exam score. Specific levels and scores for these courses can be found at: http://www.math.montana.edu/undergrad/Math_Hierarchy.pdf
MATH 065 PRE-ALGEBRA (COT)
MATH 085 PREALGEBRA
MATH 101 INTRODUCTORY ALGEBRA (COT)
MATH 103 INTRODUCTORY ALGEBRA
MATH 105 COLLEGE ALGEBRA
MATH 130 MATH FOR ELEMENTARY TEACHERS I
MATH 131Q MATH FOR ELEMENTARY TEACHERS II
MATH 149Q SECRETS OF THE INFINITE
MATH 150Q LIBERAL ARTS MATHEMATICS
MATH 151Q LANGUAGE OF MATH
MATH 160Q PRECALCULUS
MATH 170Q SURVEY OF CALCULUS
MATH 175Q CALCULUS FOR TECHNOLOGY I
MATH 176Q CALCULUS FOR TECHNOLOGY II
MATH 181Q CALCULUS & ANALYTIC GEOMETRY I
MATH 182Q CALCULUS & ANALYTIC GEOMETRY II
MATH 191Q HONORS CALCULUS & ANALYTIC GEOMETRY I
MATH 192Q HONORS CALCULUS & ANALYTIC GEOMETRY II
MATH 221 MATRIX THEORY
MATH 224Q CALCULUS OF FUNCTIONS OF SEVERAL VARIABLES
MATH 225 INTRODUCTION TO DIFFERENTIAL EQUATIONS
MATH 234Q HONORS CALCULUS OF FUNCTIONS OF SEVERAL VARIABLES
MATH 235 HONORS INTRODUCTION TO DIFFERENTIAL EQUATIONS
MATH 256 INTRODUCTION TO HIGHER MATHEMATICS
MATH 280 SPECIAL TOPICS
MATH 289R UNDERGRADUATE RESEARCH/CREATIVE ACTIVITY INSTRUCTION
MATH 290R UNDERGRADUATE RESEARCH/CREATIVE ACTIVITY
MATH 328 FOUNDATIONS OF DISCRETE MATHEMATICS
MATH 329 MODERN GEOMETRY
MATH 330 HISTORY OF MATHEMATICS
MATH 333 LINEAR ALGEBRA
MATH 348 TECHNIQUES OF APPLIED MATHEMATICS I
MATH 349 TECHNIQUES OF APPLIED MATHEMATICS II
MATH 361 ADVANCED CALCULUS I
MATH 362 ADVANCED CALCULUS II
MATH 400 SEMINAR
MATH 416 MODERN ALGEBRA
MATH 420 GEOMETRY, MEASUREMENT, AND DATA IN THE MIDDLE GRADES
MATH 421 PROBABILITY
MATH 422 MATHEMATICAL STATISTICS
MATH 424 ALGEBRAIC THINKING AND NUMBER SENSE IN THE MIDDLE GRADES
MATH 427 INTEGRATING MATHEMATICS & SCIENCE THROUGH MODELING
MATH 428 MATHEMATICAL MODELING
MATH 441 NUMERICAL LINEAR ALGEBRA & OPTIMIZATION
MATH 442 NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS
MATH 449 INTRODUCTION TO COMPLEX ANALYSIS
MATH 450 APPLIED MATHEMATICS I
MATH 451 APPLIED MATHEMATICS II
MATH 454 INTRODUCTION TO DYNAMICAL SYSTEMS I
MATH 455 INTRODUCTION TO DYNAMICAL SYSTEMS II
MATH 470 INDEPENDENT STUDY
MATH 476 INTERNSHIP
MATH 480 SPECIAL TOPICS
MATH 488 TEACHING FELLOWSHIP
MATH 489R UNDERGRADUATE RESEARCH/CREATIVE ACTIVITY INSTRUCTION
MATH 490R UNDERGRADUATE RESEARCH/CREATIVE ACTIVITY
MATH 494R RESEARCH EXPERIENCES IN APPLIED MATHEMATICS
MATH 500 SEMINAR
MATH 501 INTERMEDIATE PROBABILITY & STATISTICS
MATH 502 INTERMEDIATE MATHEMATICAL STATISTICS
MATH 503 ADVANCED LINEAR ALGEBRA
MATH 504 ABSTRACT ALGEBRA
MATH 505 PRINCIPLES OF MATHEMATICAL ANALYSIS
MATH 511 GENERAL TOPOLOGY
MATH 512 GEOMETRIC & ALGEBRAIC TOPOLOGY
MATH 516 THE LANGUAGE OF MATHEMATICS: AN ADVANCED PERSPECTIVE
MATH 517 ADVANCED MATHEMATICAL MODELING FOR TEACHERS
MATH 518 STATISTICS FOR TEACHERS
MATH 520 STANDARDS-BASED MATHEMATICS: CONCEPTS AND METHODS
MATH 521 THEORY OF LEARNING MATH
MATH 522 ASSESSMENT IN THE MATHEMATICS CLASSROOM
MATH 523 NUMBER STRUCTURE FOR TEACHERS
MATH 524 LINEAR ALGEBRA FOR TEACHERS
MATH 525 ANALYSIS FOR TEACHERS
MATH 526 DISCRETE MATHEMATICS FOR TEACHING
MATH 527 GEOMETRY FOR TEACHERS
MATH 528 CURRICULUM DESIGN
MATH 529 ASSESSMENT MODELS AND ISSUES
MATH 533 HISTORICAL STRATEGIES AND THE TEACHING OF MATHEMATICS
MATH 534 RESEARCH IN MATHEMATICS EDUCATION
MATH 535 TECHNOLOGY & THE TEACHING OF MATHEMATICS
MATH 540 INTRODUCTION TO CALCULUS ON MANIFOLDS
MATH 544 PARTIAL DIFFERENTIAL EQUATIONS I
MATH 545 PARTIAL DIFFERENTIAL EQUATIONS II
MATH 547 REAL ANALYSIS
MATH 551 COMPLEX ANALYSIS
MATH 560 METHODS OF APPLIED MATHEMATICS I
MATH 561 METHODS OF APPLIED MATHEMATICS II
MATH 570 INDEPENDENT STUDY
MATH 571 ACTION RESEARCH IN MATHEMATICS EDUCATION
MATH 572 IMPROVING MATHEMATICS EDUCATION: CAPSTONE PROPOSAL
MATH 575 RESEARCH OR PROFESSIONAL PAPER/PROJECT
MATH 576 INTERNSHIP
MATH 577 IMPROVING MATHEMATICS EDUCATION: CAPSTONE PROJECT
MATH 580 SPECIAL TOPICS
MATH 581 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS I
MATH 582 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS II
MATH 584 FUNCTIONAL ANALYSIS I
MATH 585 FUNCTIONAL ANALYSIS II
MATH 586 PROBABILITY THEORY
MATH 588 PROFESSIONAL DEVELOPMENT
MATH 589 GRADUATE CONSULTATION
MATH 590 MASTER'S THESIS
MATH 591 TOPICS IN APPLIED MATHEMATICS I
MATH 592 TOPICS IN APPLIED MATHEMATICS II
