See also: catalog description of programs, course offering plan, main student page.
To fulfill a prerequisite, a student should obtain a grade of C or higher in the prerequisite course.
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MTH 097 Elementary Algebra. Introduction to topics covered in 110. Designed for students who are unprepared for 110. Credits earned for this course do not count toward the number of credits required for graduation. Prerequisite: Assignment through Grand Valley math placement. Four credits. Offered fall and winter semesters.
MTH 110 Algebra. A symbolic, numeric, and graphic approach to intermediate algebra with an emphasis on applications. Topics include operations, equations, and inequalities of linear, exponential, logarithmic, quadratic, rational, and radical functions. May not count toward a group science major or minor. Prerequisite: 097 or assignment through Grand Valley math placement. Four credits. Offered fall, winter, and spring/summer semesters.
MTH122 College Algebra. A study of functions and their graphs, including polynomial, rational, radical, exponential, logarithmic, and inverse functions; equations of circles; sequences and series. Emphasis on applications, problem solving, and using graphic, numeric, and symbolic methods to understand and solve equations, inequalities, and systems of nonlinear equations. Prerequisite: 110 or assignment through Grand Valley math placement. Fulfills Mathematical Sciences Foundation. Three credits. Offered fall and winter semesters.
MTH 123 Trigonometry. A study of the trigonometric functions with an emphasis on graphing, identities, inverse trigonometric functions, and solving equations. Additional topics include solving triangles, vectors, complex numbers, and polar coordinates. Prerequisite: 110; Co-requisite: 122 or satisfactory score on the placement test. Fulfills Mathematical Sciences Foundation. Three credits. Offered fall and winter semesters.
MTH 125 Survey of Calculus. A study of the concepts of calculus for students majoring in business, economics, life sciences, and social sciences. Differentiation and integration of algebraic, exponential, and logarithmic functions. Emphasis on applications. Prerequisite: 110. Fulfills Mathematical Sciences Foundation. Three credits. Offered fall and winter semesters.
MTH131 Introduction to Mathematics. A survey for non-mathematics majors. Topics selected from inductive and deductive reasoning, geometry, statistics, computers, modeling, number theory, numeration systems, the mathematics of decision-making, and applications. Prerequisite: 110. Fulfills Mathematical Sciences Foundation. Three credits. Offered on sufficient demand.
MTH 180 Special Topics. Readings, lecture, discussions, or lab (or any combination) in specific mathematics topics at an introductory or elementary level. Prerequisite: Permission of the instructor. One to four credits. Offered on sufficient demand.
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MTH 201 Calculus I.* A development of the fundamental concepts of calculus using graphical, numerical, and analytic methods with algebraic and trigonometric functions of a single variable. Limits and continuity, derivatives, indefinite integrals, definite integrals, and the Fundamental Theorem of Calculus; applications of derivatives and integrals. Prerequisites: 122 and 123. Fulfills Mathematical Sciences Foundation. Five credits. Offered fall and winter semesters.
MTH 202 Calculus II. Continuation of MTH 201 using graphical, numerical, and analytic methods to study exponential, logarithmic, hyperbolic, and inverse trigonometric functions. Indeterminate forms, improper integrals, integration techniques, sequences and series, Taylor polynomials and power series. Prerequisite: 201. Four credits. Offered fall and winter semesters.
MTH 203 Calculus III. Continuation of MTH 202 using graphical, numerical, and analytic methods to study parametric equations, polar coordinates, vector algebra in two and three dimension, differentiation and integration of vector functions of a single variable and scalar functions of several variables. Prerequisite: 202. Four credits. Offered fall and winter semesters.
MTH 210 Communicating in Mathematics. A study of proof techniques used in mathematics. Intensive practice in reading mathematics, expository writing in mathematics, and constructing and writing mathematical proofs. Mathematical content includes elementary logic, congruence arithmetic, set theory, functions, equivalence relations, and equivalence classes. Prerequisites: 201 and fulfillment of the composition requirement. Three credits. Offered fall and winter semesters.
