
Approved Courses
The following list includes undergraduate courses that have been approved as of May 2014. Courses added after that date do not appear in this list. Courses eliminated after that date may still appear. Not every course is offered regularly. Students should consult the Schedule of Classes at www.testudo.umd.edu to ascertain which courses are actually offered during a given semester.
Use the search box below to view the approved courses. Courses in "MATHMathematics" MATH  Mathematics MATH 003 Developmental Mathematics (3) A review of Intermediate High School Algebra intended for students preparing for one of the credit bearing Fundamental Studies Math Courses. It is taught in special computer labs using a selfpaced computer program. The curriculum will be geared toward the student's level of algebra skills and eventual goals. There is a special fee for the course that may be applied in addition to the regular tuition charge. Students should refer to the schedule of classes for details on fees as they apply to a particular semester. The course does not carry any credit toward any degree at the University. The course is repeatable. Topics will be chosen from exponents, polynomials, linear equations, quadratic equations as well as polynomial, rational, exponential and logarithm functions and elementary probability or statistics, depending on the student. MATH 010 Algebra for MATH 110 (3) A review of Intermediate High School Algebra intended for students preparing for MATH110. It is taught 5 days per week for the first 5 weeks, then leads directly into a special section of MATH110, the same semester, which also meets 5 days per week. Continuation in MATH110 is conditional on the student passing the MATHEMATICS PLACEMENT EXAM at the appropriate level. Topics include linear equations, linear inequalities, operations on polynomials, factoring, solutions of quadratic equations, as well as exponential and logarithm functions. MATH010 does not carry any credit toward any degree at the University, nor is it graded. It leads to either MATH110 or MATH003, both of which are graded. MATH 011 Algebra for MATH 111 (3) A review of Intermediate High School Algebra intended for students preparing for MATH111. It is taught 5 days per week for the first 5 weeks, then leads directly into a special section of MATH111, the same semester, which also meets 5 days per week. Continuation in MATH 111 is conditional on the student passing the MATHEMATICS PLACEMENT EXAM at the appropriate level. Topics include exponents, polynomials, linear equations, quadratic equations, as well as polynomial, rational, exponential and logarithm functions, Venn diagrams, permutations and combinations. MATH011 does not carry any credit toward any degree at the University, nor is it graded. It leads directly to MATH111 (or MATH113 or MATH110), or MATH003, all of which are graded. MATH 013 Algebra for MATH 113 (3) A review of Intermediate High School Algebra intended for students preparing for MATH113. It is taught 5 days per week for the first 5 weeks, then leads directly into a special section of MATH113, the same semester, which also meets 5 days per week. Continuation in MATH113 is conditional on the student passing the MATHEMATICS PLACEMENT EXAM at the appropriate level. Topics include exponents, polynomials, linear equations, quadratic equations, as well as polynomial, rational, exponential, logarithm functions, and trigonometry. MATH013 does not carry any credit toward any degree at the University, nor is it graded. It leads directly to MATH113 (or MATH110), or MATH003, all of which are graded. MATH 015 Algebra for MATH 115 (3) A review of Intermediate High School Algebra intended for students preparing for MATH115. It is taught 5 days per week for the first 5 weeks, then leads directly into a special section of MATH115, the same semester, which also meets 5 days per week. Continuation in MATH115 is conditional on the student passing the MATHEMATICS PLACEMENT EXAM at the appropriate level. Topics include exponents, polynomials, linear equations in one and two variables, quadratic equations, as well as polynomial, rational, exponential, logarithm functions and trigonometry. MATH015 does not carry any credit toward any degree at the University, nor is it graded. It leads directly to MATH115 (or MATH111 or MATH113 or MATH110), or MATH003, all of which are graded. MATH 110 