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  • MTH 411: Number Theory

    4.50 Credits
    National University

    (Prerequisite: MTH 215 or MTH 216A/B or MTH 301 or placement evaluation) An examination of fundamental concepts of numbers, including divisibility, congruencies, the distrib- ution of Primes, Pythagorean triples, the Euclidean Algorithm, the Fundamental Theorem of Arithmetic, Diophantine equations and Goldbach's conjecture. Emphasis active student involvement in posing and testing conjectures, formulating counter examples, logical arguments, and proofs.
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  • MTH 412: History of Mathematics

    4.50 Credits
    National University

    (Prerequisites: MTH 215, MTH 216A/B, or MTH 301) Examines currents in the development of mathematics and throughout ancient Egypt, Babylon, China, and the Middle East. It studies math's influence on society through the major events of Europe, contemporary developments, and some projections into the future, including the women and men who played key roles in evolution of mathematics.
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  • MTH 416: Algebraic Structures

    4.50 Credits
    National University

    (Prerequisite: MTH 325 and MTH 435) A look at groups, rings and fields, as well as applications of these systems. Discusses equivalence relations, Lagrange's Theorem, homomorphisms, isomorphisms, Cayley's Theorem and quaternions. Also examines error correcting codes and issues of cryptography. Graphing calculator may be required.
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  • MTH 417: Foundations of Geometry

    4.50 Credits
    National University

    (Prerequisites: MTH 215 or MTH 216A/B and MTH 311) A discussion of fundamental ideas and processes common to Euclidean and Non-Euclidean geometries: projective, affine and metric geometry. Examines the interplay between inductive and deductive reasoning, and formal and informal proof. Addresses uses in science (transformations, scaling), art (Escher-type tessellations, projections), architecture (three-dimensional figures), and computer science (fractals, computer-aided design).
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  • MTH 418: Statistical Analysis

    4.50 Credits
    National University

    (Prerequisites: MTH 210 and MTH 220) An examination of statistical applications to business, computer science, psychology, education, social sciences, and mathematics with fundamental concepts of probability distribution, mathematical models relating independent and dependent random variables, hypothesis testing and experimental design. Includes fundamental analysis of variance, various distributions and methods of regression, analysis and scaling.
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  • MTH 432: Advanced Calculus

    4.50 Credits
    National University

    (Prerequisite: MTH 223) A look at sets, functions, and the real numbers. Topics include the Completeness axiom, cardinality, and Cantor's theorem, Limsup, and Liminf; the topology of R1 and R2, open sets, limit points, compactness and the Heine-Borel theorem, continuous functions properties, uniform continuity, the Mean- Value theorem; the Riemann integral, and Lebesgue measure.
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  • MTH 433: Differential Equations

    4.50 Credits
    National University

    (Prerequisite: MTH 223 and MTH 435) Examines systems of linear equations and matrices, elementary vector-space concepts, and geometric interpretations. Discusses finite dimensional vector spaces, linear functions and their matrix representations, determinants, similarity of matrices, inner product, rank, eigenvalues and eigenvectors, canonical form, and Gram-Schmidt process.
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  • MTH 435: Linear Algebra

    4.50 Credits
    National University

    (Prerequisites: MTH 325 and MTH 220) Examination of systems of linear equations and matrices, elementary vector-space concepts, and geometric interpretations. Discusses finite dimensional vector spaces, linear functions and their matrix representations, determinants, similarity of matrices, inner product, rank, eigenvalues and eigenvectors, canonical form, and Gram-Schmidt process. Computer software will demonstrate computational techniques with larger matrices.
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  • MTH 438: Applied Mathematical Modeling

    4.50 Credits
    National University

    (Prerequisites: MTH 433, MTH 416, and MTH 432) A capstone course intended to culminate the core mathematics major studies and should be taken at or near the end of the program. Discusses principles and methods of constructing, analyzing, interpreting, evaluating, and refining mathematical models. Compares analytic and simulation, discrete and continuous, deterministic and stochastic models.
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  • MTH 440: Numerical Analysis

    4.50 Credits
    National University

    (Prerequisite: MTH 220) An introduction to numerical computation. Discusses errors in numerical computation, truncation and discretization, and machine storage restrictions as well as function approximation, roots of nonlinear equations, systems of linear equations, algebraic eigenvalue problems, polynomial interpolation, and cubic spline interpolations, quadratures, numerical differentiation, initial and boundary-value problems.
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