MATH 595 DYNAMICAL SYSTEMS I
MATH 596 DYNAMICAL SYSTEMS II
MATH 597 TOPICS IN MATHEMATICS I
MATH 598 TOPICS IN MATHEMATICS II
MATH 689 DOCTORAL READING & RESEARCH
MATH 690 DOCTORAL THESIS
MATH 065 PRE-ALGEBRA (COT)
F,S,Su 4 cr. LEC 4
-- This instructor-taught course introduces basic concepts relating to fractions, decimals, ratios, proportions, percent, simple equations, topics of signed numbers, and 1-variable linear equations are offered as a review and/or preparation for further studies in mathematics. Offered in partnership with the COT in Bozeman. Pass/Fail course.
MATH 085 PREALGEBRA
F,S, 3 cr. LEC 3
PREREQUISITE: Available only to TRIO students.
-- Instructor-taught course covering topics in problem solving, integers, fractions, decimals, percents, variable expressions, linear equations, and selected geometry topics. Offered through TRIO Student Support Services SUB 146.
MATH 101 INTRODUCTORY ALGEBRA (COT)
F,S,Su 4 cr. LEC 4
PREREQUISITE: Qualifying admission assessment score within the past 3 years, or instructor approval.
-- This instructor-taught course initiates development in students' ability to organize thought processes and systematically solve problems while preparing students for studies in other courses. Includes manipulation of variables, exponential applications, scientific notation, polynomials, factoring trinomials, solving equations, systems of equations, and graphing quadratic equations. This course is intended for students who have not studied algebra but have a firm background in basic mathematics or who wish it as a review. Offered in partnership with the COT in Bozeman.
MATH 103 INTRODUCTORY ALGEBRA
F,S 3 cr. IND 3
PREREQUISITE: MATH 065 or MATH 085 or Math Placement Test within the past 12 months.
-- A flexible paced course designed for a wide range of students needing anything from extensive practice to a quick review of algebraic concepts and problem solving. Students have access to a variety of resources as well as a personalized course webpage to keep track of their progress. Topics include linear equations and inequalities and their graphs, systems of linear equations and inequalities, exponents, polynomials, factoring, rational expressions, and square roots.
MATH 105 COLLEGE ALGEBRA
F,S,Su 3 cr. LEC 3
PREREQUISITE: MATH 103 or Math Placement Test within the past 12 months.
-- Further development of algebraic skills through the study of linear, quadratic, polynomial, exponential, and logarithmic functions.
MATH 130 MATH FOR ELEMENTARY TEACHERS I
F,S,Su 4 cr. LEC 4
PREREQUISITE: MATH 103 or Math Placement Test within the past 12 months.
-- An introduction to problem solving, sets, functions, logic, numerations systems as a mathematical structure, introductory number theory, rational, and irrational numbers and probability for prospective elementary school teachers.
MATH 131Q MATH FOR ELEMENTARY TEACHERS II
F,S,Su 3 cr. LEC 4
PREREQUISITE: MATH 130.
-- Introductory geometry, constructions, congruence and similarity, concepts
of measurement, coordinate geometry, problem solving revisited, and computer
applications for prospective elementary school teachers.
MATH 149Q SECRETS OF THE INFINITE
F,S 3 cr. LEC 2 LAB 1
PREREQUISITE: MATH 103 or Math Placement Test within the past 12 months.
-- Intriguing problems, puzzles, and paradoxes studied from an historical perspective.
Hands-on thought experiments follow mathematical ideas as they evolved from ancient beginnings into their modern contexts. Topics vary by semester.
MATH 150Q LIBERAL ARTS MATHEMATICS
F,S,Su 3 cr. LEC 3
PREREQUISITE: MATH 103 or Math Placement Test within the past 12 months.
-- Basic skills in applicable mathematics including linear, quadratic and exponential models; financial mathematics, trigonometry and some elementary statistics.
MATH 151Q LANGUAGE OF MATH
S 3 cr. LEC 3
PREREQUISITE: MATH 103 or Math Placement Test within the past 12 months.
-- Reading comprehension and writing skills in the language of mathematics; vocabulary, grammar, syntax and logic; emphasis on understanding, expressing, proving, and thinking mathematical thoughts.
MATH 160Q PRECALCULUS
F,S,Su 4 cr. LEC 4
PREREQUISITE: MATH 105 or Math Placement Test within the past 12 months.
