# Mathematics (MATH)

### Courses

**MATH-015 ARITHMETIC AND PRE-ALGEBRA 3.00 Credits**

Preparation for MATH 023 and MATH 025. Arithmetic with whole numbers, signed numbers, fractions, and decimals. Order of operations, variables, simplifying of algebraic expressions. Concrete representations of arithmetic operations and algebraic concepts are emphasized. Particularly appropriate for students who experience anxiety when learning mathematics. Course fee.

**MATH-023 BASIC ALGEBRA FOR MATH AS A LIBERAL ART 3.00 Credits**

Brief review of integer arithmetic, fraction arithmetic, percent and order of operations. Evaluating formulas. Units and unit analysis. Solving equations in one variable and using equations in one variable to solve application problems. Graphing linear equations, intercepts, slope, writing the equation of a line. Introduction to functions. Average rate of change, introduction to linear and exponential models. Simplifying exponential expressions, scientific notation, introduction to logarithms. Introduction to sets, counting methods, and discrete probability. Pre-requisite: A grade of C or better in Math-015 or satisfactory placement score. Course fee.

**MATH-025 BASIC ALGEBRA 3.00 Credits**

Brief review of prealgebra. Solving equations and inequalities in one variable; applications. Evaluating formulas; unit analysis. Graphing linear equations, intercepts, slope, writing the equation of a line, introduction to functions. Average rate of change and linear models. Graphing linear inequalities. Systems of linear equations; applications. Exponent rules and scientific notation. Addition, subtraction, multiplication, and factoring of polynomials in one variable. Using the zero product property to solve quadratic equations in one variable. Pre-requisite: A grade of 'C' or better in MATH-015 or satisfactory placement score.

**MATH-108 INTERMEDIATE ALGEBRA 4.00 Credits**

Function emphasis. Full integration of graphing technology and computer algebra system. Systems of linear equations and linear inequalities. Absolute value equations. Polynomials and polynomial functions. Exponential and logarithmic functions. Radical equations and functions. Quadratic equations and functions. Rational equations and functions. Pre-requisite: A Grade of 'C' or better in MATH-025 or satisfactory placement score. Course fee.

**MATH-123 MATHEMATICS AS A LIBERAL ART 3.00 Credits**

This course introduces students to the form and function of mathematics as it applies to liberal-arts studies with a heavy emphasis on its applications. Topics covered include ratios, rates and proportions; properties of linear equations; graphing linear equations; constructing and using linear models; exponential and logarithmic equations and models; financial applications; and elementary probability and statistics. Pre-requisite: MATH-023, MATH-025, MTHPT-103 or MTHPT-120 with a grade or 'C' or better, or permission of the instructor.

**MATH-130 FINITE MATHEMATICS 4.00 Credits**

Systems of linear equations and inequalities, elementary matrix algebra, introduction to linear programming, elementary discrete probability and statistics. Emphasis on applications to business, economics and social sciences. Pre-requisite: A grade of 'C' or better in MATH 025 or MTHPT 103 or satisfactory placement score. Cross-listed with MTHPT-130.

**MATH-147 PRECALCULUS 5.00 Credits**

The course emphasizes functions, circular trigonometry and multilevel problem solving as preparation for calculus. Functions are treated as mathematical entities, including domain, range, algebraic operations, composition, inverses, and graphing. Polynomial, logarithmic, exponential, trigonometric, inverse trigonometric, radical and rational functions are explored. Algebraic techniques include division of polynomials, roots of polynomials, theory of equations and inequalities, complex numbers and DeMoivre's Theorem, the Fundamental Theorem of Algebra and solving systems of linear and nonlinear equations. Trigonometric identities are derived, proven, and applied. Polar coordinates, vectors and oblique triangles are introduced and used in a variety of applications. Analytic geometry focuses on circles, parabolas, distance and midpoints. MATH-147 is equivalent to MATH-147A plus MATH-147B. Pre-requisite: A grade of 'C' or better in MATH-108 or satisfactory placement score.

