Mathematics Course Descriptions

	Course Descriptions
Top	1906	1921	1936	1949	1956	2001

MATHEMATICS COURSE DESCRIPTIONS 1906

261.  Arithmetic. - Milne's Standard Arithmetic. Begin with decimal fractions and complete the subject. Five periods, first term. Required of first year students in Mechanic Arts. Mr. Holmes and Mr. Mann.

262.   Algebra. - Well's Higher Algebra. Up to quadratic equations. Five periods, second and third terms. Required of first year students in Mechanic Arts. Mr. Holmes and Mr. Mann.

263.   Algebra.- Well's Higher Algebra. Begin at quadratic equations and complete logarithms, embracing ratio and proportion, variation, the progressions, the binomial theorem, series and partial fractions. Five periods, first term; two periods, second term. Required of all Freshmen and of second year students in Mechanic Arts. Mr. Richardson and Mr. J. A. Park.

264.   Geometry. - Plane and Solid. Wentworth's Plane geometry . Three periods second term; five periods, third term. Required of all Freshmen and of second year students in Mechanic Arts. Four periods, third term. Required of all Freshmen and second year students in Mechanic Arts.

265.   Solid Geometry. -Required of Sophomores, Five periods, first term. Professor Yates, Mr. J. A. Park and Mr. Richardson.

266.   Advanced Algebra.Well's Higher Algebra. Compound interest and annuities, permutations, combinations, continued fractions, general theory of equations and the solution of higher equations, etc. Required of Sophomores, Three periods, second term. Professor Yates and Mr. J. A. Park.

267.  Trigonometry. - Phillips & Strong's Plane and Spherical Trigonometry. Plane Trigonometry. Solution of plane triangles, triangulation, etc. Spherical Trigonometry. Solution of spherical triangles. Required of Sophomores. Two periods, second term; five periods, third term. Professor Yates and Mr. J. A. Park.

268.  Analytic Geometry.- Nichols's Analytic Geometry. Conic Sections, higher plane curves, Geometry of three dimensions. Four periods, first and second terms. Required of Juniors. Professor Yates.

269.  Differential and Integral Calculus.-Osborne's Elements of Calculus. A thorough treatment of the fundamental principles and derivation of formulae; application to various problems, such as expansion into series, evaluation of indeterminate forms, maxima and minima, radius of curvature, lengths of curves, ares, volumes, etc, Four periods, third term. Required of Seniors. Professor Yates.

Course Descriptions
Top	1906	1921	1936	1949	1956	2001

MATHEMATICS COURSE DESCRIPTIONS 1921

For Four-year Courses

101 (a).  Agriculture Mathematics.  This course consists of elementary Geometry, Trigonometry, and Conic Sections, with their practical applications to Agricultural Science. Thee periods , first term. Required of Agricultural Freshman. Professors Yates and Harrelson, Assistant Professor Mock.

101 (b).  Algebra.   This course begins with quadratic equations and completes summation for series, embracing ratio and proportion, variation, the progressions, the binomial theorem, undetermined coefficients, logarithms, compound interest and annuities, permutations, combinations and continued fractions. Five credits, first term. Required of Engineering, Chemical and Textile Freshmen, and second year Mechanic Arts students. Prerequisite, entrance requirements. Assistant Professor Mock, Mr. Williams. Mr. LeRoy, Mr. Buckner, Mr. Evans.

102.   Advanced Algebra.  - Well's New Higher Algebra.   The general theory of equations, the solution of higher equations, determinants, etc. Required of Engineering, Chemical, and Textile Freshmen and second-year Mechanic Arts students. One credit, second terms. Assistant Professor Mock, Mr. Williams, Mr. LeRoy, Mr. Buckner, Mr. Evans.

104.  Solid Geometry.  - Wentworth and Smith's Plane and Solid geometry .   Three periods second term; five periods, third term. Required of all Freshmen and of second year students in Mechanic Arts. Four periods, third term. Required of all Freshmen and second year students in Mechanic Arts.

201.  Trigonometry.  Plane Trigonometry. Definitions of the trigonometric functions; derivation of formulae, with their application. Solution of plane triangles, etc. Spherical Trigonometry . Solution of spherical triangles. This course includes the solution of many practical problems. Required of Sophomores in Engineering and Chemical Courses. Five credits, first term. Professor Yates, Professor Harrelson, Assistant Professor Mock, Mr. Williams, Mr. Buckner.

202.  Analytic Geometry.  - Nichols's Analytic Geometry.   Loci of equations, straight line, circle, parabola, ellipse, hyperbola, a discussion of the general equation of the second degree, higher plane e curves, and geometry of three dimensions. Required of Sophomores in Engineering and Chemical Courses. Five credits, second term. Professor Yates, Professor Harrelson, Assistant Professor Mock, Mr. Williams, Mr. Buckner.

301-302.  Differential and Integral Calculus.  -Osborne's Elements of Calculus.  A thorough treatment of the fundamental principles and derivation of formulae; application to various problems, such as expansion into series, evaluation of indeterminate forms, maxima and minima, radius of curvature, lengths of curves, areas, volumes, etc, Four credits, first and second terms. Required of Juniors in Engineering. Elective for Seniors in Chemistry. Professor Yates, Professor Harrelson.

For Short Courses

11.   Algebra.  A thorough treatment of elementary Algebra, beginning with fractions and embracing simple equations, simultaneous equations in two or more unknowns, problem solving, involution, evolution, theory of exponents, and radicals. Required of first-year students in Auto-Mechanics, Mechanic Arts, and Textile manufacturing. First term, five credits. Mr. Williams and Mr. Evans.

12.   Plane Geometry.  A complete course in plane geometry, including numerous original exercise. Required of first-year students in Auto-Mechanics, Mechanic Arts, and Textile Manufacturing. Five credits, second term. Mr. Williams and Mr. Evans.

31-32.   Farm Mathematics.   In teaching this course, problems for solution will be of the nature of those coming up daily on the average farm, such as calculating the plant food contained in and removed by different crops when fed and when sold directly from the farm; fertilizer formulas for different crops using different classes of materials; rations with different kinds of feed and for different kinds of animals, engaged in different kinds of work; capacity of different classes of farm buildings; speed of pulleys; draft of farm implements of different kinds; size of drainage tile for different conditions; capacity of cisterns and silos; quantity of different materials needed for preserving different kinds and amounts of meats; measure of hay in the barn or stack; amounts of concrete, sand and gravel needed to construct walls or floors of different kinds; number of feet of lumber woodlands of different kinds will yield; and thousands of other practical farm problems the thoughtful farmer has to work out. Three credits, first and second terms. Required of first-year students in the two-year Practical Agricultural course. Mr. Leroy.

Course Descriptions
Top	1906	1921	1936	1949	1956	2001

MATHEMATICS COURSE DESCRIPTIONS 1936

Courses for Undergraduates

Math. 100 a-b-c.  Mathematical Analysis.		0-3-0 or 0-0-3
	Math.100-a.  Fall term (Algebra)
Review of elementary topics, such as Factoring, Fractions, Simple Equations, Solution of Higher Degree equations, Simultaneous Quadratic Equations, Logarithms, the Binomial Theorem, Arithmetic and Geometric Progressions, Permutations, Combinations, and the Elementary Theory of Probability.
	Math.100-b.  Winter term (Trigonometry)
The study of the Trigonometric Functions with their applications to the solution of the right and oblique triangles, with numerous problems. Also a brief study of Trigonometric Equations and identities and Inverse Functions. Practical Mensurations of Solids is taken up.
	Math.100-c.  Spring term (Mathematics of Finance)
The principal topics are Simple and Compound Interest, Annuities, Sinking Funds and Amortization, and the Valuation of Bonds, and other applications.
Math. 101.  Algebra .		6-0-0
Required of freshmen in the Schools of Engineering and Textile, and in the departments of Industrial Management, Industrial Arts, and Landscape Architecture. This course includes quadratic equations, the progressions, the binomial theorem, permutations and combinations, logarithms, the general theory of equations, and the solution of higher equations.
Math. 102.  Trigonometry .		0-6-0
Required of freshmen in the Schools of Engineering and Textile, and in the departments of Industrial Management, Industrial Arts, and Landscape Architecture. The trigonometric functions, derivation of formulae, the solution of plane and spherical triangles, with practical applications.
Math. 103.  Analytic Geometry .		0-0-6
Required of freshmen in the Schools of Engineering and Textile, and in the departments of Industrial Management, Industrial Arts, and Landscape Architecture. Loci of equations, the straight line, circle, parabola, ellipse, hyperbola, the general equation of the second degree, polar coordinates, transcendental curves, parametric equations, coordinates in space, planes and surfaces.

Courses for Advanced Undergraduates

Math. 201.  Differential Calculus .		4-0-0
Required of sophomores in Engineering. Prerequisite: Math. 103. An elementary course in the fundamental principles of the Calculus, including the formulae for differentiation, with applications to Geometry and to problems in rates, maxima and minima, curve tracing, and curvature.
Math. 202.  Integral Calculus I.		0-4-0
Required of sophomores in Engineering. Prerequisite: Math. 201. Methods of integration, and the study of the definite integral, with applications to problems in areas, volumes, surfaces, and lengths of arcs.
Math. 203.  Integral Calculus II.		0-0-4
Required of sophomores in Engineering. Prerequisite: Math. 202. A continuation of Integral Calculus I: the calculation of centroids, radii of gyration and moments of inertia; problems in work and liquid pressure; double and triple integrals, infinite series, hyperbolic functions, and the elements of ordinary differential equations.

