MATHEMATICS (MA)
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, and their applications. Students are required to have a scientific calculator.
Core Course.
Note: May be offered for Honors Credit.
NOTE:
MA 110 is not a Pre-requisite for nor is it intended to be preparatory for any course listed below.
MA 112 Precalculus Algebra 3 cr
The course covers algebraic, graphical and numerical properties of functions, focusing on linear, quadratic, general polynomial, absolute value, rational, exponential, and logarithmic functions. Topics also include equations, inequalities, and complex numbers. Applications of mathematics to modeling real world situations are emphasized. Credit for both MA 112 and MA 115 not allowed. Pre-requisite:
C or better in MTH 100 or sufficient Mathematics Placement Exam score.
Core Course.
NOTE: Students who do not have the Pre-requisites for MA 112 should contact Developmental Studies.
MA 113 Precalculus Trigonometry 3 cr
Continuation of MA 112. Topics include numerical, graphical and algebraic properties of trigonometric functions, inverse trigonometric functions, right angle trigonometry, parametric equations, polar coordinates, and conic sections. Development and application of mathematical models to real-world situations is emphasized. Credit for both MA 113 and MA 115 not allowed. Pre-requisite:
C or better in MA 112 or sufficient Mathematics Placement Exam score.
Core Course.
MA 115 Precalculus Algebra and Trigonometry 4 cr
This fast-paced course is designed as a review of the algebra and trigonometry needed in calculus. It covers the material of MA 112 and MA 113 in one semester. Topics include numerical, graphical and algebraic properties of polynomial, rational, exponential, logarithmic, and trigonometric functions; inverse trigonometric functions; right angle trigonometry; parametric equations; polar coordinates and conic sections. Applications of mathematics to modeling real world situations are emphasized. Pre-requisite: sufficient Mathematics Placement Exam score. Credit for both MA 112 and MA 115 not allowed; credit for both MA 113 and MA 115 not allowed.
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
encouraged to have a graphing calculator. Credit for both MA 120 and MA 125 not allowed.
Pre-requisite: C or better in MA 112 or sufficient Mathematics Placement Exam score. MA 120 is not a Pre-requisite for subsequent calculus courses. Core Course.
MA 125 Calculus I 4 cr
The course provides an introduction to calculus with emphasis on differential calculus. Topics include limits of functions, derivatives of algebraic and transcendental functions, application of the derivative to curve sketching, optimization problems, and examples in the natural sciences, engineering, and economics. The course concludes with an introduction to
anti-derivatives, definite integrals, and the fundamental theorem of calculus. Credit for both MA 120 and MA 125 is not allowed. Pre-requisite: C or better in MA 113 or MA 115 or sufficient Mathematics Placement Exam score.
Core Course. NOTE: MA 110, MA 112, MA 113, MA 115, MA 120, and MA 125 have strict Pre-requisites. To be able to enroll in these courses a student needs either to pass the Pre-requisite course with C or better or to have a sufficient Mathematics Placement Exam score.
MA 126 Calculus II 4 cr
This course is a continuation of MA 125 with emphasis on integral calculus. Topics include techniques of integration; applications of the definite integral to geometry, natural sciences, engineering, and economics; improper integrals;
infinite sequences and series; Taylor polynomials and Taylor series; parametric equations and polar coordinates. Pre-requisite:
C or better in 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.
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.
Pre-requisite:
C or better in MA 110 or MA 112 or higher level course 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.
Pre-requisite: C or better in MA 110 or MA 112 or higher level course. 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; optimization of functions of several variables; multiple integrals and their applications; parametric curves and surfaces; vector fields; line and surface integrals; vector calculus. Pre-requisite:
C or better in 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. Pre-requisite:
C or better in 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 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.
Pre-requisite: C or better in MA 113 or C or better in MA 115 or sufficient Mathematics Placement Exam score.
MA 290 Special Topics 3 cr
Selected topics in elementary undergraduate mathematics.
This course may be repeated for a maximum of six credits.
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. Pre-requisite:
C or better in 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. Pre-requisite:
C or better in 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. Pre-requisite:
C or better in MA 237.
