This course develops in the theme of "Arithmetic congruence and abstract algebraic structures". Strong emphasis on theory and proofs.
Introduction to Abstract Algebra II. Continuation of Abstract Algebra I, with emphasis on Galois theory, modules, polynomial fields, and the theory of linear associative algebra. Introduction to Number Theory. Primes and unique factorization, congruences, Chinese remainder theorem, Diophantine equations, Diophantine approximations, quadratic reciprocity.
Applications such as fast multiplication, factorization, and encryption. Probability with Applications I. Probability with Applications II. Renewal theory, Poisson processes and continuous time Markov processes, including an introduction to Brownian motion and martingales. Probability distributions, limit laws, and applications through the computer. Mathematical Statistics I. Sampling distributions, Normal, t, chi-square, and f distributions.
Moment-generating function methods, Bayesian estimation, and introduction to hypothesis testing. Mathematical Statistics II. Hypothesis testing, likelihood ratio tests, nonparametric tests, bivariate and multivariate normal distributions. Introduction to Information Theory. The measurement and quantification of information. These ideas are applied to the probabilistic analysis of the transmission of information over a channel along which random distortion of the message occurs.
Finite dimensional vector spaces, inner product spaces, least squares, linear transformations, the spectral theorem for normal transformations. Applications to convex sets, positive matrices, difference equations. Real numbers, topology of Euclidean spaces, Cauchy sequences, completeness, continuity and compactness, uniform continuity, series of functions, Fourier series. Differentiation of functions of one real variable, Riemann-Stieltjes integral, the derivative in Rn, and integration in Rn.
Topics from complex function theory, including contour integration and conformal mapping. Partial Differential Equations I. Method of characteristics for first- and second-order partial differential equations, conservation laws and shocks, classification of second-order systems and applications. Partial Differential Equations II.
Green's functions and fundamental solutions. Potential, diffusion, and wave equations. Point set topology, topological spaces and metric spaces, continuity and compactness, homotopy, and covering spaces. Introduction to Algebraic Topology. Introduction to algebraic methods in topology.
Includes homotopy, the fundamental group, covering spaces, simplicial complexes. Applications to fixed point theory and group theory. The theory of curves, surfaces, and more generally, manifolds. Curvature, parallel transport, covariant differentiation, Gauss-Bonet theorem. Dynamics and Bifurcations I. A broad introduction to the local and global behavior of nonlinear dynamical systems arising from maps and ordinary differential equations.
Dynamics and Bifurcations II. A study of linear programming problems, including the simplex method, duality, and sensitivity analysis with applications to matrix games, interger programming, and networks. Classical Mathematical Methods in Engineering. The Laplace transform and applications, Fourier series, boundary value problems for partial differential equations.
Introduction to numerical algorithms for some basic problems in computational mathematics. Discussion of both implementation issues and error analysis. Introduction to the numerical solution of initial and boundary value problems in differential equations.
Undergraduate Internship. Problems from the life sciences and the mathematical methods for solving them are presented.
The underlying biological and mathematical principles and the interrelationships are emphasized. Crosslisted with BIOL Vector and Parallel Scientific Computation. Scientific computational algorithms on vector and parallel computers.
Speed-up and algorithm complexity, interprocesses communication, synchronization, modern algorithms for linear systems, programming techniques, code optimization.
Crosslisted with CS Quantum Information and Quantum Computing. Introduction to quantum computing and quantum information theory, formalism of quantum mechanics, quantum gates, algorithms, measurements, coding, and information. Physical realizations and experiments. Crosslisted with PHYS This course enables the school of Mathematics to comply with requests for courses in selected topics. Introduction to Graduate Studies in Mathematics. This course covers practical information helping students start their careers as a professional mathematician.
Graph Theory and Combinatorial Structures. Fundamentals, connectivity, matchings, colorings, extremal problems, Ramsey theory, planar graphs, perfect graphs. Applications to operations research and the design of efficient algorithms. Topology of Euclidean Spaces. Metric spaces, normed linear spaces, convexity, and separation; polyhedra and simplicial complexes; surfaces; Brouwer fixed point theorem.
Modern Abstract Algebra I. Graduate-level linear and abstract algebra including groups, finite fields, classical matrix groups and bilinear forms, multilinear algebra, and matroids. First of two courses. Modern Abstract Algebra II. Graduate-level linear and abstract algebra including rings, fields, modules, some algebraic number theory and Galois theory. Second of two courses.