Elementary Mathematical Models (3) Prerequisite: Must have math eligibility of MATH110 or higher; and math eligibility is based on Math Placement Exam or successful completion of MATH003 with appropriate eligibility. Restriction: Not open to students majoring in mathematics, engineering, business, life sciences, and the physical sciences;; and must not have completed MATH220, MATH130, or MATH140; and must not have completed any MATH or STAT course with a prerequisite of MATH140 or MATH130 or MATH220. Credit only granted for: MATH110, MATH112, or MATH113. Topics include simple and compound interest; recursion for computing balances; installment loans and amortization; approximating data by linear models; analysis of applications to realworld collections of data; probability; conditional probability; independence; expected value; graphing and analysis of systems of inequalities; linear programming and applications. MATH 111 Introduction to Probability (3) Prerequisite: Must have math eligibility of MATH111 or higher; and math eligibility is based on Math Placement Exam or successful completion of MATH003 with appropriate eligibility. Or MATH110. Restriction: Not open to students majoring in mathematics, engineering or the physical sciences; and must not have completed STAT100; and must not have completed any MATH or STAT course with a prerequisite of MATH141. Credit only granted for: MATH111 or STAT100. Logic, Boolean algebra, counting, probability, random variables, expectation, applications of the normal probability distribution. MATH 113 College Algebra and Trigonometry (3) Prerequisite: Must have math eligibility of MATH113 or higher. Restriction: Must not have completed MATH220, MATH140, MATH112, MATH115, or MATH130; and must not have completed any course with a prerequisite of MATH140 or MATH220. Credit only granted for: Students who have credits for MATH113 may not also receive credits for MATH110, MATH112, or MATH115. Topics include elementary functions including graphs and applications of: polynomial, rational, exponential, and logarithmic functions. Systems of equations and applications. Trigonometric functions: angle and radian measure, graphs and applications. MATH 115 Precalculus (3) Prerequisite: Must have math eligibility of MATH115 or higher; and math eligibility is based on the Math Placement Exam or the successful completion of MATH003 with appropriate eligibility. Or MATH113. Restriction: Must not have completed MATH140; and must not have completed any MATH or STAT course with a prerequisite of MATH140. Credit only granted for: Students who have credits for MATH115 may not also receive credits for MATH112 or MATH113. Preparation for MATH220, MATH130 or MATH140. Elementary functions and graphs: polynomials, rational functions, exponential and logarithmic functions, trigonometric functions. Algebraic techniques preparatory for calculus. MATH 130 Calculus I for the Life Sciences (4) Prerequisite: Minimum grade of C in MATH112; or minimum grade of C in MATH113; or minimum grade of C in MATH115; or permission of CMNS undergraduate program office. Restriction: Must be in a major in CMNSBiological Sciences UG Program; and not open to students majoring in mathematics, engineering or the physical sciences. Credit only granted for: MATH130, MATH220, or MATH140. Basic ideas of differential integral calculus, with emphasis on elementary techniques and applications to the life sciences. MATH 131 Calculus II for Life Sciences (4) Prerequisite: Minimum grade of C in MATH130; or minimum grade of C in MATH140. Restriction: Must be in a major in CMNSBiological Sciences UG Program. Credit only granted for: MATH131, MATH141, or MATH221. Continuation of MATH130, including an introduction to autonomous differential equations, probability (including conditional probability and the normal and binomial distributions), and statistical reasoning (including confidence intervals). Alongside the mathematical concepts will be applications in biology. MATH 140 Calculus I (4) Prerequisite: Minimum grade of C in MATH115. Or must have math eligibility of MATH140 or higher; and math eligibility is based on the Math Placement Test. Credit only granted for: MATH130, MATH220, or MATH140. Introduction to calculus, including functions, limits, continuity, derivatives and applications of the derivative, sketching of graphs of functions, definite and indefinite integrals, and