## M

Course Equivalency Tool *(Montana University System Common Course Changes)*

Mathematics

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/documents/MHierarchy.pdf.

M 065 PREALGEBRA (Gallatin College Programs) M 066 PREALGEBRA LAB & STUDY (Gallatin College Programs) M 085 PREALGEBRA M 088 MATHEMATICAL LITERACY M 096 SURVEY OF ALGEBRA (Gallatin College Programs) M 097 SURVEY OF ALGEBRA (Mastery Learning) M 108 BUSINESS MATHEMATICS (Gallatin College Programs) M 121Q COLLEGE ALGEBRA M 132 NUMBERS & OPERATIONS FOR K-8 TEACHERS M 133Q GEOMETRY & GEOMETRIC MEASUREMENT FOR K-8 TEACHERS M 135 MATHEMATICS FOR K-8 TEACHERS I M 136Q MATHEMATICS FOR K-8 TEACHERS II M 145Q MATHEMATICS FOR THE LIBERAL ARTS M 147Q LANGUAGE OF MATHEMATICS M 149Q SECRETS OF THE INFINITE M 151Q PRECALCULUS M 161Q SURVEY OF CALCULUS M 165Q CALCULUS FOR TECHNOLOGY I M 166Q CALCULUS FOR TECHNOLOGY II M 171Q CALCULUS I M 172Q CALCULUS II M 181Q HONORS CALCULUS I M 182Q HONORS CALCULUS II M 221 INTRODUCTION TO LINEAR ALGEBRA M 234 ADVANCED TOPICS IN MATHEMATICS FOR K-8 TEACHERS M 242 METHODS OF PROOF M 273Q MULTIVARIABLE CALCULUS M 274 INTRODUCTION TO DIFFERENTIAL EQUATIONS M 283Q HONORS MULTIVARIABLES CALCULUS M 284 HONORS INTRODUCTION TO DIFFERENTIAL EQUATIONS M 290R UNDERGRADUATE RESEARCH M 291 SPECIAL TOPICS M 328 HIGHER MATHEMATICS FOR SECONDARY TEACHERS M 329 MODERN GEOMETRY M 330 HISTORY OF MATHEMATICS M 333 LINEAR ALGEBRA M 348 TECHNIQUES OF APPLIED MATHEMATICS I M 349 TECHNIQUES OF APPLIED MATHEMATICS II M 383 INTRODUCTION TO ANALYSIS I M 384 INTRODUCTION TO ANALYSIS II M 386R SOFTWARE APPLICATIONS IN MATHEMATICS M 420 GEOMETRY, MEASUREMENT, AND DATA IN THE MIDDLE GRADES M 424 ALGEBRAIC THINKING AND NUMBER SENSE IN THE MIDDLE GRADES M 428 MATHEMATICAL MODELING FOR TEACHERS M 430 MATHEMATICAL BIOLOGY M 431 ABSTRACT ALGEBRA I M 441 NUMERICAL LINEAR ALGEBRA & OPTIMIZATION M 442 NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS M 450 APPLIED MATHEMATICS I M 451 APPLIED MATHEMATICS II M 454 INTRODUCTION TO DYNAMICAL SYSTEMS I M 455 INTRODUCTION TO DYNAMICAL SYSTEMS II M 472 INTRODUCTION TO COMPLEX ANALYSIS M 490R UNDERGRADUATE RESEARCH M 491 SPECIAL TOPICS M 492 INDEPENDENT STUDY M 494 SEMINAR M 497 EDUCATIONAL METHODS:TEACHING FELLOWSHIP M 498 INTERNSHIP M 501 INTERMEDIATE PROBABILITY & STATISTICS M 502 INTERMEDIATE MATHEMATICAL STATISTICS M 503 ADVANCED LINEAR ALGEBRA M 504 ABSTRACT ALGEBRA M 505 PRINCIPLES OF MATHEMATICAL ANALYSIS M 509 STOCHASTIC PROCESSES M 511 GENERAL TOPOLOGY M 512 GEOMETRIC & ALGEBRAIC TOPOLOGY M 516 LANGUAGE OF MATHEMATICS FOR TEACHERS M 517 ADVANCED MATHEMATICAL MODELING FOR TEACHERS M 518 STATISTICS FOR TEACHERS M 520 STANDARDS-BASED MATHEMATICS FOR TEACHERS M 521 LEARNING THEORIES IN MATHEMATICS FOR TEACHERS M 522 ASSESSMENT OF MATHEMATICS FOR TEACHERS M 523 NUMBER STRUCTURE FOR TEACHERS M 524 LINEAR ALGEBRA FOR TEACHERS M 525 ANALYSIS FOR TEACHERS M 526 DISCRETE MATHEMATICS FOR TEACHING M 527 GEOMETRY FOR TEACHERS M 528 CURRICULUM DESIGN M 529 ASSESSMENT MODELS AND ISSUES M 533 HISTORY OF MATHEMATICS FOR TEACHERS M 534 RESEARCH IN MATHEMATICS EDUCATION M 535 TECHNOLOGY AND MATHEMATICS FOR TEACHERS M 540 INTRODUCTION TO CALCULUS ON MANIFOLDS M 544 PARTIAL DIFFERENTIAL EQUATIONS I M 545 PARTIAL DIFFERENTIAL EQUATIONS II M 547 MEASURE THEORY M 551 COMPLEX ANALYSIS M 560 METHODS OF APPLIED MATHEMATICS I M 561 METHODS OF APPLIED MATHEMATICS II M 570 INDEPENDENT STUDY M 571 ACTION RESEARCH IN MATHEMATICS EDUCATION M 572 IMPROVING MATHEMATICS EDUCATION: CAPSTONE PROPOSAL M 575 RESEARCH OR PROFESSIONAL PAPER/PROJECT M 576 INTERNSHIP M 577 IMPROVING MATHEMATICS EDUCATION: CAPSTONE PROJECT M 581 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS I M 582 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS II M 584 FUNCTIONAL ANALYSIS I M 585 FUNCTIONAL ANALYSIS II M 586 PROBABILITY THEORY M 588 PROFESSIONAL DEVELOPMENT M 589 GRADUATE CONSULTATION M 590 MASTER'S THESIS M 591 TOPICS IN APPLIED MATHEMATICS I M 592 TOPICS IN APPLIED MATHEMATICS II M 594 SEMINAR M 595 DYNAMICAL SYSTEMS I M 596 DYNAMICAL SYSTEMS II M 597 TOPICS IN MATHEMATICS I M 598 TOPICS IN MATHEMATICS II M 689 DOCTORAL READING & RESEARCH M 690 DOCTORAL THESIS

