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Navigation Menu Requirements for Graduation Students must fulfill both the requirements for a major and University requirements to receive a bachelor's degree from the University of Central Florida.The student must: Fulfill the requirements for the chosen major; Earn a minimum of 120 unduplicated credit hours with at least a "C" average (2.

0 GPA) for all UCF course work attempted Elizabeth is a double major in business and linguistics hailing from the very snowy   Academic Handbook is designed to help make your education your own.   Mechanical Engineering*. Optical Engineering*. Optics*. Physics. Physics and Astronomy. Statistics. SOCIAL SCIENCES. Anthropology. Business. Economics..0 GPA) for all UCF course work attempted.

Some majors require more than 120 hours; Earn at least 48 of these 120 credit hours in 3000-level courses or above (upper-division); Earn a minimum of 30 of their last 39 hours in regular courses at UCF.Credit by Examination may not be used to satisfy this requirement; Earn a minimum of 25% of the total hours required for the degree in residence at UCF.For programs that require the minimum of 120 total hours, residency will be 30 hours Need to purchase college archeology coursework 2 pages / 550 words Custom writing American Undergrad. (yrs 3-4).For programs that require the minimum of 120 total hours, residency will be 30 hours.For programs that exceed 120 hours, the specific residency requirement increases proportionally and is listed with the requirements for the specific degree program; Earn a minimum of 60 credit hours after CLEP credit has been awarded; Apply no more than 45 credit hours in any combination of exten­sion, correspondence, CLEP, University Credit by Examination and Armed Forces credits toward an undergraduate degree; Fulfill the General Education Program requirements; Fulfill the Gordon Rule requirements; Fulfill the Foreign Language requirements as defined elsewhere in this section; Earn a minimum of nine credit hours during Summer terms, if applicable; and, Be registered at UCF during the semester of graduation.

Degrees Awarded Posthumously Students will be considered for posthumous degrees by the Commencement and Convocations Committee if they are in good academic standing at the time of their death, have a 2.0 GPA or better and are within at least 15 credit hours of completion of all require­ments or are in the final term of completion of all their requirements.Choice of Catalog (Catalog Year) and Continuous Enrollment A student must graduate under the degree requirements of any UCF Undergraduate Catalog in effect since the student began continuous enrollment at UCF.However, courses may change (for example, in credit hours or in prerequisites) or be discontinued as a result of curricular review.

New Catalog policies and requirements take effect with the Summer term.

A student transferring from Florida College System institutions or state universities may use the UCF Undergraduate Catalog in effect at the time he or she began the most recent period of continuous enrollment in academic good standing at any of the Florida public institutions.Continuous enrollment is defined as being enrolled in classes without a break of two or more consecutive regular semesters/terms (i., Fall and Spring, or Spring, Summer, and Fall).Continuous enrollment is automatically broken when a student moves from one transfer institution to another following academic disqualification or exclusion.

Students who change majors between different colleges must adopt the most current Catalog.Additional information is included in the program descriptions.Students pursuing a single degree (including double majors and/or minors) must use a single catalog and cannot use a combination of catalogs for graduation.In cases when required courses are no longer taught by the University, the appropriate department, college, or Academic Services (MH 210) may designate a reasonable substitute.If a student desires to change the catalog for graduation, the student should first discuss with the advisors how such a change would affect University, college, and major requirements.

If a student decides to request a change, he or she must submit a "Catalog Year Change Request Form" to the Registrar's Office (MH 161).This form is available at the Registrar's Office or online at .Exit Exams In order to measure their effectiveness, some departments and col­leges may require graduating students to participate in an exit exam designed to measure the students' understanding of the discipline.Foreign Language Proficiency Requirement (Bachelor of Arts Degree) Students graduating with a Bachelor of Arts degree must demon­strate proficiency in a foreign language equivalent to one year of college instruction.This requirement may be met either by successful completion of the appropriate college-level course or by examination.

Languages that may be used include those taught at UCF and any others for which the University can obtain standardized proficiency tests.Students who have previously received a baccalaureate degree are exempt from this requirement.Native speakers or students who have completed appropriate advanced foreign language education abroad will be considered to have satisfied the requirement.Placement in Language Courses Placement in foreign language courses is based on one year of high school language being equivalent to one semester of college work.For example, four years of one high school foreign language place the student in the first semester of the third year.

Several departments, colleges, and schools have additional requirements.See "Special College and/or Departmental Requirements" within each listing.This requirement is for proficiency and not a requirement for a particular number of hours of course work.For example, success­ful completion of only SPN 1121C (Elementary Spanish Language and Civilization II) would satisfy the B.Appropriate scores on Advanced Placement and CLEP examinations will also satisfy the requirement.This is a University-wide requirement for all B.The Testing Administrator of the University Testing Center will offer the Foreign Language Proficiency Examination throughout each term.Students must register in advance with that office to take the examination (HPH 106).The foreign language proficiency requirement does not apply to students seeking a second baccalaureate degree.A student who is required and furnishes a passing TOEFL (Test of English as a Foreign Language) score for admission to the University is considered to have satisfied the requirements.American Sign Language Students pursuing a Bachelor of Arts Degree may substitute American Sign Language for the foreign language exit requirement, except where one or more foreign languages have been specified by a col­lege, school, or program for a specific degree (see individual degree program listings for more information).

Proficiency is met either by successful completion of ASL 4161C (previously numbered SPA 4614C) or an appropriate score on the ASL proficiency exam.Contact the Department of Communication Sciences and Disorders regarding the proficiency examination.SUS Foreign Language Admission Requirement Students who have not satisfied the Foreign Language Admission Requirement (competency of foreign language or American Sign Language equivalent to the second high school level or higher Spanish 2, Haitian Creole 2, etc.or at the elementary 2 level in one foreign language or American Sign Language at an undergraduate institution) at the time they are admitted to the University must satisfy this requirement prior to graduation.This requirement applies to all undergraduates and is separate from the UCF Foreign Language proficiency requirement.