calculation of area. The course is especially recommended for science, engineering and mathematics majors. MATH 141 Calculus II (4) Prerequisite: Minimum grade of C in MATH140. Or minimum grade of B in MATH130; and permission of CMNSMathematics department. Credit only granted for: MATH131, MATH141, or MATH221. Continuation of MATH140, including techniques of integration, improper integrals, applications of integration (such as volumes, work, arc length, moments), inverse functions, exponential and logarithmic functions, sequences and series. MATH 199 Special Topics in Mathematics (3) Prerequisite: Permission of CMNSMathematics department. Many games have a mathematical component. We will introduce several games, play them, and investigate the underlying mathematics. Students will work in teams on projects that involve developing strategies for new games. MATH 206 Introduction to Matlab (1) Prerequisite: 1 course with a minimum grade of C from (MATH141, MATH131). Credit only granted for: CMSC206, CMSC298M, MATH206, or MATH299M. This course is intended to prepare students for subsequent courses requiring computation with MATLAB. Covers basics of MATLAB including simple commands, variables, solving equations, graphing differentiation and integration, matrices and vectors, functions, Mfiles and fundamentals of programming in the MATLAB environment. When offered in Winter and Summer terms, the course is offered in a format suitable for online distance learning. MATH 212 Elements of Numbers and Operations (3) Prerequisite: Must have completed one year of college preparatory algebra. Restriction: Must be in one of the following programs (Early Childhood Education; Special Education; Elementary Education). Credit only granted for: MATH212 or MATH210. Reviews and extends topics of arithmetic and number theory related to the elementary school curriculum, particularly number systems and operations with natural numbers, integers, and rationals. MATH 213 Elements of Geometry and Measurement (3) Prerequisite: MATH212. Restriction: Must be in one of the following programs (Early Childhood Education; Special Education; Elementary Education). Credit only granted for: MATH211 or MATH213. Properties of geometric objects in two and three dimensions; parallel lines, curves and polygons; ratio, proportion, similarity; transformational geometry and measurement, constructions, justifications and proofs. MATH 214 Elements of Probability and Statistics (3) Prerequisite: MATH212. Restriction: Must be in one of the following programs (Early Childhood Education; Special Education; Elementary Education). Credit only granted for: MATH211 or MATH214. Permutations and combinations; probability; collecting and representing data; using statistics to analyze and interpret data. MATH 220 Elementary Calculus I (3) Prerequisite: MATH112, MATH113, or MATH115. Or must have math eligibility of MATH220 or higher; and math eligibility is based on the Math Placement Test. Restriction: Not open to students majoring in mathematics, engineering or the physical sciences. Credit only granted for: MATH130, MATH220, or MATH140. Basic ideas of differential and integral calculus, with emphasis on elementary techniques of differentiation and applications. MATH 221 Elementary Calculus II (3) Prerequisite: MATH220, MATH130, or MATH140. Restriction: Not open to students majoring in mathematics, engineering or the physical sciences. Credit only granted for: MATH131, MATH141, or MATH221. Differential and integral calculus, with emphasis on elementary techniques of integration and applications. MATH 240 Introduction to Linear Algebra (4) Prerequisite: Minimum grade of C in MATH131; or MATH141. Credit only granted for: MATH240, MATH341, or MATH461. Basic concepts of linear algebra: vector spaces, applications to line and plane geometry, linear equations and matrices, similar matrices, linear transformations, eigenvalues, determinants and quadratic forms. MATH 241 Calculus III (4) Prerequisite: MATH141. Credit only granted for: MATH241 or MATH340. Introduction to multivariable calculus, including vectors and vectorvalued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss. MATH 246 Differential Equations for Scientists and Engineers (3) Prerequisite: Minimum grade of C in MATH141. Credit only granted for: MATH246 or MATH341. An introduction to the basic methods of solving ordinary differential