MA 320 Foundations of Mathematics (W) 3 cr
A transition to higher mathematics with an emphasis on proof techniques. Topics include symbolic logic, elementary set theory, induction, relations, functions, and the structure of the number system. Mathematics and Statistics majors are encouraged to take MA 320 as soon as possible after completing MA 125. Pre-requisites: C or better in EH 102 or EH 105 and MA 125.
MA 321 Elementary Geometry 3 cr
The course covers the major topics from secondary school curriculum of plane and solid geometry from the modern viewpoint. Emphasis will be placed on axioms, definitions, theorems, and proofs. Students will also gain experience in solving problems and communicating mathematical ideas effectively. Pre-requisite:
C or better in 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. Pre-requisites:
C or better in 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.
Pre-requisites: C or better in MA 227
and MA 237; and in MA 320 or consent of instructor.
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.
Pre-requisite: C or better in MA 334.
MA 354 Computer Assisted Mathematical Modeling (W) (C) 3 cr
This course is intended to provide the basic ideas regarding formulation, development, testing and reporting of mathematical models of various real world problems. Deterministic and stochastic models, optimization and simulations will be covered. Emphasis will be on careful mathematical formulations and the use of computer software, such as Microsoft Excel, Mathematica and Matlab. A term project will be an important component of this course. The course is taught in a laboratory setting with computers as lab equipment. Pre-requisites: C or better in EH 102, MA 227
, and in 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. Pre-requisite:
C or better in 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.
Pre-requisite:
C or better in EH 102 and either senior standing or permission of
instructor or department chair.
MA 413
Abstract Algebra I (W) 3 cr
An introduction to group theory and ring theory. Topics include permutations and
symmetries, subgroups, quotient groups, homomophisms, as well as examples of rings, integral domains, and fields. Pre-requisites: MA 237 and
C or better in EH 102 or EH 105, and C or better in one of the following: MA 311,
MA 320,
MA 334.
MA 414
Abstract 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. Pre-requisite:
C or better in EH 102 or EH 105 and 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. Pre-requisite:
C or better in MA 334.
MA 436 Numerical Analysis 3 cr
Topics include methods of numerical solution of nonlinear equations in one variable, fixed points, contraction mapping and functional iteration methods, interpolation and approximation methods, numerical differentiation and integration, numerical solution of ordinary differential equations, analysis of error for various numerical procedures. Implementation in
Mathematica of all numerical methods discussed in class is an essential part of the course. Pre-requisite: Students should have taken or be taking MA 238.
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
of residues; conformal representation; applications. Credit for both MA 437 and MA 537 not allowed. Pre-requisite:
C or better in 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
MA 550 is not allowed. Pre-requisites:
C or better in MA 227 and MA 237.
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
systems of equations. As time permits, topics covered will include sensitivity analysis, duality, integer programming, transportation, assignment, transshipment,
and networks. Credit for both MA 458 and MA 567 is not allowed. Pre-requisites:
C or better in EH 102 or EH 105 and MA 237. MA 467 Mathematical Logic 3 cr
An introduction to formal first-order logic, first-order metatheory, and its extensions. Topics include axiom systems and their models, completeness, compactness, and recursive sets and functions. Identical with PHL 467. Credit cannot be received for both PHL 467 and MA 467. Pre-requisites: PHL 321
or C or better in any 300-level or higher MA course.
MA 481 Cryptography 3 cr
This course gives an introduction to classical and modern methods of message encryption and decryption (cryptography) as well as possible attacks to cryptosystems (cryptanalysis). Topics include information theory, classical (symmetric) cryptosystems (DES, AES), public-key (asymmetric) cryptosystems (
Diffie-Hellman, RSA, El
Gamal), one-way and trapdoor functions, Hash functions, cryptanalysis, cryptographic protocols (identification, authentication, secret sharing, oblivious transfer, zero-knowledge), e-money and e-commerce. Credit for both MA
481 and MA 581 is not allowed. Pre-requisite:
C or better in MA 311.
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. Pre-requisites: 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
used number systems. Pre-requisite:
C or better in 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. Pre-requisite: C or better in
MA 413 or permission of the instructor.
