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Introduction to calculus with applications to the life sciences, mathematical modeling, differentiation, integration and applications. Course Information: Prior ...
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MATH 077. Mathematical Reasoning Workshop. 1 hour. A refresher of the algebra used in Math 118. A more detailed reminder of algebraic techniques will be given in a student-centered environment with personalized homework and worksheets to address individual needs. Course Information: Satisfactory/Unsatisfactory grading only. No graduation credit. Extensive computer use required. Requires concurrent registration in MATH 118. MATH 088. Intermediate Algebra Workshop. 1 hour. Individualized lesson plans including: order of operations, properties of real numbers, linear equations, problem solving, graphing linear equations. Course Information: Satisfactory/Unsatisfactory grading only. No graduation credit. Extensive computer use required. Corequisites: Requires concurrent registration in MATH 090. MATH 090. Intermediate Algebra. 3 hours. Linear equations and inequalities, absolute values, linear graphs and modeling, systems of equations, functions, quadratic equations, exponents and polynomials, factoring, radicals and rational exponents. Course Information: Satisfactory/Unsatisfactory grading only. Not open to students with credit in a mathematics course at or above the 100 level. No graduation credit. Extensive computer use required. Prerequisite(s): Credit or concurrent registration in MATH 088; or appropriate score on the department placement test. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Wednesday of finals week from 6 to 8 p.m. MATH 104. Mathematical Reasoning Workshop. 1 hour. A refresher of the algebra used in Math 105. A more detailed reminder of algebraic techniques will be given in a student-centered environment with personalized homework and worksheets to address individual needs. Course Information: Satisfactory/Unsatisfactory grading only. Previously listed as MATH 077. Credit is not given for MATH 104 if the student has credit in MATH 077. Requires concurrent registration in MATH 105. MATH 105. Mathematical Reasoning. 4 hours. Mathematical problem solving with a hands-on and learn-by-doing approach, using topics from linear equations, personal finance, geometry, probability, and statistics. Course Information: Previously listed as MATH 118. May serve as a prerequisite for statistics courses in the social sciences. It does not replace Math 090 as a prerequisite for any other mathematics department course. Credit is not given for MATH 105 if the student has credit in MATH 118 or MATH 121 or MATH 160 or MATH 165 or MATH 170 or MATH 180 or the equivalent. No graduation credit for architecture, business administration, or engineering students. Prerequisite(s): Credit or concurrent registration in MATH 104; or appropriate score on the department placement test. Course Schedule Information: To be properly registered, students must enroll in one Lecture and one Laboratory-Discussion. MATH 109. College Algebra Workshop. 1 hour. A refresher of material prerequisite for and used in MATH 110, including: functions, polynomial and rational equations, graphs and transformations, exponentials and logarithms, trigonometry. Course Information: Satisfactory/Unsatisfactory grading only. Prerequisite(s): Appropriate ALEKS placement score. Corequisite(s): Requires concurrent registration in MATH 110. MATH 110. College Algebra. 4 hours. Functions, composition and inverses; graphs and transformations, polynomial and rational functions, exponential functions, logarithms and applications; circles and introduction to trigonometry. Course Information: Credit is not given for Math 110 if the student has credit in MATH 121 or MATH 165 or MATH 170 or MATH 180. Extensive computer use required. Prerequisite(s): MATH 090; credit or concurrent registration in MATH 109; or an appropriate score on the department placement test. To be properly registered, students must enroll in one Lecture and one Laboratory-Discussion. MATH 121. Precalculus Mathematics. 5 hours. Functions, graphs, exponentials and logarithms, radicals, complex numbers, trigonometry (circle and triangle approaches), trigonometric graphs and inverses, introduction to polar coordinates and vectors Course Information: No credit will be given for MATH 121 if students have credit in MATH 165 or MATH 170 or MATH 180. Extensive computer use required. Prerequisite(s): Grade of C or better in MATH 110; or appropriate score on the department placement test. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Thursday of finals week from 6 to 8 p.m. To be properly registered, students must enroll in one Laboratory-Discussion and one Lecture. MATH 122. Emerging Scholars Workshop for Precalculus Mathematics. 1 hour. Intensive math workshop for students enrolled in MATH 121. Students work together in groups to solve challenging problems. Course Information: Satisfactory/Unsatisfactory grading only. Prerequisite(s): Admission to the Emerging Scholars Program. Must enroll concurrently in MATH 121. MATH 125. Elementary Linear Algebra. 5 hours. Introduction to systems of linear equations, matrices and vector spaces, with emphasis on business applications. Course Information: Credit is not given for MATH 125 if the student has credit in MATH 160. Prerequisite(s): Grade S in Math 090 or appropriate score on the department placement test. Class Schedule Information: To be properly registered, students must enroll in one Lecture and one Discussion. During the fall and spring terms, combined section final exam will be held on Thursday of finals week from 6 to 8 p.m. To be properly registered, students must enroll in one Discussion/Recitation and one Lecture. Natural World - No Lab course. MATH 140. Arithmetic and Algebraic Structures. 4 hours. Problem solving; algebraic thinking; number systems; numeration; number theory; mathematical operations over natural, integer, and rational numbers; and proportional reasoning. Course Information: Prerequisite(s): Grade of S in Math 090 or appropriate score on the department placement test. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Monday of finals week from 6 to 8 p.m. MATH 141. Algebraic and Geometric Structures. 4 hours. Area, perimeter, volume, surface area of plane and solid figures; integers, real and rational numbers; trigonometry and extended solution of general polygons; probability. Full purpose calculators used. Course Information: Designed for students in the B.A. in Elementary Education program. Prerequisite(s): Grade of C or better in MATH 140. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Tuesday of finals week from 6 to 8 p.m.
MATH 160. Finite Mathematics for Business. 5 hours. Introduction to probability, statistics, and matrices, with emphasis on business applications. Course Information: Credit is not given for MATH 160 if the student has credit in MATH 125. Prerequisite(s): MATH 090; or Grade of C or better in MATH 110; or appropriate score on the department placement test. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Thursday of finals week from 6 to 8 p.m. To be properly registered, students must enroll in one Discussion/Recitation and one Lecture. Natural World - No Lab course. MATH 165. Calculus for Business. 5 hours. Introduction to differential and integral calculus of algebraic, exponential and logarithmic functions and techniques of partial derivatives and optimization. Emphasis on business applications. Course Information: Prior credit for MATH 170 or MATH 180 will be lost with subsequent completion of MATH 165. Prerequisite(s): Grade of C or better in MATH 110; or appropriate score on the department placement test. Class Schedule Information: During the fall and spring terms, combined section final exam will be held on Wednesday of finals week from 6 to 8 p.m. To be properly registered, students must enroll in one Discussion/Recitation and one Lecture. Natural World - No Lab course. MATH 170. Calculus for the Life Sciences. 4 hours. Introduction to calculus with applications to the life sciences, mathematical modeling, differentiation, integration and applications. Course Information: Prior credit in MATH 165 or MATH 180 will be lost with subsequent completion of MATH 170. Prerequisite(s): Grade of C or better in Math 110 or appropriate score on the department placement test. Class Schedule Information: To be properly registered, students must enroll in one Lecture and one Discussion. Natural World - No Lab course. MATH 179. Emerging Scholars Workshop for Calculus I. 1 hour. Intensive math workshop for students enrolled in MATH 180. Students work together in groups to solve challenging problems. Course Information: Satisfactory/Unsatisfactory grading only. Prerequisite(s): Admission to the Emerging Scholars Program. Must enroll concurrently in MATH 180. MATH 180. Calculus I. 4 hours. Differentiation, curve sketching, maximum-minimum problems, related rates, mean-value theorem, antiderivative, Riemann integral, logarithm, and exponential functions. Course Information: Prior credit in MATH 165 or MATH 170 will be lost with subsequent completion of MATH
