Course Descriptions
Mathematics
MATH 101
Algebra
3 Semester Hours
Polynomials, rational expressions, exponents, radicals, equations in one and two variables, the quadratic formula, functions and graphs.
MATH 102
Quantitative Skills for the Modern World
3 Semester Hours
Quantitative and analytic skills used to understand personal and social issues faced in everyday life. Topics include problem solving, computer spreadsheets, probability and statistics, and the mathematics of finance.
Corequisite: MATH 103.
MATH 103
Quantitative Skills for the Modern World Lab
0 Semester Hours
Concurrent laboratory for MATH 102.
Corequisite: MATH 102.
MATH 104
Elementary Statistics
3 Semester Hours
Introduction to methods of inferential statistics, histograms, elementary probability, and random variables and distributions.
MATH 106
Mathematics for Elementary Teachers I
3 Semester Hours
Foundations of arithmetic from an advanced standpoint: sets, numeration systems, the structure of number systems, and problem solving strategies.
For Liberal Studies majors only, or by consent of the instructor.
Prerequisite: MATH 101 with a minimum grade of C (2.0) or Mathematics Placement Examination.
MATH 107
Mathematics for Elementary Teachers II
3 Semester Hours
Geometry, metric system, and introduction to probability and statistics.
For Liberal Studies majors only, or by consent of the instructor.
Prerequisite: MATH 106.
MATH 111
Mathematical Analysis for Business I
3 Semester Hours
Systems of equations and inequalities, exponential and logarithmic functions, math of finance, linear programming.
Prerequisite: MATH 101 or Mathematics Placement Examination.
MATH 112
Mathematical Analysis for Business II
3 Semester Hours
Introduction to the differential and integral calculus of elementary functions. Applications of the methods of calculus to business and economics problems.
A laboratory fee may be required.
Prerequisite: MATH 111 or 120 or Mathematics Placement Examination.
MATH 120
Precalculus Mathematics
3 Semester Hours
Functions; polynomial, rational, trigonometric, exponential and logarithmic functions.
Prerequisite: MATH 101 or Mathematics Placement Examination.
MATH 122
Calculus for the Life Sciences I
3 Semester Hours
An introduction to calculus. Derivatives and integrals of the elementary functions, including computational techniques and applications.
Prerequisite: MATH 120 or Mathematics Placement Examination.
MATH 123
Calculus for the Life Sciences II
3 Semester Hours
Integration methods with applications, differential equations and modeling, and introduction to multivariate calculus.
Prerequisite: MATH 122 or equivalent.
MATH 131
Calculus I
4 Semester Hours
Limits, continuity, derivatives of algebraic and transcendental functions, applications of the derivative, antiderivatives, introduction to the definite integral, Fundamental Theorem of Calculus.
Prerequisite: MATH 120 or Mathematics Placement Examination.
MATH 132
Calculus II
4 Semester Hours
Techniques of integration, numerical methods of integration with error analysis, applications of the integral, improper integrals, infinite series, an introduction to parametric equations and polar coordinates.
Prerequisite: MATH 131 or equivalent.
MATH 190
Workshop in Mathematics I
2 Semester Hours
Study skills, analytical and problem solving skills, technical writing, recent fields of study, and advances in mathematics, mathematical career opportunities.
MATH 191
Workshop in Mathematics II
2 Semester Hours
A continuation of MATH 190.
MATH 198
Special Studies
1-4 Semester Hours
MATH 199
Independent Studies
1-4 Semester Hours
MATH 234
Calculus III
4 Semester Hours
Partial derivatives, multiple integrals, three-dimensional space, vectors in two- and three- dimensional space, line integrals, Green’s theorem.
Prerequisite: MATH 132 or equivalent.
MATH 245
Ordinary Differential Equations
3 Semester Hours
Differential equations as mathematical models; analytical, qualitative, and numerical approaches to differential equations and systems of differential equations; and Laplace transform techniques.
