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USA Undergraduate/Graduate Bulletin 2004-2005

 

MATHEMATICS (MA)
 
MA 100 Mathematics in Society 3 cr
An introduction and real life applications to the mathematics of finance, probability, and descriptive statistics with particular emphasis on mathematics of finance. Specific topics include geometric progressions, compound interest, annuities, perpetuities, permutations, combinations, probability measure, and statistical measures of central location and dispersion. Prerequisites: Two years of high school algebra or equivalent. This course does not satisfy the mathematics requirement for General Studies.
 
MA 101 Introduction to Mathematical Thought 3 cr
A course designed to give the nonscience major- especially humanities and fine arts majors- an appreciation of the method, content, and scope of mathematics. This course does not satisfy the mathematics requirement for General Studies.
 
MA 110 Finite Mathematics 3 cr
This course is intended to give an overview of topics in finite mathematics together with their applications. The course includes logic, sets, counting, permutations, combinations, basic probability, descriptive statistics, matrices, and their applications. Students are required to have a scientific calculator. Prerequisites: Two years of high school algebra (I & II) and a year of geometry. Core Course.
Note: May be offered for Honors Credit.
 
NOTE: The three courses listed above are not prerequisites for nor are they intended to be preparatory for any course listed below. Students who do not have the prerequisites for MA 110 or 112 should contact Developmental Studies.
 
MA 112 Precalculus Algebra 3 cr
Study of use of variable quantities to interpret information about relationships that can be expressed in mathematical terms. Linear, polynomial, absolute value, rational, exponential and logarithmic functions with emphasis on numerical, graphical and algebraic properties and applications and use in modeling real world situations. Systems of linear equations. Graphing calculator required. Credit for both MA 112 and MA 115 not allowed. Prerequisites: Two years of high school algebra (I & II) and a year of geometry. Core Course.
 
MA 113 Precalculus Trigonometry 3 cr
Continuation of MA 112. Numerical, graphical and algebraic properties of polynomial, rational and trigonometric functions. Parametric equations, right angle trigonometry, inverse trigonometric functions. Polar coordinates. Conic sections. Development and use of mathematical models to solve problems which concern real-world situations emphasized. Graphing calculator required. Credit for both MA 113 and MA 115 not allowed. Prerequisite: MA 112. Core Course.
 
MA 115 Precalculus Algebra and Trigonometry 4 cr
Study of elementary functions, their graphs and applications, including polynomial, rational, algebraic, exponential, logarithmic, and trigonometric functions. This fast-paced course is designed as a review of the algebra and trigonometry needed in calculus. Students are required to have a graphing calculator. Core Course.
 
MA 120 Calculus and Its Applications 3 cr
Introduction to calculus with an emphasis on problem solving and applications. Key concepts are presented graphically, numerically and algebraically, although the stress is on a clear understanding of graphs and tabular data. The course covers: algebraic, exponential and logarithmic functions, their properties and their use in modeling; the concepts of derivative and definite integral and their applications to marginal analysis, optimization and probability; examples of multivariable functions, partial derivatives and applications to optimization problems. Students are required to have a graphing calculator. Credit for both MA 120 and MA 125 not allowed. Prerequisite: MA 112 or equivalent. Core Course.
 
MA 125 Calculus I 4 cr
Introduction to calculus with emphasis on presenting the key concepts graphically, numerically, and algebraically. Limit of a function; the derivatives of algebraic, trigonometric, exponential, and logarithmic functions; applications of the logarithmic functions; applications of the derivative to curve sketching; optimization problems including examples in the physical/natural sciences and economics; introduction of the definite integral; Fundamental Theorem of Integral Calculus. Students are required to have a graphing calculator. Credit for both MA 120 and MA 125 not allowed. Prerequisite: MA 115 or MA 113. Core Course.
 
