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Course Descriptions

MATH 1080 QL MATH 1210 QL (MATH) I 5 5 MATH 100R * Prerequisite(s): Within the past two years, * Prerequisite(s): One of the following within Math Leap one of the following: MAT 1000 or MAT 1010 the past two years: (MATH 1050 or MATH 1 with a grade of B or better or an appropriate 1055) and MATH 1060, each with a grade of Is part of UVU’s math placement process; for math placement score. C or higher; OR MATH 1080 with a grade of C students who desire to review math topics Is an accelerated version of MATH 1050 or higher; OR appropriate placement by math in order to improve placement level before and MATH 1060. Includes functions and placement test. beginning a math course. Addresses unique their graphs including , rational, Covers limits, continuity, differentiation, strengths and weaknesses of students, by exponential, logarithmic, trigonometric, and applications of differentiation, integration, providing group problem solving activities along inverse . Covers and applications of integration, including with an individual assessment and study inequalities, systems of linear and and of polynomial plan for mastering target material. Requires nonlinear equations, matrices, determinants, functions, rational functions, exponential mandatory class attendance and a minimum and geometric sequences, the functions, logarithmic functions, trigonometric of hours per week logged into a Theorem, the unit circle, right functions, inverse trigonometric functions, and preparation , with progress monitored triangle , trigonometric equations, hyperbolic functions. Is a prerequisite for by a mentor. May be repeated for a maximum trigonometric identities, the Law of , the calculus-based sciences. of 4 credits toward graduation. May be graded , vectors, complex , credit/no credit. polar coordinates, and conic sections. MATH 121H QL Calculus I MATH 1050 QL MATH 1090 QL 5 College College Algebra for Business * Prerequisite(s): One of the following within 4 3 the past two years: (MATH 1050 or MATH * Prerequisite(s): Within the past two years * Prerequisite(s): Within the past two years 1055) and MATH 1060, each with a grade of one of the following: MAT 1000 or MAT 1010 one of the following: MAT 1000 or MAT 1010 C or higher; OR MATH 1080 with a grade of C with a grade of C or better or appropriate math with a grade of C or better or appropriate math or higher; OR appropriate placement by math placement score. placement score. placement test. Includes inequalities, functions and their Uses linear, quadratic, power, polynomial, Covers limits, continuity, differentiation, graphs, polynomial and rational functions, rational, exponential, logarithmic, and logistic applications of differentiation, integration, exponential and logarithmic functions, systems functions to analyze business applications and applications of integration, including of linear and nonlinear equations, matrices such as market equilibrium, rates of derivatives and integrals of polynomial and determinants, arithmetic and geometric change, cost-benefit , and inflation. functions, rational functions, exponential sequences, and the Binomial Theorem. May be Includes systems of linear and non-linear functions, logarithmic functions, trigonometric delivered hybrid and/or online. equations and inequalities, matrices and functions, inverse trigonometric functions, and matrix equations, sequences and , and hyperbolic functions. Is a prerequisite for MATH 1055 QL financial mathematics. Canvas Course Mats calculus-based sciences. Is an honors course College Algebra with Preliminaries $90/McGraw applies. with student projects. 5 * Prerequisite(s): Within the past two years MATH 1100 QL MATH 1220 one of the following: MAT 1000 or MAT 1010 Introduction to Calculus Calculus II with a grade of C or better or appropriate math 4 5 placement score. * Prerequisite(s): Within the past two years: * Prerequisite(s): MATH 1210 or MATH 121H Includes inequalities, functions and their MATH 1050 or MATH 1055 or MATH 1080 with a grade of C or higher graphs, polynomial and rational functions, with a grade of C or better or appropriate math Includes integration techniques, , exponential and logarithmic functions, systems placement score. area of a of revolution, moments of linear and nonlinear equations, matrices Provides an overview of the basic concepts and centers of mass, sequences and and determinants, arithmetic and geometric and techniques of differential and series, parametrization of and polar sequences, and the Binomial Theorem. May calculus. Features applications in business, coordinates, vectors in 3-space, and quadric be delivered hybrid and/or online. Lab access economics, and the life, social, and physical surfaces. fee of $30 applies. Canvas Course Mats $90/ sciences. Includes optimization techniques in McGraw applies. multivariable . MATH 122H Calculus II MATH 1060 5 Trigonometry * Prerequisite(s): MATH 1210 or MATH 121H 3 with a grade of C or higher * Prerequisite(s): Within the past two years: MATH 1050 or MATH 1055 with a grade of Includes integration techniques, arc length, C or higher or appropriate math placement area of a surface of revolution, moments score. and centers of mass, sequences and series, parametrization of curves and polar Includes the unit circle and right triangle coordinates, vectors in 3-space, and quadric definitions of the trigonometric functions, surfaces. Honors course which requires a graphing trigonometric functions, trigonometric student project. identities, trigonometric equations, inverse trigonometric functions, the Law of Sines and the Law of Cosines, vectors, complex numbers, polar coordinates, and rotation of axes.