Courses for Graduates and Advanced Undergraduates

Math. 301.  Differential Equations.		0-3-0
Required of juniors in Engineering and elective for others. Prerequisite: Math. 203. A short course to include the solutions of equations which occur in scientific work and engineering problems.
Math. 302.  Advanced Calculus for Engineers I.		0-3-0
Elective. Prerequisite: Math. 301. Text: Wood's Advanced CalculusBR> Functions, power series, partial differentiation, implicit functions, maxima and minima of functions of two variables, the definite integral.     -   Mr. Levine.
Math. 303.  Advanced Calculus for Engineers II.		0-0-3
A continuation of Math. 302. Special integrals, line integrals, partial differential equations, functions of a complex variable, elliptic integrals.     -   Mr. Levine.
Math. 311.  Graphical and Numerical Methods.		3-0-0
Elective. Prerequisite: Math. 203. Graphical and numerical approximate methods in differentiation, integration , and the solution of both ordinary and differential equations. Theory of least squares and empirical curve fitting. Numerous examples in the fields of physics, electricity, mechanics, and engineering will be solved.     -   Mr. Cell.
Math. 312.  Vector Analysis I.		0-3-0
Elective. Prerequisite: Math. 203. A study of the different vector products. The calculus of vectors with applications to geometry and mechanics.     -   Mr. Clarkson.
Math. 313.  Vector Analysis II.		0-0-3
Elective. A continuation of Math. 312.     -   Mr. Clarkson.
Math. 321.  Advanced Analytical Geometry .		0-0-3
Elective. Prerequisite: Math. 203. The elements of higher plane curves and the geometry of space.     -   Mr. Bullock.
Math. 322.  Theory of Equations.		0-3-0
Elective. Prerequisite: Math. 203. The usual topics in the theory of equations, the solution of higher equations, exponential equations, logarithmic equations, and determinant.     -   Mr. Mumford.
Math. 323.  Series.		0-0-3
Elective. Prerequisite: Math. 203. Fourier series, related series and functions, with applications to physics and engineering.     -   Mr. Levine.
Math. 401.  Applied Mathematics I.		3-0-0
Elective. For graduate students only. Prerequisite: Math. 303, or the consent of the instructor. The course will be arranged to fit the engineering interests of the students enrolled. Catenary cables, straight and curved beam problems, theory of curve fitting, probability and applications, problems in the theory of elasticity, ballistics, theory and problems, electrical circuits, Heaviside operational calculus and applications to electrical engineering and to other engineering problems, calculus of finite differences and applications.     -   Mr. Cell.
Math. 402.  Applied Mathematics II.		0-3-0
Elective. For graduate students only. Prerequisite: Math. 401. A continuation of Math. 401.     -   Mr. Cell.
Math. 403.  Applied Mathematics III.		0-0-3
Elective. For graduate students only. Prerequisite: Math. 402. A continuation of Math. 401.     -   Mr. Cell.

Course Descriptions
Top	1906	1921	1936	1949	1956	2001

MATHEMATICS COURSE DESCRIPTIONS 1949

Courses for Undergraduates

Math. 101    Algebra for Engineers	4-0-0
Required of freshmen in the School of Engineering
Quadratic equations, the progressions, the binomial theorem, logarithms, the general theory of equations, the solution of higher equations, determinants and partial fractions.
Math. 102    Trigonometry for Engineers	0-4-0
Prerequisite: Math. 101 Required of freshmen in the School of Engineering
The trigonometric functions, derivation of formulae, the solution of plane and spherical triangles, with practical applications, slide rule, complex numbers, and hyperbolic functions.
Math. 103   Analytic Geometry	0-0-6
exponents and radicals, fractions, quadratic equations in one and two unknowns, radical equations, logarithms, progressions, binomial theorem, solution of higher degree equations by linear interpolation, geometric theorems and problems, the trigonometric functions, fundamental relationships, the right triangle by tables and slide rule, simple identities and equations, the oblique triangle.
Math. 111  Algebra for Agriculture and Education Students.	4-0-0
Fundamentals of algebra, logarithms, slide-rule, simple and fractional equations, graphs and graphical solutions of equations, percentages, ratio and proportion, areas and volumes of common solids, exponents, radicals, imaginary numbers, quadratic equations, simultaneous equations, progressions, the binomial theorem, simple and compound interest, elementary statistics.
Math. 112  Trigonometry for Agriculture and Education Students.	0-4-0
Prerequisite: Math. 111
Trigonometric functions of acute angles, solutions of right triangles, solutions of general triangles, use of trigonometric tables and of the slide-rule, and logarithms in solving triangles.
Math. 113  Mathematics of Finance	0-0-4
Prerequisite: Math. 102
Simple and compound interest, annuities sinking funds and amortization, and the valuation of bonds and other applications.
Math. 201  Calculus I	4-0-0
Prerequisite: Math. 103
Required of sophomores in the School of Engineering. A course in the fundamental principles of the calculus including the formulas for differentiation, and for integration of polynomial functions with applications to geometry and to problems in rates, maxima and minima, curve tracing, curvature, areas, volumes, work, pressure, velocity and acceleration.
Math. 202  Calculus II	0-4-0
Prerequisite: Math. 201
Required of sophomores in the School of Engineering. A continuation of Calculus I. Methods of integration, and the study of the definite integral with applications to problems in areas, volumes, lengths of arcs, surfaces, centroids, moments of inertia, radii of gyration, approximate integration.
Math. 211   Calculus A	3-0-0
A continuation of Math. 112
An integrated course in the fundamentals of calculus, including formal differentiation and integration. Basic applications to geometry, rates, maxima and minima, areas, volumes, first and second moments, and centroids are included. Additional topics from analytic geometry, not covered in Math. 112, are introduced as needed as a basis for calculus.
Math. 212   Calculus B	0-3-0
A continuation of Math. 211
An integrated course in the fundamentals of calculus, including formal differentiation and integration. Basic applications to geometry, rates, maxima and minima, areas, volumes, first and second moments, and centroids are included. Additional topics from analytic geometry, not covered in Math. 112, are introduced as needed as a basis for calculus.
Math. 303  Calculus III	0-0-4
Prerequisite: Math. 202
Required of sophomores in the School of Engineering. A continuation of Calculus II. Indeterminate forms, infinite series, expansion of functions, hyperbolic functions, partial differentiation, double and triple integrals,and differential equations.
Math. 311  Approximate Methods in Mathematics	0-0-3
Prerequisite: Math. 303
Review of approximate solution of equations and of graphical and numerical differentiation and integration; Newton's interpolation method; network graphs;theory of special-purpose slide rules; elementary theory of nomographs; curve fitting and use of special coordinate paper; approximations by use of differentials. Special course will not be offered after June 1950.
Math. 313  Calculus C	0-0-3
Prerequisite: Math. 212 or 202
Elective for sophomores in Textile Chemistry and Dyeing. A continuation of Calculus B. Indeterminate forms, partial differentiation, double and triple integrals, applications.

Courses for Graduates and Advanced Undergraduates

Math. 401a  Differential Equations	3-0-0
Prerequisite: Math. 303
Required of juniors in Electrical Engineering and elective for others. Solution of standard types of equations; numerous examples in the field f Electrical Engineering.
Math. 401b  Differential Equations	3-0-0
Prerequisite: Math. 303
Elective. Principally for students in Chemical Engineering. A study of the equations that occur in Applied Chemistry. Much emphasis on graphic methods and numerical work.
Math. 402  Theory of Equations	0-3-0
Prerequisite: Math. 303
The usual topics in the theory of equations, the solution of higher equations, exponential equations, logarithmic equations, and determinants.
Math. 403  Graphical and Numerical Methods	0-0-3
Prerequisite: Math. 303
Elective. Graphical and numerical approximate methods in differentiation, integration and the solution of both ordinary and and practical differential equations. Theory of least squares and empirical curve fitting. Numerous examples in the fields of physics, electricity, mechanics, and engineering will be solved.
Math. 411  Advanced Calculus for Engineers	3-0-0
Elective. Continuity;Taylor's series with remainder; differentials, partial differentiation; directional derivative;l implicit functions; Jacobians; differentiation of integrals; improper integrals; hyperbolic functions; elliptic integrals. Applications to problems in engineering.
Math. 412  Advanced Calculus for Engineers	0-3-0
Elective. A continuation of the work in Math. 411. Gamma and Beta functions; Bessel functions; line integrals, Green's theorem, Stokes' theorem; maximum and minimum points on a surface. Applications to problems in engineering.
Math. 413  Series for Engineers	0-3-0
Elective. Review of tests for convergence of infinite series; uniform convergence; series solution of differential equations; Fourier series and applications.
Math. 421  Advanced Analytic Geometry	3-0-0
Prerequisite: Math. 303
The elements of space geometry; quadric surfaces; general equation of the second degree and its reduction to canonical form; translations and rotations in space; elements of higher plane curves and space curves.
Math. 422  Theory of Probability	0-3-0
Prerequisite: Math. 401
Definitions and fundamental relation. Binomial and multinomial distributions, Poisson and normal distributions, the probability integral, Mathematical Expectation, Bayes' Theorem. Applications to problems in engineering and statistics.
Math. 423  Vector Analysis	0-0-3
Elective.
The algebra of vectors with various vector products and applications; the calculus of vectors; partial differentiation; integration; applications to engineering problems; introduction to tensor analysis.
Math. 432  Advanced Differential Equations	0-3-0
Prerequisite: Math. 401a or 401b
Solution of circuit problems by impedance methods; hyperbolic functions of complex quantities and applications; series solutions of differential equations; Bessel functions; operational methods of solving differential equations; introduction to solution of partial differential equations and applications.
Math. 433  History of Mathematics	0-0-3
Prerequisite: Ma 303
A study will be made of the lives and contributions of certain outstanding mathematicians representative of eras in the historical development of mathematics.
Courses for Graduates Only
Math. 501  Ordinary and Partial Differential Equations	3-0-0
Prerequisite: Math. 401a or 401b
Solution of ordinary differential equations by simple operational methods; partial differential equations; functions arising from solution of differential equations; applications to problems arising in electrical, civil, and mechanical engineering.
Math. 502  Ordinary and Partial Differential Equations	0-3-0
Prerequisite: Math. 501
A continuation of the work in Math. 501. Fourier series and solution of problems in vibrations, heat flow and electricity; reducible and irreducible homogeneous equations; theory of harmonic functions, Poisson's integral and boundary value problems.
Math. 511  Complex Variable Theory and Applications	3-0-0
Prerequisite: Math. 412
Elementary functions; analytic functions and Cauchy-Riemann equations; conformal mapping and applications; Taylor and Laurent series; contour integration and residue theory; the Schwarz-Cristoffel transformation.
Math. 512  Operational Mathematics	0-3-0
Prerequisite: Math. 511
Fourier integral and applications; Laplace transforms and applications to solutions of differential equations arising from engineering problems. Fourier integral and Fourier transforms and applications.
Math. 513  Advanced Operational Mathematics	0-0-3
Prerequisite: Math. 512
Extended development of the Laplace and Fourier transforms, Hankel and other transforms in solution of problems in ordinary and partial differential equations and in difference equations; Sturm-Liouville.
Math. 522  Advanced Algebra	0-3-0
Prerequisite: Math. 303
Determinant and matrix theory; transformations; quadratic forms; characteristic equation.
Math. 523  Calculus of Finite Differences	0-0-3
Prerequisite: Math. 401a or 401b
Symbolic methods, generating functions, factorial, gamma and beta functions; binomial coefficients, methods of summation; the numbers and polynomials of Bernoulli, Boole, Euler, Sterling; Interpolation; difference equations.
Math. 531  Calculus of Variations	3-0-0
Prerequisite: Math. 401a or 401b
Necessary and sufficient conditions for existence of an extremum for an integral which is a function of one or several independent variables; specific examples such as the brachistachrone problem; Hamilton's principle and the principle of least action; brief consideration of the isoperimetric problem and the variable end-point problem.
Math. 533  Advanced Complex Variable Theory and Applications	0-0-3
Prerequisite: Math. 511
A continuation of Math. 511. Further development of theory on series, analytic continuation; mapping and the Schwartz-Christoffel transformation; applications to flow problems and other problems in engineering.

