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  • Mathematics
    and any two from Math 170A B C 175 179 Math 183 and any three from Math 170A B C 175 179 One additional sequence which may be chosen from the list 6 above or the following list Math 110A 120A 130A 110A B 120A B 152 184A 154 184A 155A B 171A B 193A B Upper division electives to complete at least thirteen four unit courses chosen from any mathematics course numbered between 100 and 194 including those taken from the requirements listed above except Up to twelve units may be taken from outside the department in an approved applied mathematical area A petition specifying the courses to be used must be approved by an applied mathematics adviser No such units may also be used for a minor or program of concentration MAE 107 and Econ 120A B C cannot be counted toward the thirteen required courses To be prepared for a strong major curriculum students should complete the last three quarters of the 20 sequence and Math 109 before the end of their sophomore year Major in Mathematics Scientific Computation This major is designed for students with a substantial interest in scientific computation The program is a specialized applied mathematics program with a concentration in computer solutions of scientific problems Required Courses Lower Division One of the following sequences Calculus Math 20A B C D E F Honors Calculus Math 31AH BH CH Math 20D Computer Programming ECE 15and CSE 8A AL B or CSE 11 Basic Computation Math 15A or CSE 20 and Math 15B or CSE 21 and CSE 12 Upper Division Mathematical Reasoning Math 109 Note Students completing Math 31CH may substitute a four unit upper division mathematics elective for Math 109 Linear Algebra Math 102 Probability and Statistics Math 183 or 180A 181A Note No credit for Math 183 if Math 180A or 181A taken prior or concurrently Analysis Math 140A B or 142A B Numerical Analysis Math 170A B C or Math 170A B Math 175 Optimization Math 171A B Scientific Computing Math 179 Additional elective upper division courses to total fifteen chosen from the following Math 107A B 110A B 120A B 130A B 131 152 155A B 170C or 175 At least fifteen upper division mathematics courses are required for the major except Up to three upper division courses may be taken outside the department in an approved scientific computation area in the sciences or engineering A petition specifying the courses to be used must be approved by a mathematics scientific computation adviser MAE 107 Econ 120A B C Math 195 196 197 199 and 199H cannot be counted toward the thirteen four unit upper division courses Major in Mathematics Probability and Statistics This major is designed for students with a substantial interest in probability theory and statistics It is useful preparation for many fields of employment as well as graduate school Required Courses Lower Division One of the following sequences Calculus Math 20A B C D E F Honors Calculus Math 31AH BH CH Math 20D Programming one of the following CSE 8A AL B Java CSE 11 Java Accelerated Pace ECE 15 Engineering Computation Upper Division Mathematical Reasoning Math 109 Note Students completing Math 31CH may substitute a four unit upper division mathematics elective for Math 109 Linear Algebra Math 102 or Math 170A Analysis Advanced Calculus Math 140A B or Math 142A B Numerical Methods Math 174 or Math 170A B Probability Math 180A B C Mathematical Statistics Math 181A B One of the following Math 181C 181E 193A 193B 194 Computational Statistics Math 185 Upper division electives to complete fifteen upper division courses from the following list Math 100A B C 103A B 110A B 120A B 130A 131 140C 152 155A B 170A B C 171A B 175 176 179 181C 181E 184A 187 188 193A B 194 At least fifteen four unit upper division mathematics courses are required except Two upper division electives may be outside the department in an approved applied mathematical area A petition approved by a math adviser is required MAE 107 Econ 120A B C Math 195 199 cannot be counted toward the upper division requirements To be prepared for a strong major curriculum students should complete the last three quarters of the 20 sequence and Math 109 before the end of their sophomore year Major in Mathematics Applied Science This major is designed for students with a substantial interest in mathematics and its applications to a particular field such as physics biology chemistry biochemistry cognitive science computer science economics management science or engineering Required Courses Lower Division One of the following sequences Calculus Math 20A B C D E F Honors Calculus Math 31AH BH CH Math 20D Programming one of the following is required CSE 8A AL B Intro to Computer Sci Java CSE 11 Intro to Computer Sci Java Accelerated Pace ECE 15 Engineering Computation Upper Division Mathematics Requirements Mathematical Reasoning Math 109 Note Students completing Math 31CH may substitute a four unit upper division mathematics elective for Math 109 Linear Algebra Math 102 or Math 170A Analysis Math 140A B or 142A B Any two quarter upper division math sequence Upper division electives to complete at least seven four unit courses chosen from any mathematics course numbered between 100 and 194 including those taken from the requirements listed above Upper Division Applied Science Requirements Seven upper division courses selected from one or two other departments these cannot be from mathematics At least three of these seven upper division courses must require calculus as a prerequisite Students must submit an individual plan for approval in advance by a mathematics department adviser and all subsequent changes to the plan must be approved by a mathematics department adviser Major in Mathematics Computer Science Graduates of this program will be mathematically oriented computer scientists who have specialized in the mathematical aspects and foundations of computer science or in the computer applications of mathematics A mathematics computer science major is not allowed

