MATH - Mathematics (MATH)
Note: The appropriate entry level in mathematics is determined by the student’s intended major and a mathematics placement examination given to all entering freshmen. Placement testing is also required for transfer students who have not completed their general education mathematics requirements.
Majors in the natural or computer sciences or mathematics who have completed three years of college preparatory mathematics and have demonstrated competence on the mathematics placement examination; should enroll in Mathematics U121, U126 or U127 as appropriate. Students who need both college algebra and trigonometry have the option of taking Mathematics U121 (with a grade of B or better) or U126, and Mathematics U127. Those who have demonstrated competence in college algebra can take Mathematics U127 to meet the calculus prerequisite. Upon successful completion of one of the precalculus options, students should enroll in Mathematics U141. Those who have completed four years of college preparatory mathematics, including trigonometry, and have demonstrated competence on the mathematics placement examination, should enroll in Mathematics U141.
Students not majoring in the natural or computer sciences, who have successfully completed high school Algebra I and II, and have demonstrated competence on the mathematics placement examination, should enroll as follows: business administration majors in the Mathematics U121, U122 sequence; elementary, early childhood, and special education majors in Mathematics U121, and U231; other majors in a mathematics course determined by their advisors.
The fundamentals of modern statistical methods, descriptive and inferential statistics, probability and sampling; primarily for students in fields other than mathematics who need a working knowledge of statistics.
Linear equations and inequalities, exponential equations, mathematics of finance, fundamental set theory, fundamentals of probability and statistics. This course may not be used to satisfy any prerequisite requirement for higher-numbered mathematics courses.
Linear equations and inequalities, exponential equations, mathematics of finance, fundamental set theory, fundamentals of probability and statistics. This course may not be used to satisfy any prerequisite requirement for higher-numbered mathematics courses.
Equations and inequalities, graphing, polynomial, rational, exponential, logarithmic, and other functions; matrices and systems of equations. Only one of MATH U121 and MATH U126 may be used to satisfy a mathematics requirement for general education or major credit. For students who need a more intensive study, an expanded version of college algebra (MATH U121A) is available. MATH U121A is open to students who have an appropriate score on the placement test, have completed MATH U120 with the mandatory lab, or if the student, in consultation with his or her advisor, determines that extra instruction is needed in order to succeed in MATH U121.
Equations and inequalities, graphing, polynomial, rational, exponential, logarithmic, and other functions; matrices and systems of equations. Only one of MATH U121 and MATH U126 may be used to satisfy a mathematics requirement for general education or major credit. Prerequisites: Appropriate score on placement test and high school Algebra I and II. For students who need a more intensive study, an expanded version of College Algebra (MATH U121A) is available.
Derivatives and integrals of elementary algebraic, exponential and logarithmic functions; maxima, minima, rate of change, area under a curve, and volume. Problems and examples are drawn from a variety of areas which include economics, psychology, biology, geography, and geology.
Subsets of the real number line; polynomial, rational, absolute value, exponential and logarithmic relations and functions. Only one of MATH U121 and MATH U126 may be used to satisfy a mathematics requirement for general education or major credit.
Trigonometric functions, trigonometric identities, solution of equations and triangles, inverse trigonometric functions, vectors, polar coordinates; analytic geometry.
Limits, continuity, the derivative, differentiation with applications in the natural sciences and engineering, antiderivatives, basic integrals with applications.
Applications of integration, techniques of integration, differential equations, parametric equations, and finite sequences and series.
Topics in basic logic; proof techniques; sets, relations, and functions; counting; and elementary number theory.
An expansion of topics taught in the first semester of elementary statistics such as hypothesis testing; inferences; correlation and regression. Additional topics to be covered include: multinomial experiments and contingency tables; analysis of variance; statistical process control; and individual projects.
The meaning of number, fundamental operations of arithmetic, the structure of the real number system and its subsystems, elementary number theory. Open only to students in early childhood, elementary, middle grades, or special education.
A continuation of the development of the real number system and its subsystems, basic concepts of probability, and elementary data analysis. Open only to students in early childhood, elementary, middle grades, or special education.
