Teaching, with Teacher Certification in Mathematics (PreschoolGrade 12) (M.A.T.)  Graduate  2012 University Catalog
You are viewing the 2012 University Catalog. Please see the newest version of the University Catalog for the most current version of this program's requirements.
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Montclair State University’s Teacher Education Program is one of the most highlyregarded teacher preparation programs in the country. It has been consistently recognized both nationally and regionally for its unique features, including its structure, partnerships, and curricular emphases. The program is considered a model for other colleges and universities and has continuously been accredited by the National Council for the Accreditation of Teacher Education (NCATE) since 1954.
The Teacher Education Program’s professional course sequence and field experiences emphasize teaching for critical thinking and culturally responsive teaching. The professional component for both graduate students addresses four broad areas: 1) student development and learning, 2) the classroom and the school, 3) the curriculum, and 4) effective teaching skills.
TEACHING (MATHEMATICS)

ADDITIONAL REQUIREMENTS FOR STATE CERT

SPEECH
Complete the following 1 course: (May be completed by examination)
CMST 101 Fundamentals of Speech: Communication Requirement (3 hours lecture) 3 
PHYSIOLOGY & HYGIENE
Pass the MSU Health Knowledge Test available through the COP or have UG equivalent course approved by advisor.

EDUCATIONAL PSYCHOLOGY
Complete 1 course from:
ELRS 580 Learning Theories (3 hours lecture) 3 PSYC 560 Advanced Educational Psychology (3 hours lecture) 3


TEACHING FIELD REQUIREMENTS
Complete 34 semester hours including the following 2 requirement(s):

MATHEMETICS CORE
Complete the following 8 courses:
CMPT 183 Foundations of Computer Science I (2 hours lecture, 2 hours lab) 3 MATH 122 Calculus I (4 hours lecture) 4 MATH 221 Calculus II (4 hours lecture) 4 MATH 222 Calculus III (4 hours lecture) 4 MATH 335 Linear Algebra (4 hours lecture) 4 MATH 340 Probability (3 hours lecture) 3 MATH 350 College Geometry (3 hours lecture) 3 MATH 431 Foundations of Modern Algebra (3 hours lecture) 3 
MATHEMATICS ELECTIVES
Complete 2 courses from the following list


PROGRAM REQUIREMENTS
Complete 36 semester hours including the following 2 requirement(s):

GRADUATE PROFESSIONAL SEQUENCE

INTRODUCTORY SEQUENCE
Complete 2 requirement(s):

Complete 1 course for 3 semester hours from the following list.
CURR 505 Teaching, Democracy, and Schooling (3 hours lecture) 3 EDFD 505 Teaching, Democracy, and Schooling (3 hours lecture) 3 
Complete for 1 semester hours.
CURR 518 Technology Integration in the Classroom (1 hour lecture) 1


DIVERSITY AND INSTRUCTIONAL SEQUENCE
Complete 5 requirement(s):

Complete 1 course for 3 semester hours from the following list.
CURR 509 Sociocultural Perspectives on Teaching and Learning (3 hours lecture) 3 EDFD 509 Sociocultural Perspectives of Teaching (3 hours lecture) 3 
Complete 1 course for 1 semester hours from the following list
CURR 516 Meeting the Needs of English Language Learners (1 hour lecture) 1 EDFD 516 Meeting the Needs of English Language Learners (1 hour lecture) 1 
Complete 1 course for 1 semester hours:
CURR 517 Inclusive Classrooms in Middle and Secondary Schools (1 hour lecture) 1 
Complete 1 course for 3 semester hours: .
READ 501 Techniques of Reading Improvement in the Secondary School (3 hours lecture) 3 
Complete 1 course for 3 semester hours from the following list.
CURR 519 Assessment for Authentic Learning (3 hours lecture) 3 EDFD 519 Assessment for Authentic Learning (3 hours lecture) 3


PEDAGOGICAL SEQUENCE I
Complete 2 requirement(s):

Complete 1 course for 3 semester hours:
CURR 526 Teaching for Learning I (3 hours lecture) 3 
Complete 1 course for 3 semester hours:
CURR 527 Fieldwork (3 hours lecture) 3


PEDAGOGICAL SEQUENCE II
Complete 2 requirement(s):