-- Functions, graphs, and the use symbols for expressing mathematical thoughts. Polynomials, rational, exponential, logarithmic, and trigonometric functions.
MATH 170Q SURVEY OF CALCULUS
F,S,Su 4 cr. LEC 4
PREREQUISITE: MATH 105 or Math Placement Test within the past 12 months.
-- A survey of basic calculus including limits, differentiation, and integration
with applications to business, biology, and social science problems.
MATH 175Q CALCULUS FOR TECHNOLOGY I
F,S 3 cr. LEC 3
PREREQUISITE: MATH 160 or Math Placement Test within the past 12 months.
-- Calculus with emphasis on problems of interest to engineering technologists. Includes analytic geometry, differentiation, and introduction to integration.
MATH 176Q CALCULUS FOR TECHNOLOGY II
F,S 3 cr. LEC 3
PREREQUISITE: MATH 175.
-- Calculus with emphasis on problems of interest to engineering technologists.
Includes integration, infinite series, and differential equations.
MATH 181Q CALCULUS & ANALYTIC GEOMETRY I
F,S,Su 4 cr. LEC 4
PREREQUISITE: MATH 160 or Math Placement Test within the past 12 months.
-- Functions, elementary transcendental functions, limits and continuity,
differentiation, applications of the derivative, curve sketching, and integration theory.
MATH 182Q CALCULUS & ANALYTIC GEOMETRY II
F,S,Su 4 cr. LEC 4
PREREQUISITE: MATH 181.
-- Methods of integration, applications of the integral, Taylor's theorem, infinite sequences and series, polar coordinates.
MATH 191Q HONORS CALCULUS & ANALYTIC GEOMETRY I
F 4 cr. LEC 4
PREREQUISITE: Math 160 with an "A" grade, 700 on the SAT Math exam, 31 on the ACT Math exam, 4 on an AP Calculus exam, or consent of the instructor .
-- Topic coverage parallels Math 181 but with a greater emphasis on theory and more difficult problems.
MATH 192Q HONORS CALCULUS & ANALYTIC GEOMETRY II
S 4 cr. LEC 4
PREREQUISITE: Math 181 with an "A" grade or Math 191 with a "B" grade.
-- Topic coverage parallels Math 182 but with a greater emphasis on theory and more difficult problems.
MATH 221 MATRIX THEORY
F,S,Su 3 cr. LEC 3
PREREQUISITE: MATH 176 or MATH 182.
-- Matrix algebra, systems of linear equations, determinants, vector algebra
and geometry in Euclidean 3-space, eigenvalues, eigenvectors.
MATH 224Q CALCULUS OF FUNCTIONS OF SEVERAL VARIABLES
F,S,Su 4 cr. LEC 4
PREREQUISITE: MATH 182.
-- Topics in two and three dimensional geometry. Manipulation and application
of vectors. Functions of several variables, contour maps, graphs, partial
derivatives, gradients, double and triple integration, vector fields,
line integrals, surface integrals, Green's Theorem, Stokes' Theorem, the
Divergence Theorem.
MATH 225 INTRODUCTION TO DIFFERENTIAL EQUATIONS
F,S,Su 4 cr. LEC 4
PREREQUISITE: MATH 182.
-- An introduction to qualitative, quantitative, and numerical methods
for ordinary differential equations. Topics include modeling via differential
equations, linear and nonlinear first order differential equations and
systems, elementary phase plane analysis, forced oscillations, and Laplace
transform techniques.
MATH 234Q HONORS CALCULUS OF FUNCTIONS OF SEVERAL VARIABLES
F 4 cr. LEC 4
PREREQUISITE: MATH 192 with a 'B' grade, MATH 182 with an 'A' grade, AP
Calculus BC exam with a 5, or consent of the instructor.
-- Honors section of MATH 224. Topic coverage parallels
MATH 224 but with a greater emphasis on theory and more
difficult problem solving.
MATH 235 HONORS INTRODUCTION TO DIFFERENTIAL EQUATIONS
S 4 cr. LEC 4
PREREQUISITE: MATH 234 with a 'B' grade, MATH 224 with an 'A' grade, or
consent of the instructor.
-- Honors section of MATH 225. Topic coverage parallels MATH 225 but with a greater emphasis on theory and more difficult problem solving.
MATH 256 INTRODUCTION TO HIGHER MATHEMATICS
F,S 3 cr. LEC 3
PREREQUISITE: MATH 182.
-- Reasoning and communication in mathematics, including logic, generalization, existence, definition, proof, and the language of mathematics. Topics include functions, relations, set theory, recursion, algebra, number theory, and other areas of mathematics.
MATH 280 SPECIAL TOPICS
On Demand 1 - 4 cr. Maximum 12 cr.
PREREQUISITE: None required but some may be determined necessary.
-- Courses not required in any curriculum for which there is a particular
one-time need, or given on a trial basis to determine acceptability and demand before requesting a regular course number.
MATH 289R UNDERGRADUATE RESEARCH/CREATIVE ACTIVITY
INSTRUCTION
F,S,Su 1 - 2 cr. RCT may be repeated. Max 4 cr.
COREQUISITE: MATH 290.
-- Classroom instruction associated with directed undergraduate research and creative activity projects.
MATH 290R UNDERGRADUATE RESEARCH/CREATIVE ACTIVITY
F,S,Su 1 - 8 cr. IND
PREREQUISITE: Consent of the department head.
-- Directed undergraduate research.
MATH 328 FOUNDATIONS OF DISCRETE MATHEMATICS
F 3 cr. LEC 3
PREREQUISITE: MATH 256 or consent of instructor.
