Undergraduate Studies

MATH _0110-Intermediate Algebra (3). Mathematics [MATH] 0110 is a preparatory course for college algebra that carries no credit towards any baccalaureate degree. However, the grade received in Mathematics [MATH] 0110 does count towards a student’s overall GPA. The course covers operations with real numbers, graphs of functions, domain and range of functions, linear equations and inequalities, quadratic equations; operations with polynomials, rational expressions, exponents and radicals; equations of lines. Emphasis is also put on problem-solving. Prerequisites: Elementary College Algebra or equivalent. Placement in Mathematics [MATH] 0110 based on the student’s ACT math score or equivalent, in addition to other criteria.

MATH 1100-College Algebra (3). A review of exponents, order of operations, factoring, and simplifying polynomial, rational, and radical expres sions. Topics include: linear, quadratic, polyno mial, rational, inverse, exponential, and logarithmic functions and their applications. Students will solve equations involving these functions, and systems of linear equations in two variables, as well as inequali ties. Prerequisite: Mathematics [MATH] 0110 or a sufficient score on the ALEKS exam. This course is offered in both 3 day and 5 day versions. See the math placement website for specific requirements. A student may receive at most 5.0 credit hours among the Mathematics courses 1100, 1120, 1140, and 1160.

MATH 1140-Trigonometry (2). Prerequisite: Math [MATH] 1100 or sufficient ALEKS score. A student may receive only 5 credits from among Math [MATH] 1100, Math [MATH] 1140, and Math [MATH] 1160. A Student may receive at most 5.0 credit hours from the Mathematics courses 1100, 1120, 1140, and 1160.

MATH 1160-Precalculus Mathematics (5). Review of elementary algebra. Background material for Mathematics 1500, including algebraic, trigonomet ric, logarithmic, exponential functions. Prerequisites: B+ or better in Math [MATH] 0110 (at MU), or Math 1100, or sufficient ALEKS score. A student may receive at most 5 credits from among Math [MATH] 1100, Math [MATH] 1140, and Math [MATH] 1160. A student may receive at most 5 credit hours from among the Mathematics courses 1100, 1120, 140, and 1160.

MATH 1300-Finite Mathematics (3). A selections of topics in finite mathematics such as: basic financial mathematics, counting methods and basic prob ability and statistics, systems of linear equations and matrices. Prerequisites: Math [MATH] 1100, or Math [MATH] 1160, or both a College Algebra exemp tion and sufficient ALEKS score. Warning: without a College Algebra exemption, a sufficient ALEKS score will not suffice unless it is a proctored exam (for Math [MATH] 1100 credit).

MATH 1320-Elements of Calculus (3). Introduc tory analytic geometry, derivatives, definite integrals. Primarily for Computer Science BA candidates, Economics majors, and students preparing to enter the College of BUS. No credit for students who have completed a calculus course. Prerequisite: Math [MATH] 1100, or Math [MATH] 1160, or sufficient ALEKS score. A student may receive credit for Math [MATH] 1320 or 1400, but not both. A student may receive at most 5 credit hours among the Mathemat ics courses 1320 or 1400 and 1500.

MATH 1360-Geometric Concepts (3). This course is primarily for education majors. This course covers topics of Euclidean geometry such as the study of points, lines, angles, polygons, circles, congruence, similarity, transformations, symmetry, area, surface area, arc length, and volume. Polyhedra, spheres, cones, and other solids are discussed. The course includes constructions and proofs, and uses inductive and deductive reasoning throughout. Prerequisite: Mathematics [MATH] 1100 or 1120 or equivalent. Math Reasoning Proficiency Course.

MATH 1400-Calculus for Social and Life Sci ences I (3). The real number system, functions, analytic geometry, derivatives, integrals, maximum- minimum problems. No credit for students who have completed a calculus course. Prerequisite: grade of C- or better in Mathematics [MATH] 1100 or 1160, or sufficient ALEKS score. A student may receive credit for Mathematics [MATH] 1320 or 1400 but not both. A student may receive at most 5 units of credit among the Mathematics [MATH] 1320 or 1400 and 1500. Math Reasoning Proficiency Course.