Complete 1 course for 6 semester hours from the following list. (CURR 514 is for inservice teachers).
CURR 514 Inservice Supervised Graduate Student Teaching 48 CURR 529 Student Teaching (6 hours lab) 6 
Complete 1 course for 3 semester hours:
CURR 543 Teaching for Learning II (3 hours lecture) 3



CONTENT AREA COURSES (MATHEMATICS)
Complete the following 2 requirement(s):

Complete 1 course from the following:
MATH 572 Contemporary Teaching of Mathematics (3 hours lecture) 3 MATH 573 Mathematics Materials for Teachers of Mathematics (3 hours lecture) 3 
Complete 1 course for 3 semester hours from the following list.



CULMINATING EXPERIENCE
Successfully complete the Comprehensive Examination.
Course Descriptions:
CMPT183: Foundations of Computer Science I (2 hours lecture, 2 hours lab)
Basic theory of digital computers. Syntax and semantics of a programming language. Algorithms: logic, design, testing and documentation. 3 sh.
Prerequisites: MATH 100, MATH 112, MATH 114, MATH 116, MATH 122 or MATH 221.
CMST101: Fundamentals of Speech: Communication Requirement (3 hours lecture)
This course introduces students to the theoretical and practical requirements of different types of public presentations and helps students develop an understanding and appreciation of the dynamic nature of the communication process. The course focuses on the basic elements of the communication process, listening, communicator and audience characteristics, basic research skills, and message composition and delivery. Students learn about the demands of public presentations in culturally and professionally diverse environments and develop presentation competence and flexibility. Meets Gen Ed 2002  Communication, Communication. Previous course SPCM 101 effective through Spring 2012. 3 sh.
CURR505: Teaching, Democracy, and Schooling (3 hours lecture)
This course brings together differing viewpoints regarding the purposes of teaching in the United States and the teacher's role in fostering democracy. It provides future teachers with the habits of mind, skills, tools and resources to analyze and evaluate the relationship between the history of public education, the evolution of teacher identity, and the roles teachers and teaching have played in shaping the United States as a society and vice versa. Using Montclair State's Portrait of a Teacher as an organizing framework, this course places particular emphasis on the idea that all students can learn regardless of their gender, ability, race, ethnicity, or economic background. Students in the course study the history, philosophy, and politics that shape differing views about the roles and responsibilities of teachers, especially as these views relate to integration and inclusion in the classroom. Cross listed with EDFD 505. May be repeated once for a maximum of 6.0 credits. 3 sh.
Prerequisites: Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
CURR509: Sociocultural Perspectives on Teaching and Learning (3 hours lecture)
This course examines how teachers, teaching, & schooling can foster the learning of pupils from diverse socioeconomic, linguistic & cultural backgrounds. Students explore the ways socialization shapes perceptions of oneself & others; reflect on their own beliefs & assumptions about their sociocultural identities & how those have been shaped through experience; examine the nature & impact of the increasing social, cultural, & linguistic diversity in K12 schools; & reflect on their capacity to bring about educational change that promotes equity & affirms diversity. They investigate ways of teaching all children successfully, particularly through a culturally responsive curriculum, & of developing positive relationships among teachers, parents, & children across diversity. Through a community study of an urban area with a predominantly poor & diverse population, students develop a framework for understanding the relationship between schools, communities, & society; cultivate skills needed to familiarize themselves with diverse communities & their residents; & envision ways they can help future students see connections between their inschool & outofschool experiences. They also develop their ability to work collaboratively with colleagues. May be repeated once for a maximum of 6.0 credits. Cross listed with EDFD 509. 3 sh.
Prerequisites: CURR 505 or EDFD 505; CURR 518. Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
CURR514: Inservice Supervised Graduate Student Teaching
Open only to postbaccalaureate and graduate students; this course replaces supervised student teaching for those already employed in teaching situations without standard certification. Joint supervision by the school district and University personnel. Student must obtain permission of department chairperson and the school district. Certain qualifications required. 4  8 sh.
Prerequisites: Departmental approval.
CURR516: Meeting the Needs of English Language Learners (1 hour lecture)
