University of Missouri - Kansas City : Mathematics

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Mathematics

MATH 100 Intermediate Algebra

Numbers and their arithmetic properties, introduction to elementary algebra including exponents and radicals, elementary geometry and formulas, linear and quadratic functions and their graphs, and equations with two unknowns. Given on credit, no-credit basis. Does not fulfill Arts and Sciences mathematics requirement. Does not count toward graduation. Fall, Winter,

3 hrs

MATH 105 The Language Of Mathematics

Reading comprehension and writing skills in the language of Mathematics; grammar, syntax and logic, understanding, expressing, proving; recognizing and employing common patterns of mathematical thought; emphasizing not what is said, but how it is said. Particularly useful to students returning to school after a long hiatus, the math-anxious, students with weak skills, and those interested in elementary or middle school teaching. Prerequisite: Three units of high school mathematics

3 hrs

MATH 110 College Algebra

Review of elementary algebra, solution of equations, functions, exponential and logarithmic functions, inequalities, systems of linear equations, equations of second degree and their graphs, binomial theorem, complex numbers, and polynomials. Credit will not be given for both MATH 110 and MATH 120. Prerequisite: Three units of high school mathematics (Algebra I and higher) or MATH 100. Fall, winter, summer.

3 hrs

MATH 116 Mathematics For Liberal Arts

A survey of elementary mathematics covering such topics as: logic, sets, counting methods, introduction to probability theory, introductory statistics, plane and coordinate geometry. The course will emphasize mathematical concepts and does not require the level of computational skill of College Algebra. Topics from the history of mathematics will be presented as well as the influence of mathematics on a variety of disciplines. Prerequisite: Three units of high school mathematics (Algebra I and higher). Offered: Fall, Winter

3 hrs

MATH 120 Precalculus

Review of elementary algebra, solution of equations, functions, inequalities, systems of linear equations, exponential and logarithmic functions, trigonometric functions, trigonometric identities, triangles, equations of second degree and their graphs, binomial theorem, complex numbers, and polynomials. Credit will not be given for both MATH 120 and MATH 110 or for both MATH 120 and MATH 125. Prerequisites: Three units of high school mathematics (Algebra I or higher) or MATH 100. Fall, Winter, Summer.

5 hrs

MATH 125 Trigonometry

Trigonometric functions, trigonometric identities, triangles, and complex numbers. Credit will not be given for both MATH 125 and MATH 120. Prerequisite: Two units of high school algebra and one unit of geometry, or MATH 110. Fall, winter, summer.

2 hrs

MATH 130 Mathematics For Teachers: Number Systems

Designed for elementary school teachers. A constructive development of the real number system beginning with the system of whole numbers; concepts from elementary number theory; applications of quantitative systems to problems in discrete mathematics. Prerequisite: High school algebra and geometry. Offered: Fall, Winter, Summer

3 hrs

MATH 140 Mathematics For Teachers: Elementary Geometry

Designed for elementary school teachers. A development from informal geometric concepts to elements of the Euclidean deductive system; groups of congruence transformations, similarity transformations and symmetries; coordinate systems and vectors. Prerequisite: High school algebra and geometry. Fall/Winter

3 hrs

MATH 202 Analytic Geometry

Coordinate plane, lines, circles, the parabola, the ellipse, the hyperbola, transformation of coordinates, equations of the second degree, curve sketching, polar coordinates and parametric equations, complex numbers, vectors and vector operations, and solid analytic geometry. Prerequisites: 4 units of high school math, or MATH 110 and credit for or concurrent enrollment in MATH 125. Offered: Fall, Winter.

3 hrs

MATH 204 Mathematics For Teachers: Mathematical Immersion

Adaptable for elementary-,middle-,or secondary-school mathematics teachers. Intensive problem solving experience. Develop confidence and enthusiasm about recognizing mathematics reasoning in oneself and in students. Combat mathematics anxiety and myths. Encourage flexibility in the mathematical knowledge of teacher candidates. Prerequisites: MATH 120, MATH 130, MATH 140, or any mathematics course numbered 200 or above. Offered: On demand

3 hrs

MATH 205 Discrete Mathematics

Logic, sets, and functions. Algorithms, especially integer algorithms. Methods of proof, especially induction and recursion, counting principles, and discrete probability. Relations and partial ordering with applications. Graphs, circuits, and paths. Prerequisite: 4 units of high school math, or MATH 110. Offered: Fall, winter, summer.