MA 503 Introduction to Analysis 3 cr
A careful look at the elements, procedures, and applications of differential and integral calculus. Pre-requisites: C or better in
MA 227 or permission of the instructor. This course is designed for students in the College of Education.
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.
Pre-requisites: C or better in
MA 321 or permission of the instructor. This course is designed for students in the College of Education.
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 Mathematics Education. Problems selected from logic, algebra, analysis, geometry, combinatorics, number theory and probability.
Pre-requisite: Permission of the instructor. This course is designed for students in the College of Education.
MA 506 Statistics for Teachers 3 cr
Prepares in-service and pre-service teachers to teach statistics in high schools using a data-based approach. Uses hands-on-activities approach and simulation of situations to teach concepts, and technology to teach
data analysis.
Pre-requisite: C or better inMA 126
or permission of the instructor. This course is designed for students in the College of Education.
MA 507 Advanced Ordinary Differential Equations 3 cr
A graduate-level introduction to ordinary differential equations and their applications in Physics and Engineering. Topics include differential equations of first and higher order, power series solutions, and Laplace transform.
MA 508 Advanced Partial Differential Equations 3 cr
A continuation of MA 507 with emphasis on partial differential equations and their applications in Physics and Engineering. Topics include Fourier series, Fourier transform, diffusion equation, wave equation, and Laplace equation.
MA 511 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, and fundamental theorem of abelian groups.
MA 512 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, and field extensions.
Pre-requisite:
C or better in MA 511.
MA 515 Number Theory 3 cr
Modular arithmetic, arithmetic functions, prime numbers, and 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. Pre-requisite:
C or better in MA 515.
MA 518 Linear Algebra I 3 cr
Fields, vector spaces, dual spaces, quotient spaces, multilinear forms, linear transformations, algebras, adjoints, and 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, and applications to analysis. Pre-requisite:
C or better in MA 518.
MA 521 Enumerative Combinatorics 3 cr
Pigeonhole principle, basic counting techniques, binomial coefficients, inclusion-exclusion principle, recurrence relations, generating functions, systems of distinct representatives, and 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, and 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, and Riemann-Stieltjes integral. Pre-requisite: 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,and an introduction to the Lebesgue integral
and differential forms as time allows. Pre-requisite:
C or better in 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; and applications. Credit for both MA 537 and MA 437 is not allowed. Pre-requisite:
C or better in 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. Pre-requisite:
C or better in 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. Pre-requisite:
C or better in 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
MA 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, homology, the Euler-Poincare formula, the Borsuk-Ulam theorem, the Lefschetz fixed-point theorem, knot theory, covering spaces,
and applications. Pre-requisites:
C or better in MA 542
or MA 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
MA 451 is not allowed. Pre-requisites: C or better in MA 227 and
MA 237.
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. Pre-requisite:
C or better in 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, and 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, and analysis of count data. Computer-assisted data analysis is used. Pre-requisite:
C or better in 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. Pre-requisite:
C or better in 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
systems of equations. As time permits, topics covered will include sensitivity analysis, duality, integer programming, transportation, assignment, transshipment,
and network
s. Credit for both MA 567 and
MA 458 is not allowed. Pre-requisites:
C or better in MA 237.
MA 568 Topics in Operations Research 3 cr
A second course in operations research, covering topics of interest to the students and instructor. Pre-requisite:
C or better in 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. Pre-requisite:
C or better in 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. Pre-requisite:
C or better in MA 536.
MA 581 Cryptography 3 cr
This course gives an introduction to classical and modern methods of message encryption and decryption (cryptography) as well as possible attacks to cryptosystems (cryptanalysis). Topics include information theory, classical (symmetric) cryptosystems (DES, AES), public-key (asymmetric) cryptosystems
(Diffie-Hellman, RSA,
ElGamal), one-way and trapdoor functions, Hash functions, cryptanalysis, cryptographic protocols (identification, authentication, secret sharing, oblivious transfer, zero-knowledge), and e-money and e-commerce. Credit for both MA 481 and MA 581 is not allowed. Pre-requisite:
C or better in MA 311.
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.
May be repeated for up to six hours of credit. Pre-requisites: Approval of the department chair.
MA 599 Thesis 1-6 cr
Pre-requisite: Approval of research prospectus by Department Graduate Committee.