MA 126 Calculus II 4 cr
A continuation of MA 125. Techniques of symbolic and numerical integration; applications of the definite integral to geometry, physics, economics, and probability; indeterminate forms; improper integrals; introduction to differential equations; sequences and series; Taylor polynomials and Taylor series. Vectors and geometry. Students are required to have a graphing calculator. Prerequisite: MA 125. Core Course.
 
MA 150 Contemporary Mathematics and Statistics 1 cr
  Seminar  
This course gives an overview of modern mathematics and statistics from the point of view of the practitioners. The course is designed for majors in mathematics and statistics at all levels as well as those students who are considering mathematics or statistics as a major or minor area of study. Topics usually included are elements of geometry, algebra, analysis, methods of statistical inference, the role of the computer in analytical sciences; these topics vary from semester to semester. This course cannot be taken for credit simultaneously with ST 150, but may be repeated in different semesters.
NOTE: May be offered for Honors Credit.
 
MA 201 Mathematics for Elementary Teachers I 3 cr
An examination of some of the major ideas encountered in the teaching of elementary mathematics. Topics include introduction to problem solving, sets, relations, logic, numeration systems, elementary number theory, properties and operations for whole numbers, integers, rational numbers, and real numbers. Prerequisites: Fulfillment of the General Studies mathematics requirement.
NOTE: MA 201 does not fulfill graduation requirements for any curriculum other than College of Education.
 
MA 202 Mathematics for Elementary Teachers II 3 cr
Topics covered are those that a prospective elementary or middle school teacher should expect to encounter in the teaching of geometry in elementary or middle school. Topics include geometric shapes, measurement, triangle congruence and similarity, coordinate geometry, geometric transformation. Prerequisite: MA 201.
NOTE: MA 202 does not fulfill graduation requirements for any curriculum other than College of Education.
 
MA 227 Calculus III 4 cr
Vectors; functions of several variables; partial derivatives; local linearity; directional derivatives; the gradient; differential of a function; the chain rule; higher order partial derivatives; quadratic approximations; optimization of functions of several variables; multiple integrals and their applications; parametric curves and surfaces; vector fields; line and surface integrals; vector calculus. Students are required to have a graphing calculator. Prerequisite: MA 126. Core Course.
 
MA 237 Linear Algebra I 3 cr
An introduction to linear algebra. Topics include vector spaces, linear transformations, determinants, the eigenvalue problem and applications. Prerequisite: MA 126. Core Course.
 
MA 238 Applied Differential Equations I 3 cr
First order differential equations. Higher order linear differential equations. Systems of first order linear differential equations. Laplace Transforms. Methods for approximating solutions to first order differential equations. Applications. Students are required to have a graphing calculator. Students should have taken or be taking MA 227. Core Course.
 
MA 267 Discrete Mathematical Structures 3 cr
This course is an introduction to discrete mathematics for students majoring in computer-related areas. Students will be introduced to concepts and methods that are essential to theoretical computer science. A strong emphasis is placed on developing skills in mathematical reasoning and understanding and writing proofs. Topics include sets, functions, induction, recursion, combinatorics and graphs. Prerequisites: MA 125 or MA 120, or consent of instructor.
 
MA 290 Special Topics 3 cr
Selected topics in elementary undergraduate mathematics.
 
MA 303 Mathematics for Elementary Teachers III 3 cr
An exploration of problem solving strategies. Problems exemplifying the various problem solving strategies studied. Emphasis on the development of problem solving skills by exploring interesting problems which demand for their solution that the student select from a wide variety of possible strategies and use a wide variety of conceptual tools. Prerequisite: MA 202.
NOTE: MA 303 does not fulfill graduation requirements for any curriculum other than elementary education.
 
MA 311 Introduction to Number Theory 3 cr
An introduction to classical number theory with a balance between theory and computation. Topics include mathematical induction, divisibility properties, properties of prime numbers, the theory of congruences, number theoretic functions, continued fractions. Prerequisite: MA 126.
 