The Gordon Rule The "Gordon Rule" (State Rule 6A-10.30) applies to students who first enrolled in any college or university after October 1982.The rule requires students to complete four courses (twelve credit hours) of writing and to complete two courses (six credit hours) of mathematics at the level of college algebra or higher.Each course must be completed with a minimum grade of "C-" (1.UCF courses that are required by the General Education Program also may be used to satisfy the Gordon Rule."Gordon Rule" requirements may be satisfied by the General Education Program as follows: Gordon Rule Requirement: Summer Attendance Requirement A student entering the State University System with fewer than 60 credit hours of credit is required to enroll in a minimum of nine hours of credit in the summer at a State of Florida university.Petition forms for exemption are available from the Academic Services website /summer-waiver/.Admission to the Upper Division To be classified as an upper division student at the University of Central Florida, a student must complete the following: A minimum of 60 credit hours of academic work; The English and mathematics requirements of the Gordon Rule; One year of college instruction in a single foreign language.

(This requirement applies to those students admitted to the University without the required two units of foreign language in high school.

Students who have not applied for graduation by the last day of classes in the term preceding the graduation term may not be listed in the Commencement Program.Graduating students must be enrolled at UCF during the term of graduation.Graduates may contact the Registrar’s Office for Commencement ceremony and guest ticket information or refer to /.Successful completion of the degree requirements stated in the Undergraduate Catalog under which the student plans to graduate shall constitute a recommendation of the respective college faculty that the degree be awarded, assuming the student is in good standing at the University.

A student must complete all requirements for a baccalaureate or graduate degree no later than the date of the Commencement.A student may not be enrolled as a transient student in another institution during the term in which the baccalaureate degree or the Associate of Arts degree is to be awarded.Correspondence Courses The University of Florida's Division of Continuing Education, Department of Independent Study by Correspondence administers all correspondence instruction for the State University System of Florida (SUS).

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College credit, high school credit, and continuing professional education courses are available through regular mail and Fax (several by email).Independent Study offers more than 150 courses to students who would like a flexible schedule or an opportunity to take extra classes.

It is possible to enroll any time during the year Help me do an coursework archeology US Letter Size 53 pages / 14575 words British 9 days.It is possible to enroll any time during the year.

In 1996, the State revised the General Provisions Rule 64-4.002, at the Bureau of Teacher Certification for the State of Florida.Any teacher in the state now can use credit correspondence courses, as appropriate, to apply toward the recertification of the teaching license Students interested in the program should plan to attend an information session in the spring of their freshman year to gather general information about the Program; at least one information session will be offered each September for students who have been unable to attend in the spring. Quick questions about the Program  .Any teacher in the state now can use credit correspondence courses, as appropriate, to apply toward the recertification of the teaching license.Moreover, there is no limit to the number of courses that may fulfill the requirements xlphp.org/report.php.

Moreover, there is no limit to the number of courses that may fulfill the requirements.

The current Catalog details enrollment procedures, fees, and course information xlphp.org/report.php.The current Catalog details enrollment procedures, fees, and course information.A copy may be obtained at no cost by calling or writing to: University of Florida, Independent Study, Suite D, 2209 NW 13th St., Gainesville, FL 32609; 352-392-1711, Ext.Double Majors A student may earn one degree, a BA or BS, with two majors, by completing the requirements for both majors.If both majors are within the same college and are of the same degree type (BA or BS), both majors will be indicated on the diploma; however, if the majors are from different colleges or are of different degree types, only one major will appear on the diploma.Students earning a double major must use the same Catalog year for both majors.Two Degrees A student may earn two degrees, a BA and a BS, by completing the requirements for both majors and earning a minimum of 150 credit hours.A student may earn two degrees, either both BA or both BS, if the degrees are earned in separate colleges and a minimum of 150 (or more) credit hours are earned.

A student may earn two degrees, either both BA or both BS, within the same college if allowed by the particular college and a mini­mum of 150 (or more) credit hours are earned.Students earning two degrees may use different Catalog years for each degree.If different Catalog years are used, the general university requirements in the latest of the two catalogs will be applied to both degrees.More Than Two Majors, or More Than Two Degrees, or a Combination Students attempting multiple majors or degrees beyond two must consult with the Registrar's Office for coordination among degree programs.Responsibility for doing so rests with the student.

The stipulations for two majors and/or two degrees will apply as well as other minimum amount of hours and prohibitions about combinations.Graduates from regionally accredited four-year U.institutions who apply for admission to work toward a second baccalaureate degree at UCF must meet the regular admission requirements of the major department and the UCF residency requirement of 30 additional credit hours for that degree.Students holding the baccalaureate degree from regionally accredited U.

institutions are considered to have complet­ed Gordon Rule, foreign languages, and General Education Program Requirements.Students who hold degrees from non-regionally accredited U.institutions and foreign institutions may be required by the Office of Academic Services (MH 210) to fulfill all or part of the UCF General Education Program requirements as stipulated in the UCF Undergraduate Catalog.

The University requirements specified in the preceding paragraphs are minimum requirements.Departments and colleges may require more than 150 credit hours for a second degree or more than 30 credit hours to be taken in residence at UCF.Students should confirm department, school, and college requirements with their academic advisors.Master of Arts in Applied Archaeology Requirements (45-46 units) Program Code: AARC The Master of Arts in Applied Archaeology is a professionally oriented program designed to prepare students for middle and upper-level careers in the archaeological sector of the cultural resource management (CRM) industry.The core of the program comprises courses in archaeology with an emphasis on combining practical experience in field and laboratory studies with an internship and research project undertaken in collaboration with a government agency or private firm that conducts archaeological investigations in the context of CRM.

Students will also obtain an in-depth understanding of archaeological theory, California archaeology, and the laws, regulations, and procedures relevant to archaeology and CRM in our region.Elective courses will enable students to pursue an interest further in history, archaeology, or historic preservation.The program is intended for evening students primarily and, therefore, classes are predominantly scheduled between 6 and 10 p.Admission to the Program In addition to the general requirements of the university, specific requirements for admission to classified graduate status are: A baccalaureate degree in anthropology or a closely related field from an accredited college or university; A minimum cumulative undergraduate grade point average of at least 2.