MTH 221 Mathematics for Elementary Teachers I. Emphasis is on concepts, relationships, problem solving, reasoning, communicating, and connecting ideas in elementary school mathematics: geometry, measurement, patterns and functions, classification, logic, probability and statistics. MTH 221 and 222 (or MTH 223) required of all elementary teachers applying to the College of Education for winter 1996 or later. Does not count toward a major or minor in mathematics. Prerequisites: 110 and at least sophomore standing. Fulfills Mathematical Sciences Foundation. (3-0-2) Four credits. Offered fall and winter semesters.
MTH 222 Mathematics for Elementary Teachers II. Emphasis is on developing and teaching number and operational concepts, modeling, strategies, relationships, algorithms, and problem solving for elementary school mathematics: whole numbers, fractions, decimals, integers, mental arithmetic, and number theory. Fieldwork to include diagnosing and tutoring elementary children. MTH 221 and 222 (or MTH 223) required of all elementary teachers applying to the College of Education for winter 1996 or later. Prerequisites: 110 and at least sophomore standing; 221 strongly recommended. (2-0-2) Three credits. Offered fall and winter semesters.
MTH 223 Mathematics for Elementary Teachers III. Emphasis is on concepts, relationships, problem solving, reasoning, communicating, and connecting ideas in elementary school mathematics: geometry, measurement, patterns and functions, classification, logic, probability, statistics, whole and rational numbers and their operations, mental arithmetic, and number theory. Fieldwork: diagnosing and tutoring. Equivalent to taking MTH 221 and 222. Prerequisite: 201. (4-0-2) Five credits. Offered winter semester.
MTH 225 Discrete Structures: Computer Science. Logic, sets, counting techniques, cardinality, relations, functions and sequences, matrices, mathematical induction, and computer science applications. Prerequisite: 122 or equivalent. Three credits. Offered fall and winter semesters.
MTH 227 Linear Algebra I. Vectors in two and three dimensional space, systems of linear equations, matrix algebra, determinants, vectors in n dimensional space, subspace, dependence, bases, linear transformations, eigenvectors and applications. Prerequisite: 202. Three credits. Offered fall and winter semesters.
MTH 229 Mathematical Activities for Secondary Teachers. Problem-solving techniques, motivational ideas, and activities suitable for the secondary classroom. Includes tutorial training and experience in the Grand Valley Mathematics Laboratory. Prerequisites: 201 and sophomore standing. (2-0-2) Three credits. Offered fall and winter semesters.
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MTH 300 Applied Analysis I. Multivariable calculus and vector analysis including the change of variables formula, line integrals, surface integrals, Green’s theorem, Stokes’ theorem, and the divergence theorem. Applications in physics. Prerequisite: 203. Three credits. Offered fall semester.
MTH 302 Linear Algebra and Differential Equations. Matrix algebra and determinants. Introduction to the theory of differential equations. Methods of solution (including Laplace transform techniques) of linear equations as well as some special types of nonlinear equations. Applications in physical, biological, and social sciences. Prerequisite: 203. Four credits. Offered fall and winter semesters.
MTH 304 Analysis of Differential Equations. Solution methods for first order and second order linear equations (including power series and numerical methods). The linear algebra of linear systems and their solutions. Qualitative analysis of linear and nonlinear systems: phase plane; existence and uniqueness; stability, applications in physical, biological, and social sciences. Prerequisites: 203and 227. Three credits. Offered winter semester.
MTH 307 Mathematics Teacher Assisting Seminar. Strategies for teaching mathematics in junior and senior high school. Coordinated and taken concurrently with ED 331. Prerequisites: CS 205 or 309, PSY 301 and at least 12 hours in the major, including 229. Three credits. Offered fall and winter semesters.