MA 316 Linear Algebra II 3 cr
A continuation of MA 237. Topics include inner product spaces, spectral theorem for symmetric operators, complex vector spaces, Jordan canonical form. Additional topics such as duality and tensor products to be included at the discretion of the instructor. Prerequisite: MA 237.
 
MA 318 Matrix Theory 3 cr
A theoretical as well as computational treatment of the notions of determinant, inverse, rank and diagonalization of a matrix with real or complex entries. Eigenvalues and eigenvectors, similarity, solutions of linear systems of algebraic equations, Jordan canonical forms. Students are required to have a graphing calculator. Prerequisite: MA 126.
 
MA 320 Foundations of Mathematics (W) 3 cr
The students will develop facility with proof through the study of logic and proof techniques as applied to various areas of mathematics. Topics include symbolic logic, proof techniques, relations, functions, and structure of the number system. Prerequisite: MA 126.
 
MA 321 Elementary Geometry 3 cr
The students will review the major topics (from secondary school curriculum) of plane and solid geometry from the modern viewpoint; axioms, undefined terms, definitions, theorems and proofs. Prerequisite: MA 320.
 
MA 332 Differential Equations II 3 cr
Series solutions of second order linear equations. Numerical methods. Nonlinear differential equations and stability. Partial differential equations and Fourier series. Sturm-Liouville problems. Prerequisites: MA 227 and MA 238.
 
MA 334 Advanced Calculus I 3 cr
This is the first of a two course sequence designed to provide students with the theoretical context of concepts encountered in MA 125 through MA 227. Topics covered include Completeness Axiom, sequences of real numbers, suprema and infima, Cauchy sequences, open sets and accumulation points in Euclidean space, completeness of Euclidean space, series of real numbers and vectors, compactness, Heine-Borel Theorem, connectedness, continuity, Extremum Theorem, Intermediate Value Theorem, differentiation of functions of one variable. Prerequisite: MA 227 and MA 237.
 
MA 335 Advanced Calculus II 3 cr
This is the second of a two course sequence designed to provide students with the theoretical context of concepts encountered in MA 125 through MA 227. Topics covered include integration of functions of one variable, pointwise and uniform convergence, integration and differentiation of series, differentiable mappings of several variables, chain rule, product rule and gradients, Mean Value Theorem, Taylor's Theorem, Inverse Function Theorem, Implicit Function Theorem. Prerequisites: MA 334.
 
MA 354 Computer Assisted Mathematical Modeling (W) (C) 3 cr
Formulation, development, testing and reporting of mathematical models of various real world problems. Deterministic and stochastic models, optimization, simulation. Emphasis on the careful mathematical formulations and the appropriate use of computer software, both as an aid in the solution of mathematical problems and as a tool in the process of model evaluation, simulation, reporting. A term project will be an important component of this course. The course is taught in a laboratory setting with computers as lab equipment. Prerequisites: MA 227 and MA 238.
 
MA 367 Combinatorial Enumeration 3 cr
An introduction to the mathematical theory of counting. Basic counting principles, permutations and combinations, partitions, recurrence relations, and a selection of more advanced topics such as generating functions, combinatorial designs, Ramsey theory, or group actions and Poyla theory. Prerequisite: MA 126 or consent of instructor.
 
MA 410 History of Mathematics (W) 3 cr
Historical survey of general development of mathematics with a balance of historical perspective and mathematical structure. Prerequisites: Senior standing or permission of department chair.
 
MA 413 Algebra I (W) 3 cr
An introduction to group theory and ring theory. Topics include permutations and symmetrics, subgroups, quotient groups, homomophisms, as well as examples of rings, integral domains, and fields. Prerequisites: MA 237 and one of the following: MA 311, 320, 334.
 
MA 414 Algebra II (W) 3 cr
A continuation of MA 413 focusing on rings and fields. Topics include rings, ideals, integral domains, fields and extension fields. Geometric constructions and Galois theory are introduced. Prerequisite: MA 413.
 
