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# Mathematics

MATH-Mathematics

Math Leap

1:1:0

Fall, Spring, Summer

For students in STEM and related fields who desire to improve problem-solving skills and/or placement level in preparation for STAT 1040 and higher-numbered MATH courses. 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.

College Algebra

4:4:0

Fall, Spring, Summer

Prerequisite(s):

Within the past two years one of the following: MAT 1000 or MAT 1010 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.

College Algebra with Preliminaries

5:5:0

Fall, Spring, Summer

Prerequisite(s):

Within the past two years one of the following: MAT 1000 or MAT 1010 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. Lab access fee of $30 applies.

Trigonometry

3:3:0

Fall, Spring, Summer

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.

Precalculus

5:5:0

Fall, Spring, Summer

Prerequisite(s):

Within the past two years, one of the following: MAT 1000 or MAT 1010 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.

College Algebra for Business

3:3:0

Fall, Spring, Summer

Prerequisite(s):

Within the past two years one of the following: MAT 1000 or MAT 1010 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.

Introduction to Calculus

4:4:0

Fall, Spring, Summer

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 an overview of the basic concepts and techniques of differential and integral calculus. Features applications in business, economics, and the life, social, and physical sciences. Includes optimization techniques in multivariable differential calculus.

Calculus I

5:5:0

Fall, Spring, Summer

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.

Calculus I

5:5:0

Fall, Spring

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.

Calculus II

5:5:0

Fall, Spring, Summer

Prerequisite(s):

MATH 1210 or MATH 121H 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, vectors in 3-space, and quadric surfaces.

Calculus II

5:5:0

Fall, Spring

Prerequisite(s):

MATH 1210 or MATH 121H 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, vectors in 3-space, and quadric surfaces. Honors course which requires a student project.

Algebraic Reasoning with Modeling

3:3:0

Fall, Spring, Summer

Prerequisite(s):

Within the past two years, one of the following: MAT 1000 or MAT 1010 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.

Mathematics for Elementary Teachers I

3:3:0

Fall, Spring, Summer

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.

Mathematics for Elementary Teachers II

3:3:0

Fall, Spring, Summer

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.

Calculus III

3:3:0

Fall, Spring, Summer

Prerequisite(s):

MATH 1220 or MATH 122H with a grade of C or higher
Includes partial derivatives, gradient, Lagrange multipliers, multiple integrals, line integrals, Green's Theorem, surface integrals, the Divergence Theorem, and Stokes' Theorem.

Calculus III

3:3:0

Fall, Spring

Prerequisite(s):

MATH 1220 or MATH 122H with a grade of C or higher
Includes 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.

Differential Equations and Linear Algebra

4:4:0

On Sufficient Demand

Prerequisite(s):

MATH 1220 or MATH 122H 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, systems of linear differential equations, and numerical methods. Introduces basic concepts of linear algebra including matrices, Gaussian elimination, determinants, linear independence, and eigenvalues and eigenvectors.

Linear Algebra

3:3:0

Fall, Spring

Prerequisite(s):

MATH 1220 or MATH 122H with a grade of C or higher
Includes matrices and systems of equations, determinants, vector spaces, linear transformations, orthogonality, and eigenvalues and eigenvectors.

Ordinary Differential Equations

3:3:0

Fall, Spring

Prerequisite(s):

MATH 2210 or MATH 221H 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.

Cooperative Work Experience

2 to 9:2 to 9:0

Fall, Spring, Summer

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.

Topics in Mathematics

3 to 5:3 to 5:0

On Sufficient Demand

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.

History of Mathematics

3:3:0

Spring

Prerequisite(s):

MATH 2210 or MATH 221H with a grade of C or higher and University Advanced Standing
Provides a survey of the history of mathematics.

Methods of Secondary School Mathematics Teaching

3:3:0

Fall

Prerequisite(s):

MATH 2210 or MATH 221H with a grade of C or higher and EDSC 4550 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.

Computer Based Mathematics for Secondary School Mathematics Teachers

3:3:0

Fall

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.

Algebra for Secondary Mathematics Teaching

3:3:0

Spring

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.

Foundations of Geometry

3:3:0

Fall, Spring

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
Prerequisite(s) or Corequisite(s):

MATH 2280
Introduces logic and mathematical proof. Offers an axiomatic development of Euclidean and non-Euclidean geometries.

Foundations of Analysis

3:3:0

Spring, Summer

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.

Complex Variables

3:3:0

Fall

Prerequisite(s):

MATH 2210 or MATH 221H 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.

Introduction to Advanced Calculus

3:3:0

Fall, Spring

Prerequisite(s):

Prerequisite(s):(MATH 2210 or MATH 221H) with a grade of C or higher and MATH 2270
with a grade of C or higher and University Advanced Standing
Prerequisite(s) 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.

