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STMATH 300 Foundations of Modern Math (5) QSR
Introduces students to mathematical argument and to reading and writing proofs. Develops elementary set theory, examples of relations, functions and operations on functions, the principle of induction, counting techniques, elementary number theory, and combinatorics. Places strong emphasis on methods and practice of problem solving. Prerequisite: minimum grade of 2.0 in B CUSP 125.
STMATH 307 Introduction to Differential Equations (5) QSR
Introduces ordinary differential equations. Includes first-and second-order equations and Laplace transform. Prerequisite: 2.0 in BCUSP 125.
STMATH 308 Matrix Algebra with Applications (5) NW
Introduces linear algebra, including systems of linear equations, Gaussian elimination, matrices and matrix algebra, vector spaces, subspaces of Euclidean space, linear independence, bases and dimension, orthogonality, eigenvectors, and eigenvalues. Applications include data fitting and the method of least squares. Equivalent to MATH 308. Prerequisite: minimum grade of 2.0 in B CUSP 124.
STMATH 310 Mathematical Game Theory (5)
Covers mathematical aspects of Game Theory, including symmetric and asymmetric games, zero-sum and non-zero-sum games, mixed and pure strategies, equilibria, and strategic moves. Examines examples from several disciplines including anthropology, philosophy, business, social psychology, and biology. Prerequisite: B CUSP 124.
STMATH 324 Multivariable Calculus (5)
Introduction to the concepts and computation techniques of multivariable calculus, including double and triple integrals, the chain rule, vector fields, parametric curves and surfaces, line integrals, surface integrals, Green's Theorem, Stoke's Theorem, and the Divergence Theorem. Prerequisite: minimum grade of 2.0 in B CUSP 126.
STMATH 350 Applied Number Theory and Cryptography (5)
Introduces number theory, including divisibility, primes, the Euclidean algorithm, modular arithmetic, Fermat's Little Theorem, and the fast power method. Emphasizes applications in cryptography, including Diffie-Hellman key exchange, public key cryptography, the ElGamal and RSA cryptosystems, and elementary elliptic curve techniques. Prerequisite: minimum grade of 2.0 in STMATH 308.
STMATH 381 Discrete Mathematical Modeling (5)
Introduction to methods of discrete mathematics, including topics from graph theory, network flows, and combinatories. Emphasis on these tools to formulate models and solve problems arising in variety of applications, such as computer science, biology, and management science. Prerequisite: minimum grade of 2.0 in STMATH 308
STMATH 390 Probability and Statistics in Engineering (5) NW
Covers concepts of probability and statistics; conditional probability, independence, random variable, and distribution functions; descriptive statistics, transformations, sampling errors, confidence intervals, least squares, and maximum likelihood; and exploratory data analysis and interactive computing. Prerequisite: STMATH 324.
STMATH 402 Abstract Algebra I (5)
Introduction to group theory. Emphasizes examples, including cyclic, dihedral, and symmetric groups. Theoretical concepts include: Cosets and Lagrange's theorem; direct products; homomorphisms, normal subgroups, quotient groups, and the fundamental isomorphism theorems; orders and Cauchy's theorem; and the structure of finitely-generated abelian groups. Prerequisite: minimum grade of 2.0 in STMATH 300.
STMATH 403 Abstract Algebra II (5) QSR
Introduction to the theory of rings and fields, including ideals, homomorphisms, quotient rings, integral domains and their fields of fractions, polynomial rings, field extensions, vector spaces, geometric constructions via straight-edge and compass, the classification of finite fields, unique factorization domains, and Euclidean domains. Prerequisite: minimum grade of 2.0 in STMATH 402.
STMATH 420 History of Math (5) NW, QSR
Surveys the historical development of mathematics from its earliest beginnings, through the emergence of calculus, and into the early 20th century. Prerequisite: minimum grade of 2.0 in either B CUSP 124 or MATH 124.
STMATH 424 Real Analysis I (5)
Introduction to real analysis: the real number system, metric spaces, the topology of real Euclidean space, the Heine-Borel Theorem, sequences, Cauchy sequences, series and tests for convergence, continuous functions, the intermediate and extreme value theorems, differentiability, the mean value theorem, power series, and Taylor's Theorem. Prerequisite: minimum grade of 2.0 in STMATH 300.
STMATH 425 Real Analysis II (5)
The Riemann-Stieljes integral and the Fundamental Theorem of Calculus. Sequences and series of functions, uniform convergence and its relationship to continuity, differentiation, and integration, the Stone-Weierstrass Theorem. Continuity and differentiability of functions of several variables, the Inverse and Implicit Function Theorems, and Rank Theorem. Prerequisite: minimum grade of 2.0 in STMATH 424.