MA 434 Topology 3 cr
An introduction to topology with emphasis on the geometric aspects of the subject. Topics covered include surfaces, topological spaces, open and closed sets, continuity, compactness, connectedness, product spaces, and identification and quotient spaces. Credit for both MA 434 and MA 542 is not allowed. Prerequisite: MA 335.
 
MA 436 Numerical Analysis 3 cr
Selected numerical algorithms are analyzed. Topics include error analysis, machine arithmetic, roundoff, root finding using fixed point methods, interpolation, numerical integration, differential equations, eigenvalue /eigenvector problems, least squares analysis, boundary value problems. Prerequisite: MA 227, credit for or concurrent registration in MA 238. Students are also required to have proficiency in a programming language.
 
MA 437 Complex Variables 3 cr
Arithmetic of complex numbers; regions in the complex plane; limits, continuity, and derivatives of complex functions; elementary complex functions; mappings by elementary functions; contour integration; power series; Taylor series; Laurent series; calculus or residues; conformal representation; applications. Credit for both MA 437 and MA 537 not allowed. Prerequisite: MA 238.
 
MA 451 Probability 3 cr
A comprehensive introduction to probability, the mathematical theory used to model uncertainty, covering the axioms of probability, random variables, expectation, classical discrete and continuous families of probability models, the law of large numbers and the central limit theorem. Credit for both MA 451 and 550 is not allowed. Prerequisites: MA 227 and either MA 237 or 318.
 
MA 458 Operations Research (W) 3 cr
An introduction to linear programming. The course will include a study of the simplex method as well as using computers to solve linear and nonlinear problems. As time permits, topics covered will include sensitivity analysis, duality, integer programming, transportation, assignment, transshipment, networks, game theory, Markov processes, queuing theory, simulation, and forecasting. Credit for both MA 458 and MA 567 is not allowed. Prerequisites: MA 227 and either MA 318 or MA 316.
 
MA 490 Special Topics 1-3 cr
Selected topics in advanced undergraduate mathematics. This course may be repeated for a maximum of six credits.
 
MA 494 Directed Studies 1-3 cr
Directed individual study. May be repeated for a maximum of six credits. Prerequisites: Permission of the department chair.
 
MA 499 Honors Senior Project 3-6 cr
With the guidance and advice of a faculty mentor, Honors Students will identify, and carry out a research project in mathematics. The outcome of the research project will include a formal presentation at the annual Honors Student Colloquium. The senior project will be judged and graded by three members of the faculty, chaired by the faculty mentor.
 
MA 501 Number Systems 3 cr
A case study of axiom systems and the deductive method for graduate students in Mathematics Education. It is expected that students in this course will practice and improve their logical skills, better understand proof as a mathematical activity, and study the similarities and differences between several commonly utilized number systems. Prerequisite: MA 321 or MA 413 or permission of the instructor.
 
MA 502 Introduction to Abstract Algebra 3 cr
An introduction to the fundamental concepts of modern algebra such as groups, rings, and fields through concrete examples. The course is designed for graduate students in the College of Education. Prerequisite: MA 501.
 
MA 503 Introduction to Analysis 3 cr
A careful look at the elements, procedures, and applications of differential and integral calculus. Prerequisites: MA 501 and one year of calculus.
 
MA 504 Introduction to Geometry 3 cr
An introduction to the foundations of geometry using both synthetic and metric approaches. Euclidean, finite, projective, and hyperbolic geometries are discussed. The axioms for various geometries are discussed.
 
MA 505 Mathematical Problem Solving 3 cr
An in-depth activity-based approach to the methods and strategies for mathematical problem solving for students in Mathematical Education. Problems selected from logic, algebra, analysis, geometry, combinatorics, number theory and probability.
 
MA 506 Statistics for Teachers 3 cr
Prepares in-service and pre-service teachers to teach statistics in high schools using data-based approach. Uses hands-on-activities approach and simulation of situations to teach concepts and technology to teach analysis. Prerequisites: MA 126.
 
