# Mathematics (MATH)

### Courses

**MATH 0900. Transitional Math I. 3 Hours.**

Designed for students with an ACT Math score of 0-12 or CPT of 0-30. For students needing to learn or review basic mathematics skills. Covers operations on whole numbers, fractions, decimals, percent with applications, ratios and proportions, signed numbers, linear equations with applications, positive integral exponents, geometry, and polynomials. Graphing and polynomial factoring will be introduced. Successful completers (Grade C or higher) will be prepared to enroll in MATH 1000. Course fee required. FA, SP.

**MATH 0920. Basic Math/Pre-Algebra. 4 Hours.**

Designed for students with an ACT Math score of 12 or lower or for students needing to learn or review basic mathematics skills. Covers operations on whole numbers, fractions, decimals, percents with applications, ratios and proportions, signed numbers, linear equations with applications, positive integral exponents, geometry, and polynominals. Graphing and polynomial factoring will be introduced. Successful completers (Grade C or higher) will be prepared to enroll in MATH 0990. This course is offered in two delivery formats--lecture and individualized. Course fee required on individualized format MATH 0920 class. FA, SP, SU.

**MATH 0990. Elementary Algebra. 4 Hours.**

Designed for students with a Math placement score 13-17, or for students needing to learn or review elementary algebra. Covers operations on integers, fractions, integral exponents, polynomials with factoring, linear and quadratic equations with applications, rational expressions, linear systems, graphing, and radicals. Successful completers (Grade C or higher) will be prepared to enroll in Math 1010. Prerequisite: Math placement score 13 or higher, OR MATH 0920 (Grade C or higher). FA, SP, SU.

**MATH 1000. Transitional Mathematics II. 3 Hours.**

Prepares students for courses that fulfill the General Education Math requirement. Concepts emphasized in this course include the properties of the real number system, sets, functions, graphs, algebraic manipulations, linear and quadratic equations, systems of equations, and story problems. Students will be expected to reason mathematically and solve mathematical problems. Successful completion of the course gives students good preparation for college-level math courses. Successful completers satisfy prerequisite for MATH 1030, MATH 1040, MATH 1050, and Mathematics prerequisite for BIOL 2030, CHEM 1110, PHYS 1010, and STAT 2040. Course fee required. Prerequisites: MATH 0900 (Grade C or higher) within two years of enrollment in this course; OR ACT or equivalent placement score 13 or higher within two years of enrollment in this course; OR Accuplacer score of 31 or higher within two years of enrollment in this course. FA, SP, SU.

**MATH 1001. FYE: Mathematics. 1 Hour.**

A First Year Experience course created to help students succeed in the Math major, and assist new freshmen and returning students to make a successful transition to being a college student. The primary objective of this course is to provide students with the resources they will need to succeed in their college careers, particularly in the Math major. Multiple listed with all other sections of First Year Experience (all 1001 courses, ENGR 1000). Students may only take one FYE course for credit. FA.

**MATH 1010. Intermediate Algebra. 4 Hours.**

Prepares students for courses that fulfill the General Education Math requirement. Concepts emphasized include the properties of the real number system, sets, functions, graphs, algebraic manipulations, linear and quadratic equations, systems of equations, and story problems. Students will be expected to reason mathematically and solve mathematical problems. Successful completion of the course gives students good preparation for college-level Math courses. Successful completers satisfy prerequisite for MATH 1030, MATH 1040, MATH 1050, MATH 1080, and Mathematics prerequisite for CHEM 1110, IT 3050, PHYS 1010, SOC 3112, and STAT 2040. Prerequisite: MATH 0900 or MATH 0990 (Grade C or higher within two years of enrollment in this course), OR ACT placement score 18 or higher or equivalent, within two years of enrollment in this course.

**MATH 1030. Quantitative Reasoning. 3 Hours.**

Fulfills General Education Mathematics requirement for students in Fine Arts, Liberal Arts and other degrees. Focuses on development of analytical problem solving skills through the application of various mathematical concepts to real-life problems. Topics of study include: modeling with algebra; geometry; logic; financial math; right triangle trigonometry (indirect measurement); probability and statistics. Students are cautioned to check degree and/or transfer requirements before taking this course. Course fee required. Prerequisite: MATH 1010 or MATH 1000 (Grade C or higher) within two years of enrollment in this course; OR ACT or equivalent placement score 23 or higher within two years of enrollment in this course. FA, SP.