MTH 310 Modern Algebra. Algebraic properties of the integers and the development of the rational, real, and complex number systems as algebraic structures. Topics from modern algebra include rings, integral domains, fields and ring isomorphisms. Further study of algebraic structures using congruence arithmetic and factorization in the ring of integers and polynomial rings. Prerequisites: 210, and 227 or 225. Three credits. Offered fall and winter semesters.
MTH 321 Number Systems and Structure. Analyze characteristics and properties of number systems, patterns, functions, variables, and algebraic structures. Integrated discussions of children’s learning, pedagogy, elementary and middle school curricula, NCTM Standards, and relevant research. Fieldwork includes writing lessons/problems and observing students. Within the mathematics major or minor, applies only to Elementary Certification Emphasis. Prerequisite: 221. (2-0-2) Three credits. Offered at least one semester per year.
MTH 322 Geometry for Elementary Teachers. Analyze characteristics and properties of geometric objects, transformations and representations, visualization and spatial reasoning, measurement systems and tools, dynamic geometric software. Integrated discussion of children’s learning, curricula, standards, and research for K–8. Fieldwork includes lesson design and implementation. Within the mathematics major or minor, applies only to Elementary Certification Emphasis. Prerequisite: 221. (2-0-2) Three credits. Offered at least one semester per year.
MTH 323 Probability and Statistics for Elementary Teachers. Analyze data and chance. Gathering, organizing, constructing, and interpreting data displays, distributions and models, making inferences and predictions. Integrated discussions of children’s learning, pedagogy, curricula, standards, and relevant research for K–8. Fieldwork includes designing/teaching activities and units. Within the mathematics major or minor applies only to Elementary Certification Emphasis. Prerequisite: 221. (2-0-2) Three credits. Offered at least one semester per year.
MTH 325 Discrete Structures: Computer Science 2. Properties of relations, equivalence relations, partial orderings, fundamental concepts of graphs, trees, digraphs, networks, and associated algorithms; computer science applications. Prerequisite: 225. Three credits. Offered fall and winter semesters.
MTH 327 Linear Algebra II. Vector spaces, bases, dimensions, linear transformations, canonical forms, eigen values and geometric applications. Prerequisites: 202 and 227. Three credits. Offered summer semester.
MTH 329 Teaching Middle Grades Mathematics. Emphasis on what mathematics is, how students learn mathematics, planning and instruction, assessment, and professional decision making. Conceptual, constructivist, and cooperative activities assist middle grades teachers in helping their students learn mathematics connecting algebra, geometry, number, measurement, statistics, and probability. 20 hours of service-learning with middle grades students required. Prerequisites: C or better in MTH 202, MTH 210, and one of MTH 229, 321, 322, or 323. Junior standing. Three credits. Offered fall and winter semesters.
MTH 330 The Mathematics of Voting and Elections. A study of voting, elections, and social choice from within the framework of mathematical modeling and problem solving. Topics include models of voter preference, election procedures, voting paradoxes, impossibility theorems, power indices, and referendum elections. Prerequisites: Math 110, Writing 150, and completion of the Mathematical Sciences Foundation. Three credits. Offered winter semesters.
MTH 341 Euclidean Geometry. Critical analysis of Euclidean geometry from transformational, algebraic, and synthetic perspectives in two and three dimensions. Coordinate and vector geometry relating transformational geometry to linear algebra. Informal study of historical development of Euclidean and non-Euclidean geometries and the questions relating to the parallel postulate to develop understanding of axiomatic systems. Prerequisites: 210 and either 227 or 322. Three credits. Offered fall and winter semesters.
MTH 345 Discrete Mathematics. Basic and advanced counting techniques, including the Pigeonhole Principle and inclusion-exclusion; recurrence relations; partial orderings; graph theory, special paths, planarity, chromatic number, networks, trees, traversals, digraphs. Algorithms and proof techniques. Prerequisite: 210. Three credits. Offered fall and winter semesters.