Course Equivalency Tool

*(Montana University System Common Course Changes)*

**M 065 PREALGEBRA (Gallatin College Programs) **

F,S 4 cr. LEC 4

-- This instructor-taught course covers basic concepts relating to fractions, decimals, ratios, proportions, percent, selected geometry topics, topics of signed numbers, and 1-variable linear equations. The course is offered as a review and/or preparation for further studies in Mathematics. Offered by Gallatin College Programs. This course is equivalent to M 085.

**M 066 PREALGEBRA LAB & STUDY (Gallatin College Programs) **

F 1 cr. RCT 1

--Students enrolled in M 065 co-enroll in this course for additional instruction and practice with M 065 curriculum and Math study skills. This course will help students understand Math concepts, practice course material, and prepare for Math tests. Offered by Gallatin College Programs. Course is offered pass/fail.

**M 085 PREALGEBRA**

F,S, 4 cr. LEC 4

PREREQUISITE: ACT Math minimum score 18, or SAT Math minimum score 440.

-- An accelerated lab-based course designed for students who need a review of prealgebra concepts and are prepared to learn in a self-paced, accelerated mode. Topics include signed numbers, fractions, decimals, ratios, proportions, percent, 1-variable linear equations, an introduction to 2-variable linear equations, and selected geometry topics. The course is offered as a review and as preparation for further studies in mathematics. Offered by Gallatin College.

**M 088 MATHEMATICAL LITERACY**

F,S, 4 cr. LEC 4

-- Develop mathematical literacy through problem solving, critical thinking, writing, and communication mathematics. Represent and solve relevant, real-world problems using various forms of numbers, equations, and graphs. Topics include proportional reasoning, algebra, and measurement. Offered by Gallatin College. This course is equivalent to M065.

**M 096 SURVEY OF ALGEBRA (Gallatin College Programs) **

F,S,Su 4 cr. LEC 4

PREREQUISITE: M 065 or M 085 or Math Placement Test within the past 12 months.

-- 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. Topics include linear equations and inequalities and their graphs, systems of linear equations, exponents, polynomials, factoring, rational expressions, and square roots. Offered by Gallatin College Programs. This course is equivalent to M 097.