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  • Mathematics
    in Area 2 Students must pass a least two exams from distinct areas with a minimum grade of provisional PhD For example a PhD pass in Real Analysis provisional PhD pass in Complex Analysis an MA pass in Algebra would NOT satisfy this requirement but a PhD pass in Real Analysis MA pass in Complex Analysis provisional PhD pass in Algebra would as would a PhD pass in Numerical Analysis provisional PhD pass in Applied Algebra and an MA pass in Real Analysis All exams must be passed by the September exam session prior to the beginning of the third year of graduate studies Thus there would be no limit on the number of attempts encouraging new students to take exams when they arrive without penalty Department policy stipulates that at least one of the exams must be completed with a provisional PhD pass or better by September following the end of the first year Anyone unable to comply with this schedule will lose their funding as a PhD student They will be terminated from the doctoral program and transferred to one of our master s programs Any master s student can submit for consideration a written request to transfer into the PhD program when the qualifying exam requirements for the PhD program have been met and a dissertation adviser is found Approval by the Qualifying Exam and Appeals Committee QEAC is not automatic however Exams are typically offered twice a year one scheduled in the spring quarter and again in early September prior to the start of fall quarter Copies of past exams are made available online or in the Graduate Office In choosing a program with an eye to future employment students should seek the assistance of a faculty adviser and take a broad selection of courses including applied mathematics such as those in Area 3 Advancement to Candidacy It is expected that by the end of the third year nine quarters students should have a field of research chosen and a faculty member willing to direct and guide them A student will advance to candidacy after successfully passing the oral qualifying examination which deals primarily with the area of research proposed but may include the project itself This examination is conducted by the student s appointed doctoral committee Based on their recommendation a student advances to candidacy and is awarded the CPhil degree Dissertation and Final Defense Submission of a written dissertation and a final examination in which the thesis is publicly defended are the last steps before the PhD degree is awarded When the dissertation is substantially completed copies must be provided to all committee members at least four weeks in advance of the proposed defense date Two weeks before the scheduled final defense a copy of the dissertation must be made available in the department for public inspection Time Limits The normative time for the PhD in mathematics is five years Students must have a dissertation adviser by the end of nine quarters Students must be advanced to candidacy by the end of eleven quarters Total university support cannot exceed six years Total registered time at UC San Diego cannot exceed seven years A student making normal progress must meet the time limits described below PhD students who fail to meet these time limits may lose their TA funding Pass qualifying exams requirement by the fall quarter of the beginning of the third year Find thesis adviser by the end of nine quarters Advance to candidacy by the end of eleven quarters Final defense by the end of the fifth year PhD in Mathematics with Specialization in Computational Science The PhD in mathematics with a specialization in computational science is designed to allow a student to obtain standard basic training in his or her chosen field of science mathematics or engineering with training in computational science integrated into those graduate studies The specialization in computational science recognizes the nation s growing and continuing need for broadly trained advanced computational scientists in academic industry and government laboratories Its graduates will be well positioned to compete effectively for the best jobs in these areas Computational science refers to the use of computer simulation and visualization for basic scientific research product development and forecasting It is an interdisciplinary field that combines mathematics mathematical modeling numerical analysis and computer science architecture programming networks graphics with one of the scientific or engineering disciplines The specialization draws upon the expertise of faculty from bioengineering biological sciences chemistry and biochemistry computers and engineering electrical and computer engineering mathematics mechanical and aerospace engineering physics Scripps Institution of Oceanography structural engineering as well as research staff from the San Diego Supercomputer Center Admission Prospective students must apply to the PhD program of a participating home department be admitted to that department and then be admitted to the specialization The five participating academic departments that have a specialization in computational science are chemistry and biochemistry computer science and engineering mathematics mechanical and aerospace engineering and physics Requirements consist of those of the admitting home department one of the five participating departments as well as the proficiency qualifying and elective course requirements as outlined below Requirements and policies relating to the home department can be found in the UC San Diego General Catalog under that department s name In the case of the mathematics department the admission requirements for the mathematics doctoral program are those outlined above Specialization in Computational Science Policies The specialization requires that students complete all home department requirements for the PhD along with satisfying the CSME proficiency qualifying and elective requirements In the case of the mathematics department the requirements and timelines for the normal mathematics PhD program are as described above CSME proficiency see below must be satisfied by the end of the first year The CSME qualifying exams must be passed by the end of the second year or on petition by end of the third year The CSME qualifying exams can be attempted repeatedly but no more than once