MTH 360 Operations Research. Mathematical modeling under conditions of certainty and uncertainty. Linear programming, duality, and sensitivity analysis. Markov chains and other stochastic processes. Applications to problems in transportation, scheduling, and resource allocation. Prerequisites: MTH 227, STA 312; (STA 312 may be taken concurrently). Offered fall of even-numbered years.
MTH 380 Special Topics. Readings, lecture, discussions, or lab (or any combination) in specific mathematics topics. Prerequisites dependent upon topic selected. Permission of the instructor required. One to four credits. Offered on sufficient demand.
MTH 399 Independent Readings. Hours, credit, topics, and time to be arranged with individual staff members with approval of the department. One to four credits. Offered fall and winter semesters.
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MTH 400 Applied Analysis II. Special topics in applied analysis, including Fourier methods, partial differential equations (heat, wave, and potential equations), calculus of variations, and orthogonal functions. Prerequisites: 300 and either 302 or 304. Three credits. Offered winter semester of even-numbered years.
MTH 402 Complex Variables. Complex arithmetic derivatives and integrals of functions of a complex variable. Infinite series. Residue calculus. Applications to real integration and fluid flows. Prerequisite: 203and either 227 or 302. Three credits. Offered winter semester of odd-numbered years.
MTH 405 Numerical Analysis. Numerical methods in solving equations of a single variable, matrix algebra, numerical differentiation and integration, numerical solution to differential equations, polynomial approximations, and error estimates. Prerequisites: 227, either 302 or 304, and CS 162. Three credits. Offered fall semester of even-numbered years.
MTH 408 Advanced Calculus I. Techniques of proof, development of the real number system and its topology, a rigorous examination of limits, continuity, differentiation, and integration of functions on one real variable. Also a development of techniques for solving problems not treated in an elementary calculus sequence. Prerequisites: 203and 210. Three credits. Offered fall semester.
MTH 409 Advanced Calculus II. Infinite series, improper integrals, development of the topology of Euclidean n-space and rigorous examination of limits, continuity, and differentiability of functions of several variables. Prerequisites: 227 and 408. Three credits. Offered winter semesters of even-numbered years.
MTH 410 Modern Algebra II. An introduction to groups, including homomorphisms and isomorphisms, LaGrange’s Theorem, quotient groups, finite groups, and the Sylow theorems. Additional topics from ring theory including polynomial rings, ideals, and quotient rings. Prerequisite: 310. Three credits. Offered winter semester.
MTH 431 Non-Euclidean Geometry. A critical examination of several non-Euclidean geometries, including finite geometries, hyperbolic geometry, and spherical geometry; their relationships to Euclidean geometry; and the historical and philosophical significance of the development of Non-Euclidean geometries. Prerequisites: 210 and either 341 or permission of the instructor. Three credits. Offered fall semester.
MTH 441 Topology. An introduction to the fundamental concepts of topology. The topology of the real number system and its generalizations to metric spaces and topological spaces. Topics include subspaces, neighborhood spaces, open and closed sets, interior and boundary of sets, continuity and homeomorphisms, connected and locally connected spaces, compact sets and spaces. Prerequisites: 203, 210, and 227. Three credits. Offered winter semester of odd-numbered years.
MTH 465 Automata and Theory of Computation. Introduction to basic mathematical models of computation and the finite representation of infinite objects. Finite automata, regular languages, non-determinism, pushdown automata, context-free languages, Turing machines and variants, halting problems, time complexity of algorithms, and NP-Complete problems. Prerequisites: CS 162 and either 325 or 345. Three credits. Offered fall semester of oddnumbered years.
MTH 480 Special Topics. Readings, lecture, discussions, or lab (or any combination) in specific mathematics topics. Prerequisites dependent upon topic selected. Permission of the instructor required. One to four credits. Offered on sufficient demand.
