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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: either elementary algebra, a score of 70-120 on the ACC-AL placement test, or a score of 0-34 on the ACC-CL placement test.

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**TMATH 107 Mathematics: A Practical Art (5) NW, QSR**

Focuses on the important ideas of mathematics and mathematical methods of investigation with application to real life problems. Covers selected topics in arithmetic, geometry, probability and statistics. For students who have at least 1.5 years of high school algebra and do not plan to take additional mathematics. Prerequisite: either TMATH 098, score of 147-155 on MPT-GS placement test, or a score of 144 on the MPT-AS placement 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: either TMATH 098, TMATH 124, MATH 124, or a minimum score of 35 on ACC-CL placement 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: either a minimum grade of 2.0 in TMATH 098 or a score of 35-79 on the ACC-CL placement 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: minimum grade of 2.0 in TMATH 115.

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

Examines polynomial, rational, exponential, and trigonometric functions. Prerequisite: either minimum grade of 2.0 in TMATH 098 or score of 35-120 on the ACC-CL placement test; cannot be taken for credit if credit earned in TMATH 121; recommended: Recommended co-requisite: TMATH 158

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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. Prerequisite: minimum grade of 2.0 in either TMATH 116 or TMATH 120, score of 68% on MPT-A placement test, score of 75% on MATHEC placement test, or score of 2 on AP test. Cannot be taken for credit if credit earned in TMATH 122; 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 2.0 in TMATH 124, score 3 on AB advanced placement test, or score of 3 on BC advanced placement test.

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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: 2.0 in TMATH 125, score of 5 on AB advanced placement test, or score of 4 on BC advanced placement test.

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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 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: TMATH 110. Offered: WSp.

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**TMATH 214 Analytical Thinking (5) QSR**

Develops problem-solving skills, decision-making methods, and precise written formulation of ideas through elementary mathematics. Emphasizes logical thinking and precise formulation of statements rather than mathematical formulae and theorems. Analyzes real life problems and situations; examines optimal decisions/solutions. No specialized mathematical skills required.

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**TMATH 221 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 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 310 Statistics for Environmental Applications (5) NW, QSR**

Investigates concepts of statistical inference specific to the environmental sciences. Includes sampling design, t-tests, ANOVA, multiple comparisons, regression, transformations, principle component analysis, chi-squared tests, and non-parametric tests, using statistical software for analysis. Prerequisite: TMATH 110.

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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 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 Mathematics Research Seminar (2) NW, 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.

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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: minimum grade of 2.0 in TMATH 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 408 Numerical Methods (2) NW, QSR**

Covers basic numerical methods and techniques. Topics include: error analysis, Newton's method, interpolation, numerical integration, Runge-Kutta methods, iterative methods for solving linear systems, discrete least squares approximation.

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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: Minimum of 2.0 in TMATH 210 and TMATH 124, or minimum 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: minimum grade of 2.0 in either TCSS 321, TMATH 125, or TMATH 402.

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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 (2) NW, 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. Prerequisite: TMATH 350.

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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 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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