MATH 496. Independent Study. 1-4 hours. Reading course supervised by a faculty member. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the instructor and the department. Class Schedule Information: This course counts toward the limited number of independent study hours accepted toward the degree and the major. MATH 502. Mathematical Logic. 4 hours. First order logic, completeness and incompleteness theorems, introduction to model theory and computability theory. Course Information: Same as PHIL 562. Prerequisite(s): MATH 430 or consent of the instructor. MATH 504. Set Theory. 4 hours. Naive and axiomatic set theory. Independence of the continuum hypothesis and the axiom of choice. Course Information: Same as PHIL
**MATH 535. Complex Analysis I. 4 hours.** Analytic functions as mappings. Cauchy theory. Power Series. Partial fractions. Infinite products. Course Information: Prerequisite(s): MATH 411. **MATH 536. Complex Analysis II. 4 hours.** Normal families, Riemann mapping theorem. Analytic continuation, Harmonic and subharmonic functions, Picard theorem, selected topics. Course Information: Prerequisite(s): MATH 535. **MATH 537. Introduction to Harmonic Analysis I. 4 hours.** Fourier transform on L(p) spaces, Wiener's Tauberian theorem, Hilbert transform, Paley Wiener theory. Course Information: Prerequisite(s): MATH 533; and MATH 417 or MATH 535. **MATH 539. Functional Analysis I. 4 hours.** Topological vector spaces, Hilbert spaces, Hahn-Banach theorem, open mapping, uniform boundedness principle, linear operators in a Banach space, compact operators. Course Information: Prerequisite(s): MATH 533. **MATH 546. Advanced Topics in Analysis. 4 hours.** Subject may vary from semester to semester. Topics include partial differential equations, several complex variables, harmonic analysis and ergodic theory. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. **MATH 547. Algebraic Topology I. 4 hours.** The fundamental group and its applications, covering spaces, classification of compact surfaces, introduction to homology, development of singular homology theory, applications of homology. Course Information: Prerequisite(s): MATH 330 and MATH 445. MATH 548. Algebraic Topology II. 4 hours. Cohomology theory, universal coefficient theorems, cohomology products and their applications, orientation and duality for manifolds, homotopy groups and fibrations, the Hurewicz theorem, selected topics. Course Information: Prerequisite(s): MATH 547. MATH 549. Differentiable Manifolds I. 4 hours. Smooth manifolds and maps, tangent and normal bundles, Sard's theorem and transversality, embedding, differential forms, Stokes's theorem, degree theory, vector fields. Course Information: Prerequisite(s): MATH 445; and MATH 310 or MATH 320 or the equivalent. MATH 550. Differentiable Manifolds II. 4 hours. Vector bundles and classifying spaces, lie groups and lie algbras, tensors, Hodge theory, Poincare duality. Topics from elliptic operators, Morse theory, cobordism theory, deRahm theory, characteristic classes. Course Information: Prerequisite(s): MATH 549. MATH 551. Riemannian Geometry. 4 hours. Riemannian metrics and Levi-Civita connections, geodesics and completeness, curvature, first and second variation of arc length, comparison theorems. Course Information: Prerequisite(s): MATH 442 and MATH 549. MATH 552. Algebraic Geometry I. 4 hours. Basic commutative algebra, affine and projective varieties, regular and rational maps, function fields, dimension and smoothness, projective curves, schemes, sheaves, and cohomology, positive characteristic. Course Information: Prerequisite(s): Grade of C or better in MATH 516 and Grade of C or better in MATH 517; and graduate standing; or consent of the instructor. MATH 553. Algebraic Geometry II. 4 hours. Divisors and linear systems, differentials, Riemann-Roch theorem for curves, elliptic curves, geometry of curves and surfaces. Course Information: Prerequisite(s): MATH 552. MATH 554. Complex Manifolds I. 4 hours. Holomorphic functions in several variables, Riemann surfaces, Sheaf theory, vector bundles, Stein manifolds, Cartan theorem A and B, Grauert direct image theorem. Course Information: Prerequisite(s): MATH 517 and MATH 535. MATH 555. Complex Manifolds II. 4 hours. Dolbeault Cohomology, Serre duality, Hodge theory, Kadaira vanishing and embedding theorem, Lefschitz theorem, Complex Tori, Kahler manifolds. Course Information: Prerequisite(s): MATH 517 and MATH
MATH 568. Topics in Algebraic Topology. 