**MATH 1040. Introduction to Statistics. 3 Hours.**

Fulfills General Education Mathematics requirement for students majoring in Communications, Social & Behavioral Sciences, Fine Arts, or Liberal Arts. Introduction to basic concepts and methods used in statistical data analysis, includes descriptive statistics, sampling, and inferential methods while emphasizing problem solving and critical thinking. StatCrunch is used to perform statistical calculations, organize and analyze data, and construct graphs. Required for Utah Level 2 Math Endorsement. Students are cautioned to check degree and/or transfer requirements before taking this course. Course fee required. Prerequisite: MATH 1010 or MATH 1000 (Grade C or higher) within two years of enrollment in this course; OR ACT or equivalent placement score 23 or higher, or CPT placement score of 89 or higher within two years of enrollment in this course. FA, SP, SU.

**MATH 1050. College Algebra / Pre-Calculus. 4 Hours.**

Fulfills General Education Mathematics requirement for students majoring in Business, Elementary Education, Health Sciences, Science, and other majors. Reviews fundamental algebra; explores polynomial and rational functions; introduces exponential and logarithmic functions and applications; trigonometric functions dealing with graphs, identities, and equations, including inverse functions. Course fee required. Prerequisite: MATH 1010 or MATH 1000 (Grade C or higher) within two years of enrollment in this course; OR ACT or equivalent placement score 23 or higher, or Accuplacer score of 89 or higher within two years of enrollment in this course. FA, SP, SU.

**MATH 1060. Trigonometry. 3 Hours.**

Fulfills General Education Mathematics requirement. Continuation of MATH 1050, utilizes unit circle and right triangle definitions, graphs of trigonometric functions, solving trigonometric equations, and verifying trigonometric identities. Involves polar and parametric functions, vectors, and conic sections. Required for Utah Level 2 and Level 3 Math Endorsements. Course fee required. Prerequisite: MATH 1050 (Grade C or higher) within two years of enrollment in this course; OR ACT or equivalent placement score 25 or higher; OR Accuplacer score of 95 or higher within two years of enrollment in this course. FA, SP, SU.

**MATH 1080. Pre-Calculus with Trigonometry. 5 Hours.**

Fulfills General Education Mathematics requirement. Provides in-depth review of college algebra and trigonometry before entering trig-based calculus by reviewing concepts taught in MATH 1050 and MATH 1060. Successful completion fulfills prerequisite for MATH 1210, and Mathematics prerequisite for PHYS 2010. Prerequisite: MATH 1010 or MATH 1000 (Grade B or higher) within two years of enrollment in this course; OR ACT or equivalent placement score 25 or higher; OR Accuplacer score of 95 or higher within two years of enrollment in this course. FA, SP.

**MATH 1100. Business Calculus. 3 Hours.**

Fulfills General Education Mathematics requirement. Required of majors in the Udvar-Hazy School of Business, as well as students majoring in Computer & Information Technology. Emphasizes functions, modeling, differentiation, applications of differentiation, exponential and logarithmic functions, integration, applications of integration, and functions of several variables. Course fee required. Prerequisite: MATH 1050 (Grade C or higher) within two years of enrollment in this course; OR ACT or equivalent placement score 25 or higher; OR Accuplacer score of 95 or higher within two years of enrollment in this course. FA, SP, SU.

**MATH 1210. Calculus I. 4 Hours.**

Fulfills General Education Mathematics requirement. Students will gain a basic understanding of calculus, the mathematics of motion and change, including limits and continuity, differentiation, applications of differentiation, integration, applications of integration, derivatives of exponential functions, logarithmic functions, inverse trigonometric functions, hyperbolic functions, and related integrals. Students must have a working knowledge of college algebra and trigonometry. Required for Utah Level 2, 3, and 4 Math Endorsements, and for students majoring in Computer Science. Successful completion fulfills prerequisite for MATH 1220, and Mathematics prerequisite for ENGR 2010 and PHYS 2210. Prerequisite: MATH 1050 AND MATH 1060 (Grade C or higher); OR MATH 1080 (Grade C or higher); OR ACT or equivalent placement score 26 or higher; OR CPT placement score of 105 or higher within two years of enrollment of this course. FA, SP, SU.

**MATH 1220. Calculus II. 4 Hours.**

Fulfills General Education Mathematics requirement. Continuation of MATH 1210, covering length, area of a surface of revolution, moments and centers of mass, integration techniques, sequences and series, parameterization of curves and polar coordinates, vectors in 3-space, quadric surfaces, and cylindrical and spherical coordinates. Required for Utah Level 3 and 4 Math Endorsements. Successful completion fulfills prerequisite for MATH 2210, and Mathematics prerequisite for ENGR 2250, ENGR 2300, and PHYS 2210. Prerequisite: MATH 1210 (Grade C or higher). FA, SP, SU.