-- Concepts, processes, and proof in discrete mathematics, including number theory, abstract algebra, combinatorics and probability.
MATH 329 MODERN GEOMETRY
S 3 cr. LEC 3
PREREQUISITE: MATH 328.
-- Euclidean, hyperbolic, spherical, projective, finite, and fractal geometries;
linear transformations and their matrix representations; computer and telecommunications tools for geometry, NCTM Standards.
MATH 330 HISTORY OF MATHEMATICS
F alternate years, to be offered even years 3 cr. LEC 3
PREREQUISITE: MATH 224 and MATH 225 or consent of instructor.
-- Topics will be selected from the entire span of history from Egyptian, Babylonian, and Greek times through the 20th century. The course may focus on milestones that lead to the development of modern mathematics as well as the contributions of great mathematicians from ancient times until
today. Some ideas will require mathematical sophistication at the upper division level.
MATH 333 LINEAR ALGEBRA
F 3 cr. LEC 3
PREREQUISITE: MATH 221.
-- Vector spaces, subspaces, bases, and dimension. Linear transformations,
representation by matrices, nullity, rank, isomorphism. Eigenvalues, eigenvectors,
and diagonalization. Inner products, ad joints, unitary, and orthogonal transformations. Jordan form and minimal polynomials.
MATH 348 TECHNIQUES OF APPLIED MATHEMATICS I
F 3 cr. LEC 3
PREREQUISITE: MATH 224 and MATH 225.
-- An introduction to advanced analytical techniques frequently used by
scientists and engineers to study ordinary differential equations and
two-point boundary value problems. Topics include series solution techniques,
method of Frobenius, Laplace transforms, Fourier series, and boundary value problems.
MATH 349 TECHNIQUES OF APPLIED MATHEMATICS II
S 3 cr. LEC 3
PREREQUISITE: MATH 348.
-- Science and engineering majors often encounter partial differential
equations in the study of heat flow, vibrations, electric circuits, and
similar areas. Topics include Sturm-Liouville theory, partial differential
equations boundary value problems, and Laplace Transform methods.
MATH 361 ADVANCED CALCULUS I
F 3 cr. LEC 3.
PREREQUISITE: MATH 224 and either MATH 256, MATH 333, or consent of instructor.
-- A rigorous development of calculus with formal proofs. Functions, sequences,
limits, continuity, differentiation, and integration.
MATH 362 ADVANCED CALCULUS II
S 3 cr. LEC 3.
PREREQUISITE: MATH 361.
-- A rigorous development of multivariate calculus. Differentiable functions,
inversion theorem, multiple integrals, line and surface integrals, infinite
series.
MATH 400 SEMINAR
On Demand 1 cr. SEM 1 Maximum 4 cr.
PREREQUISITE: Junior standing and as determined for each offering.
-- Topics offered at the upper division level which are not covered in
regular courses. Students participate in preparing and presenting material.
MATH 416 MODERN ALGEBRA
S 3 cr. LEC 3
PREREQUISITE: MATH 333.
-- Senior capstone course. The integers, integers modulo n, the
Euclidean algorithm. Groups, subgroups, normal subgroups, quotient groups,
homomorphism and isomorphism theorems, and abelian groups. Rings, ideals,
homomorphism and isomorphism theorems. Integral domains, fields, and fields
of quotients.
MATH 420 GEOMETRY, MEASUREMENT, AND DATA IN THE MIDDLE GRADES
On Demand 3 cr. LEC 3
PREREQUISITE: MATH 256 or EDSD 461 or EDSD 471, or MATH 131 and 3 credits from elementary math option.
-- Develop content knowledge necessary to teach the new middle school mathematics curricula. Investigate the underlying conceptual structure of topics in geometry,
measurement and data analysis appropriate to middle school. Explore the use of manipulative materials and technologies, and discuss related pedagogical issues and national standards.
MATH 421 PROBABILITY
F 3 cr. LEC 3
PREREQUISITE: MATH 224.
-- Fundamentals of probability; discrete and continuous random variables;
expected value; variance; joint, marginal, and conditional distributions;
conditional expectations; applications, simulations; central limit theorem,
order statistics. Also, listed as STAT 420.
MATH 422 MATHEMATICAL STATISTICS
S 3 cr. LEC 3
PREREQUISITE: STAT 421 or MATH 421.
-- Introduction to the theory of point estimation, interval estimation,
and hypothesis testing. Also, listed as STAT 424.
MATH 424 ALGEBRAIC THINKING AND NUMBER SENSE IN THE MIDDLE GRADES
Su alternate even years and on demand 3 cr.LEC 3
PREREQUISITE: MATH 256 or EDSD 461 or EDSD 471, or MATH 131 and 3 credits from elementary math option.
-- Develop algebraic knowledge necessary to teach the new middle school mathematics curricula. Investigate the underlying conceptual structure of topics in algebra and number appropriate to middle school. Explore the use of manipulative materials and technologies, and discuss related pedagogical issues and national standards.
MATH 427 INTEGRATING MATHEMATICS AND SCIENCE THROUGH MODELING
Su alternate years, to be offered odd years 3 cr. LEC 3 Distance format.
PREREQUISITE: At least junior standing in math or science education certification
program or teacher certification and consent of instructor.
-- Generally taught via the Internet. This course focuses on the mathematical
methods-broadly labeled mathematical modeling - underlying scientific
inquiry and discovery. Through hands-on exploration and reflection, students
will examine topics such as historical connections between mathematics and science, empirical modeling, model validation, proportionality, and simulation.
MATH 428 MATHEMATICAL MODELING FOR TEACHERS
F 3 cr. LEC 3
PREREQUISITE: Junior or senior standing in mathematics education, or consent
of instructor
-- Senior capstone course. The use of pre-college mathematics to explore a variety of application areas. Overview of the modeling process, review of relevant technology, strategies to initiate modeling in the secondary classroom, modeling in the secondary curricula, and the classroom assessment of modeling activities.