Course Descriptions
Top	1906	1921	1936	1949	1956	2001

MATHEMATICS COURSE DESCRIPTIONS 1956-1957

Courses for Undergraduates

MA 101    First Year Mathematics for Engineers	5(4-2) F, S
Required of freshmen in the School of Engineering
Rectangular coordinates, functions and graphs, linear equations and determinants, quadratic equations, inequalities, systems of equations involving quadratics, proportion and variation, binomial theorem, progressions, logarithms, exponential and logarithmic curves, trigonometric functions of general angle, derivation of trigonometric identities and formulas, the solution of plane triangles, with practical applications, slide rule.
MA 102    First Year Mathematics for Engineers	4(3-2) F,S
Prerequisite: MA 101 Required of freshmen in the School of Engineering
Radian measurement of angles, trigonometric curves, inverse trigonometric functions, trigonometric equations, complex numbers, theory of equations, loci of equations, the straight line, circle, parabola, ellipse, hyperbola, the general equation of second degree, curve sketching, polar coordinates, parametric equations, curve fitting, coordinates in space, planes, lines and surfaces.
MA 111   Algebra and Trigonometry	3(3-1-0) F,S
exponents and radicals, fractions, quadratic equations in one and two unknowns, radical equations, logarithms, progressions, binomial theorem, solution of higher degree equations by linear interpolation, geometric theorems and problems, the trigonometric functions, fundamental relationships, the right triangle by tables and slide rule, simple identities and equations, the oblique triangle.
MA 112   Analytic Geometry and Calculus A	3(3-1-0) F,S
Prerequisite: MA 111
A unified course, beginning with elementary ideas in analytic geometry and calculus with the introduction of additional work in trigonometry where needed, rectangular and polar coordinate systems, the fundamental locus problem, lines and conic sections, curve tracing, the derivative, with applications to geometry and simple practical problems.
MA 122  Mathematics of Finance	3(3-0-0) F,S
Prerequisite: MA 111
Simple and compound interest, annuities and their application to amortization and sinking fund problems, installment buying, calculation of premiums of life annuities and life insurance, elementary statistics.
MA 201  Calculus I	4(3-2-0) F,S
Prerequisite: MA 102
A course in the fundamentals of the Calculus including the formulas for differentiation and for differentials; the integrals of polynomial functions; applications to geometry ; maxima and minima, area, volumes, moments of area, work, fluid pressure; related rates, rectilinear an curvilinear motion; Newton's Method of approximation of roots.
MA 202  Calculus II	4(3-2-0) F,S
Prerequisite: MA 201
(A continuation of Ma 201) Methods of integration; definite integral with applications to length of arc, surface area, volumes, centroids and moments of inertia; Simpson's rule; indeterminate forms. infinite series, expansion of functions; hyperbolic functions partial differentiation; multiple integration.
MA 211, 212  Analytic Geometry and Calculus B,C	3(2-2) F,S
(A continuation of MA 112) An integrated course in the fundamentals of calculus, including formal differentiation and integration. Basic applications to geometry, rates, maxima and minima, areas, volumes, first and second moments, and centroids are included. Additional topics from analytic geometry, not covered in MA 112, are introduced as needed as a basis for calculus.
MA 401   Differential Equations	3(3-0-0) F,S
Prerequisite: Ma 202 (One year of calculus)
A first course in ordinary differential equations, handling standard types, proceeding to linear equations of higher order; some operator methods; applications to geometric growth, and solution problem, and to dynamical and electrical systems, higher degree equations of order one; special equations of order two;further special applications. (Required of juniors in Electrical Engineering. Elective for others.)
MA 402  Theory of Equations	3(3-0-0) F,S
Prerequisite: Ma 202 (One year of calculus)
Algebraic equations: isolation of roots, numerical approximations to roots, the Graeffe method; application of approximation procedures to transcendental equations; systems of linear equations, determinants and introduction to matrix theory.
MA 403  Fundamentals of Modern Algebra	3(3-0-0) F,S
Prerequisite: Ma 202 (One year of calculus)
An introduction to modern algebra: numbers, fields, rings, groups, vectors and vector spaces, linear transformations, matrices, algebra and classes, ideals and algebraic numbers.
MA 404  Fundamental Concepts of Geometry	3(3-0-0) F,S
Prerequisite: Ma 202 (One year of calculus)
Laws of logic; postulates and theorems; geometries based on different postulates, projective geometry; affine geometry; geometric transformations; Euclidean geometry; non-Euclidean geometry.

Course for Graduates and Advanced Undergraduates

MA 501  Numerical Analysis I	3(3-0-0) F
Prerequisite: Ma 202 (One year of calculus)
Construction of scales to represent functions including the construction of some special purpose slide rules and networks; alignment charts, theory of least squares and curve fitting, including periodic functions; Newton's interpolation formula; the error curve and some of its properties.
MA 502  Numerical Analysis I	3(3-0-0) S
Prerequisite: Ma 402, MA 501
Interpolation formulas of Lagrange, Bessel, and Sterling; divided differences, subtabulation; numerical differentiation and integration; numerical methods of solving ordinary and partial differential equations.
MA 511  Advanced Calculus I	3(3-0-0) F,S
Prerequisite: MA 401
Continuity; Taylor's series with remainder; infinitesimals; differentials; review of convergence tests for infinite series, hyperbolic functions; partial differentiation; directional derivatives; implicit functions; Jacobians; elements of differential geometry, differentiation of integrals; improper integrals. Application to problems in engineering.
MA 512  Advanced Calculus II	3(3-0-0) S
Prerequisite: MA 511
Gamma and Beta functions; line, surface, and space integrals; Green's theorem; Stokes's theorem; expansions of functions in Fourier series, applications to boundary value problems, introduction o the theory of functions of a complex variable, including simple mapping problems, contour integration and residue theory; elliptic integrals.
MA 514  Boundary Value Problems	3(3-0-0) F,S
Prerequisite: MA 511, 512 (One year of advanced calculus
Ordinary homogeneous and non-homogeneous differential equations with boundary values; elements of partial differential equations; applications of Fourier series and other methods to the solutions of certain boundary value problems in partial differential equations; harmonic functions.
MA 521  Advanced Geometry	3(3-0-0) F
Prerequisite: Ma 202 (One year of calculus)
Coordinates in space, direction angles and cosines; planes, lines points; matrices, surfaces and curves, quadric surfaces; transformations; analysis of general equations of degree 2; matrix algebra and its applications; introduction to algebraic geometry.
MA 522  Theory of Probability	3(3-0-0) S
Prerequisite: MA 401
Definitions, discrete and continuous sample spaces, combinatorial analysis, Sterling's formula, simple occupancy and ordering problems, conditional probability, repeated trials, compound experiments, Bayes' theorem, binomial, Poisson and normal distributions, the probability integral, random variables, expectation.
MA 532  Advanced Differential Equations	3(3-0-0) S
Prerequisite: MA 401
Series solutions of differential equations; approximate methods; the gamma functions; Bessel functions; Legendre polynomials; introduction to the solution of partial differential equations and applications.
MA 533  History of Mathematics	3(3-0-0) S
Prerequisite: Ma 202 (One year of calculus)
Evolution of the number systems; trends in the development of modern mathematics; lives and contributions of outstanding mathematicians.
MA 535  An Introduction to Computers	3(3-0-0) F
Prerequisite: Ma 401 or any other advanced course
Introduction to the theory of both analog and digital computers; numbers systems, error analysis; types of computers and memory systems; experience in programming for IBM and GEDA equipment that is on the Campus.
MA 541  Vector Analysis	3(3-0-0) S
Prerequisite: Ma 401 or any other advanced course
The algebra of vectors and dyadics; elementary space geometry in vector form; scalar and vector differentiation of scalar, vector and dyadic functions; curvilinear coordinates; line, surface, and volume integrals; integral transformations; applications.