Utah Valley University Course Catalog 2021-2022 1 Course Descriptions

MATH 2000 QL MATH 2250 MATH 3000 Algebraic Reasoning with Modeling Differential Equations and WE 3 4 3 * Prerequisite(s): Within the past two years, * Prerequisite(s): MATH 1220 or MATH 122H * Prerequisite(s): MATH 2210 or MATH 221H one of the following: MAT 1000 or MAT 1010 with a grade of C or higher with a grade of C or higher and University with a grade of C or better or an appropriate Is for engineering students. Includes separable Advanced Standing math placement score. equations, linear differential equations, Provides a survey of the history of mathematics Presents the basic ideas of sets and functions differential operators and annihilators, variation with a focus on the development of in the context of and motivated by modeling of parameters, Laplace transforms, and mathematical ideas in their historical context. bivariate . Includes basic theory such systems of linear differential equations. Includes numeration systems, the mathematics as unions, intersections, Venn diagrams, etc. Introduces basic concepts of linear algebra of the ancient world, the development of Includes the basic ideas and the algebra including matrices, Gaussian elimination, algebra, , and calculus, and the work of functions including polynomial, exponential, determinants, linear independence, and of pivotal mathematicians. and logarithmic functions. Also includes some eigenvalues and eigenvectors. basic and counting principles as MATH 3010 well as arithmetic and geometric sequences. MATH 2270 Methods of Secondary School Mathematics Culminates in a pictorial introduction to the Linear Algebra Teaching basic ideas of calculus presented with minimal 3 3 computation. * Prerequisite(s): MATH 1220 or MATH 122H * Prerequisite(s): MATH 2210 or MATH 221H with a grade of C or higher with a grade of C or higher and EDSC 455G MATH 2010 with a grade of B- or higher and University Includes matrices and systems of Advanced Standing Mathematics for Elementary Teachers I equations, determinants, vector spaces, linear 3 transformations, orthogonality, and eigenvalues Is for majors. Presents * Prerequisite(s): Within the past two years: and eigenvectors. different methods of teaching mathematical MATH 1050 or MATH 1055 or MATH 2000 ideas at the secondary school level. Includes with a grade of C or better or appropriate math MATH 2280 classroom instruction, student presentations, placement score. Ordinary Differential Equations and experiences. Studies various Is for pre-elementary education majors. 3 techniques of assessment and classroom Includes problem solving, sets, numeration * Prerequisite(s): MATH 2210 or MATH 221H management. systems, arithmetic of whole numbers, , with a grade of C or higher MATH 3020 rational numbers, real numbers, elementary Includes separable equations, linear , ratios, proportions, , differential equations, differential operators Computer Based Mathematics for and percents. and annihilators, variation of parameters, Secondary School Mathematics Teachers solutions of differential equations, 3 MATH 2020 * Prerequisite(s): (MATH 2210 and MATH Laplace transforms, systems of linear Mathematics for Elementary Teachers II 2270 each with a grade of C or higher) and differential equations, and numerical methods. 3 University Advanced Standing; MATH 2280 * Prerequisite(s): MATH 2010 with a grade of MATH 281R with a grade of C or higher is recommended C or higher Cooperative Work Experience For Mathematics Education majors. Presents Is for pre-elementary education majors. 2 to 9 one or more popular mathematical computer Includes topics on , , * Prerequisite(s): Approval of Cooperative software packages. Includes mathematical geometry and measurement. Coordinator problem solving and presentations of Designed for mathematics majors. Provides mathematical concepts using a computer as MATH 2210 paid work experiences in the student's major. an aid. Introduces appropriate programming Calculus III Course content is individualized, with the language. 3 student setting the objectives by consulting * Prerequisite(s): MATH 1220 or MATH 122H with a faculty coordinator and the on-the-job with a grade of C or higher supervisor. Credit is determined by the number Includes partial derivatives, , Lagrange of hours the student works during the semester. multipliers, multiple integrals, integrals, Repeatable for a maximum of 16 credits toward Green's Theorem, surface integrals, the graduation. May be graded credit/no credit. Theorem, and Stokes' Theorem. MATH 290R MATH 221H Topics in Mathematics Calculus III 3 to 5 3 * Prerequisite(s): Departmental approval * Prerequisite(s): MATH 1220 or MATH 122H Studies a chosen topic in mathematics; topic with a grade of C or higher will vary depending upon student demand and Includes partial derivatives, gradient vectors, course development needs. May be taken more Lagrange multipliers, multiple integrals, line than once for different topics and for a maximum integrals, Green's Theorem, surface integrals, of 6 credit hours counted toward graduation. the , and Stokes' Theorem. Is an honors course which includes a student project.

