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Mathematics (MATH) 1

MATHEMATICS (MATH)MATH 504 Dynamical Systems 3 Credit HoursThe aim of this course is to survey the standard types of differentialequations. This includes systems of differential equations, and partialdifferential equations, including for each type, a discussion of thebasic theory, examples of applications, and classical techniques ofsolution with remarks about their numerical aspects. Also included areautonomous and periodic solutions, phase space, stability, perturbationtechniques and Method of Liapunov. Additional reading assignmentsor projects will distinguish this course from its undergraduate versionMATH 404. Students cannot receive credit for both MATH 404 andMATH 504. (AY)Restriction(s):Can enroll if Level is Graduate or Rackham

MATH 5055 Integral Equations 3 Credit HoursOrigin and classifications of integral equations. Connections withdifferential equations. Integral equations of convolution type. Method ofsuccessive approximations. Singular Kernels. Elements of Hilbert space.Linear operators. Resolvents. Fredholm theory. Hilbert-Schmidt theory.Additional reading asignments or projects will distinguish this coursefrom its undergraduate version MATH 405. Students cannot receivecredit for both MATH 405 and MATH 505. (AY)Prerequisite(s): MATH 216 and (MATH 217 or MATH 227)Restriction(s):Can enroll if Class is Graduate

MATH 508 Topics for Elem and Mid Tchrs 1 to 4 Credit HoursTopics such as problem solving, calculators, microcomputers,applications, algebraic and geometric concepts, probability and statisticsare to be considered. Emphasis is on developing skills in these topics andtheir uses in the curriculum.Prerequisite(s): MATH 385

MATH 508AF Topics in Math education 2 Credit HoursTopic: Graphing Calculators in Algebra and Data Analysis. This is onethe courses for special education teachers and their general educationpartners teaching algebra at the middle or high school level. Thesequence emphasizes a deep understanding of the mathematics andof the pedagogical issues in student learning the mathematics with aparticular emphasis on the use of the graphing calculator on studentsunderstanding and fluency in algebraic thinking and data analysisconcepts. This course is for 2 credits.

MATH 508AJ Topics in Mathematics Educ 2 Credit HoursTopic: Teaching Geometry with the Nspired Dynamic Geometry Software.This course is part of a sequence of courses for teachers of secondaryschool mathematics. This course focuses on the use of the dynamicgeometry software Nspired to impact the teaching of geometry andstudent conceptual understanding of geometry. It will also discuss thepedagogical issues in the use the software. This is a two-credit course.

MATH 508N Topics in Mathematics Educ 2 Credit HoursTopic: Pedagogical Issues in Mathematics for Struggling Middle SchoolStudents. This course continues a sequence of courses for middleschool teachers of mathematics offered by the Center of MathematicsEducation in collaboration with Wayne RESA. Wayne RESA supportsthis sequence for districts and teachers who are not supported by eitherITQ or MSP grants. It is a follow-up to the course Math 508L whichfocused on issues in student understanding of algebra. This courseexpands the focus to consider surrounding pre-algebra topics such asratios and proportionality as well as geometry and measurement. Thesequence emphasizes a deep understanding of the mathematics andthe pedagogical issues in supporting struggling students attaining theexpectations of Michigan's Grade Level Content Expectations. The coursewill be for 2 credits.

MATH 508Q Topics for Elem and Mid Tchrs 2 Credit HoursTopic: Elementary School Mathematics: Data Analysis and Probability.This course focuses on topics in data analysis and probability forteachers of elementary school mathematics. The data analysis topicsinclude the construction, reading and interpretation of tables andgraphs, understanding and calculating measures of central tendencyand issues such as scaling, and maximum and minimum and range.The probability topics include the concept of probability and expressingprobabilities of simple events as fractions. Important aspects of thework are representation and problem solving. This course will be 2 credithours.

MATH 508T Topics for Elem and Mid Tchrs 2 Credit HoursTopic: Explorations and Investigations in Mathematics in the UpperElementary Grades. This course is part of a sequence of courses forupper elementary grades teachers of mathematics. The sequenceemphasizes a deep understanding of the mathematics and of thepedagogical issues in students' learning the mathematics embodied inthe upper elementary grades standards-based curricula. This coursewill emphasize the content of topics in the Everyday Math series for theupper elementary grades. Its particular focus will be the explorations andinvestigations that engage students in learning the mathematics withparticular attention paid to the use of calculators and games. This courseis for 2 credit hours.

