Mathematics Courses

MATH
005
Hours
3
Introductory Algebra

Brief review of arithmetic operations and basic algebraic concepts: factoring, operations with polynomials and rational expressions, linear equations and word problems, graphing linear equations, simplification of expressions involving radicals or negative exponents, and elementary work with quadratic equations. Grades are reported as pass/fail.

MATH
100
Hours
3
Intermediate Algebra

Prerequisites: Placement and two units of college-preparatory mathematics; if a student has previously been placed in MATH 005, a passing grade in MATH 005 is required. Intermediate-level course including work on functions, graphs, linear equations and inequalities, quadratic equations, systems of equations, and operations with exponents and radicals. The solution of word problems is stressed. NOT APPLICABLE to UA Core Curriculum mathematics requirement. Grades are reported as A, B, C or NC (No Credit).

Prerequisite(s): UA Math Placement Test Score of 190-309 or ACT Math Subscore of 18 or old SAT Math Subscore of 440 or new SAT Math Subscore of 480 or MATH 005
MATH
110
MA
Hours
3
Finite Mathematics

This course is intended to give an overview of topics in finite mathematics with applications. This course covers mathematics of finance, logic, set theory, elementary probability and statistics. This course does not provide sufficient background for students who will need to take Precalculus Algebra or Calculus. Prerequisites: Placement and two units of college-preparatory mathematics; if a student has previously been placed in MATH 005, a passing grade in MATH 005 is required.

Prerequisite(s): UA Math Placement Test Score of 190-600 or ACT Math Subscore of 18 or old SAT Math Subscore of 440 or new SAT Math Subscore of 480 or MATH 005
Mathematics
MATH
112
MA
Hours
3
Precalculus Algebra

A higher-level course emphasizing functions including polynomial functions, rational functions, and the exponential and logarithmic functions. Graphs of these functions are stressed. The course also includes work on equations, inequalities, systems of equations, the binomial theorem, and the complex and rational roots of polynomials. Applications are stressed. Grades are reported as A, B, C or NC (No Credit). Degree credit will not be granted for both MATH 115 and (MATH 112 or MATH 113).

Prerequisite(s): UA Math Placement Test Score of 310-439 or ACT Math Subscore of 24 or old SAT Math Subscore of 560 or new SAT Math Subscore of 580 or C- or higher in MATH 100
Mathematics
MATH
113
MA
Hours
3
Precalculus Trigonometry

Continuation of MATH 112. The course includes study of trigonometric functions, inverse trigonometric functions, trigonometric identities and trigonometric equations. Complex numbers, De Moivre's Theorem, polar coordinates, vectors and other topics in algebra are also addressed, including conic sections, sequences and series. Grades are reported as A, B, C or NC (No Credit). Degree credit will not be granted for both MATH 115 and (MATH 112 or MATH 113).

Prerequisite(s): C- or higher in MATH 112
Mathematics
MATH
115
MA
Hours
3
Precalc Algebra & Trig

Properties and graphs of exponential, logarithmic, and trigonometric functions are emphasized. Also includes trigonometric identities, polynomial and rational functions, inequalities, systems of equations, vectors, and polar coordinates. Grades are reported as A, B, C, or NC (No credit). Degree credit will not be granted for both MATH 115 and (MATH 112 or MATH 113).

Prerequisite(s): UA Math Placement Test Score of 370-439 or ACT Math Subscore of 28 or old SAT Math Subscore of 630 or new SAT Math Subscore of 650
Mathematics
MATH
121
MA
Hours
3
Calculus & Applications

A brief overview of calculus primarily for students in the Culverhouse College of Commerce and Business Administration. This course does not provide sufficient background for students who will need higher levels of Calculus. Note: This course does not satisfy the requirement for MATH 125 or 126. Degree credit will not be granted for both MATH 121 and MATH 125 or MATH 145.

Prerequisite(s): UA Math Placement Test Score of 440-600 or ACT Math Subscore of 30 or old SAT Math Subscore of 680 or new SAT Math Subscore of 710 or a C- or higher in MATH 112 or MATH 115.
Mathematics
MATH
125
MA
Hours
4
Calculus I

This is the first of three courses in the basic calculus sequence. Topics include the limit of a function; the derivative of algebraic, trigonometric, exponential, and logarithmic functions; and the definite integral. Applications of the derivative are covered in detail, including approximations of error using differentials, maxima and minima problems, and curve sketching using calculus. There is also a brief review of selected precalculus topics at the beginning of the course. Degree credit will not be granted for both MATH 121 and MATH 125 or MATH 145.

