# Mathematics Courses

**MATH 104: Finite Mathematics (3)***Prerequisites: ACT Math Score of 19 or higher; OR ACCUPLACER Math Score of 85 or higher; OR Successful completion of MATH 099*Topics covered include functions and their graphs, matrices, linear programming, probability, and descriptive statistics. Applications are presented from the areas of biology, business, behavioral science, economics, and the social sciences. The computer may be used as a problem solving tool.

**MATH 106: College Algebra (3)***Prerequisites: ACT Math Score of 22 or higher; OR ACCUPLACER Math Score of 85 or higher; OR Successful completion of MATH 099*An introduction to the basic techniques of algebra. Topics include functions (linear, quadratic, polynomial, root, rational, exponential, and logarithmic), systems of equations, partial fractions, synthetic division, inequalities, and complex numbers.

**MATH 107: Trigonometry and Analytic Geometry (3)***Prerequisites: Successful completion of MATH 106*An introduction to the tools and techniques of trigonometry. Topics include angles and their measure, the six trigonometric functions and their properties, inverse trigonometric functions, graphs, identities including the Law of Sines and the Law of Cosines, trigonometric equations, and solving triangles. Optional topics include complex numbers, De Moivre's Theorem, polar coordinates, and analytic geometry.

**MATH 120: Single Variable Calculus I (5)***Prerequisites: ACT Math Score of 26 or higher; OR Successful completion of MATH 107*An introduction to the calculus of functions of one real variable. Topics include limits, continuity, derivatives, graphing techniques, optimization, related rates, Newton's method, indeterminate forms and l'Hôpital's rule, antiderivatives, the definite integral, and the Fundamental Theorem of Calculus.

**MATH 121: Single Variable Calculus II (5)***Prerequisites: Successful completion of MATH 120*A continuation of the calculus of functions of one real variable. Topics include integration, applications of the definite integral, techniques of integration, improper integrals, arc length, surface area, volume, infinite series, and Taylor series.

**MATH 140: Geometry With Technology (3)***Prerequisites: ACT Math Score of 19 or higher; OR ACCUPLACER Math Score of 85 or higher; OR Successful completion of MATH 099*An introduction to powerful interactive programming environments such as Geometer's Sketchpad will enable the student to survey Euclidean Geometry using technology. This course will discuss major concepts in Euclidean Geometry.

**MATH 150: Liberal Arts Mathematics (3)***Prerequisites: ACT Math Score of 19 or higher; OR ACCUPLACER Math Score of 85 or higher; OR Successful completion of MATH 099*A quantitative and qualitative exploration of some of the great ideas and methods of mathematics. Topics covered include problem solving, infinity, logic, probability, statistics, Fibonacci numbers, the golden ratio, topology, non-Euclidean geometry, Pascal's triangle, tiling, fractals, chaos, and higher dimensions.

**MATH 205: Introduction to Statistical Methods (3)***Prerequisites: Successful completion of MATH 104, 106, 107, or 120*An introduction to the basic techniques of applied statistics. Typical topics include sampling techniques (simple random, stratified, cluster), independence, discrete and continuous random variables, distributions (normal, t, chi square, F, and sampling), regression, correlation, confidence intervals, hypothesis testing, types of error, power of tests, ANOVA, and nonparametric methods.

**MATH 220: Multivariable Calculus (4)***Prerequisites: Successful completion of MATH 121*An introduction to the calculus of functions of several real variables. Typical topics include three-dimensional analytic geometry, vectors, parametric curves and surfaces, arc length and curvature, limits, continuity, partial derivatives, gradients, directional derivatives, tangent planes, optimization problems and Lagrange multipliers, multiple integrals, vector fields, line and surface integrals, Green's theorem, Stokes' theorem, and the divergence theorem.

**MATH 250: Introduction to Mathematical Thought (3)***Minimum prerequisite of MATH 120; recommended successful completion of MATH 121 or MATH 220.*This course looks at topics central to further study in mathematics. Topics include symbolic logic, especially as it applies to mathematical proof; methods of mathematical proof such as direct proof, indirect proof, and proof by induction; use and meaning of mathematical quantifiers and predicates; sets; relations; equivalence relations and partitions; order relations; and functions and their properties.

**MATH 321: Linear Algebra (3)***Prerequisites: Successful completion of MATH 121*An introduction to linear algebra. Typical topics include solution of systems of linear equations, matrix algebra, determinants, vector spaces, linear independence, span, basis, dimension, coordinates, linear transformations, matrix representations of linear transformations, eigenvalues, eigenvectors, diagonalization, Gram-Schmidt orthogonalization, orthogonal projection, and applications.