0 ("B") in the student's undergraduate major; Completion of the graduate entrance writing requirement; EITHER: A.Completion of the following prerequisite course or its equivalent, completed with a grade of B or better:ANTH 320 OR B.Documented Field experience in archaeology under professional supervision that is deemed by the Admissions Committee as being equivalent to successful completion of ANTH 320; A brief statement (one to two double-spaced typewritten pages) describing the applicant's preparation for graduate study and professional goals; Submission of three letters of recommendation from people who are in a position to make relevant comments on the student's likely success in the program.At least one of the letters should be from a former professor who is familiar with the student's scholarly abilities.

Advancement to Candidacy Achieved classified status; Secured a graduate advisor to supervise the course of study; Completed, with the approval of the advisor, at least 12 quarter units of graduate course work at this university and achieved a minimum grade point average of 3.0 ("B") in those courses; Filed a graduate program approved by the student's advisor and the coordinator of the program.Requirements for Graduation A minimum of 45 quarter units of acceptable graduate-level work, with at least 32 quarter units completed in residence at California State University, San Bernardino.Thirty-two quarter units must be in 500- and 600-level courses; A minimum grade point average of at least 3.0 ("B") in all courses; To provide a breadth of content in this graduate program, 300- or 400-level courses may be used to satisfy some program requirements with the expectation that coursework is increased to satisfy the rigors of graduate work; Successful completion of a thesis or project (ANTH 699).

Thesis/Project: Under normal circumstances, a student must complete a thesis that is approved by his or her thesis committee.The thesis must reflect original work and show a level of competence appropriate for a master's degree.The thesis committee shall consist of two or three faculty members, including the student's advisor, mutually agreed upon by the student and faculty.By mutual agreement between the student and advisor, the third committee member may be recruited from archaeologists in the southern California CRM community holding PhDs from accredited institutions.The student should enroll in (ANTH 699) in the quarter when completion of the thesis is anticipated.

On occasion a student may be allowed to substitute a completed project for the thesis.Such a project must have a completed product and would reflect at least the same amount of work as a thesis and be completed to the same standard.The content and appropriateness of the project will be determined by a project committee constituted in the same way as a thesis committee.Degree Requirements (45-46 units) 1 The 100-level courses may have been completed during undergraduate study, and their equivalents from other universities are acceptable.2 A third coherent sequence designed by the student, subject to the approval of the graduate committee, may be considered as a substitute for Sequence 1 or 2.

3 The 200-level courses must be taken at Stanford and approved by the Department of Mathematics Ph.Emeriti: Gregory Brumfiel, Gunnar Carlsson, Robert Finn, Yitzhak Katznelson, Harold Levine, Tai-Ping Liu, R.James Milgram, Donald Ornstein, Richard Schoen, Leon Simon Chair: Eleny Ionel Professors: Daniel Bump, Emmanuel Cand s,Sourav Chatterjee, Ralph L.

Cohen, Brian Conrad, Amir Dembo, Persi Diaconis (on leave Winter), Yakov Eliashberg, Jacob Fox, S ren Galatius, Eleny Ionel, Steven Kerckhoff (on leave Winter), Jun Li (on leave Autumn), Rafe Mazzeo, George Papanicolaou (on leave Spring), Lenya Ryzhik, Kannan Soundararajan, Ravi Vakil, Andr s Vasy (on leave), Akshay Venkatesh (on leave), Brian White, Lexing Ying Professor (Teaching): Tadashi Tokieda Acting Assistant Professor: Alex Wright Courtesy Professors: Moses Charikar, Renata Kallosh Adjunct Professors: Brian Conrey, David Hoffman Szeg Assistant Professors:Laura Fredrickson, Or Hershkovits,Vladimir Kazeev, Michael Kemeny,Frederick Manners,Christopher Ohrt, Cheng-Chiang Tsai, Jennifer Wilson,Xuwen Zhu Visiting Assistant Professor: Stefan M ller Senior Lecturer: Mark Lucianovic Courses MATH 19.Introduction to differential calculus of functions of one variable.Review of elementary functions (including exponentials and logarithms), limits, rates of change, the derivative and its properties, applications of the derivative.

Prerequisites: trigonometry, advanced algebra, and analysis of elementary functions (including exponentials and logarithms).You must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.

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The definite integral, Riemann sums, antiderivatives, the Fundamental Theorem of Calculus, and the Mean Value Theorem for integrals.Integration by substitution and by parts.Area between curves, and volume by slices, washers, and shells Students will also obtain an in-depth understanding of archaeological theory, California archaeology, and the laws, regulations, and procedures relevant to   A brief statement (one to two double-spaced typewritten pages) describing the applicant's preparation for graduate study and professional goals;; Submission of three  .Area between curves, and volume by slices, washers, and shells.

Initial-value problems, exponential and logistic models, direction fields, and parametric curves.If you have not previously taken a calculus course at Stanford then you must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.Sequences, functions, limits at infinity, and comparison of growth of functions to brain imaging, UCSB students have the unique opportunity to collaborate with   3 million volumes, 60,000 square feet of new space and the Summit Café. › Inviting. Housing is guaranteed for freshmen and transfers in 8 residence halls and 6 apartments that offer ocean,   Classical Archaeology, Classical. Language and  .Sequences, functions, limits at infinity, and comparison of growth of functions.Review of integration rules, integrating rational functions, and improper integrals.Infinite series, special examples, convergence and divergence tests (limit comparison and alternating series tests).Power series and interval of convergence, Taylor polynomials, Taylor series and applications.

If you have not previously taken a calculus course at Stanford then you must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.Students attend MATH 21 lectures with different recitation sessions: two hours per week instead of one, emphasizing engineering applications.