MATH 508X Topics in Teacher Mathematics 3 Credit HoursTopic: Focal Points in Algebra and Geometry: Middle School to HighSchool. This course is part of a sequence of courses for teachers ofmiddle school mathematics. This course focuses on the applicationof recently published Michigan middle school curriculum focal pointsto support student learning and deepen teacher knowledge of themathematics undergirding the focal points. Important to this study isteacher understanding of the essential understanding students need tobe successful in high school algebra and geometry. This is a two-creditcourse.

MATH 512 First Course in Modern Algebra 3 Credit HoursIntroduction to groups, subgroups, group homomorphisms, factorgroups, simple groups, cyclic groups. Sylow theorems, rings, ideals,integral domains, field, polynomial rings, Kronecker's theorem, alsoproperties of the integral, rational, real and complex numbers. Additionalreading assignments or projects will distinguish this course from itsundergraduate version MATH 412. Students cannot receive credit forboth MATH 412 and MATH 512. (W)Restriction(s):Can enroll if Level is Rackham or Graduate

2 Mathematics (MATH)

MATH 513 Linear Algebra 3 Credit HoursVector Spaces, linear transformations and matrices, determinants,inner product spaces, bilinear and quadratic forms. Hamilton-Cayleytheorem, eigenvalues and eigenvectors spectral theorem. Additionalreading assignments or projects will distinguish this course from itsundergraduate version MATH 413. Students cannot receive credit forboth MATH 413 and MATH 513. (Y).Prerequisite(s): (MATH 200 and (MATH 217 or MATH 300) and MATH 216or MATH 227)

MATH 514 Fin Diff Meth for Diff Equat 3 Credit HoursThis course studies the numerical solution of ordinary and partialdifferential equations using finite difference methods. Topics includeconvergence, stability, efficiency, numerical simulation and applicationsof these methods. (OC).Prerequisite(s): MATH 216 and (MATH 217 or MATH 227)Restriction(s):Can enroll if Class is Graduate

MATH 515 B-Splines & Their Applications 3 Credit HoursPrerequisite(s): MATH 216 and (MATH 217 or MATH 227)Restriction(s):Can enroll if Class is Graduate

MATH 516 Fin Elemnt Meth for Diff Equat 3 Credit HoursThis course studies the numerical solution of ordinary and partialdifferential equations using finite element methods. Topics includeconvergence, stability, efficiency, numerical simulation and applicationsof these methods. (OC).Prerequisite(s): MATH 216 and (MATH 217 or MATH 227)Restriction(s):Can enroll if Class is Graduate

MATH 520 Stochastic Processes 3 Credit HoursReview of distribution theory. Introduction to stochastic processes,Markov chains and Markov processes, counting, Poisson andGaussian processes. Applications to queuing theory. Additionalreading assignments or projects will distinguish this course from itsundergraduate version MATH 420. Students cannot receive credit forboth MATH 420 and MATH 520. (AY)Prerequisite(s): MATH 217 or MATH 227Restriction(s):Can enroll if Level is Graduate or Rackham

MATH 523 Linear Algebra w/Applications 3 Credit HoursVector spaces, linear transformations of vector spaces and theirrepresentations as matrices and canonical forms for similarity. Innerproduct spaces, diagonalization of the Hermitian forms by unitarytransformations. Applications to linear programming and to the solutionof systems of differential equations. (AY)Prerequisite(s): MATH 216 and (MATH 217 or MATH 227)Restriction(s):Can enroll if Level is Graduate or Rackham

MATH 525 Mathematical Statistics II 3 Credit HoursInternal estimation and pivotal quantities; maximum likelihoodestimation; hypothesis tests; linear models and analysis of variance;bivariate normal distribution, regression and correlation analysis;nonparametric methods. Additional reading assignments or projectswill distinguish this course from its undergraduate version, MATH 425.Students cannot receive credit for both MATH 425 and MATH 525. (OC)Prerequisite(s): MATH 325Restriction(s):Can enroll if Level is Graduate or Rackham

