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Courses marked with a (*) satisfy divisional studies requirements.
Courses numbered 500 and above are listed on the graduate course
lists (see the graduate course lists from the math home page).
Mathematics Courses Primarily for Nonconcentrators
CAS MA 118 College Algebra and Trigonometry
Functions and graphs. Linear and quadratic equations. Exponents,
logarithms. Right and oblique triangles; trigonometric functions.
Optimization. Specifically intended to prepare students with insufficient
background in mathematics for the study of calculus. This course
may not be used in fulfillment of the distribution requirement.
Satisfies the mathematics requirement in the College program. 4
cr, either sem.
(*) CAS MA 120 Applied Mathematics for Social and Management Sciences
Linear equations, systems of linear equations, matrix algebra,
exponential functions and logarithms, elements of differential calculus,
optimization, probability. Applications in economics, finance, and
management. Satisfies both mathematics requirement and distribution
requirement. 4 cr, either sem.
Calculus Courses
(*) CAS MA 121 Calculus for the Life and Social Sciences
Students may receive credit for either MA 121 or 123, but not
both. Differentiation and integration of functions of one variable.
Same topics as CAS MA 123, but with less emphasis on mathematical
generality and more on application. Especially suitable for students
concentrating in the biological and social sciences. 4 cr, either
sem.
(*) CAS MA 122 Calculus for the Life and Social Sciences
Students may receive credit for not more than one of the following
courses: MA 122, MA 124, MA 127, or MA 129. Prereq: MA 121 or MA
123. Continuation of MA 121. Review of univariate calculus, calculus
of the elementary transcendental functions, elementary differential
equations, elementary multivariate calculus. Applications to exponential
growth, optimization, equilibrium, and dynamic modeling problems.
4 cr, 2nd sem.
(*) CAS MA 123 Calculus I
Limits; derivatives, differentiation of algebraic functions. Applications
to maxima, minima, and convexity of functions. The definite integral;
the fundamental theorem of integral calculus; applications of integration.
4 cr, either sem.
(*) CAS MA 124 Calculus II
Prereq: MA 121 or MA 123. Logarithmic, exponential, and trigonometric
functions. Sequences and series; Taylor's series with the remainder.
Methods of integration. Calculus I and II together constitute an
introduction to calculus of a function of a single real variable.
4 cr, either sem.
(*) CAS MA 127 Calculus: A Review
For students with prior experience in calculus. A one-semester
course that covers the topics of MA 123. 124 and prepares students
to enter MA 225 Multivariate Calculus. 4 cr, 1st sem.
(*) CAS MA 129 Honors Calculus
Prereq: consent of instructor. Alternative to MA 127 for advanced
students with a deep interest in mathematics. Continuity, degrees
of differentiability, integrability. Transcendental functions. Techniques
of differentiation and integration. Sequences, series, summability,
uniform convergence. Complex numbers, Taylor series. Application
to mechanics, probability. 4 cr, 1st sem.
CAS MA 136 Calculus with Computers 2
Prereq: MA 121 or 123. Differentiation and integration of transcendental
functions, methods of integration, and sequences and series. This
course uses the mathematics-based computer system <em>Mathematica</em>
as a vehicle to do problems that cannot be done with paper and pencil
alone. 4 cr, 2nd sem.
CAS MA 142 Introduction to Linear Algebra
Coreq: MA 122, or MA 124, or MA 127, or MA 129. Systems of linear
equations; matrices. Vector spaces and linear transformations. Determinants.
Eigenvalues and eigenvectors. Applications. (Cannot be taken for
credit in addition to MA 242 or ENG EK 402.) 2 cr, either sem.
CAS MA 193 Discrete Mathematics for Engineering
Propositional logic, set theory; relations, combinatorics, graphs.
Topics are treated with particular emphasis on applications to the
engineering discipline. Cannot be taken for credit in addition to
ENG SC 333. 2 cr, either sem.
CAS MA 225 Multivariate Calculus
Prereq: MA 124, MA 127, MA 129, or MA 136. Vectors, lines, planes.
Multiple integration, cylindrical and spherical coordinates. Partial
derivatives, directional derivatives, scalar and vector fields,
the gradient, potentials, approximation, multivariate minimization.
4 cr, either sem.
CAS MA 226 Differential Equations
Prereq: MA 225 or MA 230. First-order linear and separable equations.
