University of Missouri Department of Mathematics	Undergraduate Studies
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Listed below are most of the courses that mathematics majors take either as required courses or electives in mathematics. The variety of courses offered allows students to design programs to meet their individual needs. The department also teaches a number of additional courses students in the liberal arts or business take to meet general requirements.

The department also offers courses at the graduate level, which mathematics majors may take in their senior year as electives. In some cases, mathematics seniors obtain dual enrollment with the MU Graduate School and receive graduate credit for some courses taken in their final undergraduate year.

MATH 110 Intermediate Algebra (3). Math 0110 is a preparatory course for college algebra that carries no credit towards any baccalaureate degree. However, the grade received in 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. Prerequisite: Elementary College Algebra or equivalent. Placement in Math 110 is based on the student’s ACT math score or equivalent, in addition to other criteria.

MATH 1100 College Algebra for Calculus Bound Students (3) Math 1100 offers a solid mathematical background for students who intend to take business calculus or calculus for the social sciences. Emphasis is placed on developing math skills essential for the study of calculus and on problem-solving. Math 1100 is a college algebra course, consisting of a basic review of the laws of exponents, operations with radical expressions and rational exponents, polynomial identities, factoring, and operations with rational expressions. Students will solve linear, absolute value, quadratic, polynomial, and rational equations and inequalities; equations involving radicals, exponential and logarithmic equations, and systems of equations along with applications. The course covers equations and graphs of lines and circles; the concepts of function, domain, range, operations with functions, rigid and non-rigid transformations with functions and average rates of change along with the characteristic properties of linear, quadratic, polynomial, exponential and logarithmic functions, applications and modeling. Prerequisite: A score of 22-23 or above on the math component of the ACT or equivalent, or successful completion of Intermediate Algebra with a grade in the C range or above.

MATH 1120 College Algebra for Non-Calculus Bound Students (3) Math 1120 is a college algebra course designed for students who will not be taking calculus. It is an application-driven course, leading the student from applications to theory. Math 1120 starts with a unit on making sense of data and functions. Families of functions are used to model real-world behavior and emphasis is placed on linear, exponential, logarithmic, and quadratic functions along with their characteristic properties. Real data sets are used extensively throughout, motivating abstract concepts, and forming the basis of many exercises and examples. Mathematical modeling and curves of best fit are an integral part of the course. The course includes: a review of sets and operations with sets; the laws of exponents and radicals; the solution of linear equations and inequalities; quadratic, polynomial, radical, exponential, and logarithmic equations; and systems of linear and non-linear equations. Also covered in the course: multiple conversion factors allowing to go from one unit system to another, scientific notation, logarithmic scales, and an extensive study of average rate of change with applications. Prerequisite: A score of 22-23 or above on the math component of the ACT or equivalent, or successful completion of Intermediate Algebra with a grade in the C range or above.

MATH 1121 College Algebra Bridge Course for Calculus (1). Math 1121 is intended for students who have successfully completed Math 1120 and have decided to take Math 1320 or 1400. The topics covered in Math 1121 are a selection of topics from a traditional College Algebra course, which have not been covered or emphasized in Math 1120, but are prerequisites for the study of calculus. In this course, emphasis will be put on algebraic manipulative skills as well. A Casio FX-9750G Plus or a CFX-9850GC Plus calculator is required for this course. Prerequisites: a grade in the C range or above in Math 1120.

MATH 1140 Trigonometry (2). A student may receive at most 5 units of credit from among the mathematics courses Math 1100, 1120, 1140, 1160, 1180. Prerequisite: Math 1100 or 1120 or an ACT math score of 23 or higher.

MATH 1160 Precalculus Mathematics (5). Review of elementary algebra. Background material for Mathematics 1500, including algebraic, trigonometric, logarithmic, exponential functions. A student may receive at most 5 units of credit from among the mathematics courses 1140, 1100/1120, 1160, and 1180. Prerequisite: Math 1100 or 1120 or an ACT math score of 23 or higher.

MATH 1180 Elementary Functions (3). Review of elementary algebra. Background material for Mathematics 1500 including, algebraic, trigonometric, lograrithms, exponential functions. A student may receive at most 5 units of credit from among the mathematics courses 100, 1120, 1140, 1160, 1180. Prerequisite: 2 units high school algebra, 1 unit geometry.

MATH 1300 Finite Mathematics (3). Introduces matrices and linear programming and probability. Prerequisite: grade of C- or better in MATH 1100 or 1120 or 1160 or an ACT math score of 26 or higher.

MATH 1320 Elements of Calculus (3). Introductory 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: grade of C- or better in MATH 1100 or 1160 or an ACT math score of 26 or higher.

MATH 1340 Algebra and Number Systems for Teachers (3). This course covers the tools of problem solving, problem posing, modeling, the real number system, other number systems, functions, logic, sets, probability and statistics, with a focus on number sense. Prerequisite: Math 1100 or 1120.

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, transformation, 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: Math 1100/1120 or equivalent.

MATH 1380 The Mathematics of Finance (3). Compound interest, annuities with variety of applications; introduction to mathematics of life insurance. Prerequisite: A grade of C in Math 1100 or 1120.

MATH 1400 Calculus for Social and Natural Sciences 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 Math 1100 or 1160 or an ACT math score of 26 or higher.

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 1160 or both 1100 and 1140 or an ACT math score of 26 or higher.

MATH 1500H Analytic Geometry and Calculus I (5). Elementary analytic geometry, functions, limits, continuity, derivatives, antiderivatives, definite integrals. Prerequisite: grade of C- or better in MATH 1160 or both 1100 and 1140 or an ACT math score of 26 or higher. Honors eligibility required.

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: departmental 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: departmental 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 Math 1500.

MATH 1700H Calculus II (5). Definite integrals, applications and techniques of integration, elementary transcendental functions, infinite series. Prerequisite: A grade of C or better in Math 1500. Honors eligibility required.

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 Math 1800 and 1320, 1400 or 1500. Prerequsites: 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 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 Math 1900 and 1700 or 2100. Prerequisite: Math 1800 or instructor's consent. Graded on A/F basis only.

MATH 2100 Calculus for Social and Natural 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. Prerequisite: Math 1320 or 1400 or 1500.

MATH 2120 Elementary Matrix Algebra with Applications (3). Systems of linear equations, matrices, determinants, and properties of n-dimensional Euclidean space. Various applications will be considered. Prerequisite: one of Math 1320, 1300, 1340, or 1500.

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

MATH 2300 Calculus III (3). Vectors, solid analytic geometry, calculus of several variables. Prerequisite: A grade of C or better in Math 1700.

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

MATH 2320 Discrete Mathematical Structures (3). Sets, functions, logic, relations, inductions, recursions, counting techniques, graphs, trees, algorithms. Prerequisites:  one of Math 1700, 2340, 2140, 4060 or 4070.

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

MATH 2500 Elementary Logic and Set Theory (3). Introduction to logic, set theory, denumerable and nondenumerable sets, and cardinal arithmetic. Prerequisites:  one of Math 2300, 2120, or 2340.

MATH 4001 Topics in Mathematics-General (cr. arr.). Organized study of selected topics. Subjects and earnable credit may vary from semester to semester. Prerequisite: 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. Prerequisite: 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: 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: MATH 1320, enrollment is restricted to Math Education majors.

MATH 4080 Calculus for Teachers (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: MATH 1160, enrollment is restricted to Math Education majors.

MATH 4100 Differential Equations (3). Traditional introductory course in ordinary differential equations. Includes first and second order linear differential equations with numerous applications; Laplace transforms; power series solutions; numerical methods, linear systems. Prerequisite: Math 2300.

MATH 4110 Advanced Calculus with Applications (3). Linear mappings, Jacobi matrices and determinants, changes of variables, vector fields, line and surface integrals, theorems of Green, Gauss and Stoke's, sequences and series of functions, uniform convergence, special functions. Prerequisite: 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 and introduction to Ramsey theory. Prerequisite: 2320 or instructor’s consent.

MATH 4130 Theory of Equations (3). Study of polynomials and their zeros and elementary determinant and matrix theory. Prerequisite: Math 2300 or 2320.

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 Math 2120, 2300, 2320 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. Co/Prerequisite: Math 2300 or 2340.

MATH 4160 Mathematical Logic (3). Introduction to classical modern logics as deductive systems; applications to foundations of mathematics. Prerequisites: junior or senior standing, and interest in mathematics or philosophy.

MATH 4300 Numerical Analysis (3). Machine arithmetic, approximation and interpolation, numerical differentiation and integration, nonlinear equations, linear systems, differential equations, error analysis. Selected algorithms programmed for solutions on computers. Prerequisite: Math 2300 and familiarity iwth 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 will be programmed for solution on computers. Prerequisite: Math 2300 and prior experience writing programs in Mathematica and/or in a computer language such as Fortran, Pascal, or C. Recommended: Math 4140.

MATH 4315 Introduction to Mathematical Statistics (3) (same as STAT 4710). Introduction to the theory of probability and statistics using methods and concepts of calculus. Prerequisite: Math 2300, or instructor's consent.

MATH 4320 Introduction to Probability Theory (3) (same as STAT 4750). Probability spaces; random variables and their distributions; repeated trials; probability limit theorems. Prerequisite: Math 2300 or instructor's consent.

MATH 4325 Linear Programming (3). Linear dependence and rank in vector spaces in Rn, Farkas' Lemma, Polyhedra Decomposition. Strong duality and complementary theorems. The simplex method, revised simplex and sensitivity analysis. Primal dual simplex methods. Computational Complexity and Karmarkar's Algorithm. Prerequisite: Math 4140 or instructor'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. Prerequisite: 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: 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: 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: 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: 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: Math 2300 and Stat 2500, 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 population growth. Prerequisites: 2300 and Stat 2500, or instructor’s consent No variable credit.

MATH 4370 Actuarial Modeling I (3). This course covers the main probability tools applied to financial risks modeling, and the financial mathematics concepts used in calculating present and accumulated values for various cash flows. It is a helpful tool in preparing for the Society of Actuaries exams P (Probability) and FM (Financial Mathematics), and it is oriented towards problem solving techniques illustrated with previous exam problems. Prerequisites: MATH 2300, and 4320 or STAT 4750. Students are encouraged to take MATH 4355 prior to this course.

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: MATH 2300 and 4320 or STAT 4750. Students are encouraged to take 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: 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: Math 4100.

MATH 4510 Higher Algebra (3). Introduction to rings, integral domains, fields, groups. Prerequisite: Math 2300 or 2320.

MATH 4520 Statistical Inference I (3) (same as STAT 4751). Sampling; point estimation; sampling distribution; tests of hypotheses; regression and linear hypotheses. Prerequisite: Math 4320.

MATH 4530 Applied Modern Algebra (3). Introduction to modern algebra; emphasis on applications to computer science, engineering, related subjects. Basic concepts of modern algebra applied to computer design. Prerequisite: Math 2300 or 2320 and the ability to program in a high-level language such as Fortran, Pascal or C.

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: 4100/7100, 4140/7140, and familiarity with software such as MATHEMATICA, MATLAB, or MAPLE.

MATH 4570 Fluid Dynamics and Geo-physical Applications (3). Mathematical theory of fluid dynamics and applications to meteorology and oceanography. Prerequisite: 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 Math 4540 will be considered. Prerequisite: 3 semesters of calculus and some exposure to ordinary differential equations or instructor’s consent. 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: 2300 and Stat 2500, or instructor’s consent. Recommended: 4355. No variable credit.

MATH 4700 Advanced Calculus I (3). Basic topology of the real line, numerical sequences and series, properties of continuous functions, differentiation, Riemann-Stieltjes integration, uniform convergence. Prerequisite: Math 2300. Recommended: Math 4140 and one other mathematics course numbered above 2300.

MATH 4720 Introduction to Abstract Algebra I (3). Basic properties of integers, fundamental theorem of arithmetic, introduction to groups, rings and fields. Prerequisite: Math 2300. Recommended: Math 4140 and one other mathematics course numbered above Math 2300.

MATH 4900 Advanced Calculus II (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: 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: Math 4720.

MATH 4940 Introduction to Complex Variables (3). Complex functions, contour integration, power series, residues and poles, conformal mapping. Prerequisite: Math 4110 or 4700.

MATH 4960 Special Readings in Mathematics (1-3). Prerequisite: Math 2300 and instructor's consent.

MATH 4970 Senior Seminar (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: 4140 and another 4000 level Mathematics course, or instructor’s consent.

MATH 4996 Honors in Mathematics (3). Special work for senior BA Honors and BS Honors candidates.