4 hours. Homotopy groups and fibrations. The Serre spectral sequence and its applications. Classifying spaces of classical groups. Characteristic classes of vector bundles. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): MATH 548 or consent of the instructor. MATH 569. Advanced Topics in Geometric and Differential Topology. 4 hours. Topics from areas such as index theory, Lefschetz theory, cyclic theory, KK theory, non-commutative geometry, 3-manifold topology, hyperbolic manifolds, geometric group theory, and knot theory. Course Information: Prerequisite(s): Approval of the department. MATH 570. Advanced Topics in Differential Geometry. 4 hours. Subject may vary from semester to semester. Topics may include eigenvalues in Riemannian geometry, curvature and homology, partial differential relations, harmonic mappings between Riemannian manifolds hyperbolic geometry, arrangement of hyperplanes. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. MATH 571. Advanced Topics in Algebraic Geometry. 4 hours. Various topics such as algebraic curves, surfaces, higher dimensional geometry, singularities theory, moduli problems, vector bundles, intersection theory, arithematical algebraic geometry, and topologies of algebraic varieties. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. MATH 576. Classical Methods of Partial Differential Equations. 4 hours. First and second order equations, method of characteristics, weak solutions, distributions, wave, Laplace, Poisson, heat equations, energy methods, regularity problems, Green functions, maximum principles, Sobolev spaces, imbedding theorems. Course Information: Prerequisite(s): MATH 410 and MATH 481 and MATH 533; or consent of instructor. MATH 577. Advanced Partial Differential Equations. 4 hours. Linear elliptic theory, maximum principles, fixed point methods, semigroups and nonlinear dynamics, systems of conservation laws, shocks and waves, parabolic equations, bifurcation, nonlinear elliptic theory. Course Information: Prerequisite(s): MATH 533 and MATH 576 or consent of the instructor. MATH 578. Asymptotic Methods. 4 hours. Asymptotic series, Laplace's method, stationary phase, steepest descent method, Stokes phenomena, uniform expansions, multi-dimensional Laplace integrals, Euler-MacLaurin formula, irregular singular points, WKBJ method. Course Information: Prerequisite(s): MATH 417 and MATH 481; or consent of instructor. MATH 580. Mathematics of Fluid Mechanics. 4 hours. Development of concepts and techniques used in mathematical models of fluid motions. Euler and Navier Stokes equations. Vorticity and vortex motion. Waves and instabilities. Viscous fluids and boundary layers. Asymptotic methods. Course Information: Prerequisite(s): Grade of C or better in MATH 410 and grade of C or better in MATH 417 and grade of C or better in MATH 481. MATH 581. Special Topics in Fluid Mechanics. 4 hours. Geophysical fluids with applications to oceanography and meteorology, astrophysical fluids, magnetohydrodynamics and plasmas. Course Information: Prerequisite(s): Grade of C or better in MATH 580. MATH 582. Linear and Nonlinear Waves. 4 hours. Analysis of partial differential equations describing (non-) linear wave phenomena. In particular, dispersive and hyperbolic equations. Analytical techniques include Fourier transformation and fixed point theorems. Course Information: Prerequisite(s): Graduate standing and MATH 533 and MATH 576 OR MATH 539 or consent of the instructor. MATH 584. Applied Stochastic Models. 4 hours. Applications of stochastic models in chemistry, physics, biology, queueing, filtering, and stochastic control, diffusion approximations, Brownian motion, stochastic calculus, stochastically perturbed dynamical systems, first passage times. Course Information: Prerequisite(s): MATH 417 and MATH 481 and STAT 401, or consent of the instructor.