70 courses with the subject MATH, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
MATH 1000RMath Leap1
Is part of UVU’s math placement process; for students who desire to review math topics in order to improve placement level before beginning a math course. Addresses unique strengths and weaknesses of students, by providing group problem solving activities along with an individual assessment and study plan for mastering target material. Requires mandatory class attendance and a minimum number of hours per week logged into a preparation module, with progress monitored by a mentor. May be repeated for a maximum of 4 credits toward graduation. May be graded credit/no credit.
Subject
MATH
Credits (min)
1
Credits (max)
1
Credit unit
Credit
Type
course
Repeatable
May be repeated for a maximum of 4 credits toward graduation.
Prerequisite(s): Within the past two years one of the following: MAT 1010 or MAT 1015 with a grade of C or better or appropriate math placement score. Includes inequalities, functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, systems of linear and nonlinear equations, matrices and determinants, arithmetic and geometric sequences, and the Binomial Theorem. May be delivered hybrid and/or online.
Prerequisite(s): Within the past two years one of the following: MAT 1010 or MAT 1015 with a grade of C or better or appropriate math placement score. Includes inequalities, functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, systems of linear and nonlinear equations, matrices and determinants, arithmetic and geometric sequences, and the Binomial Theorem. May be delivered hybrid and/or online.
Prerequisite(s): Within the past two years: MATH 1050 or MATH 1055 with a grade of C or higher or appropriate math placement score. Includes the unit circle and right triangle definitions of the trigonometric functions, graphing trigonometric functions, trigonometric identities, trigonometric equations, inverse trigonometric functions, the Law of Sines and the Law of Cosines, vectors, complex numbers, polar coordinates, and rotation of axes.
Prerequisite(s): Within the past two years, one of the following: MAT 1010 or MAT 1015 with a grade of B or better or an appropriate math placement score. Is an accelerated version of MATH 1050 and MATH 1060. Includes functions and their graphs including polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Covers inequalities, systems of linear and nonlinear equations, matrices, determinants, arithmetic and geometric sequences, the Binomial Theorem, the unit circle, right triangle trigonometry, trigonometric equations, trigonometric identities, the Law of Sines, the Law of Cosines, vectors, complex numbers, polar coordinates, and conic sections.
Prerequisite(s): Within the past two years one of the following: MAT 1010 or MAT 1015 with a grade of C or better or appropriate math placement score. Uses linear, quadratic, power, polynomial, rational, exponential, logarithmic, and logistic functions to analyze business applications such as market equilibrium, rates of change, cost-benefit analysis, and inflation. Includes systems of linear and non-linear equations and inequalities, matrices and matrix equations, sequences and series, and financial mathematics. Canvas Course Mats $90/McGraw applies.
Prerequisite(s): Within the past two years: MATH 1050 or MATH 1055 or MATH 1080 with a grade of C or better or appropriate math placement score. Provides a comprehensive survey of the basic concepts and techniques of differential and integral calculus. Covers topics from both single and multivariable calculus including limits, continuity, differentiation, partial differentiation, integration, single variable and multivariate optimization. Includes the derivatives and integrals of polynomial functions, rational functions, exponential functions, and logarithmic functions, and partial differentiation of multivariate versions of these same functions. Emphasizes applications to specific disciplines such as business, computer science, and the life sciences.
Prerequisite(s): One of the following within the past two years: (MATH 1050 or MATH 1055) and MATH 1060, each with a grade of C or higher; OR MATH 1080 with a grade of C or higher; OR appropriate placement by math placement test. Covers limits, continuity, differentiation, applications of differentiation, integration, and applications of integration, including derivatives and integrals of polynomial functions, rational functions, exponential functions, logarithmic functions, trigonometric functions, inverse trigonometric functions, and hyperbolic functions. Is a prerequisite for calculus-based sciences.
Prerequisite(s): One of the following within the past two years: (MATH 1050 or MATH 1055) and MATH 1060, each with a grade of C or higher; OR MATH 1080 with a grade of C or higher; OR appropriate placement by math placement test. Covers limits, continuity, differentiation, applications of differentiation, integration, and applications of integration, including derivatives and integrals of polynomial functions, rational functions, exponential functions, logarithmic functions, trigonometric functions, inverse trigonometric functions, and hyperbolic functions. Is a prerequisite for calculus-based sciences. Is an honors course with student projects.