MATH 5385 Nmbr Sys & Oper Tchrs 2 or 3 Credit HoursThis course is designed to deepen grades 3-5 elementary teachers'understanding of the whole number and rational number systems. Majortopics include interpretations of whole number operations, the extensionof whole number operations to rational numbers, the representations ofrational numbers and the conceptual underpinnings of non-standard andstandard algorithms. Other topics include analyzing number theoreticconcepts such as prime numbers and divisibility. Pedagogical andcurriculum issues will be addressed as they relate to teaching forunderstanding and developing computational fluency. The topics of the2-credit hour course will include whole numbers and operations. The 3-credit course will extend topics covered to rational numbers. Open only tocertified teachers. (OC)Restriction(s):Can enroll if Class is Graduate

MATH 5386 Geom & Meas 1 Tchrs 2 or 3 Credit HoursThis course will provide participants an opportunity to develop a deeperunderstanding of the mathematics they teach through a thoroughdevelopment of the geometric and measurement concepts associatedwith two-dimensional figures. Topics will include characteristicsand properties of geometric shapes with an emphasis on developingmathematical arguments about geometric relationships, transformationsand use of symmetry to analyze mathematical situations, measurableattributes of objects and processes of measurement, and appropriatetechniques, tools, and formulas to determine measurements. Courseworkwill focus on developing mathematical thinking and will highlightinteractive learning styles. A three-credit course extends measurement tothe real numbers by introducing the Pythagorean Theorem. Open only tocertified teachers. (OC)

MATH 5387 Geom & Meas 2 Tchrs 2 or 3 Credit HoursThis course will provide participants an opportunity to develop a deeperunderstanding of the mathematics they teach through a thoroughdevelopment of the geometric and measurement concepts associatedwith three-dimensional figures. Topics will include characteristicsand properties of geometric shapes with an emphasis on developingmathematical arguments about geometric relationships and use ofsymmetry to analyze mathematical situations, measurable attributesof objects and processes of measurement, and appropriate techniques,tools, and formulas to determine measurements. In addition, topics to becovered include the Pythagorean Theorem. Coursework will also focus ondeveloping mathematical thinking and will highlight interactive learningstyles. Open to only certified teachers. (OC)Restriction(s):Can enroll if Class is Graduate

MATH 542 Geometry for Teachers 3 Credit HoursProperties of two and three-dimensional figures are covered, includingcongruence, symmetry, transformation, and measurement. Trigonometryfrom a geometric perspective and the use of trigonometry in problemsolving are included. Topics also include coordinate geometry andvisualization as well as the nature of axiomatic reasoning and the roleit has played in the development of mathematics. An investigativeapproach involving problem solving, reasoning and proof, connections,and communication will be emphasized. Calculator and computertechnology will support the investigation of these topics. Classroomresources and materials are considered. Different levels of geometricthinking will be explored. Open only to certified teachers or elementaryeducation students. (F, W, S,)Prerequisite(s): MATH 387Restriction(s):Can enroll if Class is Graduate


MATH 543 Algebra for Teachers 3 Credit HoursAlgebraic structure is emphasized, especially as it relates toarithmetic. Emphasis is on the development of algebraic reasoningand generalizations with appropriate pedagogy. Curriculum issuesrelevant to teaching algebra for conceptual understanding are included.Major topics include algebraic representations of linear, exponential,power and quadratic patterns, systems of equations, and applications.An investigative approach involving problem solving, reasoning andproof, connections, and communication will be emphasized. Classroomresources and materials are considered as well as calculators andcomputer technology as problem solving tools to aid in algebraicthinking. Open only to certified teachers or elementary educationstudents. (F, W, S).Prerequisite(s): MATH 386

MATH 544 Data Anlsys,Prob&Stat forTchrs 3 Credit HoursConcepts of elementary probability using both experimental andtheoretical models are considered with an emphasis on the use ofprobability models to describe physical phenomena and to make andinterpret predictions. Topics in data analysis and statistics includedrawing inferences from visual displays of data, applying techniques ofinferential statistics, sampling and simulations to generate solutions toproblems, and making appropriate inferences using best fit techniques.Evaluation of data and arguments to establish validity, interpreting,calculating and solving problems related to correlation, distributions,percentiles and standard scores are also included. An investigativeapproach involving problem solving, reasoning and proof, connectionsand communication will be emphasized. Calculator and computertechnology will support the investigation of these topics. Open only tocertified teachers or elementary education students.Prerequisite(s): MATH 387Restriction(s):Can enroll if Class is Graduate