**M 097 SURVEY OF ALGEBRA (Mastery Learning)**

F,S 3 cr. IND 3

PREREQUISITE: M 065 or M 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.

**M 108 BUSINESS MATHEMATICS** **(Gallatin College Programs)**

F 4 cr.

-- Students in this course will examine the mathematics of business ownership and will demonstrate an understanding of business decisions. Concepts include marketing, payroll, cash flow, simple and compound interest, credit, promissory notes, insurance, financial statements, ratio analysis, depreciation, annuities, and inventory valuation. Offered by Gallatin College Programs.

**M 116 MATHEMATICS FOR HEALTH CAREERS (Gallatin College Programs)**

S 3 cr. LEC 3

-- Inductive reasoning; logic; mathematical number systems; liner, quadratic, exponential, and logarithmic functions; graphing; probability; English, Apothecary and Metric systems and conversions; dosage calculations; and dimensional

**M 121Q COLLEGE ALGEBRA**

F,S,Su 3 cr. LEC 3

PREREQUISITE: M 097 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.

**M 132 NUMBERS & OPERATIONS FOR K-8 TEACHERS**

F,S 3 cr. LEC 3

PREREQUISITE: M 121 or Math Placement Test within the past 12 months.

-- The study of number and operations for prospective elementary and middle school teachers, including whole numbers, decimals, fractions, percents, integers, operations, numeration systems, and problem solving.

**M 133Q GEOMETRY & GEOMETRIC MEASUREMENT FOR K-8 TEACHERS **

F,S 3 cr. LEC 3

PREREQUISITE: M 132.

-- The study of geometry and geometric measurement for prospective elementary and middle school teachers, including synthetic, transformational, and coordinate geometry, constructions, congruence and similarity, 2-dimensional and 3-dimensional measurement, and problem solving.

**M 135 MATHEMATICS FOR K-8 TEACHERS I**

F,S on demand 4 cr. LEC 4

PREREQUISITE: M 097 or Math Placement Test within the past 12 months.

-- An introduction to problem solving, sets, rational and irrational numbers, operations functions, numeration systems as mathematical structures, and introductory number theory for prospective elementary school teachers.

**M 136Q MATHEMATICS FOR K-8 TEACHERS II**

F,S on demand 4 cr. LEC 4

PREREQUISITE: M 135.

-- Introductory coordinate geometry, constructions, congruence and similarity, concepts of measurement, problem solving, probability, and statistics for prospective elementary school teachers.

**M 145Q MATHEMATICS FOR THE LIBERAL ARTS**

F,S,Su 3 cr. LEC 3

PREREQUISITE: M 097 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.

**M 147Q LANGUAGE OF MATHEMATICS**

S 3 cr. LEC 3

PREREQUISITE: M 097 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.

**M 149Q SECRETS OF THE INFINITE**

F,S 3 cr. LEC 3

PREREQUISITE: M 097 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.

**M 151Q PRECALCULUS**

F,S,Su 4 cr. LEC 4

PREREQUISITE: M 121 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.

**M 161Q SURVEY OF CALCULUS**

F,S,Su 4 cr. LEC 4

PREREQUISITE: M 121 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.

**M 165Q CALCULUS FOR TECHNOLOGY I**

F,S 3 cr. LEC 3

PREREQUISITE: M 151 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.

**M 166Q CALCULUS FOR TECHNOLOGY II**

F,S 3 cr. LEC 3

PREREQUISITE: M 165.

-- Calculus with emphasis on problems of interest to engineering technologists. Includes integration, infinite series, and differential equations.

**M 171Q CALCULUS I**

F,S,Su 4 cr. LEC 4

PREREQUISITE: M 151 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.

**M 172Q CALCULUS II**

F,S,Su 4 cr. LEC 4

PREREQUISITE: M 171.

-- Methods of integration, applications of the integral, Taylor's theorem, infinite sequences and series, polar coordinates.

**M 181Q HONORS CALCULUS I**

F 4 cr. LEC 4

PREREQUISITE: M 151 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 .

-- Honors section of M 171. Topic coverage parallels M 171 but with a greater emphasis on theory and more difficult problems.

**M 182Q HONORS CALCULUS II**

S 4 cr. LEC 4

PREREQUISITE: M 171 with an "A" grade or M 181 with a "B" grade.