Prerequisite(s): MATH 1210 or MATH 1210H with a grade of C or higher Includes applications of integration, integration techniques, arc length, area of a surface of revolution, moments and centers of mass, sequences and series, and parametrization of curves and polar coordinates.
Prerequisite(s): MATH 1210 or MATH 1210H with a grade of C or higher Includes integration techniques, arc length, area of a surface of revolution, moments and centers of mass, sequences and series, parametrization of curves and polar coordinates. Honors course which requires a student project.
Prerequisite(s): Within the past two years, one of the following: MAT 1010 or MAT 1015 with a grade of C or better or an appropriate math placement score. Presents the basic ideas of sets and functions in the context of and motivated by modeling bivariate data. Includes basic set theory such as unions, intersections, Venn diagrams, etc. Includes the basic ideas and the algebra of functions including polynomial, exponential, and logarithmic functions. Also includes some basic combinatorics and counting principles as well as arithmetic and geometric sequences. Culminates in a pictorial introduction to the basic ideas of calculus presented with minimal computation.
Prerequisite(s): Within the past two years: MATH 1050 or MATH 1055 or MATH 2000 with a grade of C or better or appropriate math placement score. Is for pre-elementary education majors. Includes problem solving, sets, numeration systems, arithmetic of whole numbers, integers, rational numbers, real numbers, elementary number theory, ratios, proportions, decimals, and percents.
Prerequisite(s): MATH 2010 with a grade of C or higher Is for pre-elementary education majors. Includes topics on probability, statistics, geometry and measurement.
MATH 2030Calculus for Middle School Mathematics Teachers4
Prerequisite(s): MATH 1060 with a grade of C or higher Introduces students to the key ideas of calculus and is specifically designed for students seeking Middle School Mathematics endorsement from the Utah State Board of Education. Utilizes a project-based approach to create conceptual understandings of limit, derivative, integral, and the fundamental theorem of calculus and their applications. Asks students to identify misconceptions and errors and will make connections to curriculum taught in grades 6-9.
Prerequisite(s): MATH 1220 or MATH 1220H with a grade of C or higher Includes vectors in 3-space, quadric surfaces, partial derivatives, gradient, Lagrange multipliers, multiple integrals, line integrals, Green's Theorem, surface integrals, the Divergence Theorem, and Stokes' Theorem.
Prerequisite(s): MATH 1220 or MATH 1220H with a grade of C or higher Includes vectors in 3-space, quadric surfaces, partial derivatives, gradient vectors, Lagrange multipliers, multiple integrals, line integrals, Green's Theorem, surface integrals, the Divergence Theorem, and Stokes' Theorem. Is an honors course which includes a student project.
MATH 2250Differential Equations and Linear Algebra4
Prerequisite(s): MATH 1220 or MATH 1220H with a grade of C or higher Is for engineering students. Includes separable equations, linear differential equations, differential operators and annihilators, variation of parameters, Laplace transforms, and systems of linear differential equations. Introduces basic concepts of linear algebra including matrices, Gaussian elimination, determinants, linear independence, and eigenvalues and eigenvectors.
Prerequisite(s): MATH 1210 or MATH 1210H with a grade of C or higher Includes matrices and systems of equations, determinants, vector spaces, linear transformations, orthogonality, and eigenvalues and eigenvectors.
Prerequisite(s): MATH 2210 or MATH 2210H with a grade of C or higher Includes separable equations, linear differential equations, differential operators and annihilators, variation of parameters, power series solutions of differential equations, Laplace transforms, systems of linear differential equations, and numerical methods.
Prerequisite(s): Approval of Cooperative Coordinator Designed for mathematics majors. Provides paid work experiences in the student's major. Course content is individualized, with the student setting the objectives by consulting with a faculty coordinator and the on-the-job supervisor. Credit is determined by the number of hours the student works during the semester. Repeatable for a maximum of 16 credits toward graduation. May be graded credit/no credit.
Prerequisite(s): Departmental approval Studies a chosen topic in mathematics; topic will vary depending upon student demand and course development needs. May be taken more than once for different topics and for a maximum of 6 credit hours counted toward graduation.