MATH 5440 Pedagogy Content Alg Tchrs I 2 or 3 Credit HoursThis is the first in a sequence of courses for secondary school teachersof mathematics. The sequence emphasizes a deep understanding ofthe mathematics and the pedagogical issues in students learning themathematics embodied in the algebra components of secondary schoolmathematics as defined in the Michigan Merit Exam in mathematicsfor graduation from high school. The first two courses in this sequenceemphasize the algebra and the algebraic reasoning basic to studentsuccess in Algebra I, and the beginning of Algebra II. The three credithour course furthers teachers? understanding of the use of mathematicalmodels to represent quantitative relationships. Pedagogical andcurriculum issues will be addressed as they relate to teaching forstudents? understanding of patterns and algebraic content.Restriction(s):Can enroll if Class is Graduate

MATH 5441 Pedagogy Content Alg Tchrs II 2 or 3 Credit HoursThis is the second in a sequence of courses for secondary schoolteachers of mathematics. The sequence emphasizes a deepunderstanding of the mathematics and the pedagogical issues instudents learning the mathematics embodied in the algebra componentsof secondary school mathematics as defined in the Michigan Merit Examin mathematics for graduation from high school. The first two coursesin this sequence emphasize the algebra and the algebraic reasoningbasic to student success in Algebra I and the beginning of Algebra II.The three credit hour course furthers teachers? understanding of theuse of mathematical models to represent quantitative relationships.Pedagogical and curriculum issues will be addressed as they relate toteaching for students? understanding of patterns and algebraic content.Restriction(s):Can enroll if Class is Graduate

MATH 5442 Geom & Meas 3 Tchrs 2 or 3 Credit HoursThis course will provide participants an opportunity to develop adeeper understanding of the mathematics they teach through athorough development of the geometric and measurement conceptsassociated with two- and three-dimensional figures. Topics willinclude characteristics and properties of geometric shapes with anemphasis on developing mathematical arguments about geometricrelationships, transformations and use of symmetry to analyzemathematical situations, measurable attributes of objects and processesof measurement, and appropriate techniques, tools, and formulas todetermine measurements. In addition, topics to be covered includePythagorean Theorem and right-angle trigonometric concepts.Coursework will also focus on developing mathematical thinking and willhighlight interactive learning styles. Open only to certified teachers. (OC)Restriction(s):Can enroll if Class is Graduate

MATH 5443 Patterns Algebra 2 Tchrs 2 or 3 Credit HoursThis course is designed to deepen in-service teachers' understanding ofpatterns and algebraic concepts. Major topics include the representation,analysis, and generalization of a variety of linear and non-linear patterns(including exponential and quadratic) with tables, graphs, words, andsymbolic rules; the comparing and contrasting of linear and non-linearpatterns; the representation and analysis of mathematical situations andstructures using algebraic symbols; the use of mathematical models torepresent and understand quantitative relationships; and the analysisof change in various contexts. Pedagogical and curriculum issues willbe addressed as they relate to teaching for students' understanding ofpatterns and algebraic concepts. Open only to certified teachers. (OC)Restriction(s):Can enroll if Class is Graduate

MATH 5445 Nmbr Sys Oper&Prop Reas Tch 2 or 3 Credit HoursThis course is designed to deepen middle school mathematics teachers'understanding of the whole number system and its operations and itsextensions to the rational number system and their operations. Theprimary focus is on proportional reasoning as a major ingredient forsuccess in mathematics. Pedagogical and curriculum issues will beaddressed as they relate to teaching for understanding. Materials includeexemplary curriculum materials and records of student thinking. Onlyopen to certified teachers. (OC)Restriction(s):Can enroll if Class is Graduate


MATH 545 Number & Prop'l Rsng for Tchrs 3 Credit HoursThis course deepens previous work on rational number ideas andapplications and explores the concepts of ratio and proportion. Contentincludes a variety of situations involving proportions, for example,real-world problems involving ratios, rates, and percents; geometryinvolving similarity; algebra involving linearity; probability involvingassigning a probability to an event; and trigonometry involving slope.Distinguishing proportional situations from those that are not andreasoning proportionally in appropriate situations are emphasized. Thecourse includes problem solving, reasoning and proof, connections,communication, and multiple representations. Open only to certifiedteachers or elementary education students. (YR).Prerequisite(s): (MATH 442 or MATH 542) and (MATH 443 or MATH 543)Restriction(s):Can enroll if Class is Post-baccalaureate NCFD or Post-baccalaureateCert only or Graduate