Linear Algebra and Differential Calculus of Several Variables.Geometry and algebra of vectors, matrices and linear transformations, eigenvalues of symmetric matrices, vector-valued functions and functions of several variables, partial derivatives and gradients, derivative as a matrix, chain rule in several variables, critical points and Hessian, least-squares, , constrained and unconstrained optimization in several variables, Lagrange multipliers.

Prerequisite: 21, 42, or the math placement diagnostic (offered through the Math Department website) in order to register for this course.Linear Algebra and Differential Calculus of Several Variables, ACE.Students attend MATH 51 lectures with different recitation sessions: three hours per week instead of two, emphasizing engineering applications.

Iterated integrals, line and surface integrals, vector analysis with applications to vector potentials and conservative vector fields, physical interpretations.

Divergence theorem and the theorems of Green, Gauss, and Stokes.Ordinary Differential Equations with Linear Algebra.Ordinary differential equations and initial value problems, systems of linear differential equations with constant coefficients, applications of second-order equations to oscillations, matrix exponentials, Laplace transforms, stability of non-linear systems and phase plane analysis, numerical methods.This is the first part of a theoretical (i., proof-based) sequence in multivariable calculus and linear algebra, providing a unified treatment of these topics.The linear algebra content is covered jointly with MATH 61DM.

Students should know 1-variable calculus and have an interest in a theoretical approach to the subject.Prerequisite: score of 5 on the BC-level Advanced Placement calculus exam, or consent of the instructor.This is the first part of a theoretical (i., proof-based) sequence in discrete mathematics and linear algebra.Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, counting techniques, and linear algebra methods in discrete mathematics including spectral graph theory and dimension arguments.The linear algebra content is covered jointly with MATH 61CM.

Students should have an interest in a theoretical approach to the subject.Prerequisite: score of 5 on the BC-level Advanced Placement calculus exam, or consent of the sequence is not appropriate for students planning to major in natural sciences, economics, or engineering, but is suitable for majors in any other field (such as MCS ("data science"), computer science, and mathematics).A continuation of themes from MATH 61CM, centered around: manifolds, multivariable integration, and the general Stokes' theorem.This includes a treatment of multilinear algebra, further study of submanifolds of Euclidean space and an introduction to general manifolds (with many examples), differential forms and their geometric interpretations, integration of differential forms, Stokes' theorem, and some applications to topology.This is the second part of a proof-based sequence in discrete mathematics.This course covers topics in elementary number theory, group theory, and discrete Fourier analysis.For example, we'll discuss the basic examples of abelian groups arising from congruences in elementary number theory, as well as the non-abelian symmetric group of permutations.A proof-based course on ordinary differential equations, continuing themes from MATH 61CM and MATH 62CM.Topics include linear systems of differential equations and necessary tools from linear algebra, stability and asymptotic properties of solutions to linear systems, existence and uniqueness theorems for nonlinear differential equations with some applications to manifolds, behavior of solutions near an equilibrium point, and Sturm-Liouville theory.

Third part of a proof-based sequence in discrete mathematics.

This course covers several topics in probability (random variables, independence and correlation, concentration bounds, the central limit theorem) and topology (metric spaces, point-set topology, continuous maps, compactness, Brouwer's fixed point and the Borsuk-Ulam theorem), with some applications in combinatorics.The Game of Go: Strategy, Theory, and History.Strategy and mathematical theories of the game of Go, with guest appearance by a professional Go player.Capillary Surfaces: Explored and Unexplored Territory.Capillary surfaces: the interfaces between fluids that are adjacent to each other and do not mix.Recently discovered phenomena, predicted mathematically and subsequently confirmed by experiments, some done in space shuttles.Interested students may participate in ongoing investigations with affinity between mathematics and physics.Mathematics of Knots, Braids, Links, and Tangles.

Types of knots and how knots can be distinguished from one another by means of numerical or polynomial invariants.The geometry and algebra of braids, including their relationships to knots.Brief summary of applications to biology, chemistry, and physics.MDL is a discovery-based project course in mathematics.

Students work independently in small groups to explore open-ended mathematical problems and discover original mathematics.Students formulate conjectures and hypotheses; test predictions by computation, simulation, or pure thought; and present their results to classmates.No lecture component; in-class meetings reserved for student presentations, attendance mandatory.Motivated students with any level of mathematical background are encouraged to apply.

Linear algebra for applications in science and engineering: orthogonality, projections, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, least-squares, the condition number of a matrix, algorithms for solving linear systems.

(MATH 113 offers a more theoretical treatment of linear algebra.) Prerequisites: MATH 51 and programming experience on par with CS106nnMath 104 and EE103/CME103 cover complementary topics in applied linear algebra.The focus of MATH 104 is on algorithms and concepts; the focus of EE103 is on a few linear algebra concepts, and many applications.Complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy integral formula, residues, elementary conformal mappings.(MATH 116 offers a more theoretical treatment.An introductory course in graph theory establishing fundamental concepts and results in variety of topics.Topics include: basic notions, connectivity, cycles, matchings, planar graphs, graph coloring, matrix-tree theorem, conditions for hamiltonicity, Kuratowski's theorem, Ramsey and Turan-type theorem.

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Prerequisites: 51 or equivalent and some familiarity with proofs is required.

Introduction to Combinatorics and Its Applications.Topics: graphs, trees (Cayley's Theorem, application to phylogony), eigenvalues, basic enumeration (permutations, Stirling and Bell numbers), recurrences, generating functions, basic asymptotics Special Academic Options Cornell University Acalog ACMS.Topics: graphs, trees (Cayley's Theorem, application to phylogony), eigenvalues, basic enumeration (permutations, Stirling and Bell numbers), recurrences, generating functions, basic asymptotics.

Topics: elements of group theory, groups of symmetries, matrix groups, group actions, and applications to combinatorics and computing.