equations. Equations of first and second order, linear differential equations, Laplace transforms, numerical methods and the qualitative theory of differential equations. MATH 274 History of Mathematics (3) Prerequisite: MATH130, MATH140, or MATH220. An overview of aspects in the history of mathematics from its beginning in the concrete problem solving of ancient times through the development of abstraction in the 19th and 20th centuries. The course considers both mathematical ideas and the context in which they developed in various civilizations around the world. MATH 299 Selected Topics in Mathematics (13) Prerequisite: Permission of CMNSMathematics department. Topics of special interest under the general guidance of the departmental committee on undergraduate studies. MATH 307 A Condensed Introduction to Mathematical Proof (2) Prerequisite: 1 course with a minimum grade of C from (MATH241, MATH340). Recommended: MATH461, MATH240, or MATH341. Credit only granted for: MATH307 or MATH310. Additional information: Math majors may not use this course to satisfy the upperlevel math requirement. Students develop proofwriting skills including logic of proofs, induction and convergence concepts. MATH 310 Introduction to Mathematical Proof (3) Prerequisite: MATH141. Corequisite: Corequisite: MATH241 or MATH340. Restriction: Must be in a major within the CMNSMathematics department. Credit only granted for: MATH307 or MATH310. Additional information: Math majors may not use this course to satisfy an upperlevel requirement. To develop the students' ability to construct a rigorous proof of a mathematical claim. Students will also be made aware of mathematical results that are of interest to those wishing to analyze a particular mathematical model. Topics will be drawn from logic, set theory, structure of the number line, elementary topology, metric spaces, functions, sequences and continuity. MATH 312 Mathematical Reasoning and Proof for PreService Middle School Teachers (3) Prerequisite: MATH212 and MATH213. Restriction: Must be in one of the following programs (Elementary Education; Special Education; Middle School Education). Reasoning and proof as addressed in the middle school curriculum. Topics include proportional reasoning, logic and proof, types of numbers, field axioms, Euclidean and nonEuclidean geometry. MATH 314 Introduction to Probability, Data, Analysis and Statistics for Preservice Middle School Teachers (3) Prerequisite: MATH214. Restriction: Must be in one of the following programs (Elementary Education; Special Education; Middle School Education). Credit only granted for: MATH314 or STAT100. Analysis of bivariate data, probability and randomness, law of large numbers, central limit theorem, probabilities for independent and dependent events, counting techniques, random variables and probability distributions, expected values, sampling distributions, and confidence intervals. MATH 315 Algebra for Preservice Middle School Teachers (3) Prerequisite: MATH212. Restriction: Must be in one of the following programs (Elementary Education; Special Education; Middle School Education). Credit only granted for: MATH112, MATH113, or MATH315. Algebraic concepts and techniques developed in the middle grades, with their larger mathematical context. Equations, inequalities and functions (linear, polynomial, exponential, logarithmic), with multiple representations of relationships. Common misconceptions of beginning algebra students. MATH 340 Multivariable Calculus, Linear Algebra and Differential Equations I (Honors) (4) Prerequisite: MATH141 and MATH140; and permission of CMNSMathematics department; and permission will be granted only to incoming freshmen. Credit only granted for: MATH241 or MATH340. First semester of the MATH340341 sequence which gives a unified and enriched treatment of multivariable calculus, linear algebra and ordinary differential equations, with supplementary material from subjects such as differential geometry, Fourier series and calculus of variations. Students completing MATH340341 will have covered the material of MATH240, MATH241, and MATH246, and may not also receive credit for MATH240, MATH241 or MATH246. MATH 341 Multivariable Calculus, Linear Algebra, Differential Equations II (Honors) (4) Prerequisite: Minimum grade of C in MATH340. Restriction: Open to second semester Freshmen only. Credit only granted for: MATH240, MATH246, MATH341 or MATH461. A continuation of MATH340. MATH 386 Experiential Learning (36) Prerequisite: Must have learning proposal approved by the CMNS Mathematics Department. MATH 401 Applications of Linear Algebra (3) Prerequisite: 1 course with a minimum grade of C from (MATH461, MATH240, MATH341). Various applications of linear algebra: theory of finite games, linear programming, matrix methods as applied to finite Markov chains, random walk, incidence matrices, graphs and directed graphs, networks and transportation problems. MATH 402 Algebraic Structures (3) Prerequisite: MATH240, MATH341, or MATH461. Restriction: Must not be in any of the following programs (Mathematics (Master's); Mathematics (Doctoral)). Credit only granted for: MATH402 or MATH403. For students having only limited experience with rigorous mathematical proofs. Parallels MATH403. Students planning graduate work in mathematics should take MATH403. Groups, rings, integral domains and fields, detailed study of several groups; properties of integers and polynomials. Emphasis is on the origin of the mathematical ideas studied and the logical structure of the subject. MATH 403 Introduction to Abstract Algebra (3) Prerequisite: 1 course with a minimum grade of C from (MATH240, MATH461, MATH340); and 1 course with a minimum grade of C from (MATH341, MATH241); and minimum grade of C in MATH310. Or students who have taken courses with comparable content may contact the department. Credit only granted for: MATH402 or MATH403. Integers; groups, rings, integral domains, fields. MATH 404 Field Theory (3) Prerequisite: MATH403. Algebraic and transcendental elements, Galois theory, constructions with straightedge and compass, solutions of equations of low degrees, insolubility of the quintic equation, Sylow theorems, fundamental theorem of finite Abelian groups. MATH 405 Linear Algebra (3) Prerequisite: 1 course with a minimum grade of C from (MATH240, MATH461, MATH341); and minimum grade of C in MATH310. An abstract treatment of finite dimensional vector spaces. Linear transformations and their invariants. MATH 406 Introduction to Number Theory (3) Prerequisite: 1 course with a minimum grade of C from (MATH240, MATH241, MATH246, MATH340, MATH341, MATH461); or permission of CMNSMathematics department. Integers, divisibility, prime numbers, unique factorization, congruences, quadratic reciprocity, Diophantine equations and arithmetic functions. MATH 410 Advanced Calculus I (3) Prerequisite: Minimum grade of C in MATH240 and MATH241. And minimum grade of C in MATH310; or students who have taken courses with comparable content may contact the department. And permission of CMNSMathematics department. First semester of a year course. Subjects covered during the year are: sequences and series of numbers, continuity and differentiability of real valued functions of one variable, the Riemann integral, sequences of functions and power series. Functions of several variables including partial derivatives, multiple integrals, line and surface integrals. The implicit function theorem. MATH 411 Advanced Calculus II (3) Prerequisite: Minimum grade of C in MATH410; and permission of CMNSMathematics department. Credit only granted for: MATH411 or MATH412. Continuation of MATH410. MATH 412 Advanced Calculus with Applications (3) Prerequisite: Minimum grade of C in MATH410; and permission of CMNSMathematics department. Credit only granted for: MATH411 or MATH412. Analysis in several variables, and applications, from a computational perspective. MATH 416 Applied Harmonic Analysis: An Introduction to Signal Processing (3) Prerequisite: MATH141; and (MATH240, MATH461, or MATH341); and familiarity with MATLAB is required. Introduces students to the mathematical concepts arising in signal analysis from the applied harmonic analysis point of view. Topics include applied linear algebra, Fourier series, discrete Fourier transform, Fourier transform, Shannon Sampling Theorem, wavelet bases, multiresolution analysis, and discrete wavelet transform. MATH 420 Mathematical Modeling (3) Prerequisite: 1 course with a minimum grade of C from (MATH240, MATH461, MATH341); and 1 course with a minimum grade of C from (MATH241, MATH340); and 1 course with a minimum grade of C from (MATH246, MATH341); and minimum grade of C in STAT400. Also offered as: AMSC420. Credit only granted for: AMSC420 or MATH420. The course will