MATH 546 Discrete Math/Modeling for Tch 3 Credit HoursThis course interweaves the ideas of discrete mathematics with theapproaches and strategies of mathematical modeling. It gives pre- and in-service teachers opportunities to deepen their understanding and use ofmathematical models based on the concepts of discrete mathematics.Topics include recurrence, induction, permutations, combinations,binomial distributions, circuits, critical paths, minimal spanning trees,adjacency matrices, algorithm design and optimization. Systems thinkingand multiple representations are emphasized. Open only to certifiedteachers or elementary education students. (YR).Prerequisite(s): (MATH 442 or MATH 542) and (MATH 443 or MATH 543)Restriction(s):Can enroll if Class is Professional Development or Graduate

MATH 547 Microcomp in Math for Teach 2 Credit HoursUse of the microcomputer in the mathematics classroom with anemphasis on the LOGO programming language. Problem solving, hands-on activities, and a cooperative learning environment are emphasized.Open only to certified teachers or elementary education students. (S)Prerequisite(s): MATH 386

MATH 548 Problem Solving for Teachers 2 Credit HoursProblem-solving skills important to the mathematics classroom areintroduced. Both the development of these skills for those in thecourse and the implementation of them in the classroom are pursued.Resource materials for the classroom are considered. No credit for CASLconcentration, minor, or area of focus. Open onl to certified teachersor elementary education students. Additional reading assignmentsor projecs will distinguish this course from its undergraduate version,MATH 448. Students cannot receive credit for both MATH 448 andMATH 548. (F).Prerequisite(s): MATH 386Restriction(s):Can enroll if Level is Graduate or Rackham

MATH 549 Concepts of Calc for Teachers 3 Credit HoursConcepts of Calculus for Teachers focuses on calculus conceptsappropriate for middle school mathematics teachers and teacher-candidates. The course provides a deep understanding of the majorconcepts of calculus: rates of change, accumulation (net change),area, and limits. Students will experience concrete approaches to thevarious topics using problem solving, manipulatives and technology asappropriate, with the intent being to help the learners discover how theideas of calculus are useful in a variety of settings. Visual, numeric, andcommonsense approaches will be used. Open only to certified teachersor elementary education students. (YR).Prerequisite(s): (MATH 442 or MATH 542) and (MATH 443 or MATH 543)Restriction(s):Can enroll if Class is Post-baccalaureate Cert only or Post-baccalaureateNCFD or Graduate

MATH 551 Advanced Calculus I 3 Credit HoursProperties of the real number system; point set theory for the real lineincluding the Bolzano-Weierstrass theorem; sequences, functions of onevariable; limits and continuity, differentiability, Riemann integrability.Additional reading assignments or projects will distinguish this coursefrom its undergraduate version MATH 451. Students cannot receivecredit for both MATH 451 and MATH 551. (YR).Restriction(s):Can enroll if Class is Graduate

MATH 552 Advanced Calculus II 3 Credit HoursIncludes the rigorous study of two and more variables, partialdifferentiation and multiple iteration. Special topics include: TaylorSeries, Implicit Function Theorem, Weierstrass Approximation Theorem,Arzela-Ascoli Theorem. Additional reading assignments or projectswill distinguish this course from its undergraduate version MATH 452.Students cannot receive credit for both MATH 452 and MATH 552. (AY)Prerequisite(s): MATH 451 or MATH 551Restriction(s):Can enroll if Class is Graduate

MATH 554 Fourier and Boundary 3 Credit HoursFourier series and integrals. Their use in solving boundary value problemsof mathematical physics by the method of separation of variables. Sturm-Liouville theory and generalized Fourier series, including those involvingBessel functions and Legendre polynomials, with applications. Studentscannot receive credit for both MATH 454 and MATH 554. (YR).Restriction(s):Can enroll if Class is Graduate

MATH 555 Func of a Complex Var with App 3 Credit HoursComplex number system. Functions of a complex variable, theirderivatives and integrals. Taylor and Laurent series expansions. Residuetheory and applications, elementary functions, conformal mapping, andapplications to physical problems. Students cannot receive credit forboth MATH 455 and MATH 555. (F,S).

