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DIVISION OF SCIENCES AND MATHEMATICS

MATHEMATICS - TACOMA

Detailed course offerings (Time Schedule) are available for

**TMATH 098 Intermediate Algebra (0)**

Intermediate algebra equivalent to third semester of high school algebra. Extra tuition required. Prerequisite: a minimum score of 250 on the UWT modified placement test based on ACC-QAS, or a minimum score of 100 on the Tacoma Directed Self Placement Math Test.

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**TMATH 105 Mathematics Through Puzzles and Games (5) QSR**

By engaging with puzzles and games, students will gain real-life problem solving and modeling skills. Develops reasoning skills through the precise formulation, expression and communication of ideas. No specialized mathematical skills required.

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**TMATH 106 Spatial and Geometric Reasoning (5) QSR**

Develops geometric intuition, problem-solving skills, and the ability to communicate ideas and solutions with elementary mathematics precisely. Emphasizes spatial, geometric, and logical thinking along with the precise formulation of statements rather than mathematical formulae and theorems. No specialized mathematical skills required.

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**TMATH 109 Financial and Mathematical Foundations (5) QSR**

Interprets everyday financial events using quantitative and algebraic reasoning and models. Students study graphs and equations of linear, exponential, and logarithmic functions with a focus on personal finance while practicing decision making and problem-solving. Topics may include, budgeting, loans, credit cards, taxes, installment buying, mortgages, depreciation and investing. Prerequisite: a minimum score of 250 on the UWT modified placement test based on ACC-QAS, or a minimum score of 100 on the Tacoma Directed Self Placement Math Test.

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**TMATH 110 Introductory Statistics with Applications (5) NW, QSR**

Addresses introductory statistical concepts and analysis in modern society. Includes descriptive statistics, graphical displays of data, the normal distribution, data collection, probability, elements of statistical inference, hypothesis testing, and linear regression and correlation. Practical examples used to demonstrate statistical concepts. Prerequisite: a minimum grade of 2.0 in either TMATH 098, MATH 098, TMATH 109, TMATH 124, or MATH 124, a minimum score of 237 on the UWT modified placement exam based on the ACC-AAF exam, or a minimum score of 200 on the Tacoma Directed Self Placement Math Test.

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**TMATH 115 Pre-calculus I: Functions (5) QSR**

Introduces the concept of a function, its notation, and prepares student to work with piece-wise, exponential, logarithmic, polynomial, and rational functions. Emphasizes computational skills, graph reading, and problem solving. One of a two-part series. Maximum of 10 credits from TMATH 115, TMATH 116, and TMATH 120 may be counted. Prerequisite: a minimum grade of 2.0 in either TMATH 098, MATH 098, or TMATH 109, a minimum score of 237 on the UWT modified placement test based on ACC-AAF, or a minimum score of 300 on the Tacoma Directed Self Placement Math Test.

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**TMATH 116 Pre-calculus II: Trigonometry (5) NW, QSR**

Continues studying the concept of a function, its notation, and trigonometric and inverse trigonometric functions. Introduces parametrized curves, polar coordinates, and complex numbers. Emphasizes computational skills, graph reading, and problem solving techniques. Second of a two-part series. Maximum of 10 credits from TMATH 115, TMATH 116, and TMATH 120 may be counted. Prerequisite: a minimum grade of 2.0 in TMATH 115, a minimum score of 263 on the ACC-AAF placement test, or a minimum score of 400 on the Tacoma Directed Self Placement Math Test.

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**TMATH 120 Precalculus (5) NW, QSR**

Accelerated review course covering the contents of TMATH 115 and TMATH 116 in one term. Examines functions and function notation including polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric functions. Recommended co-requisite: TMATH 158. Prerequisite: a minimum grade of 2.0 in TMATH 098, a score of 42-120 on the ACC-CL placement test, a minimum score of 263 on the ACC-AAF placement test, or a minimum score of 400 Tacoma Directed Self Placement Math Test.

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**TMATH 124 Calculus with Analytic Geometry I (5) NW, QSR**

First quarter in calculus of functions of a single variable. Emphasizes differential calculus. Emphasizes applications and problem solving using the tools of calculus. Cannot be taken for credit if credit earned in TMATH 122. Prerequisite: a minimum grade of 2.0 in either TMATH 116 or TMATH 120, minimum score of 68 on the MPT-A, minimum score of 75 on the MATHEC test, minimum score of 2 on the AP MATH test (AB or BC), minimum score of 276 on the ACC-AAF test, or a minimum score of 500 on the Tacoma Directed Self Placement Math Test; recommended: Recommended co-requisite: TMATH 159.

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**TMATH 125 Calculus with Analytic Geometry II (5) NW**

Second quarter in the calculus of functions of a single variable. Emphasizes integral calculus. Emphasizes applications and problem solving using the tools of calculus. Prerequisite: either a minimum grade of 2.0 in TMATH 124, or a minimum score of 3 on the AP MATH test (AB or BC).

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**TMATH 126 Calculus with Analytic Geometry III (5) NW**

Third quarter in calculus sequence. Sequences, series, Taylor expansions, and an introduction to multivariable differential calculus. Prerequisite: either a minimum grade of 2.0 in TMATH 125 or a score of 4 on AP MATH BC exam.