Applications: rotational symmetry groups, the study of the Platonic solids, crystallographic groups and their applications in chemistry and physics The Ph.D. is conferred upon candidates who have demonstrated substantial scholarship and the ability to conduct independent research and analysis in Mathematics. Through completion of advanced course work and rigorous skills training, the doctoral program prepares students to make original contributions to the  .Applications: rotational symmetry groups, the study of the Platonic solids, crystallographic groups and their applications in chemistry and physics.Honors math majors and students who intend to do graduate work in mathematics should take 120 The Ph.D. is conferred upon candidates who have demonstrated substantial scholarship and the ability to conduct independent research and analysis in Mathematics. Through completion of advanced course work and rigorous skills training, the doctoral program prepares students to make original contributions to the  .Honors math majors and students who intend to do graduate work in mathematics should take 120.Number theory and its applications to modern cryptography.Topics: congruences, finite fields, primality testing and factorization, public key cryptography, error correcting codes, and elliptic curves, emphasizing algorithms xlphp.org/report/help-me-do-anatomy-report-american-senior-bluebook.Topics: congruences, finite fields, primality testing and factorization, public key cryptography, error correcting codes, and elliptic curves, emphasizing algorithms.Algebraic properties of matrices and their interpretation in geometric terms.The relationship between the algebraic and geometric points of view and matters fundamental to the study and solution of linear equations.Topics: linear equations, vector spaces, linear dependence, bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors and eigenvalues; diagonalization.

(MATH 104 offers a more application-oriented treatment.Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness.Implementation of numerical methods in MATLAB programming assignments.Prerequisites: MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of CS 106A or higher).The development of real analysis in Euclidean space: sequences and series, limits, continuous functions, derivatives, integrals.Honors math majors and students who intend to do graduate work in mathematics should take 171.Analytic functions, Cauchy integral formula, power series and Laurent series, calculus of residues and applications, conformal mapping, analytic continuation, introduction to Riemann surfaces, Fourier series and integrals.(MATH 106 offers a less theoretical treatment.

Notions of analysis and algorithms central to modern scientific computing: continuous and discrete Fourier expansions, the fast Fourier transform, orthogonal polynomials, interpolation, quadrature, numerical differentiation, analysis and discretization of initial-value and boundary-value ODE, finite and spectral elements.

Recommended for Mathematics majors and required of honors Mathematics majors.

Similar to 109 but altered content and more theoretical orientation.Groups acting on sets, examples of finite groups, Sylow theorems, solvable and simple groups.Fields, rings, and ideals; polynomial rings over a field; PID and non-PID.Field of fractions, splitting fields, separability, finite fields.Galois groups, Galois correspondence, examples and applications.

Prerequisite: MATH 120 and (also recommended) 113.Character tables, construction of representations.An introduction to PDE; particularly suitable for non-Math majors.

Topics include physical examples of PDE's, method of characteristics, D'Alembert's formula, maximum principles, heat kernel, Duhamel's principle, separation of variables, Fourier series, Harmonic functions, Bessel functions, spherical harmonics.Students who have taken MATH 171 should consider taking MATH 173 rather than 131P.Introduction to measure theory, Lp spaces and Hilbert spaces.Random variables, expectation, conditional expectation, conditional distribution.Uniform integrability, almost sure and Lp convergence.Stochastic processes: definition, stationarity, sample path continuity.

Examples: random walk, Markov chains, Gaussian processes, Poisson processes, Martingales.Construction and basic properties of Brownian motion.Prerequisite: STATS 116 or MATH 151 or equivalent.Mathematical Methods of Classical Mechanics.Introduction to the theory of integrable systems.

Prerequisites: 51, 52, 53, or 61CM, 62CM, 63CM.Mathematically rigorous introduction to the classical N-body problem: the motion of N particles evolving according to Newton's law.

Topics include: the Kepler problem and its symmetries; other central force problems; conservation theorems; variational methods; Hamilton-Jacobi theory; the role of equilibrium points and stability; and symplectic methods.An introductory course in hyperbolic geometry.Topics may include: different models of hyperbolic geometry, hyperbolic area and geodesics, Isometries and Mobius transformations, conformal maps, Fuchsian groups, Farey tessellation, hyperbolic structures on surfaces and three manifolds, limit sets.Prerequisites: some familiarity with the basic concepts of differential geometrynand the topology of surfaces and manifolds is strongly recommended.Geometry of curves and surfaces in three-space and higher dimensional manifolds.Parallel transport, curvature, and geodesics.An introduction to the methods and concepts of algebraic geometry.The point of view and content will vary over time, but include: affine varieties, Hilbert basis theorem and Nullstellensatz, projective varieties, algebraic curves.

Strongly recommended: additional mathematical maturity via further basic background with fields, point-set topology, or manifolds.Prerequisite: 62CM or 52 and familiarity with linear algebra and analysis arguments at the level of 113 and 115 respectively.Smooth manifolds, transversality, Sards' theorem, embeddings, degree of a map, Borsuk-Ulam theorem, Hopf degree theorem, Jordan curve theorem.Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots.Counting; axioms of probability; conditioning and independence; expectation and variance; discrete and continuous random variables and distributions; joint distributions and dependence; central limit theorem and laws of large numbers.Prerequisite: 52 or consent of instructor.Euclid's algorithm, fundamental theorems on divisibility; prime numbers; congruence of numbers; theorems of Fermat, Euler, Wilson; congruences of first and higher degrees; quadratic residues; introduction to the theory of binary quadratic forms; quadratic reciprocity; partitions.Properties of number fields and Dedekind domains, quadratic and cyclotomic fields, applications to some classical Diophantine equations.Prerequisites: 120 and 121, especially modules over principal ideal domains and Galois theory of finite fields.Topics in analytic number theory such as the distribution of prime numbers, the prime number theorem, twin primes and Goldbach's conjecture, the theory of quadratic forms, Dirichlet's class number formula, Dirichlet's theorem on primes in arithmetic progressions, and the fifteen theorem.Prerequisite: 152, or familiarity with the Euclidean algorithm, congruences, residue classes and reduced residue classes, primitive roots, and quadratic reciprocity.Basic Probability and Stochastic Processes with Engineering Applications.Calculus of random variables and their distributions with applications.