MATH 558 Introduction to Wavelets 3 Credit HoursThis course will introduce the students to theory and application ofwavelets using linear algebra. Topics will include the discrete Fouriertransform, the fast Fourier transform, linear transformations, orthogonaldecomposition, discrete wavelet analysis, the filter bank, Haar Waveletfamily, and applications. Additional reading assignments or projectswill distinguish this course from its undergraduate version MATH 458.Students cannot receive credit for both MATH 458 and MATH 558. (OC)Restriction(s):Can enroll if Class is Graduate


MATH 562 Mathematical Modeling 3 Credit HoursThe processes of constructing, implementing, and evaluatingmathematical models of "real world" phenomena are investigated.Models involving continuous and discrete mathematical constructsare considered. Deterministic and stochastic models are compared.Examples are taken from genetics, epidemiology, queuing theory, andother fields. Additional reading assignments or projects will distinguishthis course from its undergraduate version MATH 462. Students cannotreceive credit for both MATH 462 and MATH 562. (AY)Restriction(s):Can enroll if Level is Graduate or Rackham

MATH 572 Intro to Numerical Analysis 3 Credit HoursSolution of linear systems by Gaussian elimination, solution of non-linearequations by iterative methods, numerical solution of ordinary differentialequations, data fitting with spline functions, numerical integration,optimization. Additional reading assignments or projects will distinguishthis course from its undergraduate version MATH 472. Students cannotreceive credit for both MATH 472 and MATH 572. (F)Prerequisite(s): MATH 217 or MATH 227Restriction(s):Can enroll if Level is Rackham or Graduate

MATH 573 Matrix Computation 3 Credit HoursA study of the most effective methods for finding the numerical solutionof problems which can be expressed in terms of matrices, includingsimultaneous linear equations, orthogonal projections and least squares,eigenvalues and eigenvectors, positive definite matrices, and differenceand differential equations. Additional reading assignments or projectswill distinguish this course from its undergraduate version MATH 473.Students cannot receive credit for both MATH 473 and MATH 573. (AY).Prerequisite(s): MATH 217 or MATH 227Restriction(s):Can enroll if Level is Graduate or Rackham

MATH 580 History of Mathematics 3 Credit HoursA unified view of the rise of mathematics from ancient times to thepresent, as seen in its conceptual developments and developers, itsmajor themes and its applications (including computers). Additionalreading assignments or projects will distinguish this course from itsundergraduate version MATH 480. Students cannot receive credit forboth MATH 480 and MATH 580. (OC).Prerequisite(s): MATH 216 and (MATH 217 or MATH 227)Restriction(s):Can enroll if Level is Graduate or Rackham

MATH 582 Computer Algebra Systems 3 Credit HoursThe use of computer algebra in various areas of mathematics includingthe solution of algebraic and differential equations, matrix computations,approximation techniques, probability, and discrete mathematics.Programming within the system is also included. Students will beexpected to design, implement, and present a project using a computeralgebra system. (OC).Prerequisite(s): MATH 216 and (MATH 217 or MATH 227)Restriction(s):Can enroll if Class is Graduate

MATH 583 Discrete Optimization 3 Credit HoursThis is an introductory course in discrete optimization at the graduatelevel for mathematics, science, engineering, and management majors.The goal of this course is to provide an overview of the problem settingsin discrete optimization. In particular, the students will learn some ofthe fundamental combinatorial and heuristic optimization methodsused in practice. The main emphasis of the course will be on modelingoptimization problems mathematically and solveing them using standardoptimization techniques. The course will also address the limitationsand complexity of the solutions that are found. The important theoreticaland practical aspects of discrete optimization will be introduced usingstandard software packages such as Lingo and Lindo.Prerequisite(s): MATH 216 and (MATH 217 or MATH 227)Restriction(s):Can enroll if Class is Graduate

MATH 584 Applied&Algorithmic Graph Thy 3 Credit HoursSelected graph theory concepts and their application to a variety of real-world problems. A study of associated algorithms. Solution of problemsusing existing software packages. (OC)Prerequisite(s): MATH 217 or MATH 227Restriction(s):Can enroll if Class is Graduate