This course examines the best practices in educating English language learners. Students gain a greater understanding of the linguistic difficulties and resources of English language learners as well as the importance of a multicultural curriculum. Students learn how to make content comprehensible and differentiate instruction based on the language levels of individual English language learners. Students develop an understanding of the academic and affective needs of English language learners, and of strategies for meeting these needs. May be repeated once for a maximum of 2.0 credits. Cross listed with EDFD 516. 1 sh.
Prerequisites: CURR 505 or EDFD 505; CURR 518. Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
CURR517: Inclusive Classrooms in Middle and Secondary Schools (1 hour lecture)
This course presents the central issues in the inclusion of students with disabilities in United States middle and secondary schools. It focuses on best practices for providing access to the general education curriculum for students with disabilities in inclusive settings. In addition, students explore the legal, professional, and contextual influences on the implementation of inclusion. May be repeated once for a maximum of 2.0 credits. 1 sh.
Prerequisites: CURR 505 or EDFD 505; and CURR 518. Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
CURR518: Technology Integration in the Classroom (1 hour lecture)
This onecredit course introduces preservice teachers to the dimensions of educational technology for teaching and learning. Students also explore the history of educational technology with a focus on the pedagogical and practical implementation of educational technologies, youth technology culture, and emerging technologies. It enables the students to drawn upon fieldbased experiences in READ 501 to plan instructional technology environments that are studentcentered, collaborative, and inquirybased; that emphasize critical thinking; and that support specific curricular goals  as stated in institutional, state and national standards for technology in education. May be repeated once for a maximum of 2.0 credits. 1 sh.
Prerequisites: Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
CURR519: Assessment for Authentic Learning (3 hours lecture)
This course provides prospective teachers with knowledge and skills for evaluating and understanding student growth and learning across diverse educational settings. Students consider assessment practices from the point of view of learners and how they experience learning opportunities. Teacher candidates also analyze assessment policies and practices, both local and national, in order to maximize both student and teacher performance. They draw on aspects of assessment policy and practice to evaluate their own understandings of assessment and its development. May be repeated once for a maximum of 6.0 credits. Cross listed with EDFD 519. 3 sh.
Prerequisites: CURR 505 or EDFD 505, CURR 518. Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
CURR526: Teaching for Learning I (3 hours lecture)
This is the first course in a twosemester sequence (CURR 526, CURR 543). This course focuses on developing classroom practices necessary for student teaching and the beginning of a professional career in teaching, building from the knowledge and skills developed in previous courses in the professional sequence. In conjunction with CURR 527Fieldwork, students have the opportunity to observe in classrooms and to do individual, small group, and whole class teaching. Students investigate democratic classroom practice by focusing on curriculum development; creating a positive, wellstructured climate for learning in their classrooms; learning and practicing techniques for effective classroom management; and choosing appropriate teaching strategies and assessments to create successful learning experiences for their students. 3 sh.
Prerequisites: CURR 505 or EDFD 505; CURR 509 or EDFD 509; CURR 516 or EDFD 516; CURR 517; CURR 518; READ 501. Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
CURR527: Fieldwork (3 hours lecture)
Students spend 60 hours, or approximately one day per week, in a selected public school. Activities include, but are not limited to, observing classroom teachers, facilitating small group and individual instruction, participating in afterschool activities, tutoring, attending department meetings, shadowing and interviewing students and teachers, lesson planning and teaching, and assessing student work. May be repeated once for a maximum of 6.0 credits. 3 sh.
Prerequisites: CURR 505 or EDFD 505; and CURR 509 or EDFD 509; and CURR 516 or EDFD 516; and CURR 517; and CURR 518; and EDFD 519 or CURR 519; and READ 501. Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
CURR529: Student Teaching (6 hours lab)