Prerequisite(s): C- or higher in MATH 113 and C- or higher in MATH 112; or C- or higher in MATH 115
Mathematics
MATH
126
MA
Hours
4
Calculus II

This is the second of three courses in the basic calculus sequence. Topics include vectors and the geometry of space, applications of integration, integration techniques, L'Hopital's Rule, improper integrals, parametric equations, polar coordinates, conic sections and infinite series.

Prerequisite(s): C- or higher in MATH 125 or C- or higher in MATH 145
Mathematics
MATH
145
MA, UH
Hours
4
Honors Calculus I

This course covers the same material as MATH 125 but in a depth appropriate for honors students. It is the first course in the three part honors calculus sequence for students majoring in mathematics, science or engineering. Topics include limits, continuity, differentiation, applications of differentiation, and integration. Applications of the derivative are covered in detail, including approximation of errors using differentials, maxima and minima problems, curve sketching, optimization problems, and Newton’s method. Topics on integration include Riemann sums, properties of definite integrals, integration by substitution and integrals involving logarithmic exponential and trigonometric functions.

Prerequisite(s): ACT Math Subscore of 32 or old SAT Math Subscore of 730 or new SAT Math Subscore of 760 or a B- or higher in (MATH 112 and MATH 113) or MATH 115
Mathematics, University Honors
MATH
146
MA, UH
Hours
4
Honors Calculus II

This course covers the same material as MATH 126 but in a depth appropriate for honors students. It is the second course in the three part honors calculus sequence for students majoring in mathematics, science or engineering. Topics include vectors and the geometry of space, L'Hospital's Rule, applications of integration, integration techniques, improper integrals, infinite series, conic sections, plane curves, parametric equations, and polar coordinates.

Prerequisite(s): A grade of B- or higher in MATH 125 or MATH 145 or a score of 4 or 5 on AP Calculus AB or a score of 4 or 5 on AP Calculus BC: AB Subscore.
Mathematics, University Honors
MATH
208
Hours
3
Number And Operations

This course is the first of a three-course sequence designed to develop deeper understanding of elementary school mathematics content needed for teaching. The course topics include whole numbers and integers, fractions, ratio, percent, decimals and arithmetic operations within these systems. The goal of the course is to develop conceptual understanding (instead of just procedural understanding) of the number systems and operations by focusing on basic concepts and principles, exploring multiple representations and strategies, and illuminating connections among concepts and procedures. The content knowledge needed for teaching will be reinforced by engaging in inquiry-based activities, analyzing children’s ways of thinking, focusing on explanation and communication of underlying mathematical principles when solving problems, and using appropriate manipulative and technology.

Prerequisite(s): C- or higher in MATH 100 or C- or higher in MATH 112 or C- or higher in MATH 113 or C- or higher in MATH 125 or ACT Math Subscore of 22 or new SAT Math Subscore of 540
MATH
209
Hours
3
Geometry & Measurement

Properties of two- and three-dimensional shapes, rigid motion transformations, similarity, spatial reasoning, and the process and techniques of measurement. Class activities initiate investigations of underlying mathematical structure in the exploration of shape and space. Emphasis is on the explanation of the mathematical thought process. Technology specifically designed to facilitate geometric explorations is integrated throughout the course.

Prerequisite(s): C- or higher in MATH 208
MATH
210
Hours
3
Data Analysis for Elementary Teachers

Data analysis, statistics, and probability, including collecting, displaying/representing, exploring, and interpreting data, probability models, and applications. Focus is on statistics for problem-solving and decision making, rather than calculation. Class activities deepen the understanding of fundamental issues in learning to work with data. Technology specifically designed for data-driven investigations and statistical analysis related to elementary school teaching is integrated throughout the course.

Prerequisite(s): C- or higher in MATH 208
MATH
227
MA
Hours
4
Calculus III

This is the third of three courses in the basic calculus sequence. Topics include: vector functions and motion in space; functions of two or more variables and their partial derivatives; and applications of partial derivatives (including Lagrange multipliers), quadric surfaces, multiple integration (including Jacobian), line integrals, Green's Theorem, vector analysis, surface integrals and Stokes' Theorem.