**MATH-147A PRECALCULUS ALGEBRA 3.00 Credits**

Emphasis on the concept of real-valued functions as mathematical entities, including domain, range, algebraic operations, composition, inverses, and graphing. Topics include polynomial functions, division of polynomials, roots of polynomials, theory of equations, complex numbers, fundamental theorem of algebra, rational functions and asymptotes, logarithmic and exponential functions, and translation of axes. Students will engage in multi-step algebraic manipulation of complicated functional expressions. Pre-requisite: A Grade of 'C' or better in MATH-108 or satisfactory placement score.

**MATH-147B PRECALCULUS TRIGONOMETRY 2.00 Credits**

This course introduces right-triangle and circular function approaches to trigonometry. Topics include plane trigonometry, trigonometric identities, graphs of trigonometric functions, amplitude, frequency, phase shift, inverse trigonometric functions and their graphs, polar coordinates, and polar representation of complex numbers. Pre-requisite: MATH-147A.

**MATH-153 STATISTICAL REASONING 3.00 Credits**

This course introduces students to problem solving and decision making using single and multivariable statistical models. The course focuses on conceptual understanding of randomness, variability, statistical models, and inference through exploration of data. The use of technology for analysis of data is integrated throughout. Topics include descriptive statistics, probability, hypothesis testing, confidence intervals, likelihood ratios, correlation, and regression. Pre-requisite: A grade of 'C' or better in MATH-023, MATH-025, or appropriate math placement score. Cross-listed with MTHPT-153.

**MATH-153P SUPPLEMENTAL INSTRUCTION FOR MATH 153 1.00 Credit**

This course provides just-in-time preparation of the mathematical skills necessary to be successful in MATH-153 with an emphasis on problem-solving and college-readiness skills. Topics may include order of operations, fraction and decimal arithmetic, percent, scientific notation, interval notation, lines, calculator use, and use of statistical software. Pre-requisite: This course must be taken concurrently with MATH-153. MATH-015 with a grade of C or better, or satisfactory placement score.

**MATH-157 FOUNDATIONS OF ELEMENTARY MATHEMATICS 3.00 Credits**

This course provides an overview of some of the mathematics taught in grades K-8 with an emphasis on conceptual understanding and communication of mathematical principles. This is the first course in a two-course sequence of mathematics content courses which is not intended to be a methods of teaching course. Topics may include numbers and the base-ten system; fractions and problem-solving; addition, subtraction, multiplication, and division of real numbers; ratio and proportional relationships; and number theory. Pre-requisite: A grade of 'C' or better in MATH-108 or MTHPT-137 or satisfactory placement score, or placement into MATH-157P to be taken concurrently with MATH-157.

**MATH-157P SUPPLEMENTAL INSTRUCTION FOR MATH 157 1.00 Credit**

This course provides just-in-time preparation of the mathematical skills necessary to be successful in MATH-157 and MATH-257 with an emphasis on problem-solving and college-readiness skills. Topics may include accuracy vs precision, order of operations, number theory, fraction and decimal arithmetic, percent, properties of real numbers, conversions and unit analysis, geometry and measurement, factoring, mental math, exponents and scientific notation, lines and graphing, probability, and statistics. This course must be taken concurrently with MATH-157. Prerequisite: MATH-023 or MATH-025 with a grade of C or better or satisfactory placement score.

**MATH-170 CALCULUS I 4.00 Credits**

Definitions of limit, derivative, antiderivative, definite integral. Computation of the derivative, including logarithmic, exponential, and trigonometric functions. Applications of the derivative, optimization, mean value theorem. The fundamental theorem of calculus, brief introduction to applications of the integral and to computation of antiderivatives. Intended for students in engineering, mathematics, and the sciences. Pre-requisites: A grade of "C" or better in MATH-147 or MATH-147A and MATH-147B or satisfactory placement score.

**MATH-175 CALCULUS II 4.00 Credits**

Applications of the integral, symbolic and numerical techniques of integration, inverse transcendental functions. Sequences and series, with an emphasis on power series and approximation. Pre-requisite: A grade of 'C' or better in MATH-170.

**MATH-186 DISCRETE MATHEMATICS 3.00 Credits**

Topics such as sets, functions, algorithms, logic, Boolean algebra are included. This course consists of numerous topics which are particularly valuable to students pursuing a computer science minor. Pre-requisite: A grade of 'C' or better in MATH-108 or satisfactory placement score.