A study of properties and relationships of shape, size, and symmetry in two and three dimensions; explorations of concepts of motion in two and three dimensions through transformations. Open only to students in early childhood, elementary, middle grades, or special education.
Vectors and geometry of space, vector functions, partial derivatives, multiple integration, vector calculus and second order differential equations.
Ordinary differential equations of first order, higher order linear equations, Laplace transform methods, series methods; numerical solutions of differential equations; applications to the physical sciences and engineering.
Programming language and techniques designed specifically for programs that rely on the application of mathematics for solution. Topics include variables, assignment statements, expressions, vectors and matrices, MATLAB scripts, input and output, selection statements, flow control, program organization, M-files, optimizing M-files, string manipulations, data structures, advanced functions, plotting, symbolic math toolboxes, variable precision arithmetic, and tricks and tips in MATLAB programming.
Review of descriptive statistics, testing statistical hypothesis, introduction to correlation, regression and linear regression models, model building, variable selection and model diagnostics.
Graphs of functions as models, modeling using proportionality and geometric similarity, model fitting and models requiring optimization, experimental modeling, modeling using the derivative and interactive dynamic systems.
Topics in set theory, logic, elementary application of logic, methods of mathematical proofs, equivalence relations and partial orderings, functions and mappings, and number systems.
Matrices, systems of linear equations, vectors, Euclidean vector spaces, linear transformations, eigenvalues and eigenvectors.
Basic linear Partial Differential Equations (PDEs) of hyperbolic, parabolic, and elliptic types used in mathematical modeling of physical, chemical, biological and other phenomena, systems, technical devices and financial markets. Selected topics such as the boundary value and initial value problems are covered.
Group theory and introduction to rings. Topics include abelian groups, cyclic groups, permutations, group homomorphisms and isomorphisms, Cayley's theorem, normal subgroups, quotient groups, Lagrange's theorem.
Ordered field properties of the real number system; completeness; theory of limits of sequences, series and functions; continuity (including uniform continuity); introduction to theory of the derivative.
Topics selected from theoretical Boolean algebra, algebraic structures, theory of computing, advanced set theory, and recursive functions.
Supervised practical experience related to the student's major in Mathematics in an elected setting planned in conjunction with the appropriate faculty member. The course may only be applied for a maximum of three hours as an Upper Level Elective.
The methods of the numerical solutions of optimization problems arising in operational research, logistics, economics, etc. Emphasis is on the simplex and Karmarkar's polynomial-time method.
A survey of the major developments and procedures of mathematics, from its origins to the modern era, relating development with the diverse cultures and the aspects of mathematics they contributed.
Geometry as a logical system based upon postulates and undefined terms; fundamental concepts and relations of Euclidean geometry developed rigorously on the basis of a set of postulates; some topics from non-Euclidean geometry.
Vector spaces, and subspaces; bases and dimension; change of basis; linear transformations and their matrices; diagonalization; canonical forms; bilinear forms; eigenspaces.
Advanced topics in groups, rings and fields. These topics include p-groups, polynomial rings, ideals, integral domains, extension fields, isomorphism theorems for groups and rings.
Complex numbers and functions, complex integration, Taylor and Laurent series, residues, and conformal mapping.
Further development of the theory of differential and integral calculus including properties of the derivative and integral, Fundamental Theorem of Calculus, sequences and series of functions.
Difference calculus; direct and iterative techniques for matrix inversion; eigenvalue problems; numerical solutions of initial value problems in ordinary differential equations; stability; error analysis; laboratory applications.
The finite-difference and finite element methods for the numerical solution of basic linear Partial Differential Equations (PDEs) arising in mathematical modeling of physical, chemical, biological and other phenomena, systems, technical devices and financial markets.
Basic applications of PDEs, numerical methods for PDEs and scientific computing to applied problems arising in the natural sciences, industry, and financial engineering. Emphasis is on the formulation and solution of problems of heat transfer and diffusion equations, Maxwell's equations and differential equations governing the financial derivatives.
Intensive study in an area of pure or applied mathematics such as mathematical modeling. Topics are selected to meet current faculty and student interest.