Prerequisite(s): C- or higher in MATH 146 or C- or higher in MATH 126
Mathematics
MATH
237
C
Hours
3
Introduction to Linear Algebra

Fundamentals of linear algebra and matrix theory are covered. Topics include vectors in Euclidean spaces, solving systems of linear equations, matrix algebra, inverses, determinants, eigenvalues, and eigenvectors. Also vector spaces and the basic notions of span, subspace, linear independence, basis, dimension, linear transformation, kernel and range are considered. Computing proficiency is required for a passing grade in this course.

Prerequisite(s): C- or higher in MATH 126 or C- or higher in MATH 146
Computer Science
MATH
238
C, MA
Hours
3
Appld Diff Equations I

Introduction to analytic and numerical methods for solving differential equations. Topics include numerical methods and qualitative behavior of first order equations, analytic techniques for separable and linear equations, applications to population models and motion problems; techniques for solving higher order linear differential equations with constant coefficients (including undetermined coefficients, reduction of order, and variation of parameters), applications to physical models; the Laplace transform (including intial value problems with discontinuous forcing functions). Use of mathematics software is an integral part of the course. Computing proficiency is required for a passing grade in this course.

Prerequisite(s): C- or higher in MATH 126 or C- or higher in MATH 146
Computer Science, Mathematics
MATH
247
MA, UH
Hours
4
Honors Calculus III

This course covers the same material as MATH 227 but in a depth appropriate for honors students. It is the third course in the three part honors calculus sequence for students majoring in mathematics, science or engineering. Topics include analytic geometry in space, vector-valued functions and motion in space, functions of two or more variables and their partial derivatives, applications of partial differentiation (including Lagrangian multipliers), quadric and cylindrical surfaces, and multiple integration (including Jacobian) and applications, line integrals, Green's Theorem, curl and divergence, surface integrals, and Stokes’ Theorem.

Prerequisite(s): A grade of B- or higher in MATH 126 or MATH 146 or a score of 4 or 5 on AP Calculus BC exam.
Mathematics, University Honors
MATH
301
W
Hours
3
Discrete Mathematics

An introduction to mathematical logic and proof within the context of discrete structures. Topics include basic mathematical logic, elementary number theory, basic set theory, functions, and relations. Writing proficiency is required for a passing grade in this course. A student who does not write with the skill normally required of an upper-division student will not earn a passing grade, no matter how well the student performs in other areas of the course.

Prerequisite(s): MATH 125 or MATH 145
Writing
MATH
311
Hours
3
Introduction to Scientific Computing and Problem Solving

An introduction to using computer algorithms to solve mathematical problems, such as data analysis, visualization, numerical approximation and simulation. Basic programming concepts, such as variables, statements, loops, branches, functions, data structures, and debugging will be introduced in Python. A brief introduction to MATLAB tools for handling vectors, matrices, and vectorizing codes for performance, will be discussed as well in the later portion of the course. Some advanced mathematical and computational topics may be offered at the discretion of instructor.

Prerequisite(s): C- or higher in MATH 237 AND C- or higher in (CS 100 OR CS 110 OR CS 223 OR AEM 249 or MIS 221 OR RRS 101)
MATH
343
Hours
3
Appl Diff Equations II

Continuation of Appl Diff Equations I (MATH 238) and is designed to equip students with further methods of solving differential equations. Topics include initial value problems with variable coefficients, methods of infinite series, two-point boundary value problems, wave and heat equations, Fourier series, Sturm-Liouville theory, phase plane analysis, and Liapunov's second method.

Prerequisite(s): C- or higher in MATH 238
MATH
355
Hours
3
Theory Of Probability

The foundations of the theory of probability, laws governing random phenomena and their practical applications in other fields. Topics include: probability spaces; properties of probability set functions; conditional probability; and an introduction to combinatorics, discrete random variables, expectation of discrete random variables, Chebyshev's Inequality, continuous variables and their distribution functions, and special densities.