MATH 1500-Analytic Geometry and Calculus I (5). Elementary analytic geometry, functions, limits, continuity, derivatives, antiderivatives, definite integrals. Prerequisite: grade of C- or better in Math ematics [MATH] 1160 or both 1100 and 1140 or suf ficient ALEKS score. A student may receive at most 5 units of credit among the Mathematics [MATH] courses 1320 or 1400 and 1500. Math Reasoning Proficiency Course.

MATH 1500H-Analytic Geometry and Calculus I - Honors (5). Elementary analytic geometry, functions, limits, continuity, derivatives, antiderivatives, definite integrals. Prerequisites: Mathematics [MATH] 1160 or both 1100 and 1140 sufficient ALEKS score. Honors eligibility required. A student may receive at most 5 units of credit among the Mathematics [MATH] courses 1320 or 1400 and 1500. Math Reasoning Proficiency course.

MATH 1601-Selected Topics in Mathematics-General (1-3). The special topics covered may vary from term to term. This course may be repeated. Prerequisite: instructor’s consent.

MATH 1602-Selected Topics in Mathematics-Biological/Physical/Math (1-3). The special topics covered may vary from term to term. This course may be repeated. Prerequisite: instructor’s consent.

MATH 1700-Calculus II (5). Definite integrals, applications and techniques of integration, elementary transcendental functions, infinite series. Prerequisite: a grade of C- or better in Mathematics [MATH] 1500. Math Proficiency Reasoning course.

MATH 1700H-Calculus II - Honors (5). Definite integrals, applications and techniques of integration, elementary transcendental functions, infinite series. Prerequisite: a grade of C- or better in Mathematics [MATH] 1500. Honors eligibility required. Math Reasoning Proficiency course.

MATH 1800-Introduction to Analysis I (5). This course will cover the material taught in a traditional first semester calculus course at a more rigorous level. The focus of this course will be on proofs of basic theorems of differential and integral calculus. The topics to be covered include axioms of arithmetic, mathematical induction, functions, graphs, limits, continuous functions, derivatives and their applications, integrals, the fundamental theorem of calculus and trigonometric functions. Students in this class will be expected to learn to write clear proofs of mathematical assertions. Some previous exposure to calculus is helpful but not required. No credit for Mathematics [MATH] 1800 and 1320, 1400 or 1500. Prerequisites: ACT mathematics score of at least 31 and ACT composite of at least 30 or instructor’s consent. Graded on A/F basis only.

MATH 1900-Introduction to Analysis II (5). This course is a continuation of Mathematics [MATH] 1800. In this course we shall cover uniform convergence and uniform continuity, integration, and sequences and series. The topics will be covered in a mathematically rigourous manner. No credit for Mathematics [MATH] 1900 and 1700 or 2100. Prerequisite: Mathematics [MATH] 1800 or instructor’s consent. Graded on A/F basis only.

MATH 2100-Calculus for Social and Life Sciences II (3). Riemann integral, transcendental functions, techniques of integration, improper integrals and functions of several variables. No credit for students who have completed two calculus courses. Prerequisites: Mathematics [MATH] 1320 or 1400 or 1500. Math Reasoning Proficiency Course.

MATH 2140-Geometric Axioms and Structures (3). Euclidean Geometry, Axiom systems, spherical geometry, finite geometries, and explorations with technology. Prerequisite: Mathematics [MATH] 1340 or 1360.

MATH 2300-Calculus III (3). Vectors, solid analytic geometry, calculus of several variables. Prerequisite: grade of C- or better in Mathematics [MATH] 1700. Mathematics Reasoning Proficiency.

MATH 2300H-Calculus III - Honors (3). Vectors, solid analytic geometry, calculus of several variables. Prerequisite: grade of C or better in Mathematics [MATH] 1700. Honors eligibility required. Math Proficiency course.

MATH 2320-Discrete Mathematical Structures (3). Sets, functions, logic, relations, induction, recursion, counting techniques, graphs, trees, algorithms. Prerequisites: one of Mathematics [MATH] 1700, 2340, or 2140. Math Reasoning Proficiency course.

MATH 2340-Algebraic Structures (3). Introduction to axiomatic mathematics with emphasis on rings and groups. Applications to elementary number theory. Prerequisite: Mathematics [MATH] 1300 and 1320 or instructor’s consent.

MATH 3000-Introduction to Advanced Mathematics (3). Gateway to theoretical math courses. Focus on reading and writing math proofs/rigorously developing background needed in Adv Calc/Abstract Alg. Topics include logic, set theory, properties of functions and integers, the real number system, completeness of the real numbers, sequences of real numbers. Prerequisite: Mathematics [MATH] 1700 or permission of the instructor/department.