2 Course Catalog 2021-2022 Utah Valley University Course Descriptions

MATH 3030 MATH 3250 MATH 3750 Algebra for Secondary Mathematics Introduction to Advanced Calculus WE Financial Mathematics Teaching 3 3 3 * Prerequisite(s):(MATH 2210 or MATH 221H) * Prerequisite(s): (MATH 1220 or FIN 3100 * Prerequisite(s): Math 1210 with a grade B- or with a grade of C or higher and MATH 2270 each with a grade of C or higher) and higher and University Advanced Standing and with a grade of C or higher and University University Advanced Standing Mathematics Department Adviser Approval Advanced Standing Prepares students to take Exam FM/Exam For Mathematics Education Majors: Includes * Prerequisite(s) or Corequisite(s): MATH 2280 2 given by the Society of Actuaries/ the exploration of important conceptual Introduces and proof. Casualty Actuarial Society. Trains students to underpinnings, common misconceptions and Covers the first topics of advanced calculus answer complex questions under significant students' ways of thinking, appropriate use including the of the real numbers, time pressure. Teaches the principles of technology, and instructional practices sequences, , limits, and mathematics of interest, annuities, to support and assess the learning of of the real numbers, continuity, amortization, investments, financial economics, algebra. Teaches algebra as an extension differentiation, and integration. investment contracts and financial of number, operation, and quantity; various risk management. ideas of equivalence as it pertains to MATH 3300 algebraic structures; patterns of change as Foundations of MATH 4015 covariation between quantities; connections 3 Actuarial Problems Laboratory between representations (tables, graphs, * Prerequisite(s): MATH 3100 or MATH 3250 1 equations, geometric models, context); and with a grade of C or higher and University * Prerequisite(s): STAT 4710 and University the historical development of content and Advanced Standing Advanced Standing perspectives from diverse cultures. Focuses Provides an introduction to algebraic structures. Provides preparation for the first actuarial on deeper understanding of rational numbers, Covers the theory of groups including modular examination by linking concepts of probability ratios and proportions, meaning and use arithmetic, normal subgroups, factor groups, and to actuarial of variables, functions (e.g., exponential, and cyclic groups. Introduces rings, integral applications. logarithmic, , rational, quadratic), domains, and fields. and inverses. MATH 4025 MATH 3310 Actuarial Problems Finance Laboratory MATH 3100 1 Foundations of Geometry 3 * Prerequisite(s): (MATH 3750 or 3 * Prerequisite(s): MATH 1220 with a grade of Departmental Approval) and University * Prerequisite(s): MATH 2270 with a grade of C or higher and University Advanced Standing Advanced Standing C or higher and MATH 2210 with a grade of C or higher and University Advanced Standing Includes logic, sets, functions, elementary Provides preparation for the second actuarial * Prerequisite(s) or Corequisite(s): MATH 2280 number theory, mathematical induction, examination by linking concepts of finance equivalence relations, and cardinality. and derivative markets to actuarial applications Introduces logic and . Offers Emphasizes the writing of proofs. frequently found on Exam FM/2. an axiomatic development of Euclidean and non-Euclidean . MATH 3320 MATH 4030 and its Applications Geometry for Secondary Mathematics MATH 3200 3 Teaching Foundations of Analysis * Prerequisite(s): MATH 2270 with a grade of 3 3 C or higher and University Advanced Standing * Prerequisite(s): Math 3100 with a grade C or * Prerequisite(s): MATH 3100 with a grade of higher and University Advanced Standing C or higher and MATH 2280 with a grade of C Introduces