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Review of limit theorems of probability and their application to statistical estimation and basic Monte Carlo methods.Introduction to Markov chains, random walks, Brownian motion and basic stochastic differential equations with emphasis on applications from economics, physics and engineering, such as filtering and control.Prerequisites: exposure to basic probability Help me do college coursework archeology Premium Business US Letter Size Rewriting.

Prerequisites: exposure to basic probability.

Modern discrete probabilistic methods suitable for analyzing discrete structures of the type arising in number theory, graph theory, combinatorics, computer science, information theory and molecular sequence analysis.Prerequisite: STATS 116/MATH 151 or equivalent.Informal and axiomatic set theory: sets, relations, functions, and set-theoretical operations A student who seeks a bachelor's degree from Old Dominion University must, in addition to meeting other requirements of the University, earn a minimum of 25   are needed for major courses and Upper-Division General Education, students should meet those requirements during their freshman and sophomore years..Informal and axiomatic set theory: sets, relations, functions, and set-theoretical operations.The Zermelo-Fraenkel axiom system and the special role of the axiom of choice and its various equivalents.Well-orderings and ordinal numbers; transfinite induction and transfinite recursion.

Equinumerosity and cardinal numbers; Cantor's Alephs and cardinal arithmetic.Prerequisite: students should be comfortable doing proofs.Mathematics is a very peculiar human activity.It delivers a type of knowledge that is particularly stable, often conceived as a priori and necessary.Moreover, this knowledge is about abstract entities, which seem to have no connection to us, spatio-temporal creatures, and yet it plays a crucial role in our scientific endeavors.Many philosophical questions emerge naturally: What is the nature of mathematical objects? How can we learn anything about them? Where does the stability of mathematics comes from? What is the significance of results showing the limits of such knowledge, such as G del's incompleteness theorem? The first part of the course will survey traditional approaches to philosophy of mathematics ("the big Isms") and consider the viability of their answers to some of the previous questions: logicism, intuitionism, Hilbert's program, empiricism, fictionalism, and structuralism.

The second part will focus on philosophical issues emerging from the actual practice of mathematics.We will tackle questions such as: Why do mathematicians re-prove the same theorems? What is the role of visualization in mathematics? How can mathematical knowledge be effective in natural science? To conclude, we will explore the aesthetic dimension of mathematics, focusing on mathematical beauty.Prerequisite: PHIL150 or consent of instructor.How was mathematics invented? A survey of the main creative ideas of ancient Greek mathematics.Among the issues explored are the axiomatic system of Euclid's Elements, the origins of the calculus in Greek measurements of solids and surfaces, and Archimedes' creation of mathematical physics.We will provide proofs of ancient theorems, and also learn how such theorems are even known today thanks to the recovery of ancient manuscripts.Recommended for Mathematics majors and required of honors Mathematics majors.Similar to 115 but altered content and more theoretical orientation.Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology.

Prerequisite: 61CM or 61DM or 115 or consent of the instructor.Lebesgue Integration and Fourier Analysis.Similar to 205A, but for undergraduate Math majors and graduate students in other disciplines.Topics include Lebesgue measure on Euclidean space, Lebesgue integration, LPrerequisite: 171 or consent of instructor.Theory of Partial Differential Equations.A rigorous introduction to PDE accessible to advanced undergraduates.Elliptic, parabolic, and hyperbolic equations in many space dimensions including basic properties of solutions such as maximum principles, causality, and conservation laws.

Methods include the Fourier transform as well as more classical methods.

The Lebesgue integral will be used throughout, but a summary of its properties will be provided to make the course accessible to students who have not had 172 or 205A.In years when MATH 173 is not offered, MATH 220 is a recommended alternative (with similar content but a different emphasis).An introductory course emphasizing the historical development of the theory, its connections to physics and mechanics, its independent mathematical interest, and its contacts with daily life experience.Applications to minimal surfaces and to capillary surface interfaces.Spectral theory of compact operators; applications to integral equations.Geometric Methods in the Theory of Ordinary Differential Equations.First order PDE and Hamilton-Jacobi equation.Structural stability and hyperbolic dynamical systems.Topics in mathematics and problem solving strategies with an eye towards the Putnam Competition.Topics may include parity, the pigeonhole principle, number theory, recurrence, generating functions, and probability.Students present solutions to the class.

Open to anyone with an interest in mathematics.Honors math major working on senior honors thesis under an approved advisor carries out research and reading.

Satisfactory written account of progress achieved during term must be submitted to advisor before term ends.May be repeated 3 times for a max of 9 units.Contact department student services specialist to enroll.Only for undergraduate students majoring in mathematics.Students obtain employment in a relevant industrial or research activity to enhance their professional experience.Students submit a concise report detailing work activities, problems worked on, and key results.May be repeated for credit up to 3 units.

Prerequisite: qualified offer of employment and consent of department.Prior approval by Math Department is required; you must contact the Math Department's Student Services staff for instructions before being granted permission to enroll.Undergraduates pursue a reading program; topics limited to those not in regular department course offerings.Credit can fulfill the elective requirement for math majors.Approval of Undergraduate Affairs Committee is required to use credit for honors majors area requirement.Contact department student services specialist to enroll.

Basic measure theory and the theory of Lebesgue integration.Point set topology, basic functional analysis, Fourier series, and Fourier transform.Prerequisites: 171 and 205A or equivalent.

Basic commutative ring and module theory, tensor algebra, homological constructions, linear and multilinear algebra, canonical forms and Jordan decomposition.Topics in field theory, commutative algebra, and algebraic geometry.

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Prerequisites: 210A, and 121 or equivalent.

Topics in Lie groups, Lie algebras, and/or representation theory.Topics: fundamental group and covering spaces, basics of homotopy theory, homology and cohomology (simplicial, singular, cellular), products, introduction to topological manifolds, orientations, Poincare duality Get an coursework archeology confidentiality High School Writing from scratch Oxford single spaced.

Topics: fundamental group and covering spaces, basics of homotopy theory, homology and cohomology (simplicial, singular, cellular), products, introduction to topological manifolds, orientations, Poincare duality.