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  • Mathematics Courses
    Equations 4 Basic concepts and classification of partial differential equations First order equations characteristics Hamilton Jacobi theory Laplace s equation wave equation heat equation Separation of variables eigenfunction expansions existence and uniqueness of solutions Formerly Math 132A Students may not receive credit for Math 110B and Math 132A Prerequisites Math 110A or consent of instructor W 111A Mathematical Modeling I 4 An introduction to mathematical modeling in the physical and social sciences Topics vary but have included mathematical models for epidemics chemical reactions political organizations magnets economic mobility and geographical distributions of species May be taken for credit two times when topics change Prerequisites Math 20D and either Math 20F or Math 31AH and Math 109 or consent of instructor 111B Mathematical Modeling II 4 Continued study on mathematical modeling in the physical and social sciences using advanced techniques that will expand upon the topics selected and further the mathematical theory presented in Math 111A Prerequisites Math 111A or consent of instructor 120A Elements of Complex Analysis 4 Complex numbers and functions Analytic functions harmonic functions elementary conformal mappings Complex integration Power series Cauchy s theorem Cauchy s formula Residue theorem Prerequisites Math 20E or Math 31CH or consent of instructor F W 120B Applied Complex Analysis 4 Applications of the residue theorem Conformal mapping and applications to potential theory flows and temperature distributions Fourier transformations Laplace transformations and applications to integral and differential equations Selected topics such as Poisson s formula Dirichlet s problem Neumann s problem or special functions Prerequisites Math 120A or consent of instructor W S 121A Foundations of Teaching and Learning Mathematics I 4 Cross listed with EDS 121A Develop teachers knowledge base knowledge of mathematics content pedagogy and student learning in the context of advanced mathematics This course builds on the previous courses where these components of knowledge were addressed exclusively in the context of high school mathematics Prerequisites EDS 30 Math 95 Calculus 10C or 20C 121B Foundations of Teaching and Learning Math II 4 Cross listed with EDS 121B Examine how learning theories can consolidate observations about conceptual development with the individual student as well as the development of knowledge in the history of mathematics Examine how teaching theories explain the effect of teaching approaches addressed in the previous courses Prerequisites EDS 121A Math 121A 130A Ordinary Differential Equations I 4 Linear and nonlinear systems of differential equations Stability theory perturbation theory Applications and introduction to numerical solutions Three lectures Prerequisites Math 20D and either Math 20F or Math 31AH or consent of instructor F 130B Ordinary Differential Equations II 4 Existence and uniqueness of solutions to differential equations Local and global theorems of continuity and differentiabillity Three lectures Prerequisites Math 130A or consent of instructor W 140A Foundations of Real Analysis I 4 First course in a rigorous three quarter sequence on real analysis Topics include the real number system basic topology numerical sequences and series continuity Students may not receive credit for both Math 140A and Math 142A Prerequisites Math 31CH or Math 109 or consent of instructor 140B Foundations of Real Analysis II 4 Second course in a rigorous three quarter sequence on real analysis Topics include differentiation the Riemann Stieltjes integral sequences and series of functions power series Fourier series and special functions Students may not receive credit for both Math 140B and Math 142B Prerequisites Math 140A or consent of instructor 140C Foundations of Real Analysis III 4 Third course in a rigorous three quarter sequence on real analysis Topics include differentiation of functions of several real variables the implicit and inverse function theorems the Lebesgue integral infinite dimensional normed spaces Prerequisites Math 140B or consent of instructor 142A Introduction to Analysis I 4 First course in an introductory two quarter sequence on analysis Topics include the real number system numerical sequences and series limits of functions continuity Students may not receive credit for both Math 140 and Math 142A Prerequisites Math 31CH or Math 109 or consent of instructor 142B Introduction to Analysis II 4 Second course in an introductory two quarter sequence on analysis Topics include differentiation the Rieman integral sequences and series of functions uniform convergence Taylor and Fourier series special functions Students may not receive credit for both Math 140B and Math 142B Prerequisites Math 142A or Math 140A or consent of instructor 150A Differential Geometry 4 Differential geometry of curves and surfaces Gauss and mean curvatures