the most important topics of graph or higher and University Advanced Standing theory including graphs and modeling, trees, For Mathematics Education Majors. Includes paths, circuits, and connectivity, matching, the exploration of important conceptual Covers material from beginning analysis planar graphs and coloring, and applications. underpinnings, common misconceptions and including the axioms of the real numbers, students' ways of thinking, appropriate use sequences, mathematical induction, limits, MATH 3400 of technology, and instructional practices to topology of the real line, continuity, Partial Differential Equations support and assess the learning of geometry. differentiation, and integration. 3 Teaches constructions and transformations, * Prerequisite(s): MATH 2280 with a grade of congruence and similarity, , MATH 3210 C or higher and University Advanced Standing geometry, conics, trigonometry, and Complex Variables Introduction to partial differential equations. the historical development of content and 3 perspectives from diverse cultures. Makes * Prerequisite(s): MATH 2210 or MATH 221H Topics include Bessel functions, Legendre polynomials, Fourier analysis, partial differential explicit connections to various mathematical with a grade of C or higher and University content strands (modeling, complex numbers, Advanced Standing equations, and boundary value problems. function, and algebra). Introduces . Includes algebra MATH 3640 of complex numbers, analytic functions, Introduction to Optimization mapping properties of elementary functions, 3 the Cauchy integral formula, complex series, * Prerequisite(s):(MATH 2210 or MATH 221H) residues, and comformal mapping. and MATH 2270 with a grade of C or higher and University Advanced Standing; CS 1400 with a grade of C or higher is recommended. Includes linear, quadratic, and nonlinear programming, network problems, convexity, necessary and sufficient optimality conditions, numerical , and special topics.

Utah Valley University Course Catalog 2021-2022 3 Course Descriptions

MATH 4040 MATH 4250 MATH 4510 Statistics and Probability for Secondary Introduction to Dynamical Systems Foundations of Topology Mathematics Teaching 3 3 3 * Prerequisite(s): MATH 3250 with a grade * Prerequisite(s): MATH 3250 with a grade of * Prerequisite(s): Math 1210 with a grade B- of C or better, and University Advanced C or higher and University Advanced Standing or higher and STAT 2040 with a grade C or Standing. Introduces the ideas of , higher and University Advanced Standing Provides a foundation in dynamical systems. compactness, connectedness, countability, For Mathematics Education Majors. Includes Discusses fundamental topics of dynamics, separability, separation axioms, the exploration of important conceptual including graphical analysis, orbits, periodic homeomorphisms, and the Baire Category underpinnings, common misconceptions and and fixed points, convergence, bifurcations, Theorem. students' ways of thinking, appropriate use symbolic dynamics, chaos, and Sarkovskii's of technology, and instructional practices to Theorem. May include fractals, complex MATH 4610 support and assess the learning of statistics functions, and fractal . Introduction to I and probability. Focuses on summarizing and 3 representing data, study design and sampling, MATH 4310 * Prerequisite(s): MATH 2270 and MATH probability, testing claims and drawing Introduction to Modern Algebra I 2280, each with a grade of C or higher, conclusions, and the historical development of 3 an approved programming language, and content and perspectives from diverse cultures. * Prerequisite(s): MATH 3300 with a grade of University Advanced Standing C or higher and University Advanced Standing Includes numerical solutions of equations MATH 4100 Provides a deeper