Prerequisite(s): MATH 2210 or MATH 2210H with a grade of C or higher and University Advanced Standing Provides a survey of the history of mathematics with a focus on the development of mathematical ideas in their historical context. Includes numeration systems, the mathematics of the ancient world, the development of algebra, geometry, and calculus, and the work of pivotal mathematicians.
MATH 3020Computer Based Mathematics for Secondary School Mathematics Teachers3
Prerequisite(s): (MATH 2210 and MATH 2270 each with a grade of C or higher) and University Advanced Standing; MATH 2280 with a grade of C or higher is recommended For Mathematics Education majors. Presents one or more popular mathematical computer software packages. Includes mathematical problem solving and presentations of mathematical concepts using a computer as an aid. Introduces appropriate programming language.
MATH 3030Algebra for Secondary Mathematics Teaching3
Prerequisite(s): Math 1210 with a grade B- or higher and University Advanced Standing and Mathematics Department Adviser Approval For Mathematics Education Majors: Includes the exploration of important conceptual underpinnings, common misconceptions and students' ways of thinking, appropriate use of technology, and instructional practices to support and assess the learning of algebra. Teaches algebra as an extension of number, operation, and quantity; various ideas of equivalence as it pertains to algebraic structures; patterns of change as covariation between quantities; connections between representations (tables, graphs, equations, geometric models, context); and the historical development of content and perspectives from diverse cultures. Focuses on deeper understanding of rational numbers, ratios and proportions, meaning and use of variables, functions (e.g., exponential, logarithmic, polynomials, rational, quadratic), and inverses.
MATH 3050Geometry for Middle School Mathematics Teaching3
Prerequisite(s): MATH 1210 with a grade of C or higher and University Advanced Standing Explores important conceptual underpinnings, common misconceptions and students' ways of thinking, appropriate use of technology, instructional practices to support and assess the learning of geometry in grades 6-9, and designed for students seeking a Middle School Mathematics Endorsement from the Utah State Board of Education. Teaches constructions and transformations, congruence and similarity, analytic geometry, solid geometry, and the historical development of content and perspectives from diverse cultures. Makes explicit connections to various mathematical content strands (modeling, function, and algebra).
MATH 3060Statistics and Probability for Middle School Mathematics Teaching3
Prerequisite(s): MATH 1210 with a grade of C or higher and University Advanced Standing Explores important conceptual underpinnings, common misconceptions and students’ ways of thinking, appropriate use of technology, instructional practices to support and assess the learning of statistics and probability, and is designed for students seeking a Middle School Mathematics Endorsement from the Utah State Board of Education. Focuses on summarizing and representing data, study design and sampling, probability, testing claims and drawing conclusions, and the historical development of content and perspectives from diverse cultures.
MATH 3090Methods of Middle School Mathematics Teaching3
Prerequisite(s): MATH 1210 with a grade of C or higher and University Advanced Standing Presents different methods of teaching mathematical ideas at the middle school level. Includes classroom instruction, student presentations, the study of various techniques of assessment and classroom management, and is designed for students seeking a Middle School Mathematics Endorsement from the Utah State Board of Education.
Prerequisite(s): MATH 2270 with a grade of C or higher and MATH 2210 with a grade of C or higher and University Advanced Standing Pre- or Corequisite(s): MATH 2280 Introduces logic and mathematical proof. Offers an axiomatic development of Euclidean and non-Euclidean geometries.
Prerequisite(s): MATH 3100 with a grade of C or higher and MATH 2280 with a grade of C or higher and University Advanced Standing Covers material from beginning analysis including the axioms of the real numbers, sequences, mathematical induction, limits, topology of the real line, continuity, differentiation, and integration.
Prerequisite(s): MATH 2210 or MATH 2210H with a grade of C or higher and University Advanced Standing Introduces complex analysis. Includes algebra of complex numbers, analytic functions, mapping properties of elementary functions, the Cauchy integral formula, complex series, residues, and comformal mapping.