-- Honors section of M 172. Topic coverage parallels M 172 but with a greater emphasis on theory and more difficult problems.

**M 221 INTRODUCTION TO LINEAR ALGEBRA**

F,S,Su 3 cr. LEC 3

PREREQUISITE: M 166 or M 172.

-- Matrix algebra, systems of linear equations, determinants, vector algebra and geometry in Euclidean 3-space, eigenvalues, eigenvectors.

**M 234 ADVANCED TOPICS IN MATHEMATICS FOR K-8 TEACHERS**

F,S 3 cr. LEC 3

PREREQUISITE: M 132 and M 133Q.

-- The study of algebra, number theory, probability and statistics for prospective elementary and middle school teachers, including proportional reasoning, functions, elementary number theory, statistical modeling and inference, and elementary probability theory.

**M 242 METHODS OF PROOF**

F,S 3 cr. LEC 3

PREREQUISITE: M 172.

-- 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.

**M 273Q MULTIVARIABLE CALCULUS**

F,S,Su 4 cr. LEC 4

PREREQUISITE: M 172.

-- 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.

**M 274 INTRODUCTION TO DIFFERENTIAL EQUATIONS**

F,S,Su 4 cr. LEC 4

PREREQUISITE: M 172.

-- 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.

**M 283Q HONORS MULTIVARIABLE CALCULUS**

F 4 cr. LEC 4

PREREQUISITE: M 182 with a 'B' grade, M 172 with an 'A' grade, AP Calculus BC exam with a 5, or consent of the instructor.

-- Honors section of M 273. Topic coverage parallels M 273 but with a greater emphasis on theory and more difficult problem solving.

**M 284 HONORS INTRODUCTION TO DIFFERENTIAL EQUATIONS**

S 4 cr. LEC 4

PREREQUISITE: M 283 with a 'B' grade, M 273 with an 'A' grade, or consent of the instructor.

-- Honors section of M 274. Topic coverage parallels M 274 but with a greater emphasis on theory and more difficult problem solving.

**M 290R UNDERGRADUATE RESEARCH**

F,S,Su 1 - 8 cr. IND

PREREQUISITE: Consent of the department head.

-- Directed undergraduate research. Course will address responsible conduct of research.

**M 291 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.

**M 328 HIGHER MATHEMATICS FOR SECONDARY TEACHERS**

F 3 cr. LEC 3

PREREQUISITE: M 242.

-- Concepts, processes, and proof relevant to school mathematics, including number theory, abstract algebra, combinatorics and probability; NCTM Standards and a focus on content for teachers in secondary schools.

**M 329 MODERN GEOMETRY**

S 3 cr. LEC 3

PREREQUISITE: M 242.

--A study of Euclidean and non-Euclidean geometries, chosen from, hyperbolic, spherical, projective, finite, transformational, and fractal geometries; computer tools for geometry; NCTM Standards and a focus on content for teachers in secondary schools.

**M 330 HISTORY OF MATHEMATICS**

F alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE: M 273 and M 274 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.

**M 333 LINEAR ALGEBRA**

F 3 cr. LEC 3

PREREQUISITE: M 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.

**M 348 TECHNIQUES OF APPLIED MATHEMATICS I**

F 3 cr. LEC 3

PREREQUISITE: M 273 and M 274.

-- 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.

**M 349 TECHNIQUES OF APPLIED MATHEMATICS II**

S 3 cr. LEC 3

PREREQUISITE: M 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.

**M 383 INTRODUCTION TO ANALYSIS I**

F 3 cr. LEC 3.

PREREQUISITE: M 273 and either M 242, M 333, or consent of instructor.

-- A rigorous development of calculus with formal proofs. Functions, sequences, limits, continuity, differentiation, and integration.

**M 384 INTRODUCTION TO ANALYSIS II**

S 3 cr. LEC 3.

PREREQUISITE: M 383.

-- A rigorous development of multivariate calculus. Differentiable functions, inversion theorem, multiple integrals, line and surface integrals, infinite series.

**M 386R SOFTWARE APPLICATIONS IN MATHEMATICS**

S 3 cr. LEC 3.

PREREQUISITE: M 221, M 273, and M 274.

-- An introduction to modern mathematical and scientific computing. Software such as MAPLE and MATLAB will be used to explore, solve, and visualize solutions of standard mathematical problems as well as simple models of various physical and/or biological systems.