**MATH-190 DIRECTED STUDY IN MATH 1.00-12.00 Credits**

**MATH-192 SPECIAL TOPICS IN MATHEMATICS 1.00-12.00 Credits**

**MATH-240 INTRODUCTION TO LINEAR ALGEBRA 2.00 Credits**

The introduction to linear algebra course covers systems of linear equations, Gaussian elimination, matrices vector spaces, linear independence, basis, dimension, determinants, eigenvalues, and eigenvectors. Pre-requisite: MATH-170.

**MATH-253 STATISTICAL METHODS FOR THE SCIENCES 3.00 Credits**

Introduction to statistical methods for scientists including design of statistical studies, basic sampling methods, descriptive statistics, probability and sampling distributions, inference regression, and analysis of variance. Pre-requisite: A grade of 'C' or better in MATH-108 or satisfactory placement score.

**MATH-257 FOUNDATION OF ELEMENTARY MATHEMATICS II 3.00 Credits**

This course is a continuation of MATH-157 and continues an overview of some of the mathematics taught in grades K-8 with an emphasis on conceptual understanding and communication of mathematical principles. This is the second course in a two-course sequence of mathematics content courses which is not intended to be a methods of teaching course. Topics may include algebra; geometry; measurement; area of shapes; circumference; the number pi; construction proofs of the Pythagorean theorem; solid shapes and their volumes and surface areas; geometry of motion and change; statistics; and probability. Pre-requisite: MATH-157 with a grade of C or better.

**MATH-275 CALCULUS III 4.00 Credits**

Vector algebra and geometry, functions of several variables, partial and directional derivatives, gradient, chain rule, optimization, multiple and iterated integrals. Parametric curves and surfaces in 3-space, vector fields, divergence and curl, line and surface integrals. Green's, Stoke's and divergence theorems. Pre-requisite: A grade of 'C' or better in MATH-175.

**MATH-285 EUCLIDEAN GEOMETRY 3.00 Credits**

This course is designed to prepare teachers of middle and high school geometry. The course emphasizes classic geometric proof and application of geometric theorems. Topics include parallel lines, triangles, quadrilaterals, circles, and polygons. Pre-requisite: A grade of 'C' or better in MATH-147A, MATH-157, or MATH-186, or satisfactory placement score.

**MATH-290 DIRECTED STUDY IN MATHEMATICS 1.00-3.00 Credits**

Pre-requisite: A grade of 'C' or better in MATH 170 or permission of the division.

**MATH-291 WORKSHOP IN MATHEMATICS 1.00-3.00 Credits**

**MATH-292 SPECIAL TOPICS IN MATHEMATICS 1.00-3.00 Credits**

**MATH-295 PRACTICUM IN MATHEMATICS 1.00-2.00 Credits**

Tutoring in the mathematics laboratory or functioning as a teacher's aide in a lower division mathematics course. Pre-requisite: Approval of the division chair. May be repeated for a total of 4 credits.

**MATH-299 RESEARCH ASSISTANTSHIP 1.00-12.00 Credits**

**MATH-300 INTRODUCTION TO MATHEMATICAL REASONING 3.00 Credits**

Introductory topics in mathematics- logic, set theory, properties of the real line- number theory, induction, mappings, rigorous treatment of limits of sequences. Emphasis is on the concept of theorem and proof. Pre-requisite: A Grade of "C" or better in MATH 175.

**MATH-313 NUMBER THEORY 3.00 Credits**

Modular arithmetic, Pythagorean triples, prime numbers, quadratic reciprocity, Diophantine approximation, elliptic curves, and public key encryption systems. Pre-requisite: MATH-175.

**MATH-320 PROBABILITY AND STATISTICS 3.00 Credits**

Sample spaces, random variables, central limit theorems, stochastic processes, estimation and testing of hypotheses. Pre-requisite: A grade of 'C' or better in MATH-175.

**MATH-340 LINEAR ALGEBRA 3.00 Credits**

Systems of linear equations, Gaussian elimination, matrices vector spaces, linear independence, basis, dimension, inner products, orthogonal projections, orthonormal bases. Determinants, eigenvalues and eigenvectors. Positive definite matrices. Pre-requisite: A grade of 'C' or better in MATH-175.