Prerequisite: MATH 132 or equivalent.
MATH 248
Introduction to Methods of Proof
3 Semester Hours
Number theory, sets, functions, equivalence relations, cardinality, methods of proof, induction, contradiction, contraposition. Student portfolios will be collected.
Prerequisite: MATH 132 or equivalent.
MATH 250
Linear Algebra
3 Semester Hours
Systems of linear equations, Gauss and Gauss-Jordan elimination, matrices and matrix algebra, determinants. Linear transformations of Euclidean space. General vector spaces, linear independence, inner product spaces, orthogonality. Eigenvalues and eigenvectors, diagonalization. General linear transformations.
Prerequisite: MATH 248 or consent of instructor.
MATH 261
Mathematics: Contributions by Women
3 Semester Hours
A study of the biographies and mathematics of women mathematicians from the 1st through the 20th centuries. Topics include prime numbers, conic sections, cycloid curve, functions, sequences, series, polyhedra, and group theory.
Prerequisite: MATH 101, 102, or 104, or placement into MATH 106 or higher.
MATH 264
Cryptography throughout the Ages
3 Semester Hours
A study of mathematical systems used for enciphering and deciphering information and the context in which these systems arose; in particular, encryption/decryption used during World War II and modern systems, including public key cryptography. Policy issues related to cryptography also will be studied.
Prerequisite: MATH 101, 102, or 104, or placement into MATH 106 or higher.
MATH 282
Elementary Numerical Methods
3 Semester Hours
Computer solutions of applied mathematical problems using a procedural programming language and a computer algebra system. Nonlinear equations, differentiation, integration.
Prerequisite: MATH 131 or equivalent.
MATH 285
Discrete Mathematics for Engineering
3 Semester Hours
An introduction to basic counting; permutations; combinations; probability; the binomial distribution; set theory; generating functions; recurrence relations; with C programming.
Prerequisite: MATH 132 or equivalent.
MATH 288
Introduction to Biomathematics
3 Semester Hours
Introduction to mathematical and statistical concepts closely related to research problems in biology. Topics include statistical analysis of biological measurements, dynamic modeling of biological systems, and fitting models to observed data.
Prerequisites: BIOL 101 and MATH 123 or MATH 132.
MATH 293
Mathematics Teaching Field Experience
0 Semester Hours
Planned observation, instruction or tutoring experiences appropriate for future secondary or middle school mathematics teachers; related professional reading and reflections.
MATH 298
Special Studies
1-4 Semester Hours
MATH 299
Independent Studies
1-4 Semester Hours
MATH 301
Mathematical Ideas for Future Teachers I
3 Semester Hours
A selection of topics from number theory, algebra, game theory, probability, and statistics of interest to future teachers. The emphasis is on deepening students’ understanding of the methods and philosophy of mathematics. Students will actively engage in exploring mathematics through student investigations and presentations.
Prerequisites: MATH 107 and MATH 111 or 112 or 120 or 122 or 131.
MATH 302
Mathematical Ideas for Future Teachers II
3 Semester Hours
A selection of topics from geometry and topology of interest to future teachers. The emphasis is on deepening students’ understanding of the methods and philosophy of mathematics. Students will actively engage in exploring mathematics through student investigations and presentations.
Prerequisites: MATH 107 and MATH 111 or 112 or 120 or 122 or 131.
MATH 308
Mathematics for Elementary Teachers Workshop I
1 Semester Hour
Hands-on use of math manipulatives related to the elementary school concepts of sets, systems of numeration, whole numbers, integers, fractions, and decimals.
Prerequisite: MATH 106 or concurrent enrollment or consent of instructor.
MATH 309
Mathematics for Elementary Teachers Workshop II
1 Semester Hour
Hands-on use of math manipulatives related to geometry, probability, and statistics appropriate to the elementary school mathematics curriculum.
Prerequisite: MATH 107 or concurrent enrollment or consent of instructor.