MA 507 Applicable Mathematics I 3 cr
A graduate-level introduction to topics of ordinary differential equations, partial differential equations, and their applications in physics and engineering.
 
MA 508 Applicable Mathematics II 3 cr
A continuation of MA 507 with more emphasis on theory of partial differential equations, as well as their applications in physics and engineering problems.
 
MA 511 Abstract Algebra I 3 cr
A graduate level introduction to group theory. Topics include quotient groups, homomorphism, group actions, Sylow theorems, composition series, simple groups, free groups, fundamental theorem of abelian groups.
 
MA 512 Abstract Algebra II 3 cr
A graduate level introduction to ring theory and fields. Topics include ring homomorphism, quotient rings, ideals, rings of fractions, Euclidean domains, principal ideal domains, unique factorization domains, modules, finite fields, field extensions. Prerequisites: MA 511.
 
MA 515 Number Theory 3 cr
Modular arithmetic, arithmetic functions; prime numbers, algebraic number theory.
 
MA 516 Topics in Number Theory 3 cr
A second course in number theory, covering topics of interest to the students and instructor. Prerequisite: MA 515.
 
MA 518 Linear Algebra I 3 cr
Fields, vector spaces, dual spaces, quotient spaces, multilinear forms, linear transformations, algebras, adjoints, eigenvalues.
 
MA 519 Linear Algebra II 3 cr
Triangular form, nilpotence, Jordan form, inner products, self-adjoint transformations, positive transformations, isometries, Spectral Theorem, polar decomposition, applications to analysis. Prerequisite: MA 518.
 
MA 521 Discrete Mathematics 3 cr
Pigeonhole principle, basic counting techniques, binomial coefficients, inclusion-exclusion principle, recurrence relations, generating functions, systems of distinct representatives, finite fields.
 
MA 525 Graph Theory 3 cr
Fundamental concepts, connectedness, graph coloring, planarity and Kuratowski's theorem, four-color theorem, chromatic polynomial, Eulerian and Hamiltonian graphs, matching theory, network flows, NP-complete graph problems, Markov chains, matroids.
 
MA 535 Real Analysis I 3 cr
An introduction to real analysis. Topics include the metric topology of the reals, limits and continuity, differentiation, Riemann-Stieltjes integral. Prerequisite: An undergraduate course in advanced calculus.
 
MA 536 Real Analysis II 3 cr
A continuation of MA 535. Topics covered include sequences and series of functions, differentiation and integration in several variables, an introduction to differential forms and to the Lebesgue integral. Prerequisite: MA 535.
 
MA 537 Complex Analysis 3 cr
Arithmetic of complex numbers; regions in the complex plane; limits, continuity, and derivatives of complex functions; elementary complex functions; mappings by elementary functions; contour integration; power series; Taylor series; Laurent series; calculus of residues; conformal representation; applications. Credit for both MA 537 and 437 is not allowed. Prerequisite: MA 238.
 
MA 538 Topics in Complex Analysis 3 cr
A second course in complex analysis, covering topics of interest to the students and instructor. Prerequisite: MA 537.
 
MA 539 Measure Theory 3 cr
Foundations of the general theory of measure and integration, with particular attention to the Lebesgue integral. Function spaces, product measure and Fubini's theorem, the Radon-Nikodym theorem and applications to probability theory are discussed, and possibly additional topics such as Haar measure or the Ergodic Theorem. Prerequisite: MA 536.
 
MA 540 Differential Geometry 3 cr
Local and global theory of curves and surfaces in three-dimensional space.
 
MA 542 Topology I 3 cr
An introduction to topology with emphasis on the geometric aspects of the subject. Topics covered include surfaces, topological spaces, open and closed sets, continuity, compactness, connectedness, product spaces, and identification and quotient spaces. Credit for both MA 542 and 434 is not allowed.
 
