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ENGINEERING AND MATHEMATICS (BOTHELL)

SCIENCE AND TECHNOLOGY MATHEMATICS

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**STMATH 124 Calculus I (5) NW, QSR**

Studies the development of differential calculus, starting with limits, continuity, and the definition of derivative. Emphasizes differentiation techniques and their applications. Prerequisite: a minimum grade of 2.5 in either B MATH 123 or MATH 120, or a minimum score of 500 on the MTHDSP directed self-placement test. Offered: AWSpS.

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**STMATH 125 CALCULUS II (5) NW, QSR**

Integration theory and techniques with applications in science and engineering. Prerequisite: a minimum grade of 2.0 in either STMATH 124 or MATH 124, or a minimum score of 3 on AP MAB, or a minimum score of 2 on AP MBC exam. Offered: AWSpS.

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**STMATH 126 CALCULUS III (5) NW**

Studies sequences and series, including convergence tests and Taylor polynomials and series, as well as the calculus of curves in the plane and space described in polar, parametric, or vector-valued form. Prerequisite: a minimum grade of 2.0 in either STMATH 125 or MATH 125, or a score of 5 on AP MAB exam, or a minimum score of 4 on AP MBC exam. Offered: AWSpS.

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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 STMATH 125, or MATH 125.

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**STMATH 307 Introduction to Differential Equations (5) NW**

Introduces ordinary differential equations. Includes first-and second-order equations and Laplace transform. Prerequisite: minimum grade of 2.0 in either STMATH 125, or MATH 125.

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**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. Prerequisite: minimum grade of 2.0 in STMATH 125 or MATH 125

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**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: minimum grade of 2.0 in STMATH 124, or MATH 124.

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**STMATH 324 Multivariable Calculus (5)**

Introduction to the concepts and computation techniques of multivariable calculus, including partial derivative, the chain rule, double and triple integrals, vector fields, line integrals, surface integrals, Green's Theorem, Stokes' Theorem, and the Divergence Theorem. Prerequisite: minimum grade of 2.0 in STMATH 126, or MATH 126. Offered: AWSpS.

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**STMATH 330 Financial Mathematics (5)**

An introduction to the concepts of financial mathematics, and how they are applied in calculating
present and accumulated values for various streams of cash flows, as a basis for future use in: reserving; valuation; pricing; asset/liability management; investment income; capital budgeting; and valuing contingent cash flows. Prerequisite: A minimum grade of 2.0 in STMATH 125; and a minimum grade of 2.0 in B BUS 220/BIS 200.

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**STMATH 341 Introduction to Statistical Inference (5) QSR**

Stochastic concepts including probabilistic underpinnings of statistics, measures of central tendency, variability, correlation, distributions, sampling, and simulation. Exploratory data analysis including experiments, surveys, measures of association and inferential statistics. Credit is not given for both STMATH 341 and STMATH 390. Prerequisite: minimum grade of 2.0 in STMATH 124, B MATH 144, or MATH 124.

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**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.

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**STMATH 381 Discrete Mathematical Modeling (5)**

Introduction to methods of discrete mathematics, including topics from graph theory, network flows, and combinatorics. 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 or MATH 308; and minimum grade of 2.0 in CSE 142, CSS 142, CSS 161, or AMATH 301.

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**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. Credit is not given for both STMATH 341 and STMATH 390. Prerequisite: minimum grade of 2.0 in STMATH 324, or MATH 324.

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**STMATH 392 Probability (5)**

Introduction to probability theory including combinatorial analysis, conditional probability, independence, and random variables. Conditional expectation including its use in prediction, moment-generating functions, and the multivariate normal distribution. Theoretical results in probability theory such as the strong law of large numbers and the central limit theorem. Prerequisite: a minimum grade of 2.0 in STMATH 324; recommended: B BUS 220 if enrolled in the Actuarial Science Minor. Offered: W.

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**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 or MATH 300; and minimum grade of 2.0 in STMATH 308 or MATH 308.

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**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, or MATH 402.

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**STMATH 405 Numerical Analysis I (5)**

Methods and theory for numerically solving systems of equations, both linear and nonlinear. Topics include numerical error, stability and conditioning, root finding, direct and iterative methods for linear systems, linear least squares, eigenvalue problems, and nonlinear systems. Prerequisite: minimum grade of 2.0 in STMATH 308 or MATH 308; and minimum grade of 2.0 in STMATH 126 or MATH 126; and minimum grade of 2.0 in CSS 132, CSS 142, CSE 142, CSS 161, or AMATH 301.

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**STMATH 406 Numerical Analysis II (5)**

Methods and theory for numerically approximating functions, their integrals and derivatives, and solutions to ODEs. Topics include polynomial and piecewise polynomial interpolation, the Fourier transform, numerical differentiation and integration, and approximate solution of ODEs using Euler and Runge-Kutta methods. Prerequisite: Minimum grade of 2.0 in STMATH 307 and STMATH 405.

