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Engineering and Mathematics (Bothell)

SCIENCE AND TECHNOLOGY MATHEMATICS

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**STMATH 124 CALCULUS I: ORIGINS AND EARLY DEVELOPMENTS (5) NW, QSR**

Develops modern calculus by investigating the questions, problems, and ideas that motivated its discovery and practice. Studies the real number system and functions defined on it, focusing on limits, area and tangent calculations, properties and applications of the derivative, and the notion of continuity. Emphasizes problem-solving and mathematical thinking. Prerequisite: either a minimum grade of 2.5 in B MATH 123, sufficient score on approved mathematics assessment test, or a minimum score of 2 on either the AB or BC AP Calculus test.

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**STMATH 125 CALCULUS II: FOUNDATIONS AND THE EMERGENCE OF MODERN ANALYSIS (5) NW, QSR**

Focuses on the historical emergence of modern calculus, the Fundamental Theorem, area, volume, and area length calculations, properties and applications of the integral, infinite series, Taylor and Fourier expansions, and the Weierstrass definition of limit. Emphasizes problem-solving and mathematical thinking. Prerequisite: minimum grade of 2.0 in STMATH 124, score of 3 on AP MAB or AP MBC exams.

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**STMATH 126 CALCULUS WITH ANALYTIC GEOMETRY III (5) NW**

Third quarter in calculus sequence. Introduction to Taylor polynomials and Taylor series, vector geometry in three dimensions, introduction to multivariable differential calculus, double integrals in Cartesian and polar coordinates. Prerequisite: either 2.0 in MATH 125, 2.0 in MATH 145, 2.0 in MATH 146, 2.0 in STMATH 125, score of 5 on AB advanced placement test, or score of 4 on BC advanced placement test. Offered: AWSp.

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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.

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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: 2.0 in B CUSP 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 B CUSP 124.

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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: B CUSP 124.

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**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.

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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. Prerequisite: minimum grade of 2.0 in either 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 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; minimum grade of 2.0 in CSS 161.

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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. Prerequisite: STMATH 324.

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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.

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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.

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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 both STMATH 308 and CSS 161.

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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 each of STMATH 308, STMATH 324, and CSS 161.

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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: minimum grade of 2.0 in either B CUSP 124 or MATH 124.

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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.

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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 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.

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**STMATH 465 Fostering Alegbraic 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: either B CUSP 125, 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: either B CUSP 125, 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: either B CUSP 125, 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)**

Readings course covering special topics in mathematics agreed upon by student and faculty member.

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**STMATH 499 Undergraduate Research in Mathematics (1-5, max. 15)**

Undergraduate research project agreed upon by the student and faculty member.

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