Prerequisite(s): C- or higher in MATH 227 or C- or higher in MATH 247
MATH
359
Hours
3
Mathematical Theory of Data Science

An introduction to the mathematical foundations of data science and machine learning. The fundamental roles of linear algebra and probability theory in data science will be explored. Heuristics for a variety of learning tasks, such as methods for clustering, classification, regression, or deep learning will be discussed in tandem with mathematical justifications for their use and effectiveness, as well as exercises illustrating their practical use in data analysis. Theoretical models for the feasibility of machine learning and for different types of learning problems will be introduced.

Prerequisite(s): (C- or higher in MATH 237) AND (C- or higher in MATH 301) AND (C- or higher in MATH 355) AND (C- or higher in CS 101 or MATH 311)
MATH
371
Hours
3
Advanced Linear Algebra

Topics include inner product spaces, norms, self adjoint and normal operators, orthogonal and unitary operators, orthogonal projections and the spectral theorem, bilinear and quadratic forms, generalized eigenvectors, and Jordan canonical form.

Prerequisite(s): C- or higher in MATH 237 and C- or higher in MATH 301
MATH
403
Hours
3
Algebraic Structures for Secondary Teachers

Explore the interconnections between the algebraic, analytic, and geometric areas of mathematics with a focus on properties of various number systems, importance of functions, and the relationship of algebraic structures to solving analytic equations. This exploration will also include the development and sequential nature of each of these branches of mathematics and how it relates to the various levels within the algebra mathematics curriculum.

Prerequisite(s): C- or higher in MATH 237 and C- or higher in MATH 301
MATH
405
Hours
3
Geometry for Secondary Teachers

This course will give an overview of geometry from a modern point of view. Axiomatic, analytic, transformational, and algebraic approaches to geometry will be used. The relationship between Euclidean geometry, the geometry of complex numbers, and trigonometry will be emphasized.

Prerequisite(s): C- or higher in MATH 403
MATH
409
Hours
3
Data Analysis for Secondary Teachers

Concepts and techniques of posing questions and collecting, analyzing, and interpreting data. Topics include: univariate and bivariate statistics, probability, simulation, confidence intervals and hypothesis testing.

Prerequisite(s): C- or higher in MATH 125 and C- or higher in MATH 355
MATH
410
Hours
3
Numerical Linear Algebra

Further study of matrix theory, emphasizing computational aspects. Topics include direct solution of linear systems, analysis of errors in numerical methods for solving linear systems, least-squares problems, orthogonal and unitary transformations, eigenvalues and eigenvectors, and singular value decomposition.

Prerequisite(s): (C- or higher in MATH 311) OR ((C- or higher in CS 101) AND (C- or higher in MATH 237))
MATH
411
Hours
3
Numerical Analysis I

Credit will not be granted for both MATH 411 and MATH 300. An introduction to numerical methods. Topics include numerical methods for solving nonlinear equations; iterative methods for solving systems of equations; approximations and interpolations; numerical differentiation and integration; and numerical methods for solving initial value problems for ordinary differential equations.

Prerequisite(s): (C- or higher in MATH 238) AND (C- or higher in MATH 237) AND ( (C- or higher in MATH 311) OR (C- or higher in CS 101) )
MATH
420
Hours
3
Linear Optimization Theory

This course is an introduction to theory of linear programming (focused on development of theory and algorithms with only a limited coverage of examples and applications), a basic component of optimization theory. Topics include: basic theory (fundamental theorem of LP, equivalence of basic feasible solutions and extreme points, duality and sensitivity results), simplex algorithm and its variations, and special applications to transportation and network problems. Non-simplex methods are also briefly introduced.

Prerequisite(s): C- or higher in (MATH 227 or MATH 247) AND (C- or higher in MATH 237) AND ((C- or higher in MATH 311) OR (C- or higher in CS 101))
MATH
421
Hours
3
Non-Linear Optimization Theory

This course is an introduction to nonlinear programming. Topics will include necessary and sufficient conditions for optimality, as well as basic theory and numerical algorithms for several traditional optimization methods, e.g., basic descent methods, conjugate direction methods, quasi-Newton methods, penalty and barrier methods, Lagrange multiplier methods. A brief introduction to selected modern topics may be added if time permits.

Prerequisite(s): C- or higher in (MATH 227 or MATH 247) AND (C- or higher in MATH 237) AND ( (C- or higher in MATH 311) OR (C- or higher in CS 101) )
MATH
441
Hours
3
Boundary Value Problems

Methods of solving the classical second-order linear partial differential equations: Laplace's equation, the heat equation, and the wave equation, together with appropriate boundary or initial conditions. Usually offered in the fall semester.