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**TMATH 158 Pre-Calculus Collaborative Learning Seminar (1, max. 2)**

Enhances problem-solving skills for pre-calculus by having students work with a facilitator to strengthen their skills in critical thinking via group problem sessions in pre-calculus and its applications. Prerequisite: TMATH 120, which must be taken concurrently Credit/no-credit only.

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**TMATH 159 Calculus Collaborative Learning Seminar (1, max. 3)**

Enhances problem-solving skills for calculus by having students work with a facilitator to strengthen their skills in critical thinking via group problem sessions in calculus and its applications. Prerequisite: TMATH 124 which must be taken concurrently. Credit/no-credit only.

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**TMATH 171 Mathematics for Teachers I: Number Systems and Algebraic Concepts (5) QSR**

Aimed at students planning to be elementary/middle school teachers, but any student interested in exploring essential mathematical concepts, skills, and representations in a humanized way may benefit. Topics include number, algebraic relationships, algorithms and why they work. We will also explore mathematical connections to our identities as math learners.

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**TMATH 172 Mathematics for Teachers II: Statistics and Modeling (5) QSR**

Aimed at students planning to be elementary/middle school teachers, but any student interested in exploring essential mathematical concepts, skills, and representations in a humanized way may benefit. Topics include statistics, probability, and mathematical modeling. We will also explore mathematical connections to our identities as math learners.

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**TMATH 173 Mathematics for Teachers III: Geometry and Measurement (5) QSR**

Aimed at students planning to be elementary/middle school teachers, but any student interested in exploring essential mathematical concepts, skills, and representations in a humanized way may benefit. Topics include geometry, measurement, and the mathematics of art. We will also explore mathematical connections to our identities as math learners.

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**TMATH 210 Intermediate Statistics with Applications (5) NW, QSR**

Investigates intermediate concepts of statistical inference and testing using statistical software for analysis. Includes sampling and experimental design, t-tests, discrete distributions, proportions, ANOVA, regression, transformations, and chi-squared tests. Analyzes datasets from a variety of disciplines such as environmental and social science. Includes critical review of contemporary studies. Prerequisite: a minimum grade of 2.0 in TMATH 110 or STAT 220. Offered: WSp.

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**TMATH 300 Foundations of Mathematical Reasoning (5) NW, QSR**

Develops skills in making mathematical arguments and writing of proofs by studying elementary set theory; functions; logical statements and quantifiers; the principle of induction; cardinality; and properties of number systems - integers, rational, real, and complex. Investigates proofs in both discrete and continuous mathematics. Prerequisite: minimum grade of 2.0 in either TMATH 125 or TCSS 321.

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**TMATH 307 Introduction to Differential Equations (5) NW, QSR**

Explores ordinary differential equations including first- and second-order equations, Laplace transform, and systems of first-order equations. Prerequisite: minimum grade of 2.0 in either TMATH 125 or MATH 125.

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**TMATH 308 Matrix Algebra with Applications (5) NW, QSR**

Introduces linear algebra, including systems of linear equations; Gaussian elimination; matrices and matrix algebra; vectors; vector spaces; subspace 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 either TMATH 125 or TCSS 321.

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**TMATH 316 Financial Mathematics (5) QSR**

Introduces students to fundamental concepts in financial mathematics: compound and simple interest, nominal and effective rates, present and future value, discount rates, force of interest. Covers annuities with both constant and variable cash flows, loans, amortization, loan refinancing, and bonds. Studies may also include term structure of interest rates, spot rates, arbitrage, duration, convexity, and immunization. Prerequisite: minimum grade of 2.0 in TMATH 126 Offered: W.

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**TMATH 324 Multivariable Calculus (5) NW, QSR**

Introduces 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 TMATH 126.

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**TMATH 342 Applied Topology (5) QSR**

Engages with varied topics which will be chosen from differential topology, knot theory, or algebraic topology. Applications (such as chemistry, physics or engineering) will be emphasized throughout the course. Prerequisite: minimum grade of 2.0 in TMATH 324.

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**TMATH 344 Fundamentals of Geometry (5) NW, QSR**

Covers fundamentals of geometry. Presents an axiomatic treatment of geometry, including Euclidean and non-Euclidean geometry. Describes the role of Euclid's Fifth Postulate in development of non-Euclidean geometries. Develops student's ability to write rigorous proofs. Prerequisite: minimum grade of 2.0 in either TMATH 126 or TMATH 300.

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**TMATH 350 Foundations of Mathematical Research (3) QSR**

Introduces students to diverse mathematical topics through invited speakers and selected readings. Develops mathematical ways of thinking, investigating, reading, and writing. Explores future employment and graduate school options and opportunities. Co-requisite: TMATH 351. Prerequisite: either TMATH 300, TMATH 307, or TMATH 308, any of which may be taken concurrently.

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**TMATH 351 Mathematics Seminar (1, max. 2)**

Introduces students to mathematics and its applications, career paths for mathematics majors, and develops problem-solving skills. Prerequisite: TMATH 124.