**MATH 322: Algebraic Structures I (3)***Prerequisites: Successful completion of MATH 250 AND MATH 321*An introduction to the theory of groups. Typical topics include sets, mappings, binary operations, equivalence relations, partitions, the integers, induction, the well-ordering property, elementary number theory, cryptography, coding theory, groups (permutation groups, symmetry groups, matrix groups, and cyclic groups), subgroups, cosets, Lagrange's theorem, normal subgroups, homomorphisms, isomorphisms, Cayley's theorem, and the Fundamental Homomorphism Theorem.

**MATH 323: Algebraic Structures II (3)***Prerequisites: Successful completion of MATH 322*An introduction to the theory of rings and fields. Typical topics include rings, ideals, integral domains, fields, ring homomorphisms, quotient rings, polynomial rings, division algorithms, factorization of polynomials, extensions of fields, finite fields, and Galois theory.

**MATH 327: Differential Equations (3)***Prerequisites: Successful completion of MATH 121*An introduction to the study and application of ordinary differential equations. Typical topics include first order differential equations, linear differential equations, systems of equations, existence and uniqueness of solutions, bifurcations, the Laplace transform, matrix methods, and stability theorems.

**MATH 330: Numerical Analysis (3)***Prerequisites: Successful completion of MATH 121 AND successful completion of one of the following courses: CSCI 150, CSCI 208, or MATH 210*The study, development, implementation, and analysis of algorithms for obtaining numerical solutions to various mathematical problems. Typical topics include error analysis, stable and unstable computations, rates of convergence, solutions of nonlinear equations, solutions of systems of linear equations, function approximation and interpolation, optimization, numerical differentiation and integration, and numerical solutions to ordinary differential equations.

**MATH 331: Modern Geometry (3)***Prerequisites: Successful completion of MATH 121 AND MATH 250*An introduction to plane geometry intended for future teachers of mathematics. Typical topics include deductive reasoning and the axiomatic method, Euclidean geometry, parallelism, hyperbolic and other non-Euclidean geometries.

**MATH 335: History of Mathematics (3)***Prerequisites: Successful completion of MATH 121*This course traces the historical development of mathematics from ancient to modern times, placing mathematical facts into a meaningful intellectual and historical context. Typical topics include mathematics in early civilizations such as Egypt and Babylonia, early Greek mathematics from Euclid to Archimedes, the work of Diophantus, mathematics in medieval Islam and its transmission to the Latin West, the early development of algebra, the analytic geometry of Descartes and Fermat, the development of the calculus at the hands of Newton and Leibniz, the contributions of the Bernoulli family, nineteenth-century analysis from Cauchy to Weierstrass, nineteenth-century algebra from Galois through Klein, the development of non-Euclidean geometry, and Cantor's developments in set theory.

**MATH 340: Probability and Statistics (3)***Prerequisites: Successful completion of MATH 121*Application and theory of the principles of probability and statistics in the sciences and engineering. Topics include random variables, probability distributions, sampling, estimation, tests of hypothesis, and regression.

**MATH 403: Senior Assessment (3)***Prerequisites: Senior standing for BA or BS in mathematics or mathematics-computer science and department approval of senior project proposal early in the previous semester.*Students will develop a project, present the results of their research to the faculty and write a paper communicating the results of the project. Students will find a project advisor at least one semester prior to enrollment, will develop and submit a project proposal, and will have substantially completed the research before enrolling. Each student takes a comprehensive capstone examination that includes a nationally normed test over the subject area. This course may enhance content knowledge in ALL the state model content standards areas of mathematics. Which standards are addressed depends very much on the individual student project.

**MATH 420: Advanced Analysis I (3)***Prerequisites: Successful completion of MATH 220 and MATH 250*Rigorous presentation of the fundamental concepts and techniques of real analysis, including a careful study of continuity and convergence, sets and functions, sequences and series, limits and continuity, and differentiation.

**MATH 421: Advanced Analysis II (3)***Prerequisites: Successful completion of MATH 420*A continuation of Math 420 with an emphasis on integration, sequences and series of functions, uniform convergence, infinite series, and additional topics of the instructor's choosing.

**MATH 430: Complex Analysis I (3)***Prerequisites: Successful completion of MATH 220*Theory of functions of one complex variable, including derivatives, integrals, power series, residues, and conformal mappings.

**MATH 436: Research in Mathematics (1)***Prerequisites: Permission of instructor.*An independent research course. The student will work with a professor on a research project either designed by the student or the professor. The student's research must result in a professional quality paper or project and a presentation before a group of peers and professors.