treatment of topics in modern in one , numerical solutions of Curves and algebra. Covers direct products of groups of linear and nonlinear system of Surfaces and the classification of finite Abelian groups. equations, interpolations and polynomial 3 Covers the theory of rings including ideals, approximation, and approximating eigenvalues * Prerequisite(s): MATH 3250 with a grade of factor rings, various kinds of integral domains, and eigenvectors. C or higher and University Advanced Standing fields, and polynomial rings. Presents the differential geometry of curves MATH 4620 and surfaces. Includes parametrized curves, MATH 4320 Introduction to Numerical Analysis II arc length, surfaces, planes, area, Introduction to Modern Algebra II 3 , the Gauss map, vector fields, 3 * Prerequisite(s): MATH 4610 with a grade of isometries, geodesics, the Gauss-Bonnet * Prerequisite(s): MATH 4310 with a grade of C or higher and University Advanced Standing C or higher and University Advanced Standing theorem, and other curves and surfaces topics Introduction to numerical analysis II. Topics selected by the instructor. Provides a deeper treatment of topics in the will include numerical differentiation and theory of groups, rings, and fields. Covers integration, numerical solutions of initial-value MATH 4210 field extensions, algebraic extensions, finite problems and boundary-value problems for Advanced Calculus I fields, and Kronecker's Theorem. Includes ordinary differential equations, numerical. 3 applications to straightedge and compass * Prerequisite(s): MATH 3250 with a grade of geometric constructions. Covers other topics at MATH 4750 C or higher and MATH 2280 with a grade of C the instructor's discretion which may include the Life Contingencies or higher and University Advanced Standing Sylow Theorems, symmetry groups, and Galois 3 Covers and differentiation theorems, Theory. * Prerequisite(s): STAT 4710 with a grade of C L’Hopital’s rule, integration, the Fundamental or higher and University Advanced Standing MATH 4330 Theorem of Calculus, series convergence, Includes survival models, Markov Chains, , compactness, and an introduction Theory of Linear Algebra life insurance and annuities, and Poisson to the geometry and topology of Euclidean 3 processes. Prepares students for the life spaces. * Prerequisite(s): MATH 3250 with a grade of contingencies portion of Exam M of the Society C or higher and University Advanced Standing of Actuaries. MATH 4220 Covers vector spaces, linear transformations Advanced Calculus II and matrices, dual spaces, inner MATH 481R 3 spaces, orthogonality, bilinear forms, Internship in Mathematics * Prerequisite(s): MATH 4210 with a grade eigenvalues, eigenvectors and generalized 1 to 4 of C or higher, and University Advanced eigenvectors, diagonalization, and Jordan and * Prerequisite(s): Instructor Approval and Standing other canonical forms. University Advanced Standing Covers the topology of Euclidean For mathematics majors. Provides MATH 4340 spaces, vectors and linear transformations, mathematics-related work experience in multivariable limits and continuity, multivariable Introduction to Number Theory an industrial, commercial, or research differentiation, Jordan regions, multivariable 3 environment. Internship credit may not be * Prerequisite(s): MATH 3250 with a grade of Riemann integration, and Taylor series in used in fulfilling the mathematics major course C or higher and University Advanced Standing multiple variables. requirements. May be taken two times for a Covers divisibility, irreducibility and primality, maximum of 6 credits toward graduation. May linear Diophantine equations, Pell's equation, be graded credit/no credit. continued , congruences, Euler's theorem, arithmetic functions, primitive roots, quadratic reciprocity.