MATH 4001-Topics in Mathematics-General (cr. arr.). Organized study of selected topics. Subjects and earnable credit may vary from semester to semester. Prerequisites: Mathematics [MATH] 2300 and instructor’s consent. Departmental consent for repetition.

MATH 4002-Topics in Mathematics-Biological/ Physical/Math (cr.arr.). Organized study of selected topics. Subjects and earnable credit may vary from semester to semester. Prerequisites: Mathematics [MATH] 2300 and instructor’s consent. Departmental consent for repetition.

MATH 4060-Connecting Geometry to Middle and Secondary Schools (3). Euclidean foundations, logic, Euler Characteristic, congruence, area, Pick’s Theorem, volume, Cavalieri’s Principle, surface area, similarity, symmetry, transformations, matricies, introduction to spherical geometry. Prerequisites: Mathematics [MATH] 1360 or 1500.

MATH 4070-Connecting Algebra to Middle and Secondary Schools (3). A detailed study of integer and rational arithmetic and algebra. Topics include: Bionomial Theorem, induction, division algorithm, Euclid’s Algorithm, Fundamental Theorem of Arithmetic, Pythogorian triples, modular arithmetic and generalizations to polynomials, matrices and other axiomatic structures. Prerequisite: Mathematics [MATH] 1320, enrollment is restricted to Math Education majors.

MATH 4080-Calculus Connections (3). Course topics include: sequences, series, functions, limits, continuity, differentiation, optimization, curve sketching, antidifferentiation, areas of plane regions, lengths of plane curves, areas of surfaces of revolution, and volumes of solids. Prerequisites: Mathematics [MATH] 1160, enrollment is restricted to Math Education majors.

MATH 4100-Differential Equations (3). Traditional introductory course in ordinary differential equations. Includes 1st and 2nd order linear differential equations with numerous applications; Laplace transforms; power series solutions; numerical methods, linear systems. Prerequisite: Mathematics [MATH] 2300.

MATH 4110-Advanced Calculus With Applications (3). Linear mappings, Jacobi matrices and determinants, change of variables, vector fields, line and surface integrals, theorems of Green, Gauss and Stokes, sequences and series of functions, uniform convergence, special functions. Prerequisite: Mathematics [MATH] 2300.

MATH 4120-Combinatorics (3). Study of a variety of topics from combinatorial mathematics, especially graph theory and enumerative combinatorics. Topics include graph coloring, matchings and coverings, generating functions, recurrence relations, Polya’s Enumeration Theorem, introduction to Ramsey theory. Prerequisites: Mathematics [MATH] 2320, or instructor’s consent.

MATH 4140-Matrix Theory (3). Basic properties of matrices, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and Jordan normal forms. Introduction to writing proofs. Prerequisite: one of Mathematics [MATH] 2300, 2320, 2120 or 2340.

MATH 4150-History of Mathematics (3). This is a history course with mathematics as its subject. Includes topics in the history of mathematics from early civilizations onwards. The growth of mathematics, both as an abstract discipline and as a subject which interacts with others and with practical concerns, is explored. Pre- or Co-requisite: Mathematics [MATH] 2300 or 2340.

MATH 4300-Numerical Analysis (3). Machine arithmetic, approximation and interpolation, numerical differentiation and integration, nonlinear equations, linear systems, differential equations, error analysis. Selected algorithms will be programmed for solution on computers. Prerequisites: Mathematics [MATH] 2300 and familiarity with softwares such as Mathematica MatLab or Maple, etc.

MATH 4310-Numerical Linear Algebra (3). Solution of linear systems of equations by direct and iterative methods. Calculation of eigenvalues and eigenvectors of matrices. Selected algorithms programmed for solution on computers. Prerequisites: Mathematics [MATH] 2300 and familiarity with software such as Mathematica, MatLab, Maple, etc.

MATH 4315-Introduction to Mathematical Statistics (3). (same as Statistics [STAT] 4710). Introduction to theory of probability and statistics using concepts and methods of calculus. Prerequisites: Mathematics [MATH] 2300 or instructor’s consent.

MATH 4320-Introduction to Probability Theory (3). (same as Statistics {STAT] 4750). Probability spaces; random variables and their distributions; repeated trials; probability limit theorems. Prerequisites: Mathematics [MATH] 2300 or instructor’s consent.

MATH 4325-Linear Programming (3). Linear dependence and rank in vector spaces in Rn, Farkas’ Lemma, Polyhedral Decomposition. Strong duality and complementary theorems. The simplex method, revised simplex, and sensitivity analysis. Primal Dual simplex method and network simplex methods. Computational Complexity and Karmarkar’s Algorithm. Prerequisites: Mathematics [MATH] 4140 or instruc-tor’s consent.

MATH 4330-Theory of Numbers (3). Divisibility, factorization, arithmetic functions, means value theorems, distribution of prime numbers, congruences, primitive roots, character theory, Riemann zeta function, and Dirichlet L-functions. Prerequisites: Mathematics [MATH] 2300; recommended 2320 or 2340, and 4940/7940.

MATH 4335-College Geometry (3). Euclidean geometry from an advanced viewpoint. Synthetic and coordinate methods will be used. The Euclidean group of transformations will be studied. Prerequisite: Mathematics [MATH] 2300.

MATH 4340-Projective Geometry (3). Basic ideas and methods of projective geometry built around the concept of geometry as the study of invariants of a group. Extensive treatment of collineations. Prerequisite: Mathematics [MATH] 2300.

MATH 4345-Foundations of Geometry (3). Coordination of affine, projective planes by means of various kinds of algebraic structures: planar ternary rings, Veblen-Wedderburn systems, divisions rings, skew fields, and fields. Prerequisite: Mathematics [MATH] 2300.

MATH 4350-Introduction to Non-Euclidean Geometry (3). Account of rise, development of non-Euclidean geometries. Intensive study of plane hyperbolic geometry. Prerequisite: Mathematics [MATH] 2300.

MATH 4355-Investment Science I (3). Deterministic cash flow streams. The present value. Bonds, bonds’ yield, duration. The term structure of interest rates. Single-period random yield analysis. Random returns. Portfolio mean-variance analysis. Markovitz model. Prerequisites: Mathematics [MATH] 2300 and either Statistics [STAT] 2500 or Statistics [STAT] 4710/ Mathematics [MATH] 4315, or instructor’s consent.

MATH 4360-Actuarial Mathematics (3). Basic actuarial methods, mathematical population studies and models of population growth. Compound interest and annuities certain. Values of endowment and annuities, calculation of premiums, surrender values. Stochastic models of populations growth. Prerequisite: Mathematics [MATH] 2300 and either Statistics [STAT] 2500 or Statistics [STAT] 4710 Mathematics [MATH] 4315, or instructor’s consent. No variable credit.

MATH 4370-Actuarial Modeling I (3). This course covers the concepts underlying the theory of interest and their applications to valuation of various cash flows, annuities certain, bonds, and loan repayment. This course is designed to help students prepare for Society of Actuaries exam FM (Financial Mathematics). It is oriented towards problem solving techniques applied to real-life situations and illustrated with previous exam problems. Prerequisites: grade of C-or better in Mathematics [MATH] 2300.

MATH 4371-Actuarial Modeling II (3). This course covers the actuarial models and their applications to insurance and other business decisions. It is a helpful tool in preparing for the Society of Actuaries exam M (Actuarial Models), and it is oriented towards problem solving techniques illustrated with previous exam problems. Prerequisites: Mathematics [MATH] 2300 and 4320 or Statistics [STAT] 4750. Students are encouraged to take Mathematics [MATH] 4355 prior to this course.

MATH 4400-Introduction to Topology (3). Topics from topology of Euclidean spaces, generalizations to metric spaces and topological spaces. Fundamentals of point set topology. Prerequisite: Mathematics [MATH] 2300.

MATH 4500-Applied Analysis (3). Solution of the standard partial differential equations (wave, heat, Laplace’s eq.) by separation of variables and transform methods; including eigenfunction expansions, Fourier and Laplace transform. Boundary value problems, Sturm-Liouville theory, orthogonality, Fourier, Bessel, and Legendre series, spherical harmonics. Prerequisite: Mathematics [MATH] 4100.

MATH 4510-Higher Algebra (3). Introduction to rings, integral domains, fields, groups. Prerequisites: Mathematics [MATH] 2300 or 2320.

MATH 4520-Statistical Inference I (3). (same as Statistics [STAT] 4760). Sampling; point estimation; sampling distribution; tests of hypotheses; regression and linear hypotheses. Prerequisite: Mathematics [MATH] 4320.

MATH 4540-Mathematical Modeling I (3). Solution of problems from industry, physical, social and life sciences, economics, and engineering using mathematical models. Prerequisites: 3 semesters of calculus and some exposure to ordinary differential equations or instructor’s consent.

MATH 4560-Nonlinear Dynamics, Fractals and Chaos (3). Conceptual introduction to nonlinear dynamics, bifurcation and stability of steady states, chaos in nonlinear differential equations and maps, fractal dimension, strange attractors, and applications to physical science. Prerequisite: Mathematics [MATH] 4100/ 7100, 4140/7140, and familiarity with software such as MATHEMATICA, MATLAB, or MAPLE.

MATH 4570-Fluid Dynamics and Geophysical Applications (3). Mathematical theory of fluid dynamics and applications to meteorology and oceanography. Prerequisites: Mathematics [MATH] 2300 and instructor’s consent.

MATH 4580-Mathematical Modeling II (3). Solution of problems from industry, physical, social and life sciences, economics, and engineering using mathematical models. More general classes of problems than in Mathematics 4540 will be considered. Prerequisites: 3 semesters of calculus and some exposure to ordinary differential equations or instructor’s consent. Mathematics [MATH] 4540 is not a prerequisite.

MATH 4590-Investment Science II (3). Derivative securities, forward and future contracts, forward prices, hedging. Mean-variance hedging. Stochastic models of asset dynamics, random walks and binomial models. Capital budgeting, optimal portfolios. Basic option theory, put-call parity. Prerequisite: Mathematics [MATH] 2300 and Statistics [STAT] 2500 or Statistics [STAT] 4710/ Mathematics [MATH] 4315, or instructor’s consent. Recommended: Mathematics [MATH] 4355. No variable credit.

MATH 4700-Advanced Calculus of One Real Variable I (3). Basic topology of the real line, numerical sequences and series, continuity, differentiability, Riemann integration, uniform convergence, power series. Prerequisite: Mathematics [MATH] 3000.

MATH 4720-Introduction to Abstract Algebra I (3). Basic properties of integers, fundamental theorem of arithmetic, introduction to groups, rings and fields. Prerequisite: Mathematics [MATH] 3000.

MATH 4800-Advanced Calculus for One Real Variable II (4). Continuation of Advanced Calculus for functions of a single real variable. Topics include sequences and series of functions, power series and real analytic functions, Fourier series. Prerequisites: Mathematics [MATH] 4700/7700 or permission of the instructor.

MATH 4900-Advanced Multivariable Calculus (3). This is a course in calculus in several variables. The following is core material: Basic topology of n-dimensional Euclidian space; limits and continuity of functions; the derivative as a linear transformation; Taylor’s formula with remainder; the Inverse and Implicit Function Theorems, change of coordinates; integration (including transformation of integrals under changes of coordinates); Green’s Theorem. Additional material from the calculus of several variables may be included, such as Lagrange multipliers, differential forms, etc. Prerequisite: Mathematics [MATH] 4700.

MATH 4920-Introduction to Abstract Linear Algebra (3). Study of vector spaces over arbitrary fields: topics include linear maps on finite dimensional vector spaces, bilinear and multi-linear forms, invariant subspaces and canonical forms. Prerequisite: Mathematics [MATH] 4720.

MATH 4940-Introduction to Complex Variables (3). Complex functions, contour integration, power series, residues and poles, conformal mapping. Prerequisites: Mathematics [MATH] 4110 OR 4700.

MATH 4960-Special Readings in Mathematics (1-3). Prerequisites: Mathematics [MATH] 2300 and instructor’s consent.

MATH 4970-Senior Seminar in Mathematics (3). Seminar with student presentations, written projects, and problem solving. May be used for the capstone requirement. Prerequisite: 12 hours of mathematics courses numbered 4000 or above.

MATH 4980-Mathematics Problem Solving (3). Creative advanced problem solving bringing together methods such as integration, probability and Euclidean geometry. Prerequisite: Mathematics [MATH] 4140 and another 4000 level Mathematics course, or instructor’s consent.

MATH 4996-Honors in Mathematics (2). Special work for senior B.A. Honors and B.S. Honors candidates.