Topics: Basics of differentiable manifolds (tangent spaces, vector fields, tensor fields, differential forms), embeddings, tubular neighborhoods, integration and Stokes¿ Theorem, deRham cohomology, intersection theory via Poincare duality, Morse theory.

This course will be an introduction to Riemannian Geometry.

Topics will include the Levi-Civita connection, Riemann curvature tensor, Ricci and scalar curvature, geodesics, parallel transport, completeness, geodesics and Jacobi fields, and comparison techniques 26 Feb 2013 - When you have to write a college business essay, choosing the right topic isn't always easy. Here are 5 types of business essays topics you should never use if you want to succeed and get a high grade on your academic paper. Hypothetical world references. The topic of your business essay should focus  .Topics will include the Levi-Civita connection, Riemann curvature tensor, Ricci and scalar curvature, geodesics, parallel transport, completeness, geodesics and Jacobi fields, and comparison techniques.Algebraic curves, algebraic varieties, sheaves, cohomology, Riemann-Roch theorem need to order a fine art paper single spaced British Vancouver.Algebraic curves, algebraic varieties, sheaves, cohomology, Riemann-Roch theorem.Classification of algebraic surfaces, moduli spaces, deformation theory and obstruction theory, the notion of schemes.Complex structures, almost complex manifolds and integrability, Hermitian and Kahler metrics, connections on complex vector bundles, Chern classes and Chern-Weil theory, Hodge and Dolbeault theory, vanishing theorems, Calabi-Yau manifolds, deformation theory.Partial Differential Equations of Applied Mathematics.

First-order partial differential equations; method of characteristics; weak solutions; elliptic, parabolic, and hyperbolic equations; Fourier transform; Fourier series; and eigenvalue problems.Prerequisite: Basic coursework in multivariable calculus and ordinary differential equations, and some prior experience with a proof-based treatment of the material as in MATH 171 or MATH 61CM (formerly Math 51H).Image denoising and deblurring with optimization and partial differential equations methods.Imaging functionals based on total variation and l-1 minimization.Fast algorithms and their implementation.Array imaging using Kirchhoff migration and beamforming, resolution theory for broad and narrow band array imaging in homogeneous media, topics in high-frequency, variable background imaging with velocity estimation, interferometric imaging methods, the role of noise and inhomogeneities, and variational problems that arise in optimizing the performance of array imaging algorithms.Numerical Solution of Partial Differential Equations.

Hyperbolic partial differential equations: stability, convergence and qualitative properties; nonlinear hyperbolic equations and systems; combined solution methods from elliptic, parabolic, and hyperbolic problems.Examples include: Burger's equation, Euler equations for compressible flow, Navier-Stokes equations for incompressible flow.Partial Differential Equations and Diffusion Processes.Parabolic and elliptic partial differential equations and their relation to diffusion processes.First order equations and optimal control.

Emphasis is on applications to mathematical finance.

Prerequisites: MATH 136/STATS 219 (or equivalents) and MATH 131P + MATH 115/171 or MATH 173 or MATH 220.The basic limit theorems of probability theory and their application to maximum likelihood estimation.

Basic Monte Carlo methods and importance sampling.Markov chains and processes, random walks, basic ergodic theory and its application to parameter estimation.Discrete time stochastic control and Bayesian filtering.Diffusion approximations, Brownian motion and an introduction to stochastic differential equations.Examples and problems from various applied areas.

Prerequisites: exposure to probability and background in analysis.Probability, Stochastic Analysis and Applications.The basic limit theorems of probability theory and their application to maximum likelihood estimation.

Basic Monte Carlo methods and importance sampling.Markov chains and processes, random walks, basic ergodic theory and its application to parameter estimation.Discrete time stochastic control and Bayesian filtering.Diffusion approximations, Brownian motion and basic stochastic differential equations.Examples and problems from various applied areas.

Prerequisites: exposure to probability and background in analysis.Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems.

Probability: independence, Borel-Cantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers.Weak convergence; central limit theorems; Poisson convergence; Stein's method.Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 0-1 laws, Radon-Nikodym Theorem, ruin problems, etc.Other topics as time allows selected from (i) local limit theorems, (ii) renewal theory, (iii) discrete time Markov chains, (iv) random walk theory,n(v) ergodic theory.Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes.Invariance principle, random walks, LIL and functional CLT.

Probability and statistics are founded on the study of games of chance.

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This course addresses practical and theoretical aspects.Topics covered: mathematics of basic random phenomena (physics of coin tossing and roulette, analysis of various methods of shuffling cards), odds in popular games, card counting, optimal tournament play, practical problems of random number generation.An Introduction to Random Matrix Theory.

Patterns in the eigenvalue distribution of typical large matrices, which also show up in physics (energy distribution in scattering experiments), combinatorics (length of longest increasing subsequence), first passage percolation and number theory (zeros of the zeta function).Classical compact ensembles (random orthogonal matrices).The tools of determinental point processes.Background from operator theory, addition and multiplication theorems for operators, spectral properties of infinite-dimensional operators, the free additive and multiplicative convolutions of probability measures and their classical counterparts, asymptotic freeness of large random matrices, and free entropy and free dimension.Topics in Probability: Percolation Theory.An introduction to first passage percolation and related general tools and models.Topics include early results on shape theorems and fluctuations, more modern development using hyper-contractivity, recent breakthrough regarding scaling exponents, and providing exposure to some fundamental long-standing open problems.Course prerequisite: graduate-level probability.

Topics in Combinatorics: Polyhedral Techniques in Optimization.LP duality and min-max formulas; matchings, spanning trees, matroids, matroid union and intersection; packing of trees and arborescences; submodular functions, continuous extensions and optimization.Combinatorial estimates and the method of types.Large deviation probabilities for partial sums and for empirical distributions, Cramer's and Sanov's theorems and their Markov extensions.

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Applications in statistics, information theory, and statistical mechanics.This advanced course in extremal combinatorics covers several major themes in the area.