Full time student teaching in the public schools of New Jersey for the duration of a semester is required of all students who complete the regular program of certification requirements. 6 hour lab requirements. May be repeated once for a maximum of 12.0 credits. 6 sh.
Prerequisites: CURR 505 or EDFD 505; and CURR 509 or EDFD 509; and CURR 516 or EDFD 516; and CURR 517; and CURR 518; and CURR 519 or EDFD 519; and CURR 526; and CURR 527; and READ 501; and content area methods course(s). Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
CURR543: Teaching for Learning II (3 hours lecture)
This is the second course in a twosemester sequence (CURR 526, CURR 543). This course focuses on putting into practice all the knowledge and skills students have developed throughout their professional sequence in their fulltime, supervised student teaching experience. A primary focus is on planning and implementing curriculum. In addition to curriculum planning and using appropriate instructional and assessment strategies, students learn about the impact of the school and classroom culture and climate on student learning and on relationships between and among students, teachers, and other professionals in school. May be repeated once for a maximum of 6.0 credits. 3 sh.
Prerequisites: CURR 505 or EDFD 505; and CURR 509 or EDFD 509; and CURR 516 or EDFD 516; and CURR 517; and CURR 518; and CURR 526; and CURR 527; and READ 501; and content area methods course(s). Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
EDFD505: Teaching, Democracy, and Schooling (3 hours lecture)
This course brings together differing viewpoints regarding the purposes of teaching in the United States and the teacher's role in fostering democracy. It provides future teachers with the habits of mind, skills, tools and resources to analyze and evaluate the relationship between the history of public education, the evolution of teacher identity, and the roles teachers and teaching have played in shaping the United States as a society and vice versa. Using Montclair State's Portrait of a Teacher as an organizing framework, this course places particular emphasis on the idea that all students can learn regardless of their gender, ability, race, ethnicity, or economic background. Students in the course study the history, philosophy, and politics that shape differing views about the roles and responsibilities of teachers, especially as these views relate to integration and inclusion in the classroom. Cross listed with CURR 505. May be repeated once for a maximum of 6.0 credits. 3 sh.
Prerequisites: Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
EDFD509: Sociocultural Perspectives of Teaching (3 hours lecture)
This course examines how teachers, teaching, & schooling can foster the learning of pupils from diverse socioeconomic, linguistic & cultural backgrounds. Students explore the ways socialization shapes perceptions of oneself & others; reflect on their own beliefs & assumptions about their sociocultural identities & how those have been shaped through experience; examine the nature & impact of the increasing social, cultural, & linguistic diversity in K12 schools; & reflect on their capacity to bring about educational change that promotes equity & affirms diversity. They investigate ways of teaching all children successfully, particularly through a culturally responsive curriculum, & of developing positive relationships among teachers, parents, & children across diversity. Through a community study of an urban area with a predominantly poor & diverse population, students develop a framework for understanding the relationship between schools, communities, & society; cultivate skills needed to familiarize themselves with diverse communities & their residents; & envision ways they can help future students see connections between their inschool & outofschool experiences. They also develop their ability to work collaboratively with colleagues. May be repeated once for a maximum of 6.0 credits. Cross listed with CURR 509. 3 sh.
Prerequisites: CURR 505 or EDFD 505, CURR 518. Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
EDFD516: Meeting the Needs of English Language Learners (1 hour lecture)
This course examines the best practices in educating English language learners. Students gain a greater understanding of the linguistic difficulties and resources of English language learners as well as the importance of a multicultural curriculum. Students learn how to make content comprehensible and differentiate instruction based on the language levels of individual English language learners. Students develop an understanding of the academic and affective needs of English language learners, and of strategies for meeting these needs. May be repeated once for a maximum of 2.0 credits. Cross listed with CURR 516. 1 sh.
Prerequisites: CURR 505 or EDFD 505; and CURR 518. Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
EDFD519: Assessment for Authentic Learning (3 hours lecture)