Foundations of Abstract Algebra

3:3:0

Fall, Spring

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.

Discrete Mathematics

3:3:0

On Sufficient Demand

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.

Graph Theory and its Applications

3:3:0

Fall Even Year

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.

Partial Differential Equations

3:3:0

Spring

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.

Introduction to Optimization

3:3:0

Fall Odd Year

Prerequisite(s):

Prerequisite(s):(MATH 2210 or MATH 221H) 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.

Financial Mathematics

3:3:0

Fall, Spring, Summer

Prerequisite(s):

(MATH 1220 or FIN 3100 each with a grade of C or higher) and University Advanced
Standing
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. Teaches the principles and mathematics of interest, annuities, amortization, investments, financial economics, derivative investment contracts and financial risk management.

Actuarial Problems Laboratory

1:0:3

On Sufficient Demand

Prerequisite(s):

STAT 4710 and University Advanced Standing
Provides preparation for the first actuarial examination by linking concepts of probability and mathematical statistics to actuarial applications.

Actuarial Problems Finance Laboratory

1:0:3

On Sufficient Demand

Prerequisite(s):

(MATH 3750 or Departmental Approval) and University Advanced Standing
Provides preparation for the second actuarial examination by linking concepts of finance and derivative markets to actuarial applications frequently found on Exam FM/2.

Geometry for Secondary Mathematics Teaching

3:3:0

Fall

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).

Statistics and Probability for Secondary Mathematics Teaching

3:3:0

Fall

Prerequisite(s):

Math 1210 with a grade B- or higher and Math 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.

Differential Geometry of Curves and Surfaces

3:3:0

Fall Odd Year

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.

Advanced Calculus I

3:3:0

Fall

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.

Advanced Calculus II

3:3:0

Spring

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.

Introduction to Dynamical Systems

3:3:0

Fall

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.

Introduction to Modern Algebra I

3:3:0

Fall

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.

Introduction to Modern Algebra II

3:3:0

Spring

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.

Theory of Linear Algebra

3:3:0

Spring

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.

Introduction to Number Theory

3:3:0

Spring Even Year

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.

Foundations of Topology

3:3:0

Fall Even Year

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.

Introduction to Numerical Analysis I

3:3:0

Fall

Prerequisite(s):

MATH 2270 and MATH 2280, each with a grade of C or higher, an approved programming
language, 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.

Introduction to Numerical Analysis II

3:3:0

Spring

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.

Life Contingencies

3:3:0

Spring Odd Year

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.

Internship in Mathematics

1 to 4:1 to 4:0

On Sufficient Demand

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.

Undergraduate Research in Mathematics

1 to 3:1 to 3:0

On Sufficient Demand

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.

Topics in Mathematics

2 to 3:2 to 3:0

On Sufficient Demand

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.

Mathematics Capstone

2:2:0

Spring

Prerequisite(s):

Instructor approval, departmental approval, and University Advanced Standing
For mathematics majors, to be taken during the last semester before graduation. Reviews topics learned in the core undergraduate mathematics courses. Assesses student understanding through the Major's 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.

General Topology

3:3:0

Spring Odd Year

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.

Topics in Geometry and Topology

3:3:0

Fall, Spring

Prerequisite(s):

Mathematics Endorsement 4, or instructor approval
Includes manifolds, fundamental group, classification of surfaces, covering spaces, homotopy types, differential geometry, Riemannian geometry, algebraic geometry, projective geometry, and algebraic topology. May be delivered online.

Modern Algebra

3:3:0

Fall, Spring

Prerequisite(s):

Mathematics Endorsement 4, or instructor approval
Reviews the basics of ring theory. Analyzes ideals and factor rings in detail to prepare students for the study of fields. Uses the basics of field theory, including the construction of field extensions, to prove the impossibility of the three great construction problems of antiquity. Concludes with an introduction to Galois Theory.

Introduction to Combinatorics

3:3:0

Fall, Spring

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.

Topics in Ordinary Differential Equations

3:3:0

Fall, Spring

Prerequisite(s):

Mathematics Endorsement 4, or instructor approval
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.

Numerical Methods and Modeling

3:3:0

Fall, Spring

Prerequisite(s):

Mathematics Endorsement 4, or instructor approval
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.

Topics in Numerical Analysis

3:3:0

Fall, Spring

Prerequisite(s):

Mathematics Endorsement 4, or instructor approval
Develops a deeper practical and theoretical understanding of methods used to find approximate solutions of 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.

Applications of Mathematics

3:3:0

On Sufficient Demand

Prerequisite(s):

Mathematics Endorsement 4, or instructor approval
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.