These include extremal combinatorics and Ramsey theory, the graph regularity method, and algebraic methods .These include extremal combinatorics and Ramsey theory, the graph regularity method, and algebraic methods.

This is a graduate-level course on the use and analysis of Markov chains.

Emphasis is placed on explicit rates of convergence for chains used in applications to physics, biology, and statistics receive an admissions decision by January 31, 2018. Defer Decision:   we do not exceed the number of spaces available in each of the freshman-   Biology (CBS)*. Biology, Society, and Environment (CLA). Biomedical Engineering (CSE). Bioproducts & Biosystems Engineering. (CFANS, CSE)*. Business: –Accounting  .Emphasis is placed on explicit rates of convergence for chains used in applications to physics, biology, and statistics.Topics covered: basic constructions (metropolis, Gibbs sampler, data augmentation, hybrid Monte Carlo); spectral techniques (explicit diagonalization, Poincar , and Cheeger bounds); functional inequalities (Nash, Sobolev, Log Sobolev); probabilistic techniques (coupling, stationary times, Harris recurrence) receive an admissions decision by January 31, 2018. Defer Decision:   we do not exceed the number of spaces available in each of the freshman-   Biology (CBS)*. Biology, Society, and Environment (CLA). Biomedical Engineering (CSE). Bioproducts & Biosystems Engineering. (CFANS, CSE)*. Business: –Accounting  .Topics covered: basic constructions (metropolis, Gibbs sampler, data augmentation, hybrid Monte Carlo); spectral techniques (explicit diagonalization, Poincar , and Cheeger bounds); functional inequalities (Nash, Sobolev, Log Sobolev); probabilistic techniques (coupling, stationary times, Harris recurrence).A variety of card shuffling processes will be studies.Classical functional inequalities (Nash, Faber-Krahn, log-Sobolev inequalities), comparison of Dirichlet forms.Random walks and isoperimetry of amenable groups (with a focus on solvable groups).Entropy, harmonic functions, and Poisson boundary (following Kaimanovich-Vershik theory).

Introduction to Stochastic Differential Equations.Brownian motion, stochastic integrals, and diffusions as solutions of stochastic differential equations.Functionals of diffusions and their connection with partial differential equations.

Random walk approximation of diffusions.Prerequisite: 136 or equivalent and differential equations.Introduction to mathematical models of complex static and dynamic stochastic systems that undergo sudden regime change in response to small changes in parameters.Examples from materials science (phase transitions), power grid models, financial and banking systems.Special emphasis on mean field models and their large deviations, including computational issues.Dynamic network models of financial systems and their stability.European options and equivalent martingale measures.

Hedging strategies and management of risk.Term structure models and interest rate derivatives.Corequisites: MATH 236 and 227 or equivalent.Monte Carlo, finite difference, tree, and transform methods for the numerical solution of partial differential equations in finance.Emphasis is on derivative security pricing.Holomorphic functions in several variables, Hartogs phenomenon, d-bar complex, Cousin problem.Plurisubharmonic functions and pseudo-convexity.nPrerequisites: MATH 215A and experience with manifolds.Riemann surfaces and holomorphic maps, algebraic curves, maps to projective spaces.

) Prerequisites: MATH 106 or MATH 116, and familiarity with surfaces equivalent to MATH 143, MATH 146, or MATH 147.Topics of contemporary interest in algebraic geometry.Topics may include 1) subadditive and multiplicative ergodic theorems, 2) notions of mixing, weak mixing, spectral theory, 3) metric and topological entropy of dynamical systems, 4) measures of maximal entropy.Prerequisites: Solid background in "Measure and Integration" (MATH 205A) and some functional analysis, including Riesz representation theorem and Hahn-Banach theorem (MATH 205B).

Topics of contemporary interest in number theory.The theory of linear and nonlinear partial differential equations, beginning with linear theory involving use of Fourier transform and Sobolev spaces.

Topics: Schauder and L2 estimates for elliptic and parabolic equations; De Giorgi-Nash-Moser theory for elliptic equations; nonlinear equations such as the minimal surface equation, geometric flow problems, and nonlinear hyperbolic equations.

Linear symplectic geometry and linear Hamiltonian systems.Symplectic manifolds and their Lagrangian submanifolds, local properties.Relations between symplectic and contact manifolds.Applied Fourier Analysis and Elements of Modern Signal Processing.Introduction to the mathematics of the Fourier transform and how it arises in a number of imaging problems.Mathematical topics include the Fourier transform, the Plancherel theorem, Fourier series, the Shannon sampling theorem, the discrete Fourier transform, and the spectral representation of stationary stochastic processes.Computational topics include fast Fourier transforms (FFT) and nonuniform FFTs.

Applications include Fourier imaging (the theory of diffraction, computed tomography, and magnetic resonance imaging) and the theory of compressive sensing.Algebraic Combinatorics and Symmetric Functions.Theorems about permutations, partitions, and graphs now follow in a unified way.Topics: The usual bases (monomial, elementary, complete, and power sums).Representation theory of the symmetric group.Littlewood-Richardson rule, quasi-symmetric functions, combinatorial Hopf algebras, introduction to Macdonald polynomials.

Throughout, emphasis is placed on applications (e.to card shuffling and random matrix theory).Prerequisite: 210A and 210B, or equivalent.

Crystal Bases: Representations and Combinatorics.Crystal Bases are combinatorial analogs of representation theorynof Lie groups.We will explore different aspects of thesenanalogies and develop rigorous purely combinatorial foundations.Geometry and Topology of Complex Manifolds.Complex manifolds, Kahler manifolds, curvature, Hodge theory, Lefschetz theorem, Kahler-Einstein equation, Hermitian-Einstein equations, deformation of complex structures.Applications: immersion theory and its generaliazations.Differential relations and Gromov's h-principle for open manifolds.

Mappings with simple singularities and their applications.Topics in Partial Differential Equations.Covers a list of topics in mathematical physics.The specific topics may vary from year to year, depending on the instructor's discretion.

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Background in graduate level probability theory and analysis is desirable.