MATH 321
Real Variables I
3 Semester Hours
The real number system, least upper bound, sequences, Cauchy sequences, functions, limits of functions, continuity, derivatives, and Riemann integration.
Prerequisite: MATH 248.
MATH 322
Real Variables II
3 Semester Hours
Infinite series, uniform convergence, power series, and improper integrals.
Prerequisite: MATH 321.
MATH 331
Elements of Group Theory
3 Semester Hours
Group theory. Binary operations, subgroups, cyclic groups, factor groups, isomorphism, homomorphism, and Cayley’s theorem.
Prerequisite: MATH 248.
MATH 332
Elements of the Theory of Rings and Fields
3 Semester Hours
Rings, integral domains, fields, ideals, factor rings, polynomial rings, and unique factorization domains.
Prerequisite: MATH 331.
MATH 350
Advanced Linear Algebra
3 Semester Hours
Vector spaces over an arbitrary field, dual spaces, Cayley-Hamilton theorem, invariant subspaces, canonical forms for matrices, inner product spaces over C, the spectral theorem.
Prerequisites: MATH 248 and 250.
MATH 355
Methods of Applied Mathematics
3 Semester Hours
Series solutions and special functions. Orthogonal functions and Fourier series, partial differential equations and boundary value problems.
Prerequisites: MATH 234 and 245.
MATH 357
Complex Variables
3 Semester Hours
Complex variables; analytic functions, Laurent expansions and residues; evaluation of real integrals by residues; integral transforms.
Prerequisite: MATH 234.
MATH 360
Introduction to Probability and Statistics
3 Semester Hours
Descriptive statistics, probability, discrete and continuous random variables, limit theorems, sampling distributions, estimations of parameters, nonparametric methods, hypothesis testing, linear regression.
Prerequisite: MATH 123 or 132.
MATH 366
Discrete Methods
3 Semester Hours
An introduction to graph theory; trees; coloring; Eulerian circuits. Combinatorics; permutations and combinations; recurrence relations.
Prerequisites: MATH 248.
MATH 393
Mathematics Internship
1-3 Semester Hours
Internship conducted in an industrial, business, government, or educational setting involving applied mathematical work or teaching. This will involve a research project (or paper) coordinated jointly with an onsite supervisor and a Department faculty member.
Enrollment is subject to available opportunities and approval of the Department Chairperson.
MATH 397
Putnam Competition Preparation
0-1 Semester Hours
A study of problem-solving techniques and skills to prepare students to participate in the William Lowell Putnam Mathematical Competition, a prestigious national exam. The course may be repeated for credit. Grading is Credit/No Credit. The course may not be used to satisfy any of the requirements of the mathematics major or minor.
Consent of instructor required.
MATH 398
Special Studies
1-4 Semester Hours
MATH 399
Independent Studies
1-4 Semester Hours
MATH 471
Topology
3 Semester Hours
An introduction to metric and topological spaces; continuity and homeomorphism; separation properties; connectivity and compactness; examples and applications.
Prerequisite: MATH 321.
MATH 473
Differential Geometry
3 Semester Hours
Curves, parametrizations, and arc length; surfaces, differentiable functions, and the first fundamental form (area); the Gauss map; isometries, Gauss’ Theorema Egregium, geodesics, and the Gauss-Bonnet theorem.
Prerequisites: MATH 234 and 250.
MATH 490
History of Mathematics
3 Semester Hours
The development of mathematics from historical and cultural viewpoints, including both European and non-European roots of mathematics as well as contributions by women.
Prerequisite: MATH 248.
MATH 491
Senior Mathematics Seminar
3 Semester Hours
Topics in mathematics chosen by the instructor. Written and oral presentations are required.
MATH 493
Senior Seminar for Future Mathematics Educators
3 Semester Hours
Topics in high school mathematics are examined from an advanced standpoint by developing and exploring extensions and generalizations of typical high school problems, by making explicit connections between these problems and upper division mathematics courses, and by providing historical context. Current issues in secondary mathematics education will be investigated. Written and oral presentations are required.