MATH 441 NUMERICAL LINEAR ALGEBRA & OPTIMIZATION
F 3 cr. LEC 3
PREREQUISITE: MATH 221 and MATH 224.
-- Numerical solution of nonlinear equations. Numerical solutions of linear
systems and eigenvalue problems. Least squares, data smoothing, and optimization
techniques.
MATH 442 NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS
S 3 cr. LEC 3
PREREQUISITE: MATH 221 and MATH 225.
-- Numerical integration, numerical solutions of initial and boundary value problems in ordinary differential equations. Numerical solutions of partial differential equations.
MATH 449 INTRODUCTION TO COMPLEX ANALYSIS
S alternate years, to be offered even years 3 cr. LEC 3
PREREQUISITE: MATH 224.
-- An introduction to the techniques of complex analysis that are frequently
used by scientists and engineers. Topics include complex numbers, analytic
functions, Taylor and Laurent expansions, Cauchy's theorem, and evaluation
of integrals by residues.
MATH 450 APPLIED MATHEMATICS I
F alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: MATH 224 and MATH 225.
-- An introduction to modern methods in applied mathematics. Topics include
introductions to dimensional analysis and scaling, perturbation and WKB
methods, boundary layers, calculus of variations, stability, and bifurcation
analysis.
MATH 451 APPLIED MATHEMATICS II
S alternate years, to be offered even years 3 cr. LEC 3
PREREQUISITE: MATH 450.
-- This is the second semester of a course that introduces modern methods
in applied mathematics. Topics involve methods for linear and nonlinear
partial differential equations, including introductions to Green's functions,
Fourier analysis, shock waves, conservation laws, maximum and minimum
principles, and integral equations.
MATH 454 INTRODUCTION TO DYNAMICAL SYSTEMS I
F alternate years, to be offered even years 3 cr. LEC 3
PREREQUISITE: MATH 224 and MATH 225.
-- Existence and uniqueness of solutions to ordinary differential equations,
linearization, phase portraits, stability theory, and the analysis of specific examples.
MATH 455 INTRODUCTION TO DYNAMICAL SYSTEMS II
S alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: MATH 454.
-- Gradient systems, Poincare'-Bendixson theory, Poincare' maps, structural stability and chaotic systems.
MATH 470 INDEPENDENT STUDY
F,S,Su 1 - 3 cr. IND Maximum 6 cr.
PREREQUISITE: Junior standing, consent of instructor, and approval of department head.
-- Directed research and study on an individual basis.
MATH 476 INTERNSHIP
F,S,Su 2 - 12 cr. IND
PREREQUISITE: Junior standing, consent of instructor, and approval of department head.
-- An individualized assignment arranged with an agency, business, or other organization to provide guided experience in the field.
MATH 480 SPECIAL TOPICS
On Demand 1 - 4 cr. Maximum 12 cr.
PREREQUISITE: Course prerequisites as determined for each offering.
-- Courses not required in any curriculum for which there is a particular
one-time need, or given on a trial basis to determine acceptability and
demand before requesting a regular course number.
MATH 488 TEACHING FELLOWSHIP
F,S 1 - 2 cr. IND.
-- As co-teachers of a Mathematics or Statistics course, students will learn and have the opportunity to practice classroom teaching strategies as well as mentoring skills.
MATH 489R UNDERGRADUATE RESEARCH/CREATIVE ACTIVITY INSTRUCTION
F,S,Su 1 - 2 cr. RCT May be repeated. Max 4 cr.
COREQUISITE: MATH 490.
-- Classroom instruction associated with directed undergraduate research/creative
activity projects.
MATH 490R UNDERGRADUATE RESEARCH/CREATIVE ACTIVITY
F,S,Su 1 - 6 cr. IND May be repeated. Max 12 cr.
PREREQUISITE: Junior standing in mathematics and consent of department
head.
-- Directed undergraduate research/creative activity which may culminate
in a research paper, journal article, or undergraduate thesis.
MATH 494R RESEARCH EXPERIENCES IN APPLIED MATHEMATICS
S 3 cr. LEC 3
PREREQUISITE: MATH 221, MATH 224, and MATH 225.
-- Senior capstone course. An introduction to the use of modern scientific computing software to solve and investigate mathematical and scientific problems. The software package MAPLE or Mathematica will be used for visualization and computer algebra systems. Also, the software package MATLAB will be used for doing numerics and visualization.
MATH 500 SEMINAR
F,S,Su 1 cr. SEM 1 Maximum 6 cr.
PREREQUISITE: Graduate standing or seniors by petition. Course prerequisites as determined for each offering.
-- Topics offered at the graduate level which are not covered in regular courses. Students participate in preparing and presenting discussion material.
MATH 501 INTERMEDIATE PROBABILITY & STATISTICS
F 3 cr. LEC 3
PREREQUISITE: STAT 424 or MATH 362.
-- Families of probability distributions, distributions of functions of random variables, limiting distributions, order statistics. Cross-listed with STAT 501.
MATH 502 INTERMEDIATE MATHEMATICAL STATISTICS
S 3 cr LEC 3
PREREQUISITE: STAT 501.
-- Estimation, likelihood inference, statistical hypothesis tests, sufficient statistics, exponential families, Bayesian statistics. Cross-listed with STAT 502.
MATH 503 ADVANCED LINEAR ALGEBRA
S 3 cr. LEC 3
PREREQUISITE: MATH 333 or consent of instructor.
-- Topics include abstract vector spaces, diagonalization, Schur's Lemma,
Jordan canonical form and spectral theory for finite dimensional operators.