Course for Graduates Only

MA 602  Partial Differential Equations	3(3-0) S
Prerequisite: MA 511, 512 (One year of advanced calculus)
Partial differentiation, functional dependence, envelopes, eliminants, Lagrange's equation, general and complete integrals, non-linear equations of the first and higher orders; Fourier series with applications to problems in vibrations, heat and fluid flow, electricity; boundary value problems.
MA 604  Orthogonal Functions	3(3-0) F
MA 512 (One year of advanced calculus) or consent of the instructor
The development of the theory and properties of general orthogonal functions; applications to Fourier, Bessel, Legendre, Hermitian, Laguerre and Tchebycheff types of orthogonal functions. Methods developed here will be used in the solution of problems from physics and engineering.
MA 611 Complex Variable Theory and Applications	3(3-0) F
Prerequisite: MA 511, 512 (One year of advanced calculus)
Elementary functions; analytic functions and Cauchy-Riemann equations; conformal mapping and applications; Taylor and Laurent series; contour integration and residue theory; the Schwarz-Cristoffel transformation.
MA 612 Advanced Complex Variable Theory and Applications	3(3-0) F
Prerequisite: MA 611
A continuation of MA 611. Further development of residue theory; further applications of conformal mapping to flow phenomena; multiple-valued functions and Riemann surfaces; analytic continuation; elliptic functions; differential equations.
MA 622  Advanced Algebra	3(3-0) S
Prerequisite: MA 202 (One year of calculus)
Introduction to matrices; vector spaces; equivalence, rank, inverse of matrices; determinants; congruence; quadratic forms; polynomials over a field; similarity, characteristic roots.
MA 623 Calculus of Finite Differences	3(3-0) S
Prerequisite: MA 401
Symbolic methods, generating functions, factorial, gamma and beta functions; binomial coefficients, methods of summation; the numbers and polynomials of Bernoulli, Boole, Euler, Sterling; Interpolation; difference equations.
MA 632 Operational Mathematics	3(3-0) S
Prerequisite: MA 611 or consent of the instructor
Laplace transforms and applications to solutions of ordinary and partial differential equations arising from engineering problems. Fourier integral and Fourier transforms and applications.
	3(3-0) S (Alt. yrs.)
Prerequisite: MA 632
Extended development of the Laplace and Fourier transforms, Hankel and other transforms in solution of problems in ordinary and partial differential equations and in difference equations; Sturm-Liouville.
MA 635  Mathematics of Computers	3(3-0) S
Prerequisite: MA 512 and MA 535/i>
Boolean Algebra and logical design; advanced programming including abstract methods; error analysis, special techniques; applications to solution of problems in linear and nonlinear ordinary and partial differential equations, systems of simultaneous linear algebraic equations, integral equations etc.
MA 641  Calculus of Variations	3(3-0) F
Prerequisite: MA 511
The simplest problem of the Calculus of Variations in detail; variable end points; iso-permetric problems; Hamilton's Principle; Least Action Principle; generalizations.
MA 651  Expansion of Functions	3(3-0) F (Alt. yrs.)
Prerequisite: MA 611 and 632 or consent of the instructor
Expansion of functions of one or several variables in Taylor series; asymptotic series, infinite products, partial fractions, continued fractions, series of orthogonal functions; Fuchsion theory in ordinary differential equations.
MA 661  Tensor Analysis I	3(3-0) F
Prerequisite: MA 512, MA 541 (MA 521, 602, 633 recommended)
The basic theory; tensor algebra, tensor calculus; invariant theory; quadratic differential forms; covariant differentiation, curvature tensor; geometric applications, Riemannian spaces, parallelism, geodesics, normal coordinates, generalized vector analysis; physical applications: Dynamics, Lagrange's equations, generalized coordinates; the geometry of dynamics,; kinematic and action line elements, holonomic and non-holonomic systems; configuration space, dynamics in n-dimensions.
MA 662 Tensor Analysis II	3(3-0) S
Prerequisite: MA 561
Continuation of physical applications, Elasticity: finite strains, equations of compatibility, strain invariants, stress tensor, equations of motion, generalized Hook's law, isotropic stress-strain relations: Hydrodynamics: perfect fluids, viscous fluids, viscosity tensor; Equations of motion; Electromagnetic theory: Maxwell's equations, plane waves, stress-energy tensor; Relativity: Lorentz transformation, field equations, Schwarz-child solution, planetary orbits.
MA 681,682 Special Topics in Mathematics	3(3-0) F, S
Prerequisite: Graduate standing and consent of the instructor
This course provides opportunity for small groups of graduate students to study under the direction of qualified members of the professional staff, advanced topics in their special fields of interest.
MA 691  Special Topics in Mathematics	3(3-0) F, S
Prerequisite: Graduate standing and approval of advisor
Individual research in the field of mathematics.