MTH 490 Mathematics Internship Seminar. Prerequisite: Approval of the department; senior status. Two credits. Offered fall and winter semesters.
MTH 495 The Nature of Modern Mathematics (capstone). A study of mathematics as a human intellectual endeavor impacting our culture, history, and philosophy. Includes an indepth investigation, including analyses from the mathematical, historical, and philosophical perspectives, of several significant developments from various fields of mathematics. The specific developments considered will vary from semester to semester. Prerequisites: 210, 227, 310, and at least three other 300–400 level mathematics courses. Three credits. Offered fall and winter semesters.
MTH 496 Senior Thesis (capstone). A senior thesis is written to demonstrate depth and sophistication in the major. Independent library research is conducted under the supervision of a faculty member. Students produce full-fledged, professional, oral and written presentations on this research. Prerequisite: Open to senior mathematics majors in good standing. Consent of instructor required. Three credits. Offered upon arrangement.
MTH 499 Independent Study and Research. Hours, credit, topics, and time to be arranged with individual staff members with approval of the department. One to four credits. Offered fall and winter semesters.
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MTH 603 Foundations of Calculus. Study of the conceptual underpinnings of calculus through situation-based, graphical, and numerical perspectives. The foundations of limit, rate of change, and area under a curve will be explored through examination of the properties of algebraic and transcendental functions. Prerequisite: Certification in secondary mathematics. Three credits.
MTH 615 Statistics with Probability. A blend of theory and applications with emphasis on applications. This calculus-based statistics course includes such topics as probability distributions, sampling, estimation, confidence intervals, hypothesis testing, and regression. A statistical computer package will be used extensively. Prerequisite: Certification in secondary mathematics. Three credits.
MTH 620 Modern Algebra. Study of the complex number system and various subsystems in terms of structural characteristics. Proofs of theorems within algebraic structures, such as groups, rings, integral domains and fields. Development of algebraic transformations, including techniques based on the theory of equations. Applications using technology. Prerequisite: Certification in secondary mathematics. Three credits.
MTH 625 Number Theory. The mathematical treatment of the properties and the structure of the set of integers. Topics include prime numbers, divisibility, number-theoretic functions, the algebra of congruence classes, and applications. Prerequisite: Certification in secondary mathematics. Three credits.
MTH 629 Secondary Student Issues. Research, theories, and recommendations of professional groups provide the foundation for exploring appropriate content, activities, applications and teaching techniques for meeting special needs of secondary students in mathematics. Special attention will be given to mathematics anxiety and avoidance. Prerequisite: Completion of 24 credit hours in program. Three credits.
MTH 641 Modern Geometry. The study of geometry as a mathematical system, explorations of different geometries and their relations to physical space and as sources of mathematical models, investigations of geometrical thinking in problem solving in mathematics and areas outside of mathematics. Computer applications appropriate to school classrooms. Prerequisite: Certification in secondary mathematics. Three credits.
MTH 645 Discrete Mathematics. A study of discrete mathematical structures, including sets, logic, algebraic structures, relations; graphs and digraphs, trees, and networks. Prerequisites: Certification in mathematics. Three credits.
MTH 685 Mathematics Workshop for Teachers. Activities using quantitative reasoning skills, divergent, and convergent thinking to expand the perspectives on the teaching of mathematics in grades 3–9, strategies and tactics for developing mathematical concepts and problem solutions. Prerequisite: Permission of the department. One to three credits. Offered on sufficient demand.
MTH 686 High School Mathematics Workshop. Expands the perspective on the teaching of precalculus secondary mathematics. The workshop will focus on the impact of technology, general approaches to problem solving, and the use of writing in the teaching of mathematics. Prerequisite: Permission of department. One to three credits. Offered on sufficient demand.
MTH 699 Directed Readings in Mathematics. Independent supervised reading on selected topics in mathematics. Credits and topics must be prearranged with a faculty member and approved by the department. One to three credits. Offered fall and winter semesters.
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