**MATH 2010. Math for Elementary Teachers I. 3 Hours.**

The first course in a 2-semester sequence of mathematics appropriate to the needs of elementary and middle school teachers. Includes problem solving, sets, numeration systems, whole numbers, algorithms of arithmetic, number theory, rational numbers and decimal numbers. Required for Utah Elementary Education (Level 1) and Level 2 Math Endorsements. Prerequisite: MATH 1050 (Grade C or higher). FA, SP.

**MATH 2020. Math for Elemen Teachers II. 3 Hours.**

The second course in a 2-semester sequence of mathematics appropriate to the needs of elementary and middle school teachers. Continuation of Math 2010. Includes real numbers, statistics, probability, geometry, measurement, and algebra. Required for Utah Elementary Education (Level 1) and Level 2 Math Endorsements. Prerequisite: MATH 2010 (Grade C or higher). FA, SP.

**MATH 2200. Discrete Mathematics. 3 Hours.**

Introduction to proofs and writing Mathematics. Covers Logic (including Boolean), Sets, Functions, Equivalence Relations, Modular Arithmetic, and Graph Theory. Also covers prepositional calculus, combinatorics, and Counting Methods. Prerequisite: MATH 1210 (Grade C or higher). FA, SP.

**MATH 2210. Multivariable Calculus. 4 Hours.**

Fulfills General Education Mathematics requirement. Continuation of MATH 1220. Includes partial derivatives, gradient vectors, Lagrange multipliers, multiple integrals, line integrals, Green's Theorem, surface integrals, the Divergence Theorem, Stokes' Theorem. Required for Utah Level 3 and Level 4 Endorsement. Prerequisite: MATH 1220 (Grade C or higher). FA, SP.

**MATH 2270. Linear Algebra. 3 Hours.**

For Mathematics and pre-Engineering majors. Covers matrix and vector analysis and systems of equations with applications, linear dependence and independence, matrix algebra and invertibility, determinants and their applications, Cramer's Rule, diagonalization, eigenvalues and eigenvectors, linear transformations (kernel and range), inner product, orthogonality, vector spaces and subspaces, including null and column and bases as well as introducing basic proof theory. Required for Utah Level 3 and 4 Math Endorsements. Prerequisite: MATH 1210 (Grade C or higher). FA, SP.

**MATH 2280. Ordinary Differential Equation. 3 Hours.**

For Mathematics and pre-Engineering majors. Covers methods of solving ordinary differential equations with applications: separation of variables, homogeneous and non-homogeneous, exact, first and higher order, integrating factors, substitution methods, linear and non-linear, complex characteristic roots, variation of parameters, undetermined coefficients (superposition and annihilator approach), and Euler-Cauchy. Systems of equations, power series solutions, and the Laplace transform will be introduced. Required for Utah Level 4 Math Endorsement. Prerequisite: MATH 1220 (Grade C or higher). SP.

**MATH 2989. TI-89 Calculator Skills. 1 Hour.**

Designed to aid students in using the TI-89 (or similar) calculator through a study guide, demonstrations, and hands-on experience. Covered features include basic computation, matrices, graphing, and calculus applications. Each student must own or have access to a TI-89, TI-92, or TI Voyage 200 calculator. FA, SP.

**MATH 2990. Seminars in Math. 0.5-3 Hours.**

For students wishing instruction that is not available through other regularly scheduled courses in this discipline. Occasionally, either student demand for some type of non-traditional instruction, or an unanticipated opportunity for instruction presents itself. The seminar courses provides a variable credit context for these purposes. This seminar course must first be pre-approved by the department chair; second, it must provide at least nine contact hours of lab or lecture for each credit hour offered; and third, it must include some academic project or paper (i.e., credit is not given for attendance alone). This course may include standard lectures, travel and field trips, guest speakers, laboratory exercises, or other non-traditional instruction methods. Note that this course is an elective and does not fulfill general education or program requirements. Prerequisite: Instructor permission.

**MATH 3000. History of Mathematics. 3 Hours.**

Selected topics in mathematics developed from ancient to modern times and the study of biographies of prominent mathematicians. Required for Utah Level 4 Math Endorsement. Prerequisite: MATH 1220 (Grade C or higher). FA (odd).

**MATH 3100. Euclidean / Non-Euclidean Geom. 3 Hours.**

Includes axiomatic development of Euclidean and non-Euclidean geometry. Computer-based GeoGebra program is used. Required for Utah Level 3 and 4 Math Endorsements. Prerequisite: MATH 2200 (Grade C or higher). SP (odd).