Course Descriptions
Top	1906	1921	1936	1949	1956	2001

MATHEMATICS COURSE DESCRIPTIONS 2001

Courses for Undergraduates

MA 100    Precalculus by Self Study	3(0-7-0)
Preq: Algebra I
Enrollment is limited to students who have not received credit for a calculus course or higher at NC State. Freshman may attempt the course twice while all other classifications of students may take the course once. MA 100 may not be counted as credit toward meeting graduation requirements in any curriculum. Directed self study of precalculus topics to prepare students for a Mathematics Level II C Achievement Test in order to qualify for placement into the appropriate calculus course at NC STATE.
MA 101   Intermediate Algebra	4(5-0-0) F,S,Sum
Credit for MA 101 is not allowed if student has prior credit in any other mathematical MA 101 may not be counted as credit toward meeting graduation
Preparation for MA 103, MA 105, MA 107, MA 111, and MA 114. Reviews main topics from high school Algebra I and Algebra II emphasizing functions and problem solving. Other concepts and skills covered include algebraic operations, factoring, linear equations, graphs, exponents, radicals, complex numbers, quadratic equations, radical equations, inequalities, systems of equations, compound inequalities, absolute value in equations and inequalities.
	3(3-0-0) F,S,Sum
Preq: MA 101 or equivalent completed in high school
Primarily for students in Humanities and Social Sciences. Illustrations of contemporary uses of mathematics, varying from semester to semester, frequently including sets and logic, counting procedures, probability, modular arithmetic, and game theory.
MA 105  Mathematics of Finance	3(3-0-0) F,S,Sum
Preq: MA 101 or equivalent completed in high school
Simple and compound interest, annuities and their application to amortization and sinking fund problems, installment buying, calculation of premiums of life annuities and life insurance.
MA 107   Precalculus I	3(3-1-0) F,S,Sum
Preq: Placement via Achievement Test or MA 101. Credit is not allowed for both MA 107 and MA 111 Credit for MA 107 does not count toward graduation for students in Engineering, PAMS, Design, Bio and Ag Engineering (Science Program), Bio Sci (all options), Math Edu, Sci Edu, Textiles, College of Management, and B.S. degrees in CHASS
Algebra and basic trigonometry; polynomial, rational, exponential, logarithmic and trigonometric functions and their graphs.
MA 108 Precalculus II	3(3-1-0) F,S,Sum
Preq: C or better in MA 107. Credit is not allowed for both MA 108 and MA 111. Also, MA 108 should not be counted toward the GER mathematical sciences requirement Credit for MA 108 does not count toward graduation for students in Engineering, PAMS, Design, Bio and Ag Engineering (Science Program), Bio Sci (all options), Math Edu, Sci Edu, Textiles, College of Management, and B.S. degrees in CHASS
Algebra, analytic geometry and trigonometry; inequalities, conic sections, complex numbers, sequences and series, solving triangles, polar coordinates, and applications.
MA 111  Precalculus Algebra and Trigonometry	3(3-1-0) F,S,Sum
Preq: Placement via Level Two Achievement Test or MA 101; Credit is not allowed for both MA 111 and either MA 107 or MA 108 Credit in MA 111 does not count toward graduation for students in Engr., Physical & Math. Sci., Design, Biological & Ag. Engr. (Science Program), Biological Sci.(all options),Math. Edu., Forestry, & Textiles
Real numbers, functions and their graphs (special attention to polynomial, rational, exponential, logarithmic, and trigonometric functions), analytic trigonometry.
MA 114  Introduction to Finite Mathematics with Applications	3(3-0-0) F,S,Sum
Preq: MA 101 or equivalent completed in high school
Elementary matrix algebra including arithmetic operations, inverses, and systems of equations; introduction to linear programming including simplex method; sets and counting techniques, elementary probability including conditional probability; Markov chains; applications in the behavioral, managerial and biological sciences. Computer use for completion of assignments.
MA 121  Elements of Calculus	3(3-0-0) F,S,Sum
Preq: MA 107 or 111 or placement via Level Two Achievement Test
Credit is not allowed in more than one of MA 121, 131, 141. MA 121 may not be substituted for MA 131 or MA 141 as a curricular requirement
For students who require only a single semester of calculus. Emphasis on concepts and applications of calculus, along with basic skills. Algebra review, functions, graphs, limits, derivatives, integrals, logarithmic and exponential functions, functions of several variables, applications in management, applications in biological and social sciences.
MA 131  Calculus for Life and Management Sciences A	3(3-0-1) F,S,Sum
Preq: C or better in MA 107 or MA 111 or placement via Level Two Achievement Test
Credit not allowed for more than one of MA 121, 131, and 141
First order finite difference models; derivatives - limits, power rule, graphing, and optimization; exponential and logarithmic functions - growth and decay models; integrals - computation, area, total change; applications in life, management, and social sciences.
MA 132  Computational Mathematics for Life and Management Sciences	1(1-0-0) S
Preq: C or better in MA 121 or MA 131
Computational aspects of calculus for the life and management sciences; use of spreadsheets and a computer algebra system; applications to data models, differential equation models, and optimization.
MA 141  Calculus I	4(4-0-0) F,S,Sum
Preq: MA 111 with grade of C or better or placement via Level Two Achievement Test
Credit is not allowed for more than one of MA 141), 131, 121
First of three semesters in a calculus sequence for science and engineering majors. Functions, graphs, limits, derivatives, rules of differentiation, definite integrals, fundamental theorem of calculus, applications of derivatives and integrals. Use of computation tools.
MA 222  Applied Discrete Mathematics	3(3-0-0) F,S
Preq: Programming knowledge, MA 141
Formal logic. Methods of proof including induction. Introduction to grammars and finite state machines. Recurrence relations and asymptotic behavior of functions. Sets and counting. Boolean expressions and logic networks. Graphs and relations.
MA 225  Foundations of Advanced Mathematics	3(3-0-0) F,S
Preq: MA 241
Introduction to mathematical proof with focus on properties of the real number system. Elementary symbolic logic, mathematical induction, algebra of sets, relations, functions, countability. Algebraic and completeness properties of the reals.
MA 231  Calculus for Life and Management Sciences B	3(3-0-0) F,S,Sum
Preq: MA 131
MA 121 is not an accepted prerequisite for MA 231
Differential equations - population growth, flow processes, finance and investment models, systems; functions of several variables - partial derivatives, optimization, least squares, multiple integrals; Lagrange multiplier method - chain rule, gradient; Taylor polynomials and series; numerical methods.
MA 241  Calculus II	4(3-2-0) F,S,Sum
Preq: MA 141 with grade of C or better
Second of three semesters in a calculus sequence for science and engineering majors. Techniques and applications of integration, elementary differential equations, sequences, series, power series, and Taylor's Theorem. Use of computational tools.
MA 242  Calculus III	4(3-2-0) F,S,Sum
Preq: MA 241 with grade of C or better
Third of three semesters in a calculus sequence for science and engineering majors. Vectors, vector algebra, and vector functions. Functions of several variables, partial derivatives, gradients, directional derivatives, maxima and mimima. Multiple integration. Line and surface integrals, Green's Theorem, Divergence Theorems, Stokes' Theorem, and applications. Use of computational tools.
MA 293  Special Topics in Mathematics	1-6 F,S,Sum
Preq: Consent of Department Head
Freshman-sophomore level experimental course offerings or directed individual study.
	3(3-0-0)
Preq: Credit for 12 hours of calculus; primarily intended for transfer students whose calculus backgrounds do not include a study of first and second order linear differential equations
Credit not allowed if MA 241 taken previously at NCSU
First order differential equations with applications; second order linear differential equations with applications in mechanics and other areas elementary matrix algebra, systems of linear equations and applications; Laplace transforms; Fourier series.
MA 302  Numerical Applications to Differential Equations	1(1-0-0) F,S
Preq: MA 241
Numerical methods for approximating solutions for differential equations, with an emphasis on Runge-Kutta-Fehlberg methods with stepsize control. Applications to population, economic, orbital and mechanical models.
MA 303 Linear Analysis	3(3-0-0) F,S
Preq: MA 241
Credit not allowed if credit has been obtained for MA 301, 341 or 405
Linear difference equations of first and second order, compound interest and amortization. Matrices and systems of linear equations, eigenvalues, diagonalization, systems of difference and differential equations, transform methods, population problems.
MA 305  Elementary Linear Algebra	3(3-0-0) F, S, Sum
Preq: MA 241 (with corequisite MA 242) or MA 231 and MA 132
Coreq: MA 242 (with prerequisite MA 241)
Credit is not allowed for both MA 305 and MA 405
An elementary introduction to the essentials of linear algebra. Matrices and systems of linear equations, determinants, euclidean spaces as vector spaces, linear transformations of euclidean spaces, elementary treatment of eigenvalues and eigenvectors, applications to numerical solutions of equations and computer graphics.
MA 308  College Geometry	3(3-0-0)
Preq: MA 225
The axiomatic approach to mathematics. Congruences for triangles. Parallel postulate and consequences. Right triangles. Circles, tangents, chords. Area. Coordinate geometry. Lines and planes in space. Non-Euclidean geometries.
MA 314  Probability with Applications to Electrical and Computer Engineering.	3(3-0-0) F,S