**M 420 GEOMETRY, MEASUREMENT, AND DATA IN THE MIDDLE GRADES**

F alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE: M 242 or EDSD 461 or EDSD 471, or M 136 and 3 credits from elementary math option.

-- Develop content knowledge necessary to teach standards based middle school mathematics. 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.

**M 424 ALGEBRAIC THINKING AND NUMBER SENSE IN THE MIDDLE GRADES**

F alternate odd years, Su alternate even years 3 cr.LEC 3

PREREQUISITE: M 242 or EDSD 461 or EDSD 471, or M 136 and 3 credits from elementary math option.

-- Develop algebraic knowledge necessary to teach standards-based middle school mathematics. 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.

**M 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. Overview of the modeling process including simulation, review of relevant technology, relevant mathematics including difference equations and recursion, strategies to initiate modeling, activities, modeling in the secondary curricula, and the classroom assessment of modeling activities. Emphasis on technology and authentic applications using pre-college mathematics.

**M 430 MATHEMATICAL BIOLOGY**

S 3 cr. LEC 3

PREREQUISITE: M 273 and M 274 or consent of the instructor.

-- Mathematical modeling of basic biological processes in ecology, physiology, neuroscience, epidemiology and molecular biology using difference equations, differential equations, and partial differential equations.

**M 431 ABSTRACT ALGEBRA I**

S 3 cr. LEC 3

PREREQUISITE: M 333.

-- Senior capstone course. The integers, integers modulon, 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.

**M 441 NUMERICAL LINEAR ALGEBRA & OPTIMIZATION**

F 3 cr. LEC 3

PREREQUISITE: M 221 and M 273.

-- Numerical solution of nonlinear equations. Numerical solutions of linear systems and eigenvalue problems. Least squares, data smoothing, and optimization techniques.

**M 442 NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS**

S 3 cr. LEC 3

PREREQUISITE: M 221 and M 274.

-- Senior capstone course. Numerical integration, numerical solutions of initial and boundary value problems in ordinary differential equations. Numerical solutions of partial differential equations.

**M 450 APPLIED MATHEMATICS I**

F alternate years, to be offered odd years 3 cr. LEC 3

PREREQUISITE: M 273 and M 274.

-- 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.

**M 451 APPLIED MATHEMATICS II**

S alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE: M 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.

**M 454 INTRODUCTION TO DYNAMICAL SYSTEMS I**

F alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE: M 273 and M 274.

-- Existence and uniqueness of solutions to ordinary differential equations, linearization, phase portraits, stability theory, and the analysis of specific examples.

**M 455 INTRODUCTION TO DYNAMICAL SYSTEMS II**

S alternate years, to be offered odd years 3 cr. LEC 3

PREREQUISITE: M 454.

-- Gradient systems, Poincare'-Bendixson theory, Poincare' maps, structural stability and chaotic systems.

**M 472 INTRODUCTION TO COMPLEX ANALYSIS**

S alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE: M 273 and M 274.

-- 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.

**M 490R UNDERGRADUATE RESEARCH**

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. Course will address responsible conduct of research.

**M 491 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.

**M 492 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.

**M 494 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.

**M 497 EDUCATIONAL METHODS:TEACHING FELLOWSHIP**

F,S 1 - 2 cr. IND.

PREREQUISITE: Junior standing, consent of instructor, and approval of department head.

-- 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.

**M 498 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.

**M 501 INTERMEDIATE PROBABILITY & STATISTICS**

F 3 cr. LEC 3

PREREQUISITE: STAT 422 or M 382.

-- Families of probability distributions, distributions of functions of random variables, limiting distributions, order statistics. Cross-listed with STAT 501.

**M 502 INTERMEDIATE MATHEMATICAL STATISTICS**

S 3 cr LEC 3

PREREQUISITE: STAT 501 or M 501.

-- Estimation, likelihood inference, statistical hypothesis tests, sufficient statistics, exponential families, Bayesian statistics. Cross-listed with STAT 502.

**M 503 ADVANCED LINEAR ALGEBRA**

S 3 cr. LEC 3

PREREQUISITE: M 333 or consent of instructor.

-- Topics include abstract vector spaces, diagonalization, Schur's Lemma, Jordan canonical form and spectral theory for finite dimensional operators.

**M 504 ABSTRACT ALGEBRA**

S 3 cr. LEC 3

PREREQUISITE: M 431 or consent of instructor.