Prerequisite(s):(MATH 2210 or MATH 2210H) with a grade of C or higher and MATH 2270 with a grade of C or higher and University Advanced Standing Pre- or Corequisite(s): MATH 2280 Introduces mathematical logic and proof. Covers the first topics of advanced calculus including the axioms of the real numbers, sequences, mathematical induction, limits, topology of the real numbers, continuity, differentiation, and integration.
Prerequisite(s): MATH 3100 or MATH 3250 with a grade of C or higher and University Advanced Standing Provides an introduction to algebraic structures. Covers the theory of groups including modular arithmetic, normal subgroups, factor groups, and cyclic groups. Introduces rings, integral domains, and fields.
Prerequisite(s): MATH 1220 with a grade of C or higher and University Advanced Standing Includes logic, sets, functions, elementary number theory, mathematical induction, equivalence relations, and cardinality. Emphasizes the writing of proofs.
Prerequisite(s): MATH 2270 with a grade of C or higher and University Advanced Standing Introduces the most important topics of graph theory including graphs and modeling, trees, paths, circuits, and connectivity, matching, planar graphs and coloring, and applications.
Prerequisite(s): MATH 2280 with a grade of C or higher and University Advanced Standing Introduction to partial differential equations. Topics include Bessel functions, Legendre polynomials, Fourier analysis, partial differential equations, and boundary value problems.
Prerequisite(s):(MATH 2210 or MATH 2210H) 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 algorithms, and special topics.
Prerequisite(s): MATH 1220 and FIN 3100 each with a grade of C or higher and University Advanced Standing Corequisite(s): MATH 3755 Prepares students to take Exam FM/Exam 2 given by the Society of Actuaries/Casualty Actuarial Society. Trains students to answer complex questions under significant time pressure. Covers the principles and mathematics of interest, annuities, amortization, investments, financial economics, derivative investment contracts and financial risk management.
Prerequisite(s): University Advanced Standing Corequisite(s): MATH 3750 Prepares students to take the SOA Exam FM. Emphasizes practice solving problems similar to those that might appear on the SOA Exam FM.
Prerequisite(s): STAT 4710 and University Advanced Standing Provides preparation for the probability actuarial examination (Exam P) by linking concepts of probability and mathematical statistics to actuarial applications.
MATH 4030Geometry for Secondary Mathematics Teaching3
Prerequisite(s): Math 3100 with a grade C or higher and University Advanced Standing For Mathematics Education Majors. Includes the exploration of important conceptual underpinnings, common misconceptions and students' ways of thinking, appropriate use of technology, and instructional practices to support and assess the learning of geometry. Teaches constructions and transformations, congruence and similarity, analytic geometry, solid geometry, conics, trigonometry, and the historical development of content and perspectives from diverse cultures. Makes explicit connections to various mathematical content strands (modeling, complex numbers, function, and algebra).
MATH 4040Statistics and Probability for Secondary Mathematics Teaching3
Prerequisite(s): Math 1210 with a grade B- or higher and STAT 2040 with a grade C or higher and University Advanced Standing For Mathematics Education Majors. Includes the exploration of important conceptual underpinnings, common misconceptions and students' ways of thinking, appropriate use of technology, and instructional practices to support and assess the learning of statistics and probability. Focuses on summarizing and representing data, study design and sampling, probability, testing claims and drawing conclusions, and the historical development of content and perspectives from diverse cultures.
MATH 4100Differential Geometry of Curves and Surfaces3
Prerequisite(s): MATH 3250 with a grade of C or higher and University Advanced Standing Presents the differential geometry of curves and surfaces. Includes parametrized curves, arc length, surfaces, tangent planes, area, curvature, the Gauss map, vector fields, isometries, geodesics, the Gauss-Bonnet theorem, and other curves and surfaces topics selected by the instructor.
Prerequisite(s): MATH 3250 with a grade of C or higher and MATH 2280 with a grade of C or higher and University Advanced Standing Covers limit and differentiation theorems, L’Hopital’s rule, integration, the Fundamental Theorem of Calculus, series convergence, Taylor series, compactness, and an introduction to the geometry and topology of Euclidean spaces.
Prerequisite(s): MATH 4210 with a grade of C or higher, and University Advanced Standing Covers the topology of Euclidean spaces, vectors and linear transformations, multivariable limits and continuity, multivariable differentiation, Jordan regions, multivariable Riemann integration, and Taylor series in multiple variables.