This course examines the best practices in educating English language learners. Students gain a greater understanding of the linguistic difficulties and resources of English language learners as well as the importance of a multicultural curriculum. Students learn how to make content comprehensible and differentiate instruction based on the language levels of individual English language learners. Students develop an understanding of the academic and affective needs of English language learners, and of strategies for meeting these needs. May be repeated once for a maximum of 2.0 credits. Cross listed with CURR 516. 3 sh.
Prerequisites: CURR 505 or EDFD 505; and CURR 518. Students must be enrolled in a Master of Arts in Teaching (MAT), Instructional Teaching Certificate (CRI), Educational Services Certificate (CRE) or Master of Education (MED).
ELRS580: Learning Theories (3 hours lecture)
Study of the learning process and its measurement as it applies in the classroom and nonschool settings. 3 sh.
MATH122: Calculus I (4 hours lecture)
Limits, continuity; derivative and differentiation; applications of the derivative, maxima, minima, and extreme considerations; antiderivatives; Riemann integral. 4 sh.
Prerequisites: MATH 111 or MATH 112 or placement through the Montclair State University Placement Test (MSUPT) or a satisfactory score on department's Calculus Readiness Test. (Students who did not satisfy the course prerequisite at MSU and students who received a grade of D, D, or D+ in the prerequisite course taken at MSU are required to demonstrate competency on the department's Calculus Readiness Test.)
MATH221: Calculus II (4 hours lecture)
Riemann integral applications, transcendental functions, techniques of integration, improper integrals, L'Hospital's rule, infinite series. 4 sh.
Prerequisites: MATH 122.
MATH222: Calculus III (4 hours lecture)
Vector algebra; partial differentiation, and extreme considerations; polar, cylindrical, and spherical coordinates, multiple integration; introduction to line integrals. 4 sh.
Prerequisites: MATH 221.
MATH335: Linear Algebra (4 hours lecture)
The course content will cover the foundations of the algebra of vector spaces, matrix operations, matrix invertibility theorems, linear independence, span, basis, linear transformations, finite dimensional Hilbert Spaces, GramSchmidt process, projections, eigenvalues and eigenvectors, and applications. The focus of the course will be to develop advanced mathematical skills in reading and understanding abstract mathematical definitions, constructing examples, and developing mathematical proofs. Meets the University Writing Requirement for majors in Mathematics. 4 sh.
Prerequisites: MATH 222 or equivalent.
MATH340: Probability (3 hours lecture)
Chance and variability, elements of combinatorics, Bayes' theorem, random variables, binomial, poisson and normal distributions, applications to statistics. 3 sh.
Prerequisites: MATH 221.
MATH350: College Geometry (3 hours lecture)
Study of Euclidean and other geometries from an axiomatic point of view. 3 sh.
Prerequisites: MATH 221.
MATH420: Ordinary Differential Equations (4 hours lecture)
A course in the theory and applications of ordinary differential equations which emphasizes qualitative aspects of the subject. Topics include analytic and numerical solution techniques for linear and nonlinear systems, graphical analysis, existenceuniqueness theory, bifurcation analysis, and advanced topics. Prerequisite: MATH 335. 4 sh.
Prerequisites: MATH 335.
MATH423: Complex Variables (3 hours lecture)
This course is a study of the arithmetic and algebra of complex numbers, and an introduction to the differentiation and integration of complex functions. Topics include: rectangular and polar form of complex numbers, algebra of complex numbers, differentiation, CauchyRiemann equations, and contour integrals. 3 sh.
Prerequisites: MATH 335.
MATH425: Advanced Calculus I (3 hours lecture)
Properties of the real number system, limits, continuous functions, intermediate value theorem, derivative, mean value theorem, Riemann integral. 3 sh.
Prerequisites: MATH 335.
MATH426: Advanced Calculus II (3 hours lecture)
Functions of several variables, partial derivatives, Green's theorem, Stoke's theorem, divergence theorem, implicit function theorem, inverse function theorem, infinite series, uniform convergence. 3 sh.
Prerequisites: MATH 425.
MATH431: Foundations of Modern Algebra (3 hours lecture)
Fundamental concepts of algebra including groups, rings, integral domains and fields, with important examples. 3 sh.
Prerequisites: MATH 335.
MATH433: Theory of Numbers (3 hours lecture)
Properties of integers, congruences, quadratic reciprocity law, primitive roots, diophantine equations, continued fractions, algebraic numbers, lattice points and partitions. 3 sh.
Prerequisites: MATH 335.
MATH450: Foundations of Geometry (3 hours lecture)
Groups of transformations, an introduction to projective geometry. 3 sh.
Prerequisites: MATH 335.
MATH451: Topology (3 hours lecture)