Constant coefficient theory. Second-order variable coefficient equations.
Numerical methods, Laplace transforms, systems of first-order equations,
power series methods. Applications and modeling of real phenomena
included throughout. 4 cr, either sem.
CAS MA 230 Honors-Level Vector Calculus
Prereq: MA 124 or MA 127, or MA 129. Linear algebra: linear transformations
and matrices, inner products, cross products. Differentiation: tangent
spaces, directional derivatives, gradients, vector fields and flow,
divergence, curl. Integration: multiple integrals, line integrals,
Green's theorem, surface integrals, Stokes's theorem, the divergence
theorem. 4 cr, 2nd sem.
CAS MA 231 Honors-Level Differential Equations
Prereq: MA 225 or MA 230. Ordinary differential equations with
applications to mechanics, biology, and physics. First- and second-order
equations, Sturm-Louisville problems, vibrating strings, special
functions, power series solutions, regular singular points, Laplace
transforms, calculus of variations, isoperimetric problems, and
Hamilton's principle. 4 cr, 1st sem.
Principal Mathematics Courses
Although designed primarily for the various programs of the
department, these courses are open to all qualified students.
Statistics courses are listed in a separate section.
CAS 242 Linear Algebra
Coreq: MA 122, MA 124, MA 127, or MA 129. Matrix algebra, solution
of linear systems, determinants, Gaussian elimination, fundamental
theory, row-echelon form.
Vector spaces, bases, norms. Computer methods. Eigenvalues and
eigenvectors, canonical decomposition. Applications to differential
and difference equation problems. 4 cr, either sem.
CAS MA 293 Discrete Mathematics I
Propositional logic, set theory. Elementary probability theory.
Number theory. Combinatorics with applications. 4 cr, either sem.
CAS MA 294 Discrete Mathematics II
Prereq: MA 293 or consent of instructor. Graph theory and combinatorics.
Groups, rings and fields, and their applications. 4 cr, either
sem.
CAS MA 341 Introduction to Number Theory
Prereq: MA 242 or consent of instructor. Study of integers and
basic results of number theory. Topics include Linear Diophantine
equations, prime numbers and factorization, congruences, and quadratic
reciprocity. 4 cr, 2nd sem.
CAS MA 38l Elementary Probability
Prereq: MA 225 or MA 230. Combinatorial analysis, discrete and
continuous probability, random walk, treatment of data. 4 cr,
either sem.
CAS MA 401, 402 Senior Independent Work
Prereq: approval of the Honors Committee. 4 cr each, 1st &
2nd sem.
CAS MA 411 Advanced Calculus
Prereq: MA 225 or MA 230, and MA 242 or MA 442. Extends concepts
and techniques of calculus and develops further applications.
Topics include higher dimensional calculus, applications of vector
analysis, uniform convergence of series, complex series, improper
integrals, gamma and beta functions, Stirling's formula, Fourier
series and transform. 4 cr, 1st sem.
CAS MA 411 Complex Variables
Prereq: MA 225 or MA 230. Basic concepts, results, and applications
of complex analysis. Emphasis on computation and applications.
Complex plane and functions, differentiability, Cauchy-Reimann
conditions, contour integrals, Cauchy formulas, complex series,
residue calculus, applications. Extends the concepts of the calculus
to the complex setting. 4 cr, 2nd sem.
CAS MA 442 Honors Level Linear Algebra
Prereq: MA 225 or 230. A thorough development of the fundamentals
of linear algebra. Systems of linear equations; matrices, linear
transformations, duality; determinants, characteristic and minimal
polynomials; diagonalization and normal forms of linear transformations;
inner products, unitary and self-adjoint operators, and spectral
theory. Applications to physics, probability, and statistics.
4 cr, either sem.
CAS MA 471 Chaotic Dynamical Systems
Prereq: MA 225 or MA 230, and CS 101 or CS 111 (or equivalent
computer experience). Iteration of functions in one and higher
dimensions. Periodic points; hyperbolicity; recurrence; topological
conjugacy and structural stability; chaotic dynamics. Some numerical
experimentation involving personal computers. 4 cr, 1st sem.
CAS MA 491, 492 Directed Study
Prereq: consent of
instructor and application made through the Mathematics Department.
Variable cr, 1st & 2nd sem.
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