Advanced Classical Probability Theory. Classical introduction to probability theory including expectation, notions of convergence, laws of large numbers, independence, large deviations, conditional expectation, martingales, and Markov chains. Stochastic Processes in Finance II. Advanced mathematical modeling of financial markets, derivative securities pricing, and portfolio optimization.
Concepts from advanced probability and mathematics are introduced as needed. Develops the probability basis requisite in modern statistical theories and stochastic processes.
Topics of this course include measure and integration foundations of probability, distribution functions, convergence concepts, laws of large numbers, and central limit theory. Topics of this course include results for sums of independent random variables, Markov processes, martingales, Poisson processes, Brownian motion, conditional probability and conditional expectation, and topics from ergodic theory.
Second of two classes. Advanced Statistical Inference I. Basic theories of statistical estimation, including optimal estimation in finite samples and asymptotically optimal estimation. A careful mathematical treatment of the primary techniques of estimation utilized by statisticians. Testing Statistical Hypotheses. Basic theories of testing statistical hypotheses, including a thorough treatment of testing in exponential class families.
A careful mathematical treatment of the primary techniques of hypothesis testing utilized by statisticians. Linear Statistical Models. Basic unifying theory underlying techniques of regression, analysis of variance and covariance, from a geometric point of view. Modern computational capabilities are exploited fully. Students apply the theory to real data through canned and coded programs. Multivariate Statistical Analysis. Multivariate normal distribution theory, correlation and dependence analysis, regression and prediction, dimension-reduction methods, sampling distributions and related inference problems, selected applications in classification theory, multivariate process control, and pattern recognition.
Ordinary Differential Equations I. This sequence develops the qualitative theory for systems of ordinary differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, normal forms. Ordinary Differential Equations II. This sequence develops the qualitative theory for systems of differential equations.
Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, and normal forms. In , engineering educators presented an engineering alternative to the general studies curriculum GSC that modified the Act to specific needs of engineering colleges statewide.
The engineering alternative was unanimously approved by the statewide Articulation and General Studies Committee in December and was made a part of GSC. For guidance on selecting elective courses, students should work with their assigned advisor. Click here for details regarding The University of Alabama's policy on grades and grade points.
If a grade lower than C- minus is received in a prerequisite course, that course must be repeated. A grade of C- minus of higher must be earned before the student enrolls in the subsequent course. Changes should be made before the beginning of the next term, and they must be made before the deadline for adding courses. Failure to make the changes on time will result in administrative withdrawal from the course. Students who are administratively withdrawn from a course after the deadline to add a course may not add another course in replacement.
For academic planning assistance, students should work with their assigned advisor. The mission of the Engineering Advising Center is to educate students on the importance of academic advising by fostering a working advisor-student partnership designed to support students in achieving academic and personal goals. Engineering advisors aim to empower students to take ownership of their educational experiences by understanding and using the available resources through communication and involvement with the advising center.
Students are assigned an advisor based on their major program of study. Advising in the College of Engineering is mandatory, so students must be advised each semester prior to registering for courses. For more information on advising services, students are encouraged to visit the Engineering Advising Center website. Click here for details regarding The University of Alabama's policy on repeating courses.
Undergraduate students in the College of Engineering are limited to a maximum of three attempts per course offered by the College of Engineering, excluding withdrawals.
Senior design course s for all BS Engineering and Computer Science programs must be taken at UA and cannot be transferred from another institution. The University of Alabama College of Engineering will be a nationally-recognized leader in student-centered education, research and innovation. The mission of the College of Engineering is to serve the state, nation, and global community by advancing the boundaries of knowledge through innovative research and education of the next generation of leaders.
For more information about the College of Engineering and its programs and services, call or write: The University of Alabama, College of Engineering, Box , Tuscaloosa, AL ; ; eng. Search Everything Go. Search UA Courses Go. Search UA Programs Go. Catalog Home ua. The third element is a group project in which seniors work under the direction of a student chief engineer on a year-long comprehensive design.
In conjunction with these projects, there are required written and oral presentations and required computer applications integrated throughout the curriculum. Completion of these projects also trains students to work in groups of different sizes and gives them experience in self-directed learning.
Additionally, in the senior year, elements of professional practice, ethics, and safety are introduced in the classroom. The chemical engineering curriculum also contains a significant laboratory component aimed at reinforcing the knowledge gained in the classroom. In addition to basic chemistry and physics laboratories, the chemical engineering laboratories include a laboratory course that reinforce material taught in the junior year, followed by a two-semester laboratory sequence in the senior year in which the principles of experimental design, laboratory and safety procedures, data analysis, and report writing are stressed.
Please use this link to view a list of courses that meet each GEF requirement. Please see the curriculum requirements listed below for details on which GEFs you will need to select.