Prerequisite(s): MATH 3250 with a grade of C or better, and University Advanced Standing. Provides a foundation in dynamical systems. Discusses fundamental topics of dynamics, including graphical analysis, orbits, periodic and fixed points, convergence, bifurcations, symbolic dynamics, chaos, and Sarkovskii's Theorem. May include fractals, complex functions, and fractal dimension.
Prerequisite(s): MATH 3300 with a grade of C or higher and University Advanced Standing Provides a deeper treatment of topics in modern algebra. Covers direct products of groups and the classification of finite Abelian groups. Covers the theory of rings including ideals, factor rings, various kinds of integral domains, fields, and polynomial rings.
Prerequisite(s): MATH 4310 with a grade of C or higher and University Advanced Standing Provides a deeper treatment of topics in the theory of groups, rings, and fields. Covers field extensions, algebraic extensions, finite fields, and Kronecker's Theorem. Includes applications to straightedge and compass geometric constructions. Covers other topics at the instructor's discretion which may include the Sylow Theorems, symmetry groups, and Galois Theory.
Prerequisite(s): MATH 3250 with a grade of C or higher and University Advanced Standing Covers vector spaces, linear transformations and matrices, dual spaces, inner product spaces, orthogonality, bilinear forms, eigenvalues, eigenvectors and generalized eigenvectors, diagonalization, and Jordan and other canonical forms.
Prerequisite(s): MATH 3250 with a grade of C or higher and University Advanced Standing Covers divisibility, irreducibility and primality, linear Diophantine equations, Pell's equation, continued fractions, congruences, Euler's theorem, arithmetic functions, primitive roots, quadratic reciprocity.
Prerequisite(s): MATH 3250 with a grade of C or higher and University Advanced Standing Introduces the ideas of topologies, compactness, connectedness, countability, separability, separation axioms, homeomorphisms, and the Baire Category Theorem.
Prerequisite(s): MATH 2270, MATH 2280, and CS 1400, each with a grade of C or higher, and University Advanced Standing Includes numerical solutions of equations in one variable, numerical solutions of linear and nonlinear system of equations, interpolations and polynomial approximation, and approximating eigenvalues and eigenvectors.
Prerequisite(s): MATH 4610 with a grade of C or higher and University Advanced Standing Introduction to numerical analysis II. Topics will include numerical differentiation and integration, numerical solutions of initial-value problems and boundary-value problems for ordinary differential equations, numerical.
Prerequisite(s): STAT 4710 with a grade of C or higher and University Advanced Standing Includes survival models, Markov Chains, life insurance and annuities, and Poisson processes. Prepares students for the life contingencies portion of Exam M of the Society of Actuaries.
Prerequisite(s): Instructor Approval and University Advanced Standing For mathematics majors. Provides mathematics-related work experience in an industrial, commercial, or research environment. Internship credit may not be used in fulfilling the mathematics major course requirements. May be taken two times for a maximum of 6 credits toward graduation. May be graded credit/no credit.
MATH 4890RUndergraduate Research in Mathematics1-3
Prerequisite(s): MATH 3250 with a grade of C or better, Departmental Approval, and University Advanced Standing Allows research on a project determined by a faculty member and approved by the department chair. Emphasizes proof, modeling, or other activities associated with mathematical research. May be used as part of a senior project. May be Graded Credit/No Credit. May be repeated for a maximum of 3 credits toward graduation.
Subject
MATH
Credits (min)
1
Credits (max)
3
Credit unit
Credits
Type
course
Repeatable
May be repeated for a maximum of 3 credits toward graduation.
Prerequisite(s): Departmental approval and University Advanced Standing Studies a chosen topic in mathematics. The topic will vary depending upon student demand. Course may be taken more than once for different topics and for a maximum of 6 credit hours counted toward graduation.
Prerequisite(s): Instructor approval, departmental approval, and University Advanced Standing Is for mathematics majors and is to be taken during the last semester before graduation. Reviews topics learned in the core undergraduate mathematics courses. Assesses student understanding through the Major Field Test. Provides an opportunity for senior mathematics majors to participate in mathematical research under the supervision of a faculty member. Offers a setting in which students prepare a research paper and give oral presentations that describe their research.
