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 grade of "C-" or higher 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.

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 a C- or higher in MATH 100
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): MATH 113 and MATH 112; or 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): MATH 125 or MATH 131 or 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

Arithmetic of whole numbers and integers, fractions, proportion and ratio, and place value. Class activities initiate investigations underlying mathematical structure in arithmetic processes and include hands-on manipulatives for modeling solutions. Emphasis is on the explanation of the mathematical thought process. Students are required to verbalize explanations and thought processes and to write reflections on assigned readings on the teaching and learning of mathematics.

Prerequisite(s): MATH 100 or MATH 110 or MATH 112 or MATH 113 or MATH 125
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): MATH 208
MATH
210
Hours
3
Data Analysis Probabil Stats

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 is integrated throughout the course.

Prerequisite(s): 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): MATH 146 or MATH 126
Mathematics
MATH
237
C, MA
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): (MATH 126 or MATH 146) and CS 102
Computer Science, Mathematics
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): (MATH 126 or MATH 146) and CS 102
Prerequisite(s) with concurrency: MATH 227 or MATH 247
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
300
Hours
3
Intro Numerical Analysis

Credit will not be granted for both MATH 300 and MATH 411. A beginning course in numerical analysis. Topics include number representation in various bases, error analysis, location of roots of equations, numerical integration, interpolation and numerical differentiation, systems of linear equations, approximations by spline functions, and approximation methods for first-order ordinary differential equations and for systems of such equations.

Prerequisite(s): (MATH 227 or MATH 247) and (CS 100 or AEM 249 or ECE 285 or RRS 101)
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 within this discipline is required for a passing grade in this course.

Prerequisite(s): MATH 125 or MATH 145
Writing
MATH
302
Hours
1
Topics in Discrete Mathematics

A supplemental course in discrete mathematics covering select topics of interest in computer science. Topics include graphs and trees, finite state automata and regular expressions, efficiency of algorithms.

Prerequisite(s): MATH 301
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): 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): MATH 227 or MATH 247
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): MATH 237
MATH
382
Hours
3
Advanced Calculus

Further study of calculus with emphasis on theory. Topics include limits and continuity of functions of several variables; partial derivatives; transformations and mappings; vector functions and fields; vector differential operators; the derivative of a function of several variables as a linear transformation; Jacobians; change of variables in multiple integrals; line and surface integrals; and Green's, Stokes', and Divergence Theorems.

Prerequisite(s): MATH 227 or MATH 247; and MATH 237.
MATH
402
Hours
3
History Of Mathematics

Survey of the development of some of the central ideas of modern mathematics, with emphasis on the cultural context. Writing proficiency within this discipline is required for a passing grade in this course.

MATH
403
Hours
3
Adv Math Connections & Devlpmn

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): MATH 237 and MATH 301
MATH
404
Hours
1
Topics Math Secondary Teachers

This is a seminar style course focusing on various mathematical topics related to the high school curriculum. Topics will vary depending upon instructor.

Prerequisite(s): MATH 301
MATH
405
Hours
3
Geometry For Teachers

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

Prerequisite(s): MATH 403
MATH
409
Hours
3
Advanced Data Analysis

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): MATH 125 and ST 260
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): MATH 237 and (CS 100 or AEM 249 or ECE 285 or RRS 101)
MATH
411
Hours
3
Numerical Analysis I

Credit will not be granted for both MATH 411 and MATH 300. A rigorous 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): MATH 237 and MATH 238 and (CS 100 or AEM 249 or ECE 285 or RRS 101)
MATH
412
Hours
3
Numerical Analysis II

This is the second course in the numerical analysis sequence for senior students in mathematics, science, or engineering. Topics include numerical methods for solving boundary value problems, ordinary differential equations, and partial differential equations, multistep methods for initial value problems, and approximation theory (least-squares problems,fast Fourier Transforms).

Prerequisite(s): MATH 343 and MATH 411
MATH
420
Hours
3
Linear Optimization Theory

In-depth theoretical development and analysis of linear programming. Topics include formulation of linear programs, various simplex methods, duality, sensitivity analysis, transportation and networks and various geometric concepts.

Prerequisite(s): (MATH 227 OR MATH 247) AND MATH 237 AND (CS 100 OR AEM 249 OR ECE 285 OR RRS 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): MATH 237 and (MATH 227 or MATH 247) and (CS 100 or AEM 249 or ECE 285 or RRS 101)
MATH
422
Hours
3
Mathematics For Finance I

Topics include the basic no-arbitrage principle, binomial model, time value of money, money market, risky assets such as stocks, portfolio management, forward and future contracts, and interest rates.

Prerequisite(s): (MATH 227 or MATH 247) and MATH 355
MATH
432
Hours
3
Graph Theory & Applictns

Survey of several of the main ideas of general theory with applications to network theory. Topics include oriented and nonoriented linear graphs, spanning trees, branching and connectivity, accessibility, planar graphs, networks and flows, matching, and applications.

Prerequisite(s): MATH 237 or MATH 257
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: MATH 343, or consent of the department.

Prerequisite(s): MATH 343
MATH
442
Hours
3
Integral Transf & Asympt

Complex variable methods, integral transforms, asymptotic expansions, WKB method, Airy's equation, matched asymptotics, and boundary layers.

Prerequisite(s): C- or higher in MATH 441
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): MATH 237 and 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): 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): 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): MATH 486
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): 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): MATH 470
MATH
474
Hours
3
Cryptography

Introduction to rapidly growing area of cryptography, an application of algebra, especially number theory. Usually offered in the Fall semester.

Prerequisite(s): 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): MATH 227
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): 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): MATH 486
MATH
495
Hours
1-3
Seminar Directed Reading

Offered as needed.

MATH
499
Hours
1-3
Undergraduate Research Experience

Independent or collaborative research experience in mathematics.