MATH 586 Sec School Math for Teachers 3 Credit HoursBasic concepts, relationships, generalizations, and applications fromthe secondary school mathematics curriculum are discussed both froman advanced viewpoint and from the standpoint of the learner. Includedare the roles of technology, problem solving, and current thinking onthe teaching of secondary mathematics topics. Open only to certifiedteachers or secondary education students. (OC).Prerequisite(s): MATH 217 or MATH 227Restriction(s):Can enroll if Level is Graduate or Rackham

MATH 590 Topics in Math & Stat 3 Credit HoursA course designed to offer selected topics in different areas ofmathematics. The specific topic or topics will be announced togetherwith the prerequisites when offered. Course may be repeated for creditwhen specific topic differs. (OC).Prerequisite(s): MATH 216 and (MATH 217 or MATH 227)Restriction(s):Can enroll if Class is Graduate

MATH 590A Topics in Mathematics and Stat 3 Credit HoursTopic: Introduction to Wavelets. This course will intorduce students tothe theory and applications of wavelets. Topics will include discreteFourier analysis, the Fast Fourier Transform, linear transformations,orthogonal decomposition, discrete wavelets analysis, the filter bank,HAAR Wavelet family, and applications.

MATH 591 Topics in Math for Teachers 1 to 3 Credit HoursA course designed to offer selected topics in different areas ofmathematics for teachers of mathematics. The specific topic or topicswill be announced together with the prerequisites when offered. Coursemay be repeated for credit when specific topics differ. (OC).


MATH 591A Topics in Math and Statistics 1 Credit HourTOPIC TITLE: Algebraic Reasoning for Teachers This course wil engageparticipants in activities that foster algebraic reasoning. Work willfocus on observing patterns of change in real-life and mathematicalsituations, on describing and recording patterns of change, and ongeneralizing patterns. Ways of representing patterns of change, suchas, verbal descriptions, tables and graphs as well as symbolic ruleswill be discussed. Advantages and disadvantages of the variousrepresentation for promoting understanding of relationships andpatterns. Understanding the relationship between two variables isfundamental to the understanding of functions. Initial consideration willbe given to linear relationships; that is, a relationship in which, as onevariable changes, the other changes a constant amount. To extend andbroaden understanding of functions, patterns will be explored in whichthe rate of change is predictavle, but not constant. Using an investigative,team-based approach, teachers will participate in learning activities thatmodel MCF Learning and Teaching Standards. Discussions will revolvearound how exploring patterns and making generalizations will developa deeper and broader undersganding of fundamental algebraic concepts.Participants will experience rich mathematical content and constructivistinstructional approaches.

MATH 591B Topics in Math and Statistics 1 Credit HourTOPIC TITLE: Number Systems: The How and the Why This coursewill examine number systems and their properties from an advancedstandpoint. It will consider the development of the real number systembeginning with the whole numbers and continuing through the integers,rational numbers and irrational numbers. The topical threads includehistoric mitivation, number sense and estimation, models for theoperations, development of algorithms, field properties, representations,and fundamental relationships. The Michigan Curriculum Framewrokand the NCTM Standards 2000 will inform the content. Class time willbe spent in cooperative learning groups, guided discorvery lessons, andwhole class discussions.

MATH 591C Topics in Math and Statistics 1 Credit HourTOPIC TITLE: Transformational Geometry and the Geometer's SkethpadThis course is based on the Institute for Advanced Study's SummerGeometry Institutes for high school teachers. The goal is to enableteachers of secondary school mathematics to deepen and broaden theirunderstanding of topics relevant to grades 7-12 and to experience the useof synamic geometry software which engages students in inquiry-basedlessons. The theme for this course will be transformational geometrywith extensive use of the Geometer's Sketchpad. No experience withthe software is expected. Using an investigative, team-based approach,teachers will participate in learning activities that model MichiganCurriculum Framework Learning and Teaching Standards.