MATH 504 ABSTRACT ALGEBRA
S 3 cr. LEC 3
PREREQUISITE: MATH 416 or consent of instructor.
-- The theory of groups, rings and fields with particular emphasis on
finite groups, polynomial rings and fields of characteristic zero.
MATH 505 PRINCIPLES OF MATHEMATICAL ANALYSIS
F 3 cr. LEC 3
PREREQUISITE: MATH 362 or consent of instructor.
-- Principles of analysis in Euclidean spaces and metric spaces.
MATH 511 GENERAL TOPOLOGY
F 3 cr. LEC 3
PREREQUISITE: MATH 362 or consent of instructor.
-- Definition of a topology, relative topology, metric topology, quotient topology, and the product topology. Connectedness, local connectedness, components and path components. Compactness and local compactness, countability and separation axioms, the Urysohn Lemma, metrization and compactification.
MATH 512 GEOMETRIC & ALGEBRAIC TOPOLOGY
S 3 cr. LEC 3
PREREQUISITE: MATH 511 or consent of instructor.
-- Topics in continua theory, topics in dimension theory, covering spaces and the fundamental group, simplicial complexes, topics in homology and cohomology theory.
MATH 516 THE LANGUAGE OF MATHEMATICS: AN ADVANCED PERSPECTIVE
Su alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: Graduate standing in mathematics education, teaching endorsement
in mathematics, or consent of instructor.
-- The features of the language of mathematics, particularly as they apply
to high school and middle school curricula. Includes grammar, syntax,
vocabulary, synonyms, negation, sentence structure, paragraph structure,
logic, and proof. Comparison of oral and written modes of communication.
MATH 517 ADVANCED MATHEMATICAL MODELING FOR TEACHERS
S alternate years, to be offered odd years 3 cr. LEC 3 Distance format.
PREREQUISITE: Graduate standing in mathematics education, teaching endorsement in mathematics, or consent of instructor.
-- Hands-on focus on the use of modeling to solve real-world problems. Topics include the modeling process, an overview of relevant technology, strategies to initiate modeling in the secondary classroom, and classroom assessment of modeling activities. Extensive use of mathematics to explore application areas, leading to the construction of original models.
MATH 518 STATISTICS FOR TEACHERS
Su 3 cr. LEC 3 Distance format.
PREREQUISITE: Graduate standing in mathematics or science education, teaching endorsement
in mathematics or science, or consent of instructor.
-- Stochastic concepts including probabilistic underpinnings of statistics, measures of central tendency, variability, correlation, distributions, sampling, and simulation. Exploratory data analysis including experiments, surveys, measures of association and inferential statistics. Discussion of methods for teaching statistics in secondary mathematics and science.
MATH 520 STANDARDS-BASED MATHEMATICS: CONCEPTS AND METHODS
On Demand 3 cr. LEC/RCT
PREREQUISITE: Graduate standing in mathematics education, teaching endorsement in mathematics, or consent of instructor.
-- Study of key content themes and connections in algebra, geometry, probability/data
analysis, number, and measurement with a focus on the NCTM process standards. Exploring, extending, designing, and teaching standards-based classroom activities for middle/high school students and reflecting on student outcomes.
MATH 521 THEORY OF LEARNING MATH
S alternate years, to be offered odd years 3 cr. LEC/RCT 3 Distance format
PREREQUISITE: EDSD 461 and graduate standing in mathematics education, or consent of instructor.
-- Examine theories of learning as they apply to the mathematics classroom. The course focuses on theories of and research about learning, human development, personality and motivation. The theories and research are used (a) to understnd mathematics learning among students of all cultural, linguistic and socioeconomic backgrounds, and (b) to formulate effective teaching and learning strategies.
MATH 522 ASSESSMENT IN THE MATHEMATICS CLASSROOM
S alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: EDCI 360 or Equivalent
--Connects assessment theory and models to teachers' practice through classroom observations and hand-on activities. Focus on assessment practices consistent with standard-based mathematics, classroom assessment of student learning, evaluation of mathematics programs and curricula, and standardized testing practices.
MATH 523 NUMBER STRUCTURE FOR TEACHERS
F alternate years, to be offered even years 3 cr. LEC 3
PREREQUISITE: EDSD 410
-- Develop the relationship and distinction between mathematics behind the structure of number and learning and teaching of number structure in schools. Educational ideas of representation and abstraction examined via relevant and timely research about learning about the structure of number.
MATH 524 LINEAR ALGEBRA FOR TEACHERS
Su alternate years, to be offered even years 3 cr. LEC 3
PREREQUISITE: MATH 224 or MATH 328, EDSD 361.
-- Algebraic systems, special matrices, determinants, vector spaces, linear
programming with applications, graph theory, transportation, economics
and engineering using computer software such as MATLAB.
MATH 525 ANALYSIS FOR TEACHERS
Su alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: MATH 224 and EDSD 361.
-- A study of calculus reform and concepts from graphical, numerical and algebraic perspectives. Extensive use of activities and projects. Modeling and technology are incorporated throughout the course.
MATH 526 DISCRETE MATHEMATICS FOR TEACHERS
Su alternate years, to be offered even years 3 cr. LEC 3
PREREQUISITE: MATH 256 or MATH 516, EDSD 361 or EDSD 371 or equivalent, and K-14 teaching experience.
--Investigations of paradigm problems from the history of math.
MATH 527 GEOMETRY FOR TEACHERS
S alternate years, to be offered even years 3 cr. LEC 3 Distance format.
PREREQUISITE: MATH 329 and EDSD 361.
-- Geometry of transformations including Euclidean motions and similarity,
projective geometry, geometric topology and geometry of inversion.