Prerequisite(s): C- or higher in MATH 343
MATH
451
Hours
3
Math Stats W/Applictn I

Introduction to mathematical statistics. Topics include bivariate and multivariate probability distributions, functions of random variables, sampling distributions and the central limit theorem, concepts and properties of point estimators, various methods of point estimation, interval estimation, tests of hypotheses and Neyman-Pearson lemma with some applications.

Prerequisite(s): C- or higher in MATH 237 and C- or higher in MATH 355
MATH
452
Hours
3
Math Stats W/Applictn II

Further applications of the Neyman-Pearson Lemma, Likelihood Ratio tests, Chi-square test for goodness of fit, estimation and test of hypotheses for linear statistical models, analysis of variance, analysis of enumerative data, and some topics in nonparametric statistics.

Prerequisite(s): C- or higher in MATH 451
MATH
457
Hours
3
Stochastic Processes I

Introduction to the basic concepts and applications of stochastic processes. Markov chains, continuous-time Markov processes, Poisson and renewal processes, and Brownian motion. Applications of stochastic processes including queueing theory and probabilistic analysis of computational algorithms.

Prerequisite(s): C- or higher in MATH 355
MATH
460
Hours
3
Intro Differential Geom

Introduction to basic classical notions in differential geometry: curvature, torsion, geodesic curves, geodesic parallelism, differential manifold, tangent space, vector field, Lie derivative, Lie algebra, Lie group, exponential map, and representation of a Lie group. Usually offered in the spring semester.

Prerequisite(s): C- or higher in (MATH 227 or MATH 247), and C- or higher in MATH 371
MATH
465
Hours
3
Intro General Topology

Basic notions in topology that can be used in other disciplines in mathematics. Topics include topological spaces, open sets, basis for a topology, continuous functions, seperation axioms, compactness, connectedness, product spaces, quotient spaces.

Prerequisite(s): MATH 486
MATH
466
Hours
3
Intro Algebraic Topology

Homotopy, fundamental groups, covering spaces, covering maps, and basic homology theory, including the Eilenberg Steenrod axioms.

Prerequisite(s): MATH 465
MATH
470
Hours
3
Prin Modern Algebra I

A first course in abstract algebra. Topics include groups, cyclic groups, non-abelian groups, Lagrange's theorem, subgroups, cosets, homomorphisms, isomorphisms, rings.

Prerequisite(s): C- or higher in MATH 237 and C- or higher in MATH 301
MATH
471
Hours
3
Prin Modern Algebra II

An introduction to ring theory. Topics include rings, polynomial rings, matrix rings, modules, fields and semi-simple rings. Usually offered in the fall semester.

Prerequisite(s): C- or higher in MATH 470
MATH
485
Hours
3
Intro Complex Variables

Some basic notions in complex analysis. Topics include analytic functions, complex integration, infinite series, contour integration, and conformal mappings.

Prerequisite(s): C- or higher in MATH 227 or C- or higher in MATH 247
MATH
486
Hours
3
Introduction to Real Analysis I

Rigorous development of the calculus of real variables. Topics include the topology of the real line, sequences and series, limits, limit suprema and infima, continuity, and differentiation.

Prerequisite(s): C- or higher in MATH 301
MATH
487
Hours
3
Introduction to Real Analysis II

A continuation of MATH 486. Topics include Riemann integration, sequences and series of functions, uniform convergence, power series, Taylor series. Optional topics may include the Reimann-Stieltjes integration, Weierstrass Approximation Theorem and the Arzela-Ascoli Theorem, metric spaces, multi-variable calculus.

Prerequisite(s): C- or higher in MATH 486
MATH
493
Hours
3
Capstone in Data Science

A project-based course that integrates the skills and abilities developed throughout the curriculum for the Data Science major. The course will require the analysis of a real world data set, a plan for conducting that analysis, a report on the analysis, and an oral presentation of the results and reasoning behind them.

Prerequisite(s): (C- or higher in MATH 359) AND (C- or higher in CS 451)
MATH
495
SP
Hours
1-3
Seminar Directed Reading

Offered as needed.

Special Topics Course
MATH
499
Hours
1-3
Undergrad Research Exp

Independent or collaborative research experience in mathematics.