-- The theory of groups, rings and fields with particular emphasis on finite groups, polynomial rings and fields of characteristic zero.

**M 505 PRINCIPLES OF MATHEMATICAL ANALYSIS**

F 3 cr. LEC 3

PREREQUISITE: M 382 or consent of instructor.

-- Principles of analysis in Euclidean spaces and metric spaces.

**M 509 STOCHASTIC PROCESSES**

S alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE: STAT 421.

-- Conditional probability theory, discrete and continuous time markov chains including birth and death processes and long run behavior; Poisson processes; queueing systems; system reliability. Cross-listed with STAT 509.

**M 511 GENERAL TOPOLOGY**

F 3 cr. LEC 3

PREREQUISITE: M 382 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.

**M 512 GEOMETRIC & ALGEBRAIC TOPOLOGY**

S 3 cr. LEC 3

PREREQUISITE: M 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.

**M 516 LANGUAGE OF MATHEMATICS FOR TEACHERS**

S 3 cr. LEC 3

PREREQUISITE: M 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.

**M 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.

-- 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.

**M 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.

**M 520 STANDARDS-BASED MATHEMATICS FOR TEACHERS**

S alternate years, to be offered even years 3 cr. LEC 3. Distance format.

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.

**M 521 LEARNING THEORIES IN MATHEMATICS FOR TEACHERS **

F 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.

-- 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 understand mathematics learning among students of all cultural, linguistic and socioeconomic backgrounds, and (b) to formulate effective teaching and learning strategies.

**M 522 ASSESSMENT OF MATHEMATICS 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.

--Connects assessment theory and models to teachers' practice through classroom observations and hand-on activities. Focus on assessment practices consistent with standards-based mathematics, classroom assessment of student learning, evaluation of mathematics programs and curricula, and standardized testing practices.

**M 523 NUMBER STRUCTURE FOR TEACHERS**

F alternate years, to be offered even years 3 cr. LEC 3 Distance format.

PREREQUISITE: Graduate standing in mathematics education, teaching endorsement in mathematics, or consent of instructor.

-- Develop the relationship and distinction between the mathematics that underlies the structure of number and the learning and teaching of number structure in schools. Explore representation, abstraction, and basic proof in the context of number and operations. Develop foundations of the real number system and examine relevant research about students' understanding of number.

**M 524 LINEAR ALGEBRA FOR TEACHERS**

Su alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE:Graduate standing in mathematics education, teaching endorsement in mathematics, or consent of instructor.

-- Algebraic systems, special matrices, determinants, vector spaces, and linear programming. Includes applications relevant to industry and business and connections to topics in secondary mathematics.

**M 525 ANALYSIS FOR TEACHERS**

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.

-- A study of calculus concepts and processes from graphical, numerical and algebraic perspectives. Extensive use of activities and projects. Modeling and technology are incorporated throughout the course.

**M 526 DISCRETE MATHEMATICS FOR TEACHERS**

Su alternate years, to be offered even years 3 cr. LEC 3 Distance format.

PREREQUISITE: Graduate standing in mathematics education, teaching endorsement in mathematics, or consent of instructor.

--A study of classical topics in discrete mathematics, chosen from combinatorics, probability, graph theory, and other areas relevant to secondary mathematics. Emphasis on problem solving and justification.

**M 527 GEOMETRY FOR TEACHERS**

S alternate years, to be offered even years 3 cr. LEC 3 Distance format.

PREREQUISITE: Graduate standing in mathematics education, teaching endorsement in mathematics, or consent of instructor.

-- Geometry of transformations including Euclidean motions and similarity, projective geometry, geometric topology and geometry of inversion.

**M 528 CURRICULUM DESIGN**

S alternate years, to be offered even years 3 cr. LEC 3 Distance format.

PREREQUISITE: Graduate standing in mathematics education, teaching endorsement in mathematics, or consent of instructor.

--Focuses on the design, implementation, and evaluation of curricula in mathematics. Includes historical changes and trends in mathematics curriculum and an examination of current research.

**M 529 ASSESSMENT MODELS AND ISSUES**

F 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.

--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.

**M 533 HISTORY OF MATHEMATICS FOR TEACHERS**

F 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.

-- Focus on the history of mathematics as a context for classroom instruction. Includes the changing nature of mathematics, classical problems, proofs and mathematical processes, and the development of teaching units that incorporate the history of mathematics.