Prerequisite: Senior standing or consent of instructor.
MATH 495
Mathematical Modeling
3 Semester Hours
Introduction to various modeling techniques, design and implementation of algorithms, organization and presentation of results, introduction to problem solving using computer algebra systems. Written and oral presentations are required.
Senior standing or consent of instructor required.
MATH 497
Senior Thesis
3 Semester Hours
This course is intended to provide the student with an opportunity to complete a substantive research project under the guidance of a faculty member. The student will prepare a written report and an oral presentation on the project at the end of the semester.
Senior standing and the consent of both the Chairperson and a faculty thesis advisor required.
MATH 498
Special Studies
1-3 Semester Hours
MATH 499
Independent Studies
1-3 Semester Hours
MATH 511
Mathematics and Gender Issues
3 Semester Hours
Historical and current gender issues in mathematics examined through 1) the lives and mathematical work of women mathematicians from the 4th to the 21st centuries and 2) equity issues in K-12 mathematics education and math-related careers. Mathematical topics include prime numbers, conic sections, functions, sequences and series, polyhedra and group theory.
Prerequisites: MATH 107 and 111 or 112 or 120 or 122 or 131 or consent of instructor.
MATH 550
Fundamental Concepts of Geometry
3 Semester Hours
Euclidean and non-Euclidean planar geometries, axiomatic systems, synthetic and analytic representations, relationships with algebra, and selected topics and applications.
Prerequisites: MATH 248 and 250.
MATH 560
Advanced Topics in Probability and Statistics
3 Semester Hours
Material to be covered will be determined by the instructor. Consult with the instructor for the specific topics in probability and statistics that will be covered in any given semester.
Prerequisites: MATH 234 and 360.
MATH 561
Computational Methods in Linear Algebra
3 Semester Hours
Numerical solutions of linear systems of equations, Gauss elimination and iterative methods, eigenvalues and eigenvectors.
Prerequisites: CMSI 185 or MATH 282, and MATH 250 or consent of instructor.
MATH 562
Numerical Analysis
3 Semester Hours
Numerical solutions of non-linear equations, interpolation, numerical differentiation, integration, and solution of differential equations.
Prerequisites: CMSI 185 or ENGR 240 or MATH 282, and MATH 245 or consent of instructor.
MATH 568
Mathematical Methods of Operations Research
3 Semester Hours
Linear and dynamic programming, network analysis, inventory control.
Prerequisite: MATH 360.
MATH 575
Introduction to Orbit Determination
3 Semester Hours
A brief introduction to Banach and Hilbert spaces, the Projection Theorem, linear minimum variance estimates, the Kalman filter, variational equations and orbit determination examples. The final exam is a computer problem that involves tracking a spacecraft orbiting an asteroid by means of Doppler measurements.
Prerequisites: MATH 245, 250, and consent of instructor.
MATH 582
Analysis of Algorithms
3 Semester Hours
Design, comparison, and analysis of mathematical algorithms, including implementation and testing using Fortran.
Prerequisite: CMSI 185 or ENGR 240 or MATH 282 or consent of instructor.
MATH 590
History of Mathematics for Secondary Teachers
3 Semester Hours
The development of mathematics from historical and cultural viewpoints, including both European and non- European roots of mathematics as well as contributions by women. Course content will be connected to the secondary classroom.
Prerequisite: MATH 248.
MATH 598
Special Studies
1-3 Semester Hours
MATH 599
Independent Studies
1-3 Semester Hours
MATH 695
MAT Final Project
0 Semester Hours
The student will prepare and submit a proposal for a substantive project to the MAT Director, who will submit it to the Education Liaison Committee, complete the proposal as approved by the Education Liaison Committee under the guidance of a faculty member, prepare a written report, and give an oral presentation on the project.
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