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**TMATH 390 Probability and Statistics in Engineering and Science (5) NW, QSR**

Investigates probability and statistics using exploratory data analysis and interactive computing. Study topics including conditional probability, independence, random variables, distribution functions, descriptive statistics, transformations, sampling errors, confidence intervals, least squares, and maximum likelihood. Prerequisite: a minimum grade of 2.0 in either TMATH 126 or MATH 126.

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**TMATH 402 Introduction to Abstract Algebra I (5) NW**

Focuses on group theory with a brief introduction to rings and fields. Emphasizes proofs. Topics include cosets; Lagrange's theorem; homomorphisms; normal subgroups; quotient groups; the isomorphism theorems; cyclic and symmetric groups; Cauchy's theorem; automorphisms; and elementary properties of rings and fields. Prerequisite: minimum grade of 2.0 in TMATH 300.

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**TMATH 403 Abstract Algebra II (5) NW, QSR**

Continues studying the theory of rings and fields, including ideals; homomorphisms; quotient rings; integral domains and fields of fractions; polynomial rings; vector spaces; field extensions; 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 TMATH 402.

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**TMATH 410 Regression Modeling with Applications (5) QSR**

Investigates regression models with applications; including multiple linear regression, model selection, residual analysis, variable transformations and categorical data. Studies may also include generalized linear models, nonlinear regression, matrix formulation, and mixed models. Prerequisite: either a minimum grade of 2.0 in TMATH 210 and TMATH 124, or a minimum grade of 2.0 in TMATH 390.

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**TMATH 412 Cryptography: Theory and Practice (5) QSR**

Covers "classical" cryptosystems and their cryptoanalysis, Shannon's approach to cryptography including entropy and perfect secrecy, block ciphers and AES. Contains RSA cryptosystem, public key cryptography based on discrete logarithms, and signature schemes. Breaks simple ciphers using a computer. Prerequisite: a minimum grade of 2.0 in either TCSS 321, TMATH 300, or TMATH 308.

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**TMATH 413 Coding Theory (5) QSR**

Deals with electronic communication over noisy channels where some bits of information may get corrupted. Covers using codes in designing ciphers secure in the era of quantum computers. Topics include error-detection/correction, various types of codes, and McEliece cipher. Prerequisite: minimum grade of 2.0 in either TMATH 308 or TCSS 321.

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**TMATH 420 History of Mathematics (5) I&S, QSR**

Surveys the history and development of mathematics from its earliest beginnings into the early twentieth century. Focuses on the effect math discovery and literacy has had on human, social, and cultural behaviors. Prerequisite: minimum grade of 2.0 in either TMATH 126, TMATH 300, TMATH 307, or TMATH 308.

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**TMATH 424 Introduction to Real Analysis I (5) NW, QSR**

Introduces set theory; the construction of the real numbers; infima and suprema; metric spaces and Euclidean distance; topology of the reals numbers; formal treatment of limits; Cauchy sequences; continuity; uniform convergence; and the derivative. Prerequisite: minimum grade of 2.0 in TMATH 300.

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**TMATH 425 Introduction to Real Analysis II (5) QSR**

Provides rigorous treatment of the derivative of a function of one variable; Contraction Mapping Theorem; Riemann integral, Fundamental Theorem of Calculus, Cauchy existence criterion; sequences of functions, pointwise and uniform convergence; power series; differentiation of functions on Euclidean spaces, total derivative; and Implicit Function Theorem. Prerequisite: minimum grade of 2.0 in TMATH 424.

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**TMATH 427 Complex Analysis (5) QSR**

Introduces concept of Complex numbers; Power series and Complex functions; Mobius transformations; Riemann sphere; Cauchy-Riemann equations; Complex differentiation and integration; Residue theorem; Cauchy integral formula; Conformal mapping. Prerequisite: Minimum grade of 2.0 in TMATH 300 or TMATH 324.

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**TMATH 450 Mathematics Capstone (4) QSR**

Synthesizes mathematics studies and presentations skills in an individual or group project researching new topics or continuing beyond coursework. Includes research presentations of capstone experiences. Co-requisite: TMATH 351.

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**TMATH 490 Special Topics in Quantitative Studies (1-7, max. 21) NW, QSR**

Advanced course offerings in quantitative studies designed to respond to faculty and student interests and needs.

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**TMATH 495 Collaborative Mathematics Research Experience (3) QSR**

Provides opportunities to complete collaborative mathematics or statistics projects within a structured course.

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**TMATH 496 Mathematics Internship (1-5, max. 10)**

Provides opportunity for a mathematical internship in the public or private sector with the supervision of a faculty member in mathematics or a related discipline. Prerequisite: minimum grade of 2.0 in each of TMATH 300, TMATH 307, TMATH 308, and TMATH 324. Credit/no-credit only.

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**TMATH 498 Directed Readings in Mathematics (1-5, max. 10)**

Allows students to engage in an in-depth study of any area of mathematics or related area under faculty supervision.

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**TMATH 499 Undergraduate Research in Mathematics (1-5, max. 10) QSR**

Engages students in original research in mathematics or related area under faculty supervision.

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