**MATH-345 ORDINARY DIFFERENTIAL EQUATIONS 3.00 Credits**

Separation of variables, variations of parameters- methods of characteristic roots, undetermined coefficients- systems of differential equations. Laplace transform, and power series. Pre-requisite: A Grade of "C" or better in MATH-175.

**MATH-386 POSTULATIONAL GEOMETRY 3.00 Credits**

This course is an introduction to axiomatic geometry with an emphasis on understanding high school geometry. Topics include postulates of Euclid and Hilbert, non-Euclidian geometry, and projective geometry. Pre-requisite: MATH-170 with a grade of C or better.

**MATH-390 DIRECTED STUDY IN MATHEMATICS 1.00-3.00 Credits**

**MATH-391 WORKSHOP IN MATHEMATICS 1.00-3.00 Credits**

**MATH-392 SPECIAL TOPICS IN MATHEMATICS 1.00-3.00 Credits**

**MATH-395 PRACTICUM IN MATHEMATICS 1.00-2.00 Credits**

**MATH-399 RESEARCH ASSISTANTSHIP 1.00-12.00 Credits**

**MATH-450 COMPLEX ANALYSIS 3.00 Credits**

Complex numbers and functions, complex derivatives and integrals, residue theory, conformal mappings and uniform convergence. Pre-requisite: A grade of 'C' or better in MATH-300.

**MATH-460 ABSTRACT ALGEBRA I 3.00 Credits**

This is the first course in a two-course sequence that provides an introduction to abstract algebra. Topics include groups, subgroups, permutation groups, isomorphisms, homomorphisms, quotient groups, and the fundamental theorem of finite abelian groups. Pre-requisite: MATH-300 with a grade of C or better.

**MATH-461 ABSTRACT ALGEBRA II 3.00 Credits**

This is the second course in a two-course sequence that provides an introduction to abstract algebra. Topics include rings, subrings, ideals, quotient rings, polynomial rings, vector spaces, fields, extension fields, and Galois theory. Pre-requisite: MATH-460 with a grade of C or better.

**MATH-470 GENERAL TOPOLOGY 3.00 Credits**

An introduction to the fundamental concepts of general topology including set theory, metrics, neighborhoods, bases, subspaces, mappings, continuity, separation axioms, compactness and connectedness. Pre-requisite: A grade of 'C' or better in MATH-300.

**MATH-480 REAL ANALYSIS I 3.00 Credits**

This course is the first course in a two-course sequence that provides a theory of the real line, properties of real numbers, and real-valued functions. Topics include convergence of sequences; open and closed sets; density of sets; Cauchy sequences; monotone convergence theorem; pointwise and uniform convergence of functions; continuity; mean value theorem; intermediate value theorem; compactness; and differentiability. Pre-requisite: MATH-300 with a grade of C or better.

**MATH-481 REAL ANALYSIS II 3.00 Credits**

This course is the second course in a two-course sequence on the theory of real-valued functions. Topics include sequences and series of functions, Weierstrass M-test, power series, Taylor series, Riemann integrability, metric spaces, convergence in metric spaces, and differentiability of functions with higher dimensional domains. Pre-requisite: MATH-480 with a grade of C or better.

**MATH-490 DIRECTED STUDY IN MATHEMATICS 1.00-3.00 Credits**

Pre-requisite: A grade of 'C' or better in MATH-170 or permission of the division.

**MATH-491 WORKSHOP IN MATHEMATICS 1.00-3.00 Credits**

**MATH-492 SPECIAL TOPICS IN MATHEMATICS 1.00-3.00 Credits**

**MATH-495 PRACTICUM IN MATHEMATICS 1.00-2.00 Credits**

Tutoring in the mathematics laboratory or functioning as a teacher's aide in a lower division mathematics course. Pre-requisite: Approval of the division chair. May be repeated for a total of 4 credits.

**MATH-499 RESEARCH PROJECT AND SEMINAR IN MATH 1.00-3.00 Credits**

Students will conduct and communicate the results of a research project in the Natural Sciences Division. Topics may include the historical, philosophical, cultural and environmental aspects, and the processes of natural science. Requirements of students include satisfactory oral presentation and defense of their research and submission of a written report approved by their advisor to the Natural Sciences Division. Prerequisite: NS-398.