**MATH 3150. Introduction to Partial Differential Equations. 3 Hours.**

First-Order Partial Differential Equations (PDEs), Second-Order PDEs, Fourier Series, The Heat Equation, The Wave Equation, Laplace's Equation, The Fourier Transform Methods for PDEs. Prerequisite: MATH 2210 and MATH 2270 and MATH 2280 (all Grade C or higher). FA (odd).

**MATH 3200. Introduction to Analysis I. 3 Hours.**

For students interested in advanced Mathematics. Introduces the construction of rigorous proofs of mathematical claims in beginning analysis. Required for Utah Level 4 Math Endorsement. Prerequisite: MATH 2200 (Grade C or higher); AND MATH 2210 (Grade C or higher). FA (odd years).

**MATH 3210. Introduction to Analysis II. 3 Hours.**

Continuation of MATH 3200. Includes continuity, differentiation, chain rule, Riemann integration, Fubini's theorem, and change of variable formula. Prerequisite: MATH 3200. SP (even).

**MATH 3400. Probability & Statistics. 3 Hours.**

Mathematics- based statistics. Topics include: Concepts in probability, discrete, continuous and bivariate distributions, distributions of functions of random variables, point and interval estimation, tests of hypothesis, and regression. Calculators with statistical functions is required. Required for Utah Level 3 and 4 Math Endorsement. Prerequisite: MATH 1220 (Grade C or higher). SP (odd).

**MATH 3500. Numerical Analysis. 3 Hours.**

Includes numerical solutions of nonlinear equations, interpolation and approximation, numerical integration and differentiation, and solutions of linear systems, numerical solutions of ordinary and partial differential equations, using Maple software to implement various algorithms numerically. Prerequisites: MATH 2270 AND MATH 2280. FA (even).

**MATH 3900. Number Theory. 3 Hours.**

Overview of number theory and its applications, including the integers, factorizations, modular arithmetic, congruencies, Fermat's and Euler's Theorems, diophantine equations, cryptography, and RSA algorithm. Required for Utah Level 4 Math Endorsement. Prerequisite: MATH 2200. SP (even).

**MATH 4000. Foundations of Algebra. 3 Hours.**

For students in all Math-related majors. Covers an introduction to algebraic systems including group rings, fields and sets. Required for Utah Level 3 and 4 Math Endorsements. Prerequisite: MATH 2200. FA (even).

**MATH 4010. Abstract Algebra. 3 Hours.**

Continuation of MATH 4000. Topics include Sylow Theory for finite groups, Galois Theory, factorization in commutative rings. Prerequisite: MATH 4000. SP (odd).

**MATH 4100. Introduction to Topology. 3 Hours.**

Overview of elementary point-set topology. Includes topological spaces, compactness, connectedness, metric spaces, and Hausdorff spaces. Prerequisites: MATH 2200 AND MATH 2210. FA (odd).

**MATH 4200. Introduction to Complex Analysis. 3 Hours.**

Overview of basic theory and applications of complex variables, including analytic functions, contour integration, and conformal mappings. Prerequisite: MATH 3200. SP (even).

**MATH 4500. Methods Teach Secondary Math. 3 Hours.**

Designed for pre-service secondary math teachers or those seeking Utah Level 2, 3, 4 Mathematics Endorsement. Course content includes use of curriculum and research in the 7- 12 grade classroom, development of math pedagogical skills, accommodations for diverse learners, factors of motivation, and professional growth. Technology will include graphing calculators, classroom on-line learning systems, and mathematical instructional software. Required for Utah Level 2, 3, and 4 Math Endorsements. Prerequisite: MATH 1210 (Grade C or higher). FA.

**MATH 4890R. Independent Research. 1-3 Hours.**

Designed to meet the individual needs of advanced students in the Math Department who wish to perform an independent research to answer a specific mathematical question. This course is offered by arrangement with an individual faculty, based on preparation and interest, and allows close interaction between the student and faculty member to address specific mathematical problems. Projects are at the discretion of the faculty member, in line with the student's interests in the various mathematics subject areas. The student and faculty will set expectations and grading policies at the beginning of the term. Students are expected to meet with the faculty mentor each week and to provide the faculty mentor with progress reports and assignment development for feedback. Prerequisite: Instructor permission required. FA, SP, SU.

**MATH 4900. Senior Capstone Seminar. 3 Hours.**

Independent Study. Required of all Mathematics majors in the senior year. Emphasizes the ability to analyze and communicate mathematically through projects to include researching topics, summarizing journal articles, using a technical documentation system such as LaTeX or Equation Editor, and making oral class presentations. Preparation for and completion of standardized exit exam is required. Prerequisite: Senior standing; and Mathematics major. SP.