Topological spaces, metric spaces, continuity, compactness, connectedness, and separability properties; topological generalizations of basic continuity theorems of advanced calculus. 3 sh.
Prerequisites: MATH 425.
MATH463: Numerical Analysis (3 hours lecture)
Finite differences, approximation theory, linear and nonlinear equations, error analysis. 3 sh.
Prerequisites: MATH 222 and 335.
MATH464: Operations Research I (3 hours lecture)
Linear programming, transportation problem, assignment problem, duality, sensitivity analysis, network flows, dynamic programming, nonlinear programming, integer programming. 3 sh.
Prerequisites: MATH 335.
MATH465: Operations Research II (3 hours lecture)
Game theory, queuing models, inventory models, Markov processes, reliability theory and applications. 3 sh.
Prerequisites: MATH 335 and 340.
MATH469: Mathematical Modeling (3 hours lecture)
The art of constructing mathematical models for "real world" problems, solving the model, and testing the accuracy of the model. Problems will be selected from business, science, computer science, and the social sciences. 3 sh.
Prerequisites: MATH 335, and MATH 340, and MATH 464 or STAT 330.
MATH471: Selected Topics in Modern Mathematics (3 hours lecture)
Professionalized view of junior and senior high school mathematics topics: functions, real and complex numbers, analytic geometry, absolute value and inequalities, sets and logic, flow charting, linear programming. 3 sh.
Prerequisites: Admission to Teacher Education Program and MATH 335.
MATH475: History of Mathematics (3 hours lecture)
Histories of geometry, number theory, algebra, calculus and infinite processes. 3 sh.
Prerequisites: MATH 335.
MATH485: Applied Combinatorics and Graph Theory (3 hours lecture)
Problem solving by counting, enumeration, and graph theory. Permutation, combinations, binomial coefficients, generating functions, and recurrence relations, partitions, inclusionexclusion, Polya's formula, graph theoretic models, trees, circuits, networks, matching, and their applications to puzzles, games, tournaments, traffic patterns, transportation. 3 sh.
Prerequisites: MATH 340.
MATH490: Honors Seminar (3 hours seminar)
This course will concentrate on subject matter not usually covered within standard mathematics courses. A written and oral report are required. 3 sh.
Prerequisites: MATH 335 and departmental approval.
MATH495: Topics for Undergraduates
Study of advanced topics in undergraduate mathematics. May be repeated once for a maximum of 6.0 credits as long as the topic is different. 1  3 sh.
Prerequisites: MATH 335 and departmental approval.
MATH497: Research I
Individual research in a mathematical area agreed upon by the student and the instructor. The results of the research will be a basis of a seminar or colloquium to be given by the student. Students must not accumulate more than 6 credits total in courses MATH 497, 498. 1  3 sh.
Prerequisites: MATH 335 and departmental approval.
MATH498: Research II
Individual research in a mathematical area agreed upon by the student and the instructor. The results of the research will be a basis of a seminar or colloquium to be given by the student. Students must not accumulate more than 6 credits total in courses MATH 497, 498. 1  3 sh.
Prerequisites: MATH 335 and departmental approval.
MATH520: Set Theory (3 hours lecture)
Historical development, paradoxes, ordered sets, SchroderBernstein theorem, axiom of choice, transfinite induction, cardinal and ordinal numbers. 3 sh.
Prerequisites: MATH 222 and permission of graduate program coordinator.
MATH521: Real Variables I (3 hours lecture)
Real number system, Lebesgue measure and integration, differentiation, Fourier series, LP, metric, normed vector, Banach and Hilbert spaces. 3 sh.
Prerequisites: MATH 426 and permission of graduate program coordinator.
MATH525: Complex Variables I (3 hours lecture)
Integration and differentiation in the complex domain, Cauchy's theorem, Cauchy's integral formula, Laurent expansion, residues, elements of conformal mapping, series and product representations. 3 sh.
Prerequisites: MATH 426 and permission of graduate program coordinator.
MATH526: Complex Variables II (3 hours lecture)
Integration and differentiation in the complex domain, Cauchy's theorem, Cauchy's integral formula, Laurent expansion, residues, elements of conformal mapping, series and product representations. 3 sh.
Prerequisites: MATH 525, permission of graduate program coordinator.
MATH530: Mathematical Computing (3 hours lecture)
Introduction to mathematical computing techniques using a computer algebra system and algorithmic approach to solving mathematical problems. Mathematical applications taken from various areas of mathematics, the sciences, engineering, and business. 3 sh.
Prerequisites: Permission of the graduate program coordinator or consent of the instructor.
MATH531: Abstract Algebra I (3 hours lecture)
Basic algebraic structures including groups, rings, fields, modules and lattices. 3 sh.