develop skills in mathematical modeling through practical experience. Students will work in groups on specific projects involving reallife problems that are accessible to their existing mathematical backgrounds. In addition to the development of mathematical models, emphasis will be placed on the use of computational methods to investigate these models, and effective oral and written presentation of the results. MATH 424 Introduction to the Mathematics of Finance (3) Prerequisite: Minimum grade of C in MATH141; and 1 course with a minimum grade of C from (STAT400, STAT410); and permission of CMNSMathematics department. Recommended: MATH246, MATH240, MATH241, MATH340, or MATH341. Credit only granted for: BMGT444, MATH424. Introduction to the mathematical models used in finance and economics with emphasis on pricing derivative instruments. Designed for students in mathematics, computer science, engineering, finance and physics. Financial markets and instruments; elements from basic probability theory; interest rates and present value analysis; normal distribution of stock returns; option pricing; arbitrage pricing theory; the multiperiod binomial model; the BlackScholes option pricing formula; proof of the BlackScholes option pricing formula and applications; trading and hedging of options; Delta hedging; utility functions and portfolio theory; elementary stochastic calculus; Ito's Lemma; the BlackScholes equation and its conversion to the heat equation. MATH 430 Euclidean and NonEuclidean Geometries (3) Prerequisite: 1 course with a minimum grade of C from (MATH240, MATH341, MATH461). Hilbert's axioms for Euclidean geometry. Neutral geometry: the consistency of the hyperbolic parallel postulate and the inconsistency of the elliptic parallel postulate with neutral geometry. Models of hyperbolic geometry. Existence and properties of isometries. MATH 431 Geometry for Computer Graphics (3) Prerequisite: MATH461, MATH240, or MATH341. Topics from projective geometry and transformation geometry, emphasizing the twodimensional representation of threedimensional objects and objects moving about in the plane and space. The emphasis will be on formulas and algorithms of immediate use in computer graphics. MATH 432 Introduction to Topology (3) Prerequisite: MATH410. Metric spaces, topological spaces, connectedness, compactness (including HeineBorel and BolzanoWeierstrass theorems), Cantor sets, continuous maps and homeomorphisms, fundamental group (homotopy, covering spaces, the fundamental theorem of algebra, Brouwer fixed point theorem), surfaces (e.g., Euler characteristic, the index of a vector field, hairy sphere theorem), elements of combinatorial topology (graphs and trees, planarity, coloring problems). MATH 436 Differential Geometry of Curves and Surfaces I (3) Prerequisite: MATH241 or MATH340; and (MATH461, MATH240, or MATH341); and must have completed two 400level MATH courses (not including MATH461, 478, and 480's). Curves in the plane and Euclidean space, moving frames, surfaces in Euclidean space, orientability of surfaces; Gaussian and mean curvatures; surfaces of revolution, ruled surfaces, minimal surfaces, special curves on surfaces, "Theorema Egregium"; the intrinsic geometry of surfaces. MATH 437 Differential Forms (3) Prerequisite: MATH241 or MATH340; and (MATH461, MATH240, or MATH341). Recommended: MATH405, MATH403, MATH436, MATH410, or MATH432. Introduction to differential forms and their applications, and unites the fundamental theorems of multivariable calculus in a general Stokes Theorem that is valid in great generality. It develops this theory and technique to perform calculations in analysis and geometry. Topics include an introduction to topological spaces, the GaussBonnet Theorem, Gauss's formula for the linking number, and the Cauchy Integral Theorem. Applications include Maxwell's equations of electromagnetism, connections and gauge theory, and symplectic geometry and Hamiltonian dynamics. MATH 445 Elementary Mathematical Logic (3) Prerequisite: MATH141. Elementary development of propositional and predicate logic, including semantics and deductive systems and with a discussion of completeness, incompleteness and the decision problem. MATH 446 Axiomatic Set Theory (3) Prerequisite: MATH403 or MATH410. Development of a system of axiomatic set theory, choice principles, induction principles, ordinal arithmetic including discussion