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**STMATH 407 Linear Programming (5)**

Maximize and minimize linear functions subject to constraints consisting of linear equations and inequalities. Define linear optimization models from problem description. Solve linear programming problems using the simplex method. Conduct duality and sensitivity analysis for linear programming. Prerequisite: minimum grade of 2.0 in STMATH 308 or MATH 308; and minimum grade of 2.0 in STMATH 126 or MATH 126; and minimum grade of 2.0 in CSS 132, CSS 142, CSE 142 or AMATH 301.

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**STMATH 408 Nonlinear Optimization (5) QSR**

Maximize and minimize nonlinear functions, constrained and unconstrained; nonlinear programming problems and methods. Topics include: Lagrange multipliers, Kuhn-Tucker conditions, convexity, quadratic programming, steepest-descent method, and Newton and quasi-Newton methods. Prerequisite: minimum grade of 2.0 in STMATH 308 or MATH 308; and minimum grade of 2.0 in STMATH 324 or MATH 324; and minimum grade of 2.0 in STMATH 300; and minimum grade of 2.0 in CSS 132, CSS 142, CSE 142 or AMATH 301.

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**STMATH 409 Advanced Linear Algebra (5)**

A mathematically rigorous treatment of vector spaces; linear transformations and matrices; matrix operations and linear systems; determinants; eigenvalues, eigenvectors, and diagonalization; canonical forms; and special matrices including permutation and nonnegative matrices. Prerequisite: minimum grade of 2.0 in each of STMATH 300 and STMATH 308; recommended: STMATH 300 and STMATH 308.

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**STMATH 420 History of Mathematics (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: a minimum grade of 2.0 in either STMATH 126 or MATH 126; and a minimum grade of 2.0 in either STMATH 300 or MATH 300.

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**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 or MATH 300.

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**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.

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**STMATH 427 Complex Analysis (5)**

Complex numbers; analytics functions; sequences and series; complex integration; Cauchy integral formula; Taylor and Laurent series; uniform convergence; residue theory; conformal mapping. Prerequisite: Minimum grade of 2.0 in STMATH 300 or MATH 300; and minimum grade of 2.0 in STMATH 324 or MATH 324.

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**STMATH 441 Topology (5)**

Topological spaces, product spaces, quotient spaces, metric spaces, convergence, continuity, separation and countability axioms, connectedness, and compactness. Prerequisite: Minimum grade of 2.0 in STMATH 424.

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**STMATH 444 Foundations of Geometry (5)**

Studies classical geometry, including topics from neutral geometry of the triangle, non-neutral Euclidean geometry, spherical geometry, hyperbolic geometry, projective geometry, and symmetries. Emphasizes proof writing. Prerequisite: minimum grade of 2.0 in STMATH 300 or MATH 300

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**STMATH 465 Fostering Algebraic Reasoning (5) NW, QSR**

Focuses on methods of teaching algebra from a developmental perspective, including research-based methods for developing students' algebraic thinking and structure and processes used in algebra. Prerequisite: minimum grade of 2.0 in STMATH 125 or MATH 125. Offered: jointly with B EDUC 465.

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**STMATH 466 Fostering Geometric Thinking (5) NW, QSR**

Focuses on methods of teaching geometry from a developmental perspective, including research-based methods for developing students' geometric thinking and structure and processes used in geometry including proof. Prerequisite: minimum grade of 2.0 in STMATH 125 or Math 125. Offered: jointly with B EDUC 466.

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**STMATH 467 Fostering Statistical Thinking, Data, and Graphical Analysis (5) NW, QSR**

Focuses on methods of teaching data and graphical analysis and statistical thinking from a developmental perspective, including how to foster secondary students' statistical thinking, and using technological tools to teach key concepts in secondary mathematics using big data sets, graphical analysis, and dynamic visualization. Prerequisite: minimum grade of 2.0 in STMATH 125 or Math 125. Offered: jointly with B EDUC 467.

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**STMATH 493 Special Topics in Mathematics (1-5, max. 15)**

Covers special topics in advanced mathematics in a classroom setting not currently taught in the mathematics curriculum. Prerequisite: minimum grade of 2.0 in either STMATH 300 or MATH 300.

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**STMATH 498 Independent Study in Mathematics (1-5, max. 15)**

Advanced special topic in mathematics. Topic guided by an articulated need or interest and not covered in regularly scheduled courses.

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**STMATH 499 Undergraduate Research in Mathematics (1-5, max. 5)**

Undergraduate research project agreed upon by student and a mathematics faculty member. This course is intended to produce a quality research artifact (e.g., a poster presentation, a research article, a conference presentation, etc.). Cannot be taken for credit if credit received for either MATH 399 or MATH 499.

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