Preq: MA 242
Fundamentals of discrete and continuous probability: conditional probability, independence, random variables, density and distribution functions, expected value and variance, common discrete and continuous distributions, joint distributions, and introduction to simple stochastic processes. Applications to electrical engineering; reliability of series and parallel circuits, models for waiting time phenomena.
MA 325  Introduction to Applied Mathematics	3(3-0-0) S
Preq: MA 231 or MA 242
Introduces studentswith multivariable calculus to five different areas of applied mathematics. These areas will be five three-week modules, which lead to higher level courses in the application areas. Topics will vary, and examples of modules are heat and mass transfer, biology and population, probability and finance, acoustic models, cryptography as well as others.
	3(3-0-0) F
Preq: LOG 201 or MA 225
Introduction to modern symbolic logic; the concept of proof, mathematical induction, recursion and the relationship between formal and informal theories (examples: group theory, Peano arithmetic). The GÖdel Theorems and the mathematical study of logic.
	3(3-0-0) F, S, Sum
Preq: MA 242 or (MA 132 and MA 231)
Credit is not allowed for both MA 301 and MA 341
Differential equations and systems of differential equations. Methods for solving ordinary differential equations including Laplace transforms, phase plane analysis, and numerical methods. Matrix techniques for systems of linear ordinary differential equations.
MA 351  Introduction to Discrete Mathematical Models	3(3-0-0) F,S
Preq: MA 224, 222, 231 or 241
Basic concepts of discrete mathematics, including graph theory, Markov chains, game theory, with emphasis on applications; problems and models from areas such as traffic flow, genetics, population growth, economics, and ecosystem analysis.
MA 401  Applied Differential Equations II	3(3-0-0) F,S,Sum
Preq: MA 341 or 301
Credit for both MA 401 and MA 501 will not be given
Wave, heat and Laplace equations. Solutions by separation of variables and expansion in Fourier Series or other appropriate orthogonal sets. Sturm-Liouville problems. introduction to methods for solving some classical partial differential equations.Use of power series as a tool in solving ordinary differential equations.
MA 402 Computational Mathematics: Models, Methods and Analysis	3(3-0-0) F
Preq: Fortran or C or Pascal, Physics
Introduction to high performance computing and numerical modeling. Matrix models and boundary value problems with an emphasis on heat and mass transfer. Assessments of all approximations in the computational engineering and science process.
MA 403  Introduction to Modern Algebra	3(3-0-0) F,S,Sum
Preq: MA 222
Credit is not allowed for both MA 403 and MA 407
Sets and mappings, equivalence relations, rings, integral domains, ordered integral domains, ring of integers. Other topics selected from fields, polynomial rings, real and complex numbers, groups, permutation groups, ideals, and quotient rings.
MA 405  Introduction to Linear Algebra and Matrices	3(3-0-0) F,S,Sum
Preq: MA 241
Coreq: MA 242
Credit is not allowed for both MA 305 and MA 405
Linear equations operations with matrices, row echelon form, determinants, vector spaces, linear independence, bases, dimension, orthogonality, eigenvalues, reduction of matrices to diagonal forms, applications to differential equations and quadratic forms.
MA 407  Introduction to Modern Algebra for Mathematics Majors	3(3-0-0)
Preq: MA 225
Credit is not allowed for both MA 403 and MA 407
Elementary number theory, equivalence relations, groups, homomorphisms, cosets, Cayley's Theorem, symmetric groups, rings, polynomial rings, quotient fields, principal ideal domains, Euclidean domains.
MA 408  Foundations of Euclidean Geometry	3(3-0-0) F,S
Coreq: MA 403 or MA 407
An examination of Euclidean geometry from a modern perspective. The axiomatic approach with alternative possibilities explored using models.
MA 410  Theory of Numbers	3(3-0-0) S
Preq: One year of calculus
Arithmetic properties of integers. Congruences, arithmetic functions, diophantine equations. Other topics chosen from quadratic residues, the quadratic reciprocity Law of Gauss, primitive roots, and algebraic number fields.
MA 414  Introduction to Differential Geometry	3(3-0-0) S
Preq: MA 242 and MA 405
Introduction to the geometry of curves in space, arc length, curvature, and torsion of curves; introduction to the geometry of surfaces in space; calculus of functions on surfaces, covariant derivatives, shape operators, metrics, curvatures of surfaces, geodesics, holonomy and other geometrical properties. Applications in the physical sciences and/or projects using computer algebra.
MA (CSC) 416  Introduction to Combinatorics	3(3-0-0) S, Alt yrs
Preq: MA 242 or CSC 224, and proficiency in a programming language
Basic principles of counting: addition and multiplication principles, generating functions, recursive methods, inclusion-exclusion, pigeonhole principle; basic concepts of graph theory: graphs, digraphs,connectedness, trees; additional topics from: Polya theory of counting, Ramsey theory; combinatorial optimization - matching and covering, minimum spanning trees, minimum distance, maximum flow; sieves; mobius inversion; partitions; Gaussian numbers and q-analogues; bijections and involutions; partially ordered sets.
MA 421  Introduction to Probability	3(3-0-0) F,S,Sum
Preq: MA 242 or MA 231
Credit for both MA 421 and MA 314 is not allowed
Axioms of probability, conditional probability and independence, basic combinatorics, discrete and continuous random variables, joint densities and mass functions, expectation, central, limit theorem, simple stochastic processes.
MA 422  Long-Term Actuarial Models	3(3-0-0) F
Preq: MA 241 or MA 231
Coreq: MA 421, BUS(ST)350,ST 301,ST 311, ST 361, ST 370, ST 371, ST 380 or equivalent
Long-term probability models for risk management systems. Theory and applications of compound interest, probability distributions of failure time random variables, present value models of future contingent cash flows, applications to insurance, health care, credit risk, environmental risk, consumer behavior and warranties.
MA 423 Short-Term Actuarial Models	3(3-0-0) S
Preq: MA 241 or MA 231, and one of MA 421, ST 301, ST 370, ST 371, ST 380, ST 421, or equivalent
Short-term probability models for risk management systems. Frequency distributions, loss distributions, the individual risk model, the collective risk model, stochastic process models of solvency requirements, applications to insurance and businessdecisions.
MA 425  Mathematical Analysis I	3(3-0-1) F,S
Preq: MA 225 (MA 407 desirable)
Real number system, functions and limits, topology on the real line, continuity, differential and integral calculus for functions of one variable. Infinite series, uniform convergence.
MA 426  Mathematical Analysis II	3(3-0-0) S
Preq: MA 425 and 405
Calculus of several variables, topology in n-dimensions, limits, continuity, differentiability, implicit functions, integration.
MA (CSC) 427  Introduction to Numerical Analysis I	3(3-0-0) F
Preq: MA 341 or 301 and programming language efficiency
Theory and practice of computational procedures including approximation of functions by interpolating polynomials, numerical differentiation and integration, and solution of ordinary differential equations including both initial value and boundary value problems. Computer applications and techniques.
MA (CSC) 428  Introduction to Numerical Analysis II	3(3-0-0) S
Preq: MA 405 and programming language proficiency. MA (CSC) 427 is not a prerequisite
Computational procedures including direct and iterative solution of linear and nonlinear equations, matrices and eigenvalue calculations, function approximation by least squares, smoothing functions, and minimax approximations.
MA 430  Mathematical Models in the Physical Sciences	3(3-0-0) F
Preq: MA 341 or 301; and MA 405
Application of mathematical techniques to topics in the physical sciences. Problems from such areas as conservative and dissipative dynamics, calculus of variations, control theory, and crystallography.
MA 432  Mathematical Models in Life and Social Sciences	3(3-0-0) S
Preq: MA 301 or 341, 305 or 405., programming language proficiency
Coreq: MA 421 or ST 371
Topics from differential and difference equations, probability, and matrix algebra applied to formulation and analysis of mathematical models in biological and social science (e.g., population growth).
MA 433  History of Mathematics	3(3-0-0) F,S
Preq: One year of calculus
Development of mathematical thought and evolution of mathematical ideas examined in a historical setting. Biographical and historical content supplemented and reinforced by study of techniques and procedures used in earlier eras.
MA 435 Major Topics in the Development of Mathematics	3(3-0-0)
Preq: MA 242
Coreq: MA 403 or MA 407 or MA 425
Great themes in mathematics, in their cultural and historical framework from an advanced undergraduate mathematical viewpoint. Biographical/mathematical snapshots of famous mathematicians.
MA 437  Applications of Algebra	3(3-0-0) S
Preq: MA 403 or 407, MA 405
Error correcting codes, cryptography, crystallography, enumeration techniques, exact solutions of linear equations, and block designs.
MA 491  Reading in Honors Mathematics	2-6 F,S
Preq: Membership in honors program, consent of department
A reading (independent study) course available as an elective for students participating in the mathematics honors program.
MA 493  Special Topics in Mathematics	1-6 F,S
Preq: Consent of department
Directed individual study or experimental course offerings.
MA 499  Independent Research in Mathematics	1-6 F,S,Sum
Consent of Department Head. Honors Program should enroll in MA 491H. At most 6 hours total of MA 499 and 491H credit can be applied towards an undergraduate degree.
Study and research in mathematics. Topics for theoretical, modeling or computational investigation.