MATH 591D Topics in Math and Statistics 1 Credit HourTOPIC TITLE: Principles and Concepts of Data Analysis and Statisticsfor Teachers This course will help high school teachers gain a deeperunderstanding of topics of descriptive statistics and data analysis.Teh Michigan Curriculum Framework (MCF) and the College Board'sAdvanced Placement Statistics curriculm guide the content. Topics willinclude interpreting visual displays of data; interpreting measures ofcentral tendency and dispersion; interpreting, calculating and solvingproblems related to correlation, distributions, percentile and standardscores; recognizing the effects of transformations applied to data;effective use of sampling techniques and methods for reporting data;making approriate inferences, interpolations nd extrapolations usingbest fit techniques. Calculator and computer technology will supportthe investigation of these topics. Using an investigative, team-basedapproach, teachers will participate in learning activities that model MCFLearning and Teaching Standards. Emphasis will be placed on waysthat statistical analysis can be used as a tool for improving studentunderstanding in topics in secondary school mathematics.

MATH 591E Topics in Math and Statistics 1 Credit HourTOPIC TITLE: Geometric Reading for Teachers This course is intended forteachers of grades 5-9. It will explore the recurring themes of geometryand their internal elegance. The van Hiele levels and their instructionalimplimications for understanding student's contruction of geometricknowledge will be used. The Michigan Curriculum Framework and theNCTM Standards 2000 guide the content. Participants will work withgeometry software such as Sketchpad and online resources. Using aninvestigative, team-based approach, teachers will participate in learningactivities that model MCF Learning and Teaching Standards. Emphisiswill be placed on deep understanding of opic. The goal will be forparticipants to teach geomety concepts with new consistency and newenthusiasm and to push their students to operate at higher intellectuallevels, with the expectation that the student academic achievement willincrease.

MATH 591J Topics in Math and Statistics 1 Credit HourTOPIC TITLE: Summer Geometry Workshop for Teachers: Part 1 Teacherparticipants will deepen and broaden their understanding of geometrutopics important to secondary school mathematics. Teacher participantswill enhance their skills using paper folding and construction tools inInvestigative activities and in designing classroom lessons that usethese skills. Teacher participants will enhance their understandingof Geometer's Sketchpad and how this dynamic software tool can beused effectively in enhancing the understanding of geometry throughinvestigations that encourage discovery and use an inductive process.Teacher participants will learn what research says about the brain andteaching and learning; and apply this understanding to enhance theirteaching and their student learning of mathematics. Teacher participantswill experience the deep learning that takes place through substantivediscourse with colleagues.

MATH 591K Topics in Math and Statistics 1 Credit HourTOPIC TITLE: Summer Geometry Workshop for Teachers Part 2

MATH 592 Introduction to Topology 3 Credit HoursMetric spaces, topological spaces, continuous maps, connectedness,compactness, separation axioms. Additional reading assignments orprojects will distinguish this course from its undergraduate versionMATH 492. Students cannot receive credit for both MATH 492 andMATH 592. (OC).Prerequisite(s): MATH 451 or MATH 551Restriction(s):Can enroll if Level is Rackham or Graduate


MATH 595 Master's Project Seminar 3 Credit HoursStudents will do a project involving a problem which may be fromeither an industrial or academic source. It may involve searching forappropriate techniques developed by others or the development of one'sown methods. Part of the project will be both written report and an oralpresentation to the seminar. In the case that the problem arises from anindustrial source there should also be a written and/or oral report to thesponsoring group. (OC).Restriction(s):Can enroll if Class is Graduate

MATH 597 Indep Studies in Mathematics 1 to 3 Credit HoursIndependent Study in mathematics for topics at the graduate level.Topics and objectives chosen bt agreement between students andinstructor.

MATH 598 Indep Study in Math Education 1 to 6 Credit HoursIndependent study project in Mathematics Education under thesupervision of a faculty member.Restriction(s):Can enroll if Class is Post-baccalaureate NCFD or Post-baccalaureateCert only or Graduate

MATH 599 Independent Research Project 1 to 3 Credit HoursIndependent research project in applied mathematics or statistics witha faculty or industrial collaborator under the supervision of a facultymember. (YR).Restriction(s):Can enroll if Class is Graduate

* An asterisk denotes that a course may be taken concurrently.

Frequency of Offering

The following abbreviations are used to denote the frequency of offering:(F) fall term; (W) winter term; (S) summer term; (F, W) fall and winterterms; (YR) once a year; (AY) alternating years; (OC) offered occasionally

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