MATH 528 CURRICULUM DESIGN
F alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: MATH 522 or EDCI 532 or equivalent.
--Focuses on the design and evaluation of curriculum in mathematics and science. Historical changes in mathematics and science curriculum as well as research results are studied in depth. This course is an on-line course.
MATH 529 ASSESSMENT MODELS AND ISSUES
S alternate years, to be offered even years 3 cr. LEC 3
--Examines critical K-12 issues including; alignment and interaction of assessment with standards, curriculum, and instruction; role of assessment systems at local, state, and national levels; evaluation of assessment tools and programs; equity considerations in assessment. This is an online course.
MATH 533 HISTORICAL STRATEGIES AND THE TEACHING OF MATHEMATICS
F alternate years, to be offered odd years 3 cr. LEC 3 Distance format.
PREREQUISITE: EDSD 361 and graduate standing in mathematics education, or consent of instructor.
-- Advanced teaching strategies in the field of middle grades, secondary and college
level mathematics, with a focus on the history of mathematics as a context for classroom instruction. Course content includes the changing nature of mathematics, historical problems and processes, and the development of teaching units that incorporate the history of mathematics.
MATH 534 RESEARCH IN MATHEMATICS EDUCATION
F alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: EDCI 506.
-- Quantitative and qualitative research methodology in mathematics education.
Review of the literature. Writing for publication and proposals.
MATH 535 TECHNOLOGY & THE TEACHING OF MATHEMATICS
F alternate years to be offered even years 3 cr. LEC 3 Distance format.
PREREQUISITE: Graduate standing or consent of instructor.
-- Calculator, computer, CD-ROM and telecommunications (internet) technologies
for K-16 mathematics education, software, curricular materials and online
high performance computers, analysis of impact of technology on K-12 math
curriculum. Emphasis on classroom implementation vis-a-vis corequisite course.
MATH 540 INTRODUCTION TO CALCULUS ON MANIFOLDS
F alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: MATH 503 and MATH 505 or consent of instructor.
-- An introduction to: manifolds and their atlases, fiber bundles, vector fields, tensor fields and differential forms, the exterior and Lie derivatives, Stokes Theorem, and de'Rham cohomology.
MATH 544 PARTIAL DIFFERENTIAL EQUATIONS I
F alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: MATH 362 and MATH 451, or consent of instructor.
-- An extended survey of the origins of a large number of scientific and
mathematical partial differential equations and an overview of the theoretical
techniques which are available to solve them.
MATH 545 PARTIAL DIFFERENTIAL EQUATIONS II
S alternate years, to be offered even years 3 cr. LEC 3
PREREQUISITE: MATH 544 and MATH 547.
-- Linear partial differential equations and the function spaces and functional analysis which one uses to study them. Topics include: Holder and Sobolev functions, Sobolev and Poincare inequalities, embedding density, semigroup theory for evolution equations.
MATH 547 REAL ANALYSIS
F 3 cr. LEC 3
PREREQUISITE: MATH 362 or MATH 505.
-- Lebesgue measure, and the Lebesgue integral of functions of a real
variable. General measure and integration theory. Lebesgue-Stieltjes integral and product measures.
MATH 551 COMPLEX ANALYSIS
S 3 cr. LEC 3
PREREQUISITE: MATH 505.
-- Analytic functions and conformal maps, contour integrals, Cauchy's theorem, Cauchy's integral formula, the maximum modulus theorem, harmonic functions, Taylor's theorem and Laurent series. Classification of singularities, the residue theorem and evaluation of definite integrals, Rouche's theorem and the argument principle.
MATH 560 METHODS OF APPLIED MATHEMATICS I
F alternate years, to be offered even years 3 cr. LEC 3
PREREQUISITE: MATH 451.
-- Finite dimensional vector spaces, spectral theory, Fredholm theorem of matrices, pseudo-inverses. Integral equations, Fredholm alternative and resolvent kernels, singular integral equations. Differential equations and Green's functions, eigenvalue expansions for differential operators.
MATH 561 METHODS OF APPLIED MATHEMATICS II
S alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: MATH 560.
-- Calculus of variations, Hamilton's principle, asymptotic and perturbation
methods, transform techniques and scattering theory. Partial differential
equations,Green's functions, separation of variables and transform methods.
MATH 570 INDEPENDENT STUDY
F,S,Su 1 - 3 cr. IND Maximum 6 cr.
PREREQUISITE: Graduate standing, consent of instructor, approval of department head and Dean of Graduate Studies.
-- Directed research and study on an individual basis.
MATH 571 ACTION RESEARCH IN MATHEMATICS EDUCATION
Su 2 cr. LEC
PREREQUISITE: Graduate standing and consent of instructor.
-- Prepares practicing mathematics teachers to study a mathematics education problem within their classroom, school or district with supervision by an MSU faculty member. Course topics include how to interpret educational research and literature; design and implement reliable and valid action research; identify worthwhile problems; and formulate questions that can be addressed through action research.
MATH 572 IMPROVING MATHEMATICS EDUCATION: CAPSTONE PROPOSAL
F 2 cr. LEC
PREREQUISITE: MATH 571 and Graduate standing and consent of instructor.
-- With guidance from faculty, students pursue a problem in the context of their classroom, school or district which impinges on student achievement in mathematics. Students work with a faculty advisor to characterize the problem, complete a review of relevant literature, and create an action research proposal to address the problem and evaluate outcomes of the proposed intervention.
MATH 575 RESEARCH OR PROFESSIONAL PAPER/PROJECT
F,S,Su 1 - 4 cr. IND, Maximum 6 cr.
PREREQUISITE: Graduate standing.
-- A research or professional paper or project dealing with a topic in the field. The topic must have been mutually agreed upon by the student and his or her major advisor and graduate committee.