Courses for Graduates and Advanced Undergraduates

	3(3-0-0) F,S,Sum
Preq: MA 341
Credit for this course and MA 401 is not allowed
Survey of mathematical methods for engineers and scientists. Ordinary differential equations and Green's functions; partial differential equations and separation of variables; special functions, Fourier series. Applications to engineering and science. Not for credit by mathematics majors.
MA 502  Advanced Mathematics for Engineers and Scientists II	3(3-0-0) F,S,Sum
Preq: MA 341.
Any student receiving credit for MA 502 may receive credit for, at most, one of the following: MA 405, MA 512, MA 513
Determinants and matrices; line and surface integrals, integral theorems; complex integrals and residues; distribution functions of probability. Not for credit by mathematics majors.
MA (OR) 504  Introduction To Mathematical Programming	3(3-0-0) S
Preq: MA 242, MA 405
Basic concepts of linear, nonlinear and dynamic programming theory. Not for majors in OR at Ph.D. level.
MA (IE) (OR) 505  Linear Programming	3(3-0-0) F,S
Preq: MA 405
Mathematical methods applied to problems of planning. Linear programming covered in detail. For those who desiring an in-depth and detailed study. Provision for rigorous and complete development of theoretical and computational aspects of this technique as well as a discussion of a number of applications.
MA 507  Analysis For Secondary Teachers	3(3-0-0) F,Sum,Alt yrs
Preq: Grad. standing
A course to update and broaden secondary teacher's capability and point-of-view with respect to topics in analysis. Historical development, logical refinement and applications of concepts such as limits, continuity, differentiation and integration. May be taken for graduate credit for certificate renewal by secondary school teachers. Credit towards graduate degree may be allowed only for students in mathematics education.
MA 508  Geometry For Secondary Teachers	3(3-0-0) S,Sum,Alt yrs
Preq: Grad. standing
Topics in geometry of concern to secondary teachers in their work and provision for background and enrichment. Various approaches to study of geometry, including vector geometry, transformational geometry and axiomatics. Course may be taken for graduate credit and for certificate renewal by secondary school teachers. Credit towards a graduate degree may be allowed only for students in mathematics education.
MA 509  Abstract Algebra For Secondary Teachers	3(3-0-0) F,Sum,Alt yrs
Preq: Grad. standing
From advanced viewpoint, an investigation of topics in algebra from high school curriculum. Theory of equations, polynomial rings, rational functions and elementary number theory. Course may be taken for graduate credit for certificate renewal by secondary school teachers. Credit towards a graduate degree may be allowed only for students in mathematics education.
MA 510  Selected Topics In Mathematics For Secondary Teachers	3(3-0-0) S,Sum, Alt yrs
Preq: Grad. standing
Coverage of various topics in mathematics of concern to secondary teachers. Topics selected from areas such as mathematics of finance, probability, statistics, linear programming and theory of games, intuitive topology, recreational math, computers and applications of mathematics. Course may be taken for graduate credit for certification renewal by secondary school teachers. Credit towards a graduate degree may be allowed only for students in mathematics education.
MA 511  Advanced Calculus I	3(3-0-0) F,S,Sum
Preq: MA 301
Credit for both MA 425 and MA 511 is not allowed
Fundamental theorems on continuous functions; convergence theory of sequences, series and integrals; the Riemann integral.
MA 512  Advanced Calculus II	3(3-0-0) F,S,Sum
Preq: MA 301. Credit for both MA 426 and MA 512 is not allowed
General theorems of partial differentiation; implicit function theorems; vector calculus in 3-space; line and surface integrals; classical integral theorems.
MA 513  Introduction To Complex Variables	3(3-0-0) F,S,Sum
Preq: MA 242
Operations with complex numbers, derivatives, analytic functions, integrals, definitions and properties of elementary functions, multivalued functions, power series, residue theory and applications, conformal mapping.
MA 515  Analysis I	3(3-0-0) F,S
Preq: MA 426
Metric spaces: contraction mapping principle, Tietze extension theorem, Ascoli-Arzela lemma, Baire category theorem, Stone-Weierstrass theorem, LP spaces. Banach spaces: linear operators, Hahn-Banach theorem, open mapping and closed graph theorems. Hilbert spaces: projection theorem, Riesz representation theorem, Lax-Milgram theorem, complete orthonormal sets.
MA 518  Introduction To Manifold Theory	3(3-0-0)
Preq: MA 426 or MA 512
Theory of differentiable manifold. Definitions and examples; tangent vectors and tangent spaces; maps between manifolds submanifolds, submersions, immersions, product and quotient manifolds; cotangent vectors and cotangent spaces; differentials forms; vector fields on a manifold, integral curves and flows of vector fields, and Lie derivatives; tangent and cotangent bundles.
MA 520  Linear Algebra	3(3-0-0) F
Preq: MA 405
Vector spaces. Bases and dimension. Changes of basis. Linear transformations and their matrices. Linear functionals. Simultaneous triangularization and diagonalization. Rational and Jordan canonical forms. Bilinear forms.
MA 521  Abstract Algebra I	3(3-0-0) F,S
Preq: MA 405 and MA 407
Groups, normal subgroups, quotient groups, Cayley's theorem, Sylow's theorem. Rings, ideals and quotient rings, polynomial rings. Elements of field theory.
MA 522  Computer Algebra	3(3-0-0) S
Preq: MA 407 or MA 521 and MA 405 or MA 520
Basic techniques and algorithms of computer algebra. Integer arithmetic, primality tests and factorization of integers, polynomial arithmetic, polynomial factorization, Groebner bases, integration in finite terms.
MA 523  Linear Transformations and Matrix Theory	3(3-0-0) F
Preq: MA 405
Vector spaces, linear transformations and matrices, orthogonality, orthogonal transformations with emphasis on rotations and reflections, matrix norms, projectors, least squares, generalized inverses, definite matrices, singular values.
MA 530  Numerical Analysis II	3(3-0-0)
Preq: MA 580
Approximation and interpolation, Fast Fourier Transform, numerical differentiation and integration, numerical solution of initial value problems for ordinary differential equations.
MA (E) (OR) 531  Dynamic Systems and Multivariable Control I	3(3-0-0) F
Preq: MA 341, MA 405
Introduction to modeling, analysis and control of linear discrete-time and continuous-time dynamical systems. State space representations and transfer methods. Controllability and observability. Realization. Applications to biological, chemical, economic, electrical, mechanical and sociological systems.
MA 532  Ordinary Differential Equations I	3(3-0-0) F,S
Preq: MA 341, 405, 425 or 511
Coreq: MA 426 or 512
Existence and uniqueness theorems, systems of linear equations, fundamental matrices, matrix exponential, nonlinear systems, plane autonomous systems, stability theory.
MA 534  Introduction To Partial Differential Equations	3(3-0-0) F
Preq: MA 425 or MA 511, MA 341
Coreq: MA 426 or 512
Linear first order equations, method of characteristics. Classification of second order equations. Solution techniques for the heat equation, wave equation and Laplace's equation. Maximum principles. Green's functions and fundamental solutions.
MA 535  Stability and Time Optimal Control Of Hereditary Systems	3(3-0-0) F
Preq: MA 341, MA 425 or MA 511.
Theory of stability and of time optimal control of hereditary systems. Lyapunov stability theory, time optimal, minimum fuel and effort control synthesis of systems. Applications: spread of epidemics, growth of global economy, automatic steering of aircraft, control of wind tunnels, and of flexible structures.
MA 537  Nonlinear Dynamics and Chaos	3(3-0-0) S
Preq: MA 341 and MA 405
Usage of computer experiments for demonstration of nonlinear dynamics and chaos and motivation of mathematical definitions and concepts. Examples from finance and ecology as well as traditional science and engineering. Difference equations and iteration of functions as nonlinear dynamical systems. Fixed points, periodic points and general orbits. Bifurcations and transition to chaos. Symbolic dynamics, chaos, Sarkovskii's Theorem, Schwarzian derivative, Newton's method and fractals.
MA 544  Computer Experiments In Mathematical Probability	3(3-0-0) S
Preq: MA 421
Exposure of student to practice of performing mathematical experiments on computer, with emphasis on probability. Programming in an interactive language such as APL, MATLAB or Mathematica. Mathematical treatment of random number generation and application of these tools to mathematical topics in Monte Carlo method, limit theorems and stochastic processes for purpose of gaining mathematical insight.
MA (ST) 546  Probability and Stochastic Processes I	3(3-0-0) F
Preq: MA 421 and MA 425 or MA 511
Modern introduction to Probability Theory and Stochastic Processes. The choice of material is motivated by applications to problems such as queueing networks, filtering and financial mathematics. Topics include: review of discrete probability and continuous random variables, random walks, markov chains, martingales, stopping times, erodicity, conditional expectations, continuous-time Markov chains, laws of large numbers, central limit theorem and large deviations.
MA 547  Financial Mathematics	3(3-0-0) S
Preq: MA(ST) 546
Stochastic models of financial markets. No-arbitrage derivativepricing. From discrete to continuous time models. Brownian motion, stochastic calculus, Feynman-Kac formula and tools for European options and equivalent martingale measures. Black-Scholes formula. Hedging strategies and management of risk. Optimal stopping and American options. Term structure models and interest rate derivatives. Stochastic volatility models.
MA 551  Introduction to Topology	3(3-0-0) F
Preq: MA 426
Set theory, topological spaces, metric spaces, continuous functions, separation, cardinality properties, product and quotient topologies, compactness, connectedness.
MA 555  Introduction to Manifold Theory	3(3-0-0) F
Preq: MA 426 or MA 512
Theory of differentiable manifold. Definitions and examples; tangent vectors and tangent spaces; maps between manifolds submanifolds, submersions, immersions, product and quotient manifolds; cotangent vectors and cotangent spaces; differentials forms; vector fields on a manifold, integral curves and flows of vector fields, and Lie derivatives; tangent and cotangent bundles.
MA 561  Set Theory and Foundations Of Mathematics	3(3-0-0) S
Preq: MA 407
Logic and axiomatic approach, the Zermelo-Fraenkel axioms and other systems, algebra of sets and order relations, equivalents of the Axiom of Choice, one-to-one correspondences, cardinal and ordinal numbers, the Continuum Hypothesis.
MA (CSC) (OR) 565  Graph Theory	3(3-0-0) F
Preq: CSC 224 or MA 351.
Basic concepts of graph theory, including: paths and connectivity, Euler tours and Hamilton cycles, matchings and independence, graph coloring, planarity, directed graphs and network flows, vector spaces associated with a graph, and applications with emphasis on organizing problems for computer solution.
MA (BMA) 573  Mathematical & Experimental Modeling of Physical Processes I	3(3-0-0) F
Preq: MA 341, MA 405, knowledge of high-level programg. lang
In-depth treatment of case studies in application of mathematics to problems currently under investigation in industrial and governmental laboratories. Background information for each case study; development of mathematical models; analytical and computational methods appropriate to models; model validation using experimental data collected during field trips to laboratories. Case studies involve problems in mechanics, thermodynamics, and hydrodynamics.
MA (BMA) 574  Mathematical & Experimental Modeling of Physical Processes II	3(3-0-0) S
Preq: MA 341, MA 405, knowledge of high-level programg. lang
In-depth treatment of case studies in the application of mathematics to problems currently under investigation in industrial and governmental laboratories. Background information for each case study; development of mathematical models; analytical and computational methods appropriate to the models; model validation using experimental data collected during field trips to the laboratories. Problems in biology & electromagnetism.
MA (PY) 575  Mathematical Introduction to Celestial Mechanics	3(3-0-0) F
Preq: MA 301
Central orbits, N-body problem, 3-body problem, Hamilton-Jacobi theory, perturbation theory, applications to motion of celestial bodies.
MA (PY) 576  Orbital Mechanics	3(3-0-0) S
Preq: MA 341, 405, knowledge of elementary mechanics and computer programming
Keplerian motion, iterative solutions, numerical integration, differential corrections and space navigation, elements of probability, least squares, sequential estimation, Kalman filter.
MA (CSC) 580  Numerical Analysis I	3(3-0-0) F,S
Preq: MA 405; MA 425 or MA 511; high-level computer language
Algorithm behavior and applicability. Effect of roundoff errors, systems of linear equations and direct methods, least squares via Givens and Householder transformations, stationary and Krylov iterative methods, the conjugate gradient and GMRES methods, convergence of method.
MA (CSC) 583  Introduction to Paralell Computing	3(3-0-0) S
Preq: CSC 302 or MA 402 or MA/CSC 428 or MA/CSC 580
Introduction to basic paralell architectures, algorithms and programming paradigms; message passing collectives and communicators; paralell matrix products, domain decomposition with direct and iterative methods for linear systems; analysis of efficiency, complexity and errors; applications such as 2D heat and mass transfer.
MA 584  Numerical Solution of Partial Differential Equations--Finite Difference Methods	3(3-0-0) F
Preq: MA 501; knowledge of a high level programming language
Survey of finite difference methods for partial differential equations including elliptic, parabolic and hyperbolic PDE's. Consideration of both linear and nonlinear problems. Theoretical foundations described; however, emphasis on algorithm design and implementation.
MA 587  Numerical Solution of Partial Differential Equations--Finite Element Method	3(3-0-0) S
Preq: MA 501; knowledge of a high level programming language
Introduction to finite element method. Applications to both linear and nonlinear elliptic and parabolic partial differential equations. Theoretical foundations described; however, emphasis on algorithm design and implementation.
MA 591  Special Topics	1-6 F,S
Preq: Consent of department
MA 676  Master's Project	3(3-0-0) F,S,Sum
Investigation of some topic in mathematics to a deeper and broader extent than typically done in a classroom situation. For the applied mathematics student the topic usually consists of a realistic application of mathematics to student's minor area.A written and oral report on the project required.
MA 685  Master's Supervised Teaching	1-3 F,S,Sum
Preq: Master's students
Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.
MA 690  Master's Examination	1-6 F,S,Sum
Preq: Master's student
For students in non thesis master's programs who have completed all other requirements of the degree except preparing for and taking the final master's exam.
MA 693  Master's Supervised Research	1-9 F,S,Sum
Preq: Master's Student
Instruction in research and research under the mentorship of a member of the Graduate Faculty.