**M 534 RESEARCH IN MATHEMATICS EDUCATION**

F alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE: EDCI 506.

-- Examination of quantitative and qualitative research findings and methodology in mathematics education. Review of current trends and literature. Writing for publication and proposals.

**M 535 TECHNOLOGY AND MATHEMATICS FOR TEACHERS**

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.

-- Calculator, computer and Web-based technologies for K-12 mathematics education. Analysis of the influence of technology on the K-12 mathematics curriculum, instruction, and assessment.

**M 540 INTRODUCTION TO CALCULUS ON MANIFOLDS**

F alternate years, to be offered odd years 3 cr. LEC 3

PREREQUISITE: M 503 and M 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.

**M 544 PARTIAL DIFFERENTIAL EQUATIONS I**

F alternate years, to be offered odd years 3 cr. LEC 3

PREREQUISITE: M 382 and M 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.

**M 545 PARTIAL DIFFERENTIAL EQUATIONS II**

S alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE: M 544 and M 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.

**M 547 MEASURE THEORY**

F 3 cr. LEC 3

PREREQUISITE: M 382 or M 505.

-- Lebesgue measure, and the Lebesgue integral of functions of a real variable. General measure and integration theory. Lebesgue-Stieltjes integral and product measures.

**M 551 COMPLEX ANALYSIS**

S 3 cr. LEC 3

PREREQUISITE: M 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.

**M 560 METHODS OF APPLIED MATHEMATICS I**

F alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE: M 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.

**M 561 METHODS OF APPLIED MATHEMATICS II**

S alternate years, to be offered odd years 3 cr. LEC 3

PREREQUISITE: M 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.

**M 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.

**M 571 ACTION RESEARCH IN MATHEMATICS EDUCATION**

Su 2 cr. LEC 2

PREREQUISITE: Graduate standing in mathematics education and consent of instructor.

-- Prepares practicing mathematics teachers to study a mathematics education problem within their classroom, school or district with supervision by a 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.

**M 572 IMPROVING MATHEMATICS EDUCATION: CAPSTONE PROPOSAL**

F 2 cr. LEC 2 Distance format.

PREREQUISITE: M 571, graduate standing in mathematics education 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.

**M 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.

**M 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.

**M 577 IMPROVING MATHEMATICS EDUCATION: CAPSTONE PROJECTS**

Su 3 cr. LEC 3

PREREQUISITE: M 571/572 sequence, graduate standing in mathematics education, teaching endorsement in mathematics 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 presented orally to peers and faculty.

**M 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.

**M 581 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS I**

F 3 cr. LEC 3

PREREQUISITE: M 442.

-- Finite difference and finite element solution techniques for elliptic, parabolic, and hyperbolic partial differential equations, numerical linear algebra.

**M 582 NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS II**

S 3 cr. LEC 3

PREREQUISITE: M 581.

-- A continuation of topics from M 581.

**M 584 FUNCTIONAL ANALYSIS I**

F alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE: M 547.

-- Banach spaces, fixed point theorems, Hilbert spaces, the Dirichlet principle, generalized Fourier series, and spectral theory.

**M 585 FUNCTIONAL ANALYSIS II**

S alternate years, to be offered odd years 3 cr. LEC 3

PREREQUISITE: M 584.

-- The Hahn Banach theorem, variational principles, weak convergence, uniform boundedness theorem, the open mapping theorem and the implicit function theorem.

**M 586 PROBABILITY THEORY**

S alternate years, to be offered odd years 3 cr. LEC 3

PREREQUISITE: M 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.

**M 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.

**M 589 GRADUATE CONSULTATION**

F,S,Su 3 cr. IND 3

PREREQUISITE: Master's standing.

-- 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.

**M 590 MASTER'S THESIS**

F,S,Su 1-10 cr. IND Maximum credits unlimited.

PREREQUISITE: Master's standing.

**M 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.

**M 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.

**M 594 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.

**M 595 DYNAMICAL SYSTEMS I**

F alternate years, to be offered odd years 3 cr. LEC 3

PREREQUISITE: M 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.

**M 596 DYNAMICAL SYSTEMS II**

S alternate years, to be offered even years 3 cr. LEC 3

PREREQUISITE: M 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.

**M 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.

**M 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.

**M 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 doctoral thesis research.

**M 690 DOCTORAL THESIS**

F,S,Su 1-10 cr. IND Maximum credits unlimited.

PREREQUISITE: Doctoral standing.