MATH 5010Methods of Secondary School Mathematics Teaching3
Prerequisite(s): MATH 2210 or MATH 2210H with a grade of C or higher and EDSC 4550G with a grade of B- or higher and University Advanced Standing Is for Mathematics Education majors. Presents different methods of teaching mathematical ideas at the secondary school level. Includes classroom instruction, student presentations, and field experiences. Studies various techniques of assessment and classroom management.
Prerequisite(s): MATH 4510 or MATH 4210 with a grade of C or higher Introduces the fundamentals of general topology, including topological spaces, separation axioms, continuity, compactness, connectedness, metric spaces, product spaces, metrization and ordinals.
Prerequisite(s): Department Approval Reviews essential undergraduate mathematics for students seeking admission to the MS-Mathematics Education program. Reviews Calculus, Linear Algebra, Differential Equations, Geometry, Advanced Calculus, and Modern Algebra. May be graded credit/no credit.
Prerequisite(s): Matriculation into the Mathematics Education, M.S. program or Matriculation into the Mathematics Graduate Certificate program, or approval of graduate program director. Includes manifolds, fundamental group, classification of surfaces, covering spaces, homotopy types, differential geometry, Riemannian geometry, algebraic geometry, projective geometry, and algebraic topology.
Prerequisite(s): Matriculation into the Mathematics Education, M.S. program or Matriculation into the Mathematics Graduate Certificate program, or approval of graduate program director. Introduces students to fundamental analytic tools used across all of mathematics. Presents a proof based approach to analysis in Euclidean space and analysis in the general setting of metric spaces. Includes sequences, series, limits in Rn, metric spaces, topology, differentiation, and integration.
Prerequisite(s): Matriculation into the Mathematics Education, M.S. program or Matriculation into the Mathematics Graduate Certificate program, or approval of graduate program director. Covers advanced topics from group, ring, and field theory.
Prerequisite(s): Matriculation into the Mathematics Education, M.S. program or Matriculation into the Mathematics Graduate Certificate program, or approval of graduate program director. Presents a proof and computation based approach to the theory of vector spaces, including bases, dimension, linear transformations, rank-nullity theorem, dual spaces, inner products, and canonical forms.
Prerequisite(s): Mathematics Endorsement 4, or instructor approval Enumerates permutations and combinations of sets and multi-sets, inclusion-exclusion, recurrence relations, generating functions, Polya theory, and combinatorial structures.
MATH 6410Topics in Ordinary Differential Equations3
Prerequisite(s): Matriculation into the Mathematics Education, M.S. program or Matriculation into the Mathematics Graduate Certificate program, or approval of graduate program director. Includes the theory of linear and nonlinear ordinary differential equations and dynamical systems; the initial-value problems and behavior of solutions; the existence, uniqueness, perturbations, continuous dependence of solution on initial conditions, and introduction of nonlinear dynamical systems with applications.
Prerequisite(s): Matriculation into the Mathematics Education, M.S. program or Matriculation into the Mathematics Graduate Certificate program, or approval of graduate program director. Investigates modelling and numerical topics. Investigates topics from college algebra, calculus, linear algebra, and differential equations from a theoretical as well as numerical perspective. Expounds on algorithms and modelling through software packages in a hands-on approach.
Prerequisite(s): Matriculation into the Mathematics Education, M.S. program or Matriculation into the Mathematics Graduate Certificate program, or approval of graduate program director. Develops a deeper practical and theoretical understanding of methods used to find approximate solutions to a variety of mathematical problems and of the relationships between these algorithms. Compares accuracy, efficiency, and stability of methods used to solve nonlinear equations and large systems of linear and nonlinear algebraic equations; ordinary and partial differential equations; and to perform numerical differentiation, integration, interpolation and more general approximation of functions. Provides experience programming and applying many of the central algorithms that have powered modern advances in math and the sciences.
Prerequisite(s): Matriculation into the Mathematics Education, M.S. program or Matriculation into the Mathematics Graduate Certificate program, or approval of graduate program director. Introduces various areas of mathematics that can be applied to other fields such as the sciences, arts, industry, etc. Includes topics such as game theory, graph theory, knot theory, number theory, etc.