Prerequisites: MATH 431 and permission of graduate program coordinator.
MATH532: Abstract Algebra II (3 hours lecture)
Basic algebraic structures including groups, rings, fields, modules and lattices. 3 sh.
Prerequisites: MATH 531, permission of graduate program coordinator.
MATH535: Linear Algebra I (3 hours lecture)
Vector spaces and linear transformations, including inner product, matrix representations, binary and quadratic forms, eigenvectors, canonical forms, and functions of matrices. 3 sh.
Prerequisites: MATH 335 and permission of graduate program coordinator.
MATH536: Linear Algebra II (3 hours lecture)
Vector spaces and linear transformations, including inner product, matrix representations, binary and quadratic forms, eigenvectors, canonical forms, and functions of matrices. 3 sh.
Prerequisites: MATH 535, permission of graduate program coordinator.
MATH537: Mathematical Logic (3 hours lecture)
Propositional and predicate calculus, model theory, Godel's completeness theorems and decidability. 3 sh.
Prerequisites: MATH 425 and permission of graduate program coordinator.
MATH540: Probability (3 hours lecture)
Sample spaces and events, combinatorial analysis, conditional probability and stochastic independence, random variables and probability distributions, expected value and variance, probability generating functions, continuous random variables. 3 sh.
Prerequisites: MATH 340 and permission of graduate program coordinator.
MATH551: Topology (3 hours lecture)
Basic pointset topology, topological spaces, homeomorphisms, compactness, connectedness, separation properties, uniformities, metrizability, introductory algebraic topology, homology groups and homotopy. 3 sh.
Prerequisites: MATH 425, and permission of graduate program coordinator.
MATH554: Projective Geometry (3 hours lecture)
Projective planes and spaces are studied by synthetic and analytic approaches. Topics covered include the theorems of Desargues and Pappus, harmonic sequences, projectivities, coordinatization, finite planes, and conics. 3 sh.
Prerequisites: MATH 335 and permission of graduate program coordinator.
MATH555: Differential Geometry (3 hours lecture)
Application of vectors to the study of classical threedimensional geometry. Topics include: plane and space curves, first and second fundamental forms, lines of curvature, asymptotic lines, geodesics. 3 sh.
Prerequisites: MATH 222 and permission of graduate program coordinator.
MATH560: Numerical Analysis (3 hours lecture)
Error analysis, interpolation and approximation theory, numerical solution of linear and nonlinear equations, numerical differentiation and integration, numerical solution of differential equations. 3 sh.
Prerequisites: MATH 335, and permission of graduate program coordinator.
MATH564: Ordinary Differential Equation (3 hours lecture)
Linear and nonlinear equations, Green's functions, power series solutions, autonomous systems, existence and uniqueness, singularities, SturmLiouville systems. 3 sh.
Prerequisites: MATH 335, and 420, and permission of graduate program coordinator.
MATH566: Partial Differential Equations (3 hours lecture)
First order equations, separation of variables, series solutions, hyperbolic, parabolic and elliptic equations, characteristics, transform methods. 3 sh.
Prerequisites: MATH 335, and 420, and permission of graduate program coordinator.
MATH568: Applied Mathematics: Continuous (3 hours lecture)
Formulation, manipulation and evaluation of mathematical models of continuous systems. Topics selected from: conservation principles and the classical equations of mathematical physics, applications of the qualitative and quantitative theory of ordinary and partial differential equations, optimization, calculus of variations, stability theory, stochastic models. 3 sh.
Prerequisites: MATH 335, and 340, and 420, and 425, and permission of graduate program coordinator.
MATH569: Applied Mathematics: Discrete (3 hours lecture)
Introduction to the basic ideas of discrete mathematics and its applications. Counting principles, permutations, combinations, algorithms, complexity, graphs, trees, searching and sorting, recurrence relations, generating functions, inclusionexclusion, the pigeonhole principle, chromatic number, eulerian chains and paths, hamiltonian chains and paths, flows in networks, finite Markov chains. 3 sh.
Prerequisites: MATH 335, and 340, and 425, and permission of graduate program coordinator.
MATH570: Administration and Supervision of Mathematics (3 hours lecture)
Problems of organization, administration and supervision in the mathematics program of the school. Functions, duties and qualifications of the supervisor investigated. Current problems and research findings. 3 sh.
Prerequisites: Permission of graduate program coordinator.
MATH572: Contemporary Teaching of Mathematics (3 hours lecture)