4 Course Catalog 2021-2022 Utah Valley University Course Descriptions

MATH 489R MATH 6100 MATH 6410 Undergraduate Research in Mathematics Topics in Geometry and Topology Topics in Ordinary Differential Equations 1 to 3 3 3 * Prerequisite(s): MATH 3250 with a grade * Prerequisite(s): Matriculation into the * Prerequisite(s): Matriculation into the of C or better, Departmental Approval, and Mathematics Education, M.S. program or Mathematics Education, M.S. program or University Advanced Standing Matriculation into the Mathematics Graduate Matriculation into the Mathematics Graduate Allows research on a project determined Certificate program, or approval of graduate Certificate program, or approval of graduate by a faculty member and approved by the program director. program director. department chair. Emphasizes proof, modeling, Includes , , Includes the theory of linear and or other activities associated with mathematical classification of surfaces, covering spaces, nonlinear ordinary differential equations research. May be used as part of a senior homotopy types, differential geometry, and dynamical systems; the initial-value project. May be Graded Credit/No Credit. May , , problems and behavior of solutions; be repeated for a maximum of 3 credits toward projective geometry, and . the existence, uniqueness, perturbations, graduation. continuous dependence of solution on initial MATH 6210 conditions, and introduction of nonlinear MATH 490R dynamical systems with applications. Topics in Mathematics 3 2 to 3 * Prerequisite(s): Matriculation into the MATH 6610 * Prerequisite(s): Departmental approval and Mathematics Education, M.S. program or Numerical Methods and Modeling University Advanced Standing Matriculation into the Mathematics Graduate 3 Certificate program, or approval of graduate * Prerequisite(s): Matriculation into the Studies a chosen topic in mathematics. The program director. Mathematics Education, M.S. program or topic will vary depending upon student demand. Course may be taken more than once for Introduces students to fundamental analytic Matriculation into the Mathematics Graduate Certificate program, or approval of graduate different topics and for a maximum of 6 credit tools used across all of mathematics. Presents program director. hours counted toward graduation. a proof based approach to analysis in and analysis in the general Investigates modelling and numerical topics. MATH 4999 setting of metric spaces. Includes sequences, Investigates topics from college algebra, Mathematics Capstone WE series, limits in Rn, metric spaces, topology, calculus, linear algebra, and differential 2 differentiation, and integration. equations from a theoretical as well as * Prerequisite(s): Instructor approval, numerical perspective. Expounds on algorithms departmental approval, and University MATH 6310 and modelling through software packages in a Advanced Standing Modern Algebra hands-on approach. Is for mathematics majors and is to be 3 taken during the last semester before * Prerequisite(s): Matriculation into the MATH 6620 graduation. Reviews topics learned in the Mathematics Education, M.S. program or Topics in Numerical Analysis Matriculation into the Mathematics Graduate 3 core undergraduate mathematics courses. Certificate program, or approval of graduate * Prerequisite(s): Matriculation into the Assesses student understanding through the program director. Mathematics Education, M.S. program or Major Field Test. Provides an opportunity for senior mathematics majors to participate in Covers advanced topics from group, , and Matriculation into the Mathematics Graduate Certificate program, or approval of graduate mathematical research under the supervision field theory. program director. of a faculty member. Offers a setting in which students prepare a research paper and give oral MATH 6330 Develops a deeper practical and theoretical presentations that describe their research. Advanced Linear Algebra understanding of methods used to find 3 approximate solutions to a variety of MATH 5510 * Prerequisite(s): Matriculation into the mathematical problems and of the relationships Mathematics Education, M.S. program or between these algorithms. Compares accuracy, 3 Matriculation into the Mathematics Graduate efficiency, and stability of methods used to * Prerequisite(s): MATH 4510 or MATH 4210 Certificate program, or approval of graduate solve nonlinear equations and large systems with a grade of C or higher program director. of linear and nonlinear algebraic equations; Introduces the fundamentals of general Presents a proof and computation based ordinary and partial differential equations; and topology, including topological spaces, approach to the theory of vector to perform numerical differentiation, integration, separation axioms, continuity, compactness, spaces, including bases, dimension, linear interpolation and more general approximation connectedness, metric spaces, product spaces, transformations, rank-nullity theorem, dual of functions. Provides experience programming metrization and ordinals. spaces, inner products, and canonical forms. and applying many of the central algorithms that have powered modern advances in math and MATH 6000 MATH 6350 the sciences. Mathematics Core Review Introduction to Combinatorics 3 3 MATH 6700 * Prerequisite(s): Department Approval * Prerequisite(s): Mathematics Endorsement 4, Applications of Mathematics or instructor approval 3 Reviews essential undergraduate mathematics * Prerequisite(s): Matriculation into the for students seeking admission to Enumerates permutations and Mathematics Education, M.S. program or the MS-Mathematics Education program. of sets and multi-sets, inclusion-exclusion, Matriculation into the Mathematics Graduate Reviews Calculus, Linear Algebra, Differential recurrence relations, generating functions, Certificate program, or approval of graduate Equations, Geometry, Advanced Calculus, and Polya theory, and combinatorial structures. program director. Modern Algebra. May be graded credit/no credit. Introduces various areas of mathematics that can be applied to other fields such as the sciences, arts, industry, etc. Includes topics such as , graph theory, knot theory, number theory, etc.

Utah Valley University Course Catalog 2021-2022 5