MATH 576 INTERNSHIP
F,S,Su 2 - 12 cr. IND Maximum credits unlimited
PREREQUISITE: Graduate standing, consent of instructor and approval of department head.
-- An individualized assignment arranged with an agency, business or other organization to provide guided experience in the field.
MATH 577 IMPROVING MATHEMATICS EDUCATION: CAPSTONE PROJECTS
Su 3 cr. LEC
PREREQUISITE: Graduate standing, MATH 571/572 sequence, and consent of instructor.
-- With guidance from faculty,
students conduct action research
addressing a problem in the
context of their classroom,
school or district which impinges
on student achievement in
mathematics. Students work
with a faculty advisor to
implement an intervention,
collect and analyze data resulting
from the intervention, and
summarize results. Findings
are written up for Web publication
and presented orally to peers
at a capstone seminar.
MATH 580 SPECIAL TOPICS
On Demand 1 - 4 cr. Maximum 12 cr.
PREREQUISITE: Upper division courses and others as determined for each offering.
-- Courses not required in any curriculum for which there is a particular one time need, or given on a trial basis to determine acceptability and demand before requesting a regular course number.
MATH 581 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS I
F 3 cr. LEC 3
PREREQUISITE: MATH 442.
-- Finite difference and finite element solution techniques for elliptic, parabolic, and hyperbolic partial differential equations, numerical linear algebra.
MATH 582 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS II
S 3 cr. LEC 3
PREREQUISITE: MATH 581.
-- A continuation of topics from MATH 581.
MATH 584 FUNCTIONAL ANALYSIS I
F alternate years, to be offered even years 3 cr. LEC 3
PREREQUISITE: MATH 547.
-- Banach spaces, fixed point theorems, Hilbert spaces, the Dirichlet principle, generalized Fourier series, and spectral theory.
MATH 585 FUNCTIONAL ANALYSIS II
S alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: MATH 584.
-- The Hahn Banach theorem, variational principles, weak convergence, uniform boundedness theorem, the open mapping theorem and the implicit function theorem.
MATH 586 PROBABILITY THEORY
S alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: MATH 547.
-- Combinatorial probability and measure theoretic foundations of probability;
axioms for probability spaces. Borel-Cantelli Lemmas, weak and strong laws of large numbers, and the central limit problem.
MATH 588 PROFESSIONAL DEVELOPMENT
On Demand 1 - 3 cr. May be repeated; maximum 3 cr.
PREREQUISITE: Graduate standing, teaching experience and/or current employment
in a school organization, consent of instructor and Dean of Graduate Studies.
-- Courses offered on a one time basis to fulfill professional development needs of inservice educators. A specific focus is given to each course which is appropriately subtitled.
MATH 589 GRADUATE CONSULTATION
F,S,Su 3 cr. IND
PREREQUISITE: Master's standing and approval of the Dean of Graduate Studies.
-- This course may be used only by students who have completed all of their course work (and thesis, if on a thesis plan) but who need additional faculty or staff time or help.
MATH 590 MASTER'S THESIS
F,S,Su 1-10 cr. IND Maximum credits unlimited.
PREREQUISITE: Master's standing.
MATH 591 TOPICS IN APPLIED MATHEMATICS I
F 3 cr. LEC 3
PREREQUISITE: Graduate standing and consent of instructor.
-- Topics may include numerical solution of linear and nonlinear problems, eigenvalue problems, continuation methods, numerical optimization, computational mechanics, spectral methods, bifurcation theory, invariant manifold theory, index theory, nonlinear analysis, reaction-diffusion equations, nonlinear oscillations, asymptotic methods and perturbation methods.
MATH 592 TOPICS IN APPLIED MATHEMATICS II
S 3 cr. LEC 3
PREREQUISITE: Graduate standing and consent of instructor.
-- Topics may include numerical solution of linear and nonlinear problems,
eigenvalue problems, continuation methods, numerical optimization, computational
mechanics, spectral methods, bifurcation theory, invariant manifold theory,
index theory, nonlinear analysis, reaction-diffusion equations, nonlinear
oscillations, asymptotic methods and perturbation methods.
MATH 595 DYNAMICAL SYSTEMS I
F alternate years, to be offered odd years 3 cr. LEC 3
PREREQUISITE: MATH 503.
-- Topics in differential equations including existence and uniqueness, continuous dependence on parameters, extendability, the existence and stability of equilibria and limit cycles and the Poincare-Bendixon theorem.
MATH 596 DYNAMICAL SYSTEMS II
S alternate years, to be offered even years 3 cr. LEC 3
PREREQUISITE: MATH 595.
-- Topics include Hartman's theorem, invariant manifold theory, Smale-Birkhoff theorem, horseshoe chaos, and the Melnikov method. Topics in discrete dynamical systems may also be covered.
MATH 597 TOPICS IN MATHEMATICS I
F 3 cr. LEC 3
PREREQUISITE: Graduate standing and consent of instructor.
-- Topics selected from: differential topology, differential geometry and complex dynamics.
MATH 598 TOPICS IN MATHEMATICS II
S 3 cr. LEC 3
PREREQUISITE: Graduate standing and consent of instructor.
-- Topics selected from: continuum theory, symbolic dynamics, ergodic theory and low dimensional topology.
MATH 689 DOCTORAL READING & RESEARCH
F,S,Su 3 - 5 cr. IND Maximum 15 cr.
PREREQUISITE: Doctoral standing.
-- This course may be used by doctoral students who are reading research publications in the field in preparation for beginning doctoral thesis research.
MATH 690 DOCTORAL THESIS
F,S,Su 1-10 cr. IND Maximum credits unlimited.
PREREQUISITE: Doctoral standing.
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