Pedagogy, resources, and research related to the teaching of standardsbased mathematics in grades 612. Emphasis is on creating studentcentered learning environments, resources and materials for contemporary mathematics classrooms, models of effective teaching and learning, alternative assessment, appropriate uses of technology and multicultural aspects of mathematics. 3 sh.
Prerequisites: Permission of graduate program coordinator.
MATH573: Mathematics Materials for Teachers of Mathematics (3 hours lecture)
The construction, adaptation and effective use of classroom materials and activities designed to enhance and expand the teaching of mathematics and mathematical thinking in the middle and high school grades with special attention given to basic commercial and simple teacher and studentmade manipulatives and models with broad use from the development of concepts and skills to their maintenance, review, and extension plus applications to problem solving. 3 sh.
Prerequisites: Permission of graduate program coordinator.
MATH574: Problem Analysis in Secondary Mathematics (3 hours lecture)
Psychology and techniques of problemsolving. Discovery and heuristic methods. Intuitive and inductive reasoning in the solution of nonroutine problems from high school mathematics. Problem formation and solution. 3 sh.
Prerequisites: MATH 222 and permission of graduate program coordinator.
MATH575: Selected Topics in Mathematics Education (3 hours lecture)
Selection of topics associated with secondary and early college years of mathematics investigated from an advanced point of view. Topics selected to give the teacher a professionalized subject matter viewpoint of such areas as algebra, geometry, number theory, real and complex analysis, probability and history of mathematics. 3 sh.
Prerequisites: MATH 222 and permission of graduate program coordinator.
MATH579: Approaching School Mathematics Through Applications (3 hours lecture)
Topics in middle grade and secondary mathematics are explored with an emphasis on their application to both traditional and more recently developed areas. Applied problems are used to motivate mathematical topics, and mathematical knowledge is used to explore solutions to applied problems. 3 sh.
Prerequisites: Permission of graduate program coordinator.
MATH580: Combinatorial Mathematics (3 hours lecture)
Arrangements and selections, binomial coefficients, Stirling numbers, generating functions, recurrence relations, inclusionexclusion, Polya enumeration formula, combinatorial graph theory, combinatorial geometries. 3 sh.
Prerequisites: MATH 222 and graduate program coordinator's permission.
MATH581: Graph Theory (3 hours lecture)
Graphs, digraphs, and trees. Connectivity, separability, planarity, and colorability. Cliques, independent sets, matchings, flows and tours. Graphs as mathematical models; graph algorithms. 3 sh.
Prerequisites: MATH 222, and 335, and graduate program coordinator's permission.
MATH584: Operations Research (3 hours lecture)
An indepth study of one or at most two topics in operations research, selected from linear programming and game theory, linear and nonlinear programming, queuing theory, inventory theory, simulation models. 3 sh.
Prerequisites: MATH 425 and STAT 440 and permission of graduate program coordinator.
PSYC560: Advanced Educational Psychology (3 hours lecture)
A comprehensive treatment of the cognitive and affective characteristics of the learner and the processes of learning and teaching provide the framework for this course. Behavioral, cognitive and informationprocessing theory are presented and their applicability to instructional strategies and classroom dynamics is discussed. Other areas included are the origins of individual differences including heredity and environment, early childhood education, cultural differences, student motivation, classroom management, measurement and evaluation, exceptional children and other topics. 3 sh.
READ501: Techniques of Reading Improvement in the Secondary School (3 hours lecture)
Techniques of Reading Improvement in the Secondary School introduces preservice and inservice teachers to an array of crosscontent literacy strategies for the improvement of nonclinical reading difficulties. Students learn how to ground literacy strategies in purposeful and meaningful curricular and pedagogical projects. 3 sh.
STAT441: Statistical Computing (3 hours lecture)
This course is designed: (1) to acquaint students with the use of the computer in solving statistical problems, and (2) to develop intermediate level statistical methodology. Several statistical computing packages and the student's own programs will be utilized. 3 sh.
Prerequisites: STAT 330 or STAT 401 and computer experience.
STAT443: Introduction to Mathematical Statistics (3 hours lecture)
Develops statistical methods from probability theory. Topics discrete and continuous probability distributions, estimation, inference and hypothesis testing. 3 sh.
Prerequisites: MATH 340 and either STAT 330 or STAT 401.