Please note that not all of the GEF courses are offered at all campuses. Students should consult with their advisor or academic department regarding the GEF course offerings available at their campus. Students must meet the following criteria to qualify for a Bachelor of Science in Chemical Engineering degree:. It is important for students to take courses in the order specified as much as possible; all prerequisites and concurrent requirements must be observed.
A typical B. E degree program that completes degree requirements in four years is as follows. The Chemical and Biomedical Engineering Department uses an outcomes-assessment plan for continuous program improvement.
Course work and design projects, in conjunction with yearly interviews provide the measures of learning outcomes. These outcomes-assessment results provide feedback to the faculty to improve teaching and learning processes. CHE Introduction to Chemical Engineering. Overview of traditional and emerging areas of chemical engineering, projects involving computational and programming tools, design projects, written and oral presentation of results, discussions of professional and ethical behavior relating to the engineering professions.
Engages students in active learning strategies that enable effective transition to college life at WVU. Students will explore school, college and university programs, policies and services relevant to academic success.
Provides active learning activities that enable effective transition to the academic environment. Students examine school, college and university programs, policies and services. Introduction to chemical engineering fundamentals and calculation procedures, industrial stoichiometry, real gases and vapor-liquid equilibrium,heat capacities and enthalpies, and unsteady material balances and energy balances.
Continuation of CHE Theory and application of reaction kinetics, analysis of rate data, reaction equilibrium, and catalysis. The application of these phenomena to industrial relevant systems will be emphasized. Numerical Methods for Chemical Engineering. Numerical solution of algebraic and differential equations with emphasis on process material and energy balances.
Statistical methods optimization, and numerical analysis. PR: Consent. Investigation of topics not covered in regularly scheduled courses.
Fluid statics, laminar and turbulent flow, mechanical energy balance, Bernoulli equation, force balance, friction, flow in pipes, pumps, metering and transportation of fluids, flow through packed beds and fluidized beds.
Conductive heat transfer, convective heat transfer, design and selection of heat exchange equipment, evaporation, and radiation. PR: CHE Equilibrium stage and multiple stage operations, differential countercurrent contracting, membrane separations, fluid-particle separations.
Chemical Engineering Transport Analysis. Development of fundamental relationships for momentum, heat and mass transfer for flow systems to include chemical reactions, interphase transport, and transient phenomena. Development and use of microscopic and macroscopic balance equations.
Chemical Engineering Thermodynamics. First and second laws of thermodynamics. Engineering Mechanical Engineering, B. Surveying Engineering, B. Print Options. Program Description The mission of the faculty of the undergraduate computer engineering program at Penn State is to provide students with the knowledge and experience needed to pursue a productive lifelong career in industry or to engage in further study at the graduate level.
What is Computer Engineering? You excel in math and physics and have an interest in designing and constructing computer hardware You want to build and analyze physical computing devices that go beyond traditional computers You want to understand how current computer hardware and software work and how to design the next generation hardware and its supporting software You want to design computing systems that impact and improve everyday lives.
Entrance to Major This program currently has administrative enrollment controls. General Education Connecting career and curiosity, the General Education curriculum provides the opportunity for students to acquire transferable skills necessary to be successful in the future and to thrive while living in interconnected contexts.
Foundations grade of C or better is required. Cultures Requirement 6 credits are required and may satisfy other requirements United States Cultures: 3 credits International Cultures: 3 credits Writing Across the Curriculum 3 credits required from the college of graduation and likely prescribed as part of major requirements. Total Minimum Credits A minimum of degree credits must be earned for a baccalaureate degree. Quality of Work Candidates must complete the degree requirements for their major and earn at least a 2.
Limitations on Source and Time for Credit Acquisition The college dean or campus chancellor and program faculty may require up to 24 credits of course work in the major to be taken at the location or in the college or program where the degree is earned.
Requirements for the Major To graduate, a student enrolled in the major must earn a grade of C or better in each course designated by the major as a C-required course, as specified by Senate Policy ECON CMPEN EE Integrated B. Stay current through professional conferences, certificate programs, post-baccalaureate degree programs, or other professional educational activities.
Student Outcomes Student outcomes describe what students are expected to know and be able to do by the time of graduation. Suggested Academic Plan The suggested academic plan s listed on this page are the plan s that are in effect during the academic year. Career Paths Computer engineering graduates understand all aspects of computing hardware, are well-studied in the use of modern tools used to design and analyze hardware, are able to think at multiple levels of abstraction when working with system-level design, and have a solid foundation in software development.
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