3 hrs

MATH 206 Brief Calculus And Matrix Algebra

Brief review of selected topics in algebra. Introduction to matrix algebra. Introduction to differential calculus and optimization. Applications to problems in business. Credit will not be given for both MATH 160 and MATH 206 Prerequisite: MATH 110, or equivalent Offered: Every semester

3 hrs

MATH 210 Calculus I

Functions and graphs, rational, trigonometric, exponential functions, composite and inverse functions, limits and continuity, differentiation and its applications, integration and its applications. Prerequisite: Four units of high school mathematics including trigonometry, or MATH 120, or MATH 110 and MATH 125, or MATH 202. Offered: Fall, Winter, and Summer

4 hrs

MATH 214 Mathematics For Teachers: Algebra

Designed for middle school mathematics teachers. Algebraic reasoning, patterns and inductive reasoning, arithmetic and algebra of integers, algebraic systems, algebraic modeling in geometry, axiomatic mathematics. Prerequisites: MATH 110, MATH 130, and one of MATH 140 or MATH 224 Offered: Fall/Winter

3 hrs

MATH 220 Calculus II

Techniques of integration, applications of the definite integral, improper integrals, sequences and series, power series. Taylor series and convergence, analytic geometry in calculus. Prerequisite: MATH 210. Fall, Winter, Summer.

4 hrs

MATH 224 Mathematics For Teachers: Geometry

Designed for middle school mathematics teachers to connect middle school and college mathematics. Geometric reasoning, Euclidean geometry, congruence, area and volume, similarity, rigid motions and symmetry, vectors and transformations, some other geometries. Prerequisites: MATH 110 and MATH 130; MATH 140 is recommended. Offered: Fall/Winter

3 hrs

MATH 244 Mathematics For Teachers: Calculus

Designed for elementary-and middle-school mathematics teachers. Elementary calculus, beginning with sequences and series, proceeding to functions, limits, continuity, differentiation and integration. Focus on concepts and applications with a discovery and inquiry approach. Prerequisites: Four units of high school mathematics including Trigonometry, or MATH 120, or MATH 110 and MATH 125. Offered: Winter

3 hrs

MATH 250 Calculus III

Vectors, solid analytic geometry, vector functions and multiple variable functions, partial derivatives, multiple integrals, line and surface integrals with applications. Prerequisite: MATH 220. Fall, Winter, Summer

4 hrs

MATH 300 Linear Algebra I

Vectors, matrices, linear equations, matrix algebra, determinants, vector spaces, linear transformations, vector spaces with an inner product. Prerequisite: MATH 250, or consent of instructor Offered: Fall, Winter

3 hrs

MATH 301 On Solid Ground: Sets And Proofs

Transition to advanced mathematics, elements of set theory and cardinality of sets, logic, mathematical proof techniques, induction, functions, elementary proofs in various subjects such as algebra, number theory, calculus, and others as time permits. Satisfies a state requirement for teacher certification. Prerequisite: MATH 220

3 hrs

MATH 345 Ordinary Differential Equations

First order equations, linear second order differential equations, Taylor series and power series solutions, Laplace transforms, elementary systems of differential equations, numerical methods, and Fourier series and boundary value problems. Prerequisite: MATH 250. Fall, winter, summer.

4 hrs

MATH 400 Introduction To Number Theory

Congruences and residue classes. The theorems of Euler and Fermat. Primitive roots and indices. Quadratic residues. The Legendre and Jacobi symbols, the law of quadratic reciprocity. Number theoretic functions: the Euler phi-function, the Moebius inversion formula. Quadratic forms. The approximation of irrationals by rationals. Prerequisite: MATH 301

3 hrs

MATH 402 Advanced Analysis I

Numerical sequences and completeness of the real numbers, numerical series, continuity and differentiation of real-valued functions of a real variable, integration and the fundamental theorem of calculus. Prerequisite: MATH 250 and MATH 301

3 hrs

MATH 406 Partial Differential Equations

Separation of variables, boundary value problems, Fourier series and integrals, wave equation, heat equation, potential equation, problems in several dimensions, and Bessel's differential equation. Prerequisite: MATH 345. Offered: Winter.