MA 543 Topology II 3 cr
A continuation of MA 542. Topics covered include the fundamental group, triangulations, classification of surfaces, simplicial homology, the Euler-Poincare formula, the Borsuk-Ulam theorem, the Lefschetz fixed-point theorem, knot theory, and covering spaces. Prerequisites: MA 542 and 434 and permission of the instructor.
 
MA 550 Probability 3 cr
A comprehensive introduction to probability, the mathematical theory used to model uncertainty, covering the axioms of probability, random variables, expectation, classical discrete and continuous families of probability models, the law of large numbers and the central limit theorem. Credit for both MA 550 and 451 is not allowed. Prerequisites: MA 227 and 237 or 318.
 
MA 551 Theory of Statistics 3 cr
A comprehensive introduction to the mathematical foundations of statistics. Sufficient statistics and information, parameter estimation, maximum likelihood and moment estimation, optimality properties of estimators and confidence intervals. Hypothesis testing, likelihood ratio tests and power functions. Credit for both MA 551 and ST 470 is not allowed. Prerequisite: MA 451 or MA 550.
 
MA 555 Statistical Analysis I 3 cr
A first course in an integrated two-course sequence in applied statistical theory and methods for research workers in technical fields. Coverage includes probability and basic probability models, mathematical expectations, random sampling processes and central limit theorem, estimation, hypothesis testing and power analysis, some applications of the theory of least squares. Computer assisted data analysis is used.
 
MA 560 Statistical Analysis II 3 cr
A second course (continuation of MA 555) in an integrated two-course sequence in applied statistical theory and methods for research workers in technical fields. Coverage includes regression analysis, design and analysis of experiments, factorial experiments, analysis of covariance, nonparametric analytical techniques, analysis of count data. Computer assisted data analysis is used. Prerequisite: MA 555.
 
MA 565 Numerical Analysis 3 cr
An introduction to Numerical Analysis. Topics include error analysis, systems of linear equations, nonlinear equations, integration, ordinary differential equations among others. Prerequisite: MA 535.
 
MA 567 Operations Research 3 cr
An introduction to linear programming. The course will include a study of the simplex method as well as using computers to solve linear and nonlinear problems. As time permits, topics covered will include sensitivity analysis, duality, integer programming, transportation, assignment, transshipment, network, game theory, Markov processes, queuing theory, simulation, and forecasting. Credit for both MA 567 and 458 is not allowed. Prerequisites: MA 227 and either MA 318 or 316.
 
MA 568 Topics in Operations Research 3 cr
A second course in operations research, covering topics of interest to the students and instructor. Prerequisite: MA 567.
 
MA 571 Ordinary Differential Equations 3 cr
An introduction to ordinary differential equations from a dynamical systems perspective. Topics include existence and uniqueness theorems, dependence on initial data, linear systems and exponential of operators, stability of equilibria, Poincare-Bendixon theorem. Additional topics such as applications to population dynamics, classical mechanics, periodic attractors among others will be included at the discretion of the instructor. Prerequisite: MA 518.
 
MA 572 Partial Differential Equations 3 cr
An introduction to partial differential equations emphasizing spectral methods. Topics include elementary Hilbert spaces, Fourier series and integrals and their applications to the study of the basic partial differential equations of mathematical physics. More advanced topics such as asymptotic properties and regularity of solutions and nonlinear equations among others will be included at the discretion of the instructor. Prerequisite: MA 536.
 
MA 590 Special Topics 1-3 cr
Selected topics in elementary graduate mathematics. This course may be repeated for a maximum of six credits.
 
MA 592 Seminar 1 cr
Student seminar. Topics covered vary. This course may be repeated indefinitely, but only two credits count towards the degree. Grading system: satisfactory/unsatisfactory.
 
MA 594 Directed Studies 1-3 cr
Directed individual study. Prerequisites: Approval of the department chair.
 
MA 599 Thesis 1-6 cr
Prerequisite: Approval of research prospectus by Department Graduate Committee.
 
 

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