Course for Graduates Only

695  Master's Thesis Research	1-9 F,S,Sum
Preq: Master's Student
Thesis Research
MA 696 Summer Thesis Research	1(1-0-0) Sum
Preq: Master's student
For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.
MA 699  Master's Thesis Preparation	1-3 F,S,Sum
Preq: Master's Student
Credits Arranged
For students who have completed all credit hour requirements and full-time enrollment for the master's degree and are writing and defending their thesis.
MA (OR) (ST) 706  Nonlinear Programming	3(3-0-0) S
Preq: OR(IE,MA) 505 and MA 425 or equivalent
An advanced mathematical treatment of analytical and algorithmic aspects of finite dimensional nonlinear programming. Including an examination of structure and effectiveness of computational methods for unconstrained and constrained minimization. Special attention directed toward current research and recent developments in the field.
MA (IE) (OR) 708  Integer Programming	3(3-0-0) S, Alt yrs
Preq: MA 405, OR (MA,IE) 505
Coreq: Some familiarity with computers (e.g., CSC 112)
General integer programming problems and principal methods of solving them. Emphasis on intuitive presentation of ideas underlying various algorithms rather than detailed description of computer codes. Students have some "hands on" computing experience that should enable them to adapt ideas presented in course to integer programming problems they may encounter.
MA 711  Analytic Function Theory I	3(3-0-0) F
Preq: MA 426
Rigorous introduction to theory of functions of a complex variable. Complex plane, functions, Mobius transformations, exponential and logarithmic functions, trigonometric functions, infinite series, integration in the complex plane, Cauchy's theoremand its consequences.
MA 712  Analytic Function Theory II	3(3-0-0) S
Preq: MA 711
A continuation of MA 611. Taylor and Laurent series. The residue theorem, the argument principle, harmonic functions and the Dirichlet problem, analytic continuation and the monodromy theorem, entire and meromorphic functions, the Weierstrass product representation and the Mittag-Leffler partial fraction representation, special functions, conformal mapping and the Picard theorem.
MA 713  Techniques of Complex Analysis	3(3-0-0) S
Preq: MA 513 or 711
Applications of complex analysis to mathematical problems in physical science in the setting of potential equation and other partial differential equations: contour integrals, special functions of mathematical physics from line integral point of view, solution of problems in potential theory, asymptotic methods including WKB and Wiener-Hopf techniques.
MA 715  Analysis II	3(3-0-0) S
Preq: MA 515
Integration: Legesgue measure and integration, Lebesgue-dominated convergence and monotone convergence theorems, Fubini's theorem, extension of the fundamental theorem of calculus. Banach spaces: Lp spaces, weak convergence, adjoint operators, compact linear operators, Fredholm-Fiesz Schauder theory and spectral theorem.
MA 716  Advanced Functional Analysis	3(3-0-0) F, Alt yrs
Preq: MA 715
Advanced topics in functional analysis such as linear topological spaces; Banach algebra, spectral theory and abstract measure theory and integration.
MA 719  Vector Space Methods in System Optimization	3(3-0-0) F
Preq: MA 405, 511 or equivalent
Introduction to algebraic and function-analytic concepts used in system modeling and optimization: vector space, linear mappings, spectral decomposition, adjoints, orthogonal projection, quality, fixed points and differentials. Emphasis on geometricinsight. Topics include least square optimization of linear systems, minimum norm problems in Banach space, linearization in Hilbert space, iterative solution of system equations and optimization problems. Broad range of applications in operations research and system engineering including control theory, mathematical programming, econometrics, statistical estimation, circuit theory and numerical analysis.
MA 720  Lie Algebras	3(3-0-0) S
Preq: MA 520, MA 521
Definition of Lie algebras and examples. Nilpotent, solvable and semisimple Lie algebras. Engel's theorem, Lie's Theorem, Killing form and Cartan's criterion. Weyl's theorem on complete reducibility. Representations of s1(2,C). Root space decomposition of semisimple Lie algebras. Root system and Weyl group.
MA 721  Abstract Algebra II	3(3-0-0) S
Preq: MA 521
Field extensions, Galois theory, modules, tensor products, exterior products.
MA 723  Theory of Matrices and Applications	3(3-0-0) S
Preq: MA 520 or 523
Canonical forms, functions of matrices, variational methods, perturbation theory, numerical methods, nonnegative matrices, applications to differential equations, Markov chains.
MA (E) (OR) 731  Dynamic Systems and Multivariable Control II	3(3-0-0) S
Preq: MA 531
Stability of equilibrium points for nonlinear systems. Liapunov functions. Unconstrained and constrained optimal control problems. Pontryagin's maximum principle and dynamic programming. Computation with gradient methods and Newton methods. Multidisciplinary applications.
	3(3-0-0) S
Preq: MA 532
Coreq: MA 515
Existence-uniqueness theory, periodic solutions, invariant manifolds, bifurcations, Fredholm's alternative.
MA 734  Partial Differential Equations	3(3-0-0) S
Preq: MA 534
Coreq: MA 515
Linear second order parabolic, elliptic and hyperbolic equations. Initial value problems and boundary value problems. Iterative and variational methods. Existence, uniqueness and regularity. Nonlinear equations and systems.
MA 735 Stability and Time Optimal Control of Hereditary Systems II	3(3-0-0) S
Preq: MA 535
Topics: time optimal control of linear delay systems; minimum fuel control synthesis; nonlinear controllability theory; stability of large-scale systems and applications to growth of the national/global economy.
MA 746  Introduction to Stochastic Processes	3(3-0-0) S
Preq: MA 405 and MA(ST) 546 or ST 521
Markov chains and Markov processes, Poisson process, birth and death processes, queuing theory, renewal theory, stationary processes, Brownian motion.
MA 747  Probability and Stochastic Processes II	3(3-0-0) S
Preq: MA(ST) 546
Fundamental mathematical results of probabilistic measure theory needed for advanced applications in stochastic processes. Probability measures, sigma-algebras, random variables, Lebesgue integration, expectation and conditional expectations w.r.t.sigma algebras, characteristic functions, notions of convergence of sequences of random variables, weak convergence of measures, Gaussian systems, Poisson processes, mixing properties, discrete-time martingales, continuous-time markov chains.
MA 748  Stochastic Differential Equations	3(3-0-0) F
Preq: MA(ST) 747
Theory of stochastic differential equations driven by Drownian motions. Current techniques in filtering and financial mathematics. Construction and properties of Brownian motion, wiener measure, Ito's integrals, martingale representation theorem, stochastic differential equations and diffusion processes, Girsanov's theorem, relation to partial differential equations, the Feynman-Kac formula.
MA 751  Topology	3(3-0-0) S
Preq: MA 551
Separation and cardinality properties, countable and sequential compactness, compactification, paracompactness and normality, metrization and metrizability theorems.
MA 753  Algebraic Topology	3(3-0-0) S, Alt yrs
Preq: MA 551
Homotopy, fundamental group, covering spaces, classification of surfaces, homology and cohomology.
MA 755  Introduction To Riemannian Geometry	3(3-0-0) S, Alt yrs
Preq: MA 555
Tensor algebra on vector spaces and tensor fields on manifolds; Koszul connections; parallel transport; torsion and curvature of connections; the Bianchi identities; metric tensor fields; metric and Levi-Civita connections; the Riemannian curvature,Ricci and Einstein tensors. Special topics: general relativity, embedding theory, integration on manifolds, the Gauss-Bonnet theorem, De Rahm cohomology.
MA 756  Geometrical Structures On Fiber Bundles	3(3-0-0) F, Alt yrs
Preq: MA 755
Principal fiber bundles, subbundles, associated bundles; Frobenius theory of distributions; the frame bundle LM of a manifold, the soldering 1-form, linear connections, curvature and torsion forms on LM, the Bianchi identities, reduction of connections; affine frame bundle and generalized affine connections. Special topics: Yang-Mills theory, electro-weak theory, magnetic monopoles, geometric quantization.
	3(2-2-0) S
Preq: OR(IE,MA) 505 or equivalent
Study of problems of flows in networks. These problems include the determination of shortest chain, maximal flow and minimal cost flow in networks. Relationship between network flows and linear programming developed as well as problems with nonlinear cost functions, multi-commodity flows and problem of network synthesis.
MA 771 Biomathematics I	3(3-0-0) F
Preq: Advanced calculus, reasonable background in biology or Consent of Instructor
Role of theory construction and model building in development of experimental science. Historical development of mathematical theories and models for growth of one-species populations (logistic and off-shoots), including considerations of age distributions (matrix models, Leslie and Lopez; continuous theory, renewal equation). Some of the more elementary theories on the growth of organisms (von Bertalanffy and others; allometric theories; cultures grown in a chemostat). Mathematical theories oftwo and more species systems (predator-prey, competition, symbosis; leading up to present-day research) and discussion of some similar models for chemical kinetics. Much emphasis on scrutiny of biological concepts as well as of mathematical structure of models in order to uncover both weak and strong points of models discussed. Mathematical treatment of differential equations in models stressing qualitative and graphical aspects, as well as certain aspects of discretization. Difference equationmodels.
MA 772  Biomathematics II	3(3-0-0) S
Preq: BMA 771, elementary probability theory
Continuation of topics of BMA 771. Some more advanced mathematical techniques concerning nonlinear differential equations of types encountered in BMA 771: several concepts of stability, asymptotic directions, Liapunov functions; different time-scales. Comparison of deterministic and stochastic models for several biological problems including birth and death processes. Discussion of various other applications of mathematics to biology, some recent research.
	3(3-0-0) S,Alt Yrs
Preq: BMA 772 or ST (MA) 746
Survey of modeling approaches and analysis methods for data from continuous state random processes. Emphasis on differential and difference equations with noisy input. Doob-Meyer decomposition of process into its signal and noise components. Examples from biological and physical sciences, and engineering. Student project.
MA 774  Partial Differential Equation Modeling in Biology	3(3-0-0) S
Preq: BMA 771 or MA/OR 731; BMA 772 or MA 401 or MA 501
Modeling with and analysis of partial differential equations as applied to real problems in biology. Review of diffusion and conservation laws. Waves and pattern formation. Chemotaxis and other forms of cell and organism movement. Introduction to solid and fluid mechanics/dynamics. Introductory numerical methods. Scaling. Perturbations, Asymptotics, Cartesian, polar and spherical geometries. Case studies.
MA 775  Mathematical Methods in the Physical Sciences I	3(3-0-0) F
Preq: MA 405, 511 and either MA 401 or 501
Green's functions and two-point boundary value problems; elementary theory of distributions; generalized Green's functions. Finite and infinite dimensional inner product spaces; Hilbert spaces; completely continuous operators; integral equations; the Fredholm alternative; eigenfunction expansions; applications to potential theory. Nonsingular and singular Sturm-Liouville problems; Weil's theorem.
MA 776  Mathematical Methods in the Physical Sciences II	3(3-0-0) S
Preq: MA 775
Distribution theory in n-space; Fourier transforms; partial differential equations, generalized solutions, fundamental solutions, Cauchy problem, wave and heat equations, well-set problems. Laplace's equations, the Dirichlet and Neumann problems, integral equations of potential theory. Green's functions, eigen function expansions.
MA 777  Exact and Approximate Solutions In Particle Transport Theory	3(3-0-0) S
Preq: MA 501 or MA 511
Method of elementary solutions used to solve exactly basic problems in neutron-transport theory and related topics. In addition, development and usage of FN method to establish concise approximate solutions in the realm of particle transport theory.
MA 778  Measure Theory and Advanced Probability	3(3-0-0) F,S
Preq: MA 426; ST 521 or MA(ST) 546 or equivalent
Modern measure and integration theory in abstract spaces. Probability measures, random variables, expectations. Distributions and characteristic functions. Modes of convergence. Independence, zero-one laws, laws of large numbers, three-series theorem. Central limit problem. Conditional expectations, martingales and martingale convergence theorems.
MA 779  Measure Theory and Advanced Probability	3(3-0-0) F,S
Preq: ST 778
Modern measure and integration theory in abstract spaces. Probability measures, random variables, expectations. Distributions and characteristic functions. Modes of convergence. Independence, zero-one laws, laws of large numbers, three-series theorem. Central limit problem. Conditional expectations, martingales and martingale convergence theorems.
MA 780  Numerical Analysis II	3(3-0-0) S
Preq: MA 580
Approximation and interpolation, Fast Fourier Transform, numerical differentiation and integration, numerical solution of initial value problems for ordinary differential equations.
MA 782  Advanced Numerical Linear Algebra	3(3-0-0) S
Preq: MA 580
Mathematical and numerical investigation of direct, iterative and semi-iterative methods for solution of linear systems. Singular algebraic systems and least squares computations. Methods for calculation of eigenvalues and eigenvectors. Careful mathematical analysis of these techniques.
MA 783  Parallel Algorithms and Scientific Computation	3(3-0-0) F (Alt yrs-odd)
Preq: MA/CSC 583, or MA/CSC 580 and some paralell computing
Multiprocessing and vector architectures including current hardware and software. Parallel implementations of numerical inear algebra algorithms for matrix products, linear systems as well as nonlinear algebraic systems and eigenvalue problems. Applications to science and engineering including 3D space and system models.
MA 784  Nonlinear Equations and Unconstrained Optimization	3(3-0-0) S,Alt yrs
Preq: MA 580
Newton's method and Quasi-Newton methods for nonlinear equations and optimization problems, globally convergent extensions, methods for sparse problems, applications to differential equations, integral equations and general minimization problems. Methods appropriate for boundary value problems.
MA 785  Numerical Solution of Ordinary Differential Equations	3(3-0-0) S
Preq: MA 511 or 512
Numerical methods for initial value problems including predictor-corrector, Runge-Kutta, hybrid and extrapolation methods; stiff systems; shooting methods for two-point boundary value problems; weak, absolute and relative stability results.
MA 788  Numerical Nonlinear Partial Differential Equations	3(3-0-0) S,Alt yrs
Preq: MA 405 or 520 and MA 501 or 534; knowledge of a high level programming language
Nonlinear discrete equations; Newton and monotone methods for nonlinear equations; computational algorithms and applications; finite difference method-convergence, stability and error estimates; multiplicity of solutions and bifurcation; asymptotic behavior of solutions; and coupled systems of equations.
MA 790  Advanced Special Topics System Optimization	1-3 F,S
Advanced topics in some phase of system optimization using traditional course format. Identification of various specific topics and prerequisties for each section from term to term.
MA 791  Special Topics In Real Analysis	1-6 F,S
MA 792  Special Topics In Algebra	1-6 F,S
MA 793  Special Topics In Differential Equations	1-6
MA 795  Special Topics In Topology	1-6
MA 796  Special Topics In Combinatorial Analysis	1-6
MA 797  Special Topics In Applied Mathematics	Credits Arranged
MA 798  Special Topics In Numerical Analysis	1-6
MA 810  Special Topics	1-3 F,S
MA 812  Special Topics In Mathematical Programming	NULL S,Alt yrs
Preq: IE(MA,OR) 505
Study of special advanced topics in area of mathematical programming. Discussion of new techniques and current research in this area. The faculty responsible for this course select areas to be covered during semester according to their preference and interest. This course not necessarily taught by an individual faculty member but can, on occasion, be joint effort of several faculty members from this university as well as visiting faculty from other institutions. To date, a course of Theory of Networks and another on Integer Programming offered under the umbrella of this course. Anticipation that these two topics will be repeated in future together with other topics.
MA 816  Advanced Special Topics System Optimization	1-3 F,S
Advanced topics in some phase of system optimization. Identification of various specific topics and prerequisite for each section from term to term.
MA 885  Doctoral Supervised Teaching	1-3 F,S,Sum
Preq: Doctoral Student
Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.
MA 890  Doctoral Preliminary Examination	1-9 F,S,Sum
Preq: Doctoral Student
For students who are preparing for and taking written and/or oral preliminary exams.
MA 893 Doctoral Supervised Research	1-9 F,S,Sum
Preq: Doctoral Student
Instruction in research and research under the mentorship of a member of the Graduate Faculty.
MA 895  Doctoral Dissertation Research	1-9 F,S,Sum
Preq: Doctoral Student
Dissertation Research
MA 896  Summer Dissertation Research	1(1-0-0) Sum
Preq: Doctoral student
For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.
MA 899  Doctoral Dissertation Preparation	1-3 F,S,Sum
Preq: Doctoral Student
For students who have completed all credit hour requirements, full-time enrollment, preliminary examination, and residency requirements for the doctoral degree, and are writing and defending their dissertations.

Top of Page

Department of Mathematics, Box 8205, NC State University, Raleigh, NC 27695-8205