of cancellation laws, divisibility, canonical expansions, cardinal arithmetic including connections with the axiom of choice, Hartog's theorem, Konig's theorem, properties of regular, singular and inaccessible cardinals. MATH 452 Introduction to Dynamics and Chaos (3) Prerequisite: Minimum grade of C in MATH246; and 1 course with a minimum grade of C from (MATH240, MATH461). Or minimum grade of C in MATH340 and MATH341. Also offered as: AMSC452. Credit only granted for: AMSC452 or MATH452. An introduction to mathematical dynamics and chaos. Orbits, bifurcations, Cantor sets and horseshoes, symbolic dynamics, fractal dimension, notions of stability, flows and chaos. Includes motivation and historical perspectives, as well as examples of fundamental maps studied in dynamics and applications of dynamics. MATH 456 Cryptology (3) Prerequisite: Must have completed two 400level MATH courses (not to include MATH 461, 478, and 480's) with a minimum grade of C. Or minimum grade of C in CMSC351 and CMSC330; and permission of CMNSMathematics department. Also offered as: CMSC456. Credit only granted for: MATH456 or CMSC456. Importance in protecting data in communications between computers. The subject lies on the border between mathematics and computer science. Mathematical topics include number theory and probability. Computer science topics include complexity theory. MATH 461 Linear Algebra for Scientists and Engineers (3) Prerequisite: MATH141; and must have completed any MATH or STAT course with a prerequisite of MATH141. Credit only granted for: MATH240, MATH341, or MATH461. Additional information: This course may not be used towards the upper level math requirements for MATH/STAT majors. Basic concepts of linear algebra. This course is similar to MATH 240, but with more extensive coverage of the topics needed in applied linear algebra: change of basis, complex eigenvalues, diagonalization, the Jordan canonical form. MATH 462 Partial Differential Equations (3) Prerequisite: MATH241 or MATH340; and (MATH246 or MATH341). Linear spaces and operators, orthogonality, SturmLiouville problems and eigenfunction expansions for ordinary differential equations. Introduction to partial differential equations, including the heat equation, wave equation and Laplace's equation. Boundary value problems, initial value problems and initialboundary value problems. MATH 463 Complex Variables for Scientists and Engineers (3) Prerequisite: MATH241 or MATH340. The algebra of complex numbers, analytic functions, mapping properties of the elementary functions. Cauchy integral formula. Theory of residues and application to evaluation of integrals. Conformal mapping. MATH 464 Transform Methods for Scientists and Engineers (3) Prerequisite: MATH246 or MATH341. Fourier transform, Fourier series, discrete fast Fourier transform (DFT and FFT). Laplace transform. Poisson summations, and sampling. Optional Topics: Distributions and operational calculus, PDEs, Wavelet transform, Radon transform and applications such as Imaging, Speech Processing, PDEs of Mathematical Physics, Communications, Inverse Problems. MATH 470 Mathematics for Secondary Education (3) Prerequisite: MATH141 and MATH140; and must have completed one 400level MATH course (not to include MATH461, 478, and 480's). An advanced perspective on some of the core mathematics underlying high school mathematics courses. Topics include number systems, functions of one variable, equations, inequalities, trigonometric functions, curve fitting, and polynomials. The course includes an analysis of alternate approaches to mathematical ideas and problems, and makes connections between ideas that may have been studied separately in different high school and college courses. MATH 475 Combinatorics and Graph Theory (3) Prerequisite: MATH240 or MATH341; and (MATH241 or MATH340); and permission of CMNSMathematics department. Also offered as: CMSC475. Credit only granted for: MATH475 or CMSC475. General enumeration methods, difference equations, generating functions. Elements of graph theory, matrix representations of graphs, applications of graph theory to transport networks, matching theory and graphical algorithms. MATH 478 Selected Topics For Teachers of Mathematics (13) Prerequisite: Permission of CMNSMathematics department. Additional information: Math majors may not use this course to fulfill the upperlevel math requirement. MATH 480 Algebra for Middle School Teachers (3) Prerequisite: MATH214. Restriction: Must be a middle school teacher; and permission of CMNSMathematics department. Credit only granted for: MATH480 or MATH483. Additional information: Not applicable to MATH/STAT major or minor requirements. Prepares teachers with elementary certification to teach Algebra 1 in middle school. Focuses on basic algebra concepts and related theoretical ideas. MATH 481 Statistics and Data Analysis for Middle School Teachers (3) Prerequisite: MATH214. Restriction: Must be a middle school teacher; and permission of CMNSMathematics department. Credit only granted for: MATH481 or MATH485. Additional information: Not applicable to MATH/STAT major or minor requirements. Prepares teachers with elementary certification to teach simple data analysis and probability in middle school. Focuses on understanding basic statistics, data analysis, and related theoretical ideas. MATH 482 Geometry for Middle School Teachers (3) Prerequisite: MATH214. Restriction: Must be a middle school teacher; and permission of CMNSMathematics department. Credit only granted for: MATH482 or MATH484. Additional information: Not Applicable to MATH/STAT major or minor requirements. Prepares teachers with elementary certification to teach geometry in middle school. Focuses on understanding basic geometry concepts and related theoretical ideas. MATH 483 Algebra for High School Teachers (3) Prerequisite: MATH141. Restriction: Senior standing. Credit only granted for: MATH483 or MATH480. Additional information: May not be used towards the upper level math requirements for the MATH minor. Focuses on concepts related to algebra and trigonometry, including functions, equations, inequalities, and data analysis. Assumes a good understanding of calculus. MATH 484 Geometry for High School Teachers (3) Prerequisite: MATH141; or students who have taken courses with comparable content may contact the department. Restriction: Senior standing. Credit only granted for: MATH482, MATH484, or MATH498E. Formerly: MATH498E. Focuses on concepts related to geometry, including several geometry axiom schemes, transformations, and similarity. Includes constructions with Geometer's Sketchpad. MATH 485 Statistics for High School Teachers (3) Prerequisite: MATH141; or students who have taken courses with comparable content may contact the department. Credit only granted for: MATH481 or MATH485. Additional information: May not be used towards the upper level math requirements for the MATH minor. Focuses on concepts related to statistics and data analysis, including probability, sampling, distribution of data, and inference. MATH 486 Calculus for High School Teachers (3) Prerequisite: MATH141; and cannot be used toward the upper level math requirements for MATH/STAT majors. Focuses on concepts related to onevariable calculus including limits, continuity, derivative, integrals, series, and applications of these topics. MATH 487 Number for Middle Grades Teachers (3) Prerequisite: Must have admission to M.A. or M.Ed. with concentration in Mathematics Education; or permission of CMNSMathematics department. Restriction: This course may not be used towards the upper level math requirements for the MATH/STAT major. Credit only granted for: MATH487 or MATH498K. Formerly: MATH498K. The rational number and proportional reasoning concepts developed in the middle grades and the larger mathematical context for these. Multiple representations of relationships, including verbal descriptions, diagrams, tables, graphs, and equations. Common misconceptions. MATH 489 Research Interactions in Mathematics (13) Prerequisite: Permission of CMNSMathematics department. Repeatable to 10 credits if content differs. Students participate in a vertically integrated (undergraduate, graduate and/or postdoctoral, faculty) mathematics research group. Format varies. Students and supervising faculty will agree to a contract which must be approved by the department. Up to three credits of MATH489 may be applied to the mathematics degree requirements. See the department's MATH489 online syllabus for further information. MATH 498 Selected Topics in Mathematics (19) Repeatable to 9 credits if content differs. Topics of special interest to advanced undergraduate students will be offered occasionally under the general guidance of the departmental committee on undergraduate studies. 