3 hrs

MATH 407 Introduction To Complex Variables

Complex numbers, complex differentiation, elementary functions, contour integration and the Cauchy integral formula, Taylor series and Laurent series, residue calculus and its applications, and special functions. Prerequisites: MATH 250, and one of MATH 300, MATH 301, or MATH 345, with MATH 301 recommended Offered: Fall

3 hrs

MATH 410 Modern Algebra

Groups, rings, integral domains, fields and polynomial rings. Prerequisite: MATH 300 and MATH 301.

3 hrs

MATH 412 Advanced Analysis II

Topics in advanced analysis such as sequences and series of functions, power series and elementary functions, Fourier series, metric spaces, analysis in Euclidean spaces, or advanced integration. Prerequisite: MATH 402 or consent of instructor Offered: Winter

3 hrs

MATH 414 Mathematics For Secondary Teachers: Algebra And Analysis

Designed for secondary-school teachers. Examine high school mathematics from a higher point of view. Real and complex numbers, functions, algebraic structures of equations, integers and polynomials, number system structures; analyses of alternate approaches, extensions, and applications of mathematical ideas, discussion of historical contexts and connections between ideas that may have been studied separately in different courses, relationships of ideas studied in secondary-school to those students may encounter in later study. When taken for graduate credit as MATH 5514, an extra project is required. Prerequisites: MATH 220, MATH 301, and one of MATH 402 or MATH 410 Offered: Winter

3 hrs

MATH 420 Linear Algebra II

Vector spaces and linear transformations, eigenvalues and eigenvectors, vector spaces with an inner product, orthogonality, least squares approximation, quadratic forms singular value decomposition, the theory of determinants. Prerequisite: MATH 300 Offered: Winter

3 hrs

MATH 424 Mathematics For Secondary Teachers: Geometry

Designed for secondary-school teachers. Examine high school mathematics from a higher point of view. Congruence, distance and similarity, trigonometry, area and volume, axiomatics and Euclidean geometry; analyses of alternate approaches, extensions, and applications of mathematical ideas, discussion of historical contexts and connections between ideas that may have been studied separately in different courses, relationships of ideas studied in secondary-school to those students may encounter in later study. When taken for graduate credit as MATH 5524, an extra project is required. Prerequisite: MATH 220, MATH 301, and one of MATH 402 or MATH 410 Offered: Fall or Winter as needed

3 hrs

MATH 430 Numerical Analysis I

Error analysis, solutions of equations of one variable, interpolation and polynomial approximation, numerical integration and differentiation, numerical solutions of initial-value problems. Prerequisite: MATH 250

3 hrs

MATH 440 Numerical Analysis II

Direct and iterative methods for solving linear systems, introduction to approximation theory, approximating eigenvalues and eigenvectors, solution of systems of nonlinear equations. Prerequisites: MATH 300 and MATH 430, or consent of instructor Offered: Winter

3 hrs

MATH 444 Modern Geometries

Modern axiomatic development of Euclidean geometry and neutral geometry, followed by examination of non-Euclidean geometries; geometric transformations, and other geometries as time permits. Satisfies a state requirement for teacher certification. Prerequisites: MATH 300 and MATH 301

3 hrs

MATH 464 WI History Of Mathematics

Topics in the History of Mathematics from Babylonian times through the invention and consolidation of Calculus, with some modern subjects as time permits. The course will emphasize proofs, ideas, and arguments as given in original sources (in translation) from around the world and throughout history. In this writing intensive course, one or two term papers, in addition to several short essays and historical proof explications are required. A field trip will be taken to the Linda Hall Library Rare Book Room. This course is of special interest to secondary mathematics teachers as well as mathematics majors. Prerequisites: MATH 300 or MATH 301. MATH 301 is recommended.

3 hrs

MATH 490 Special Topics

Selected topics in various fields of mathematics. May be repeated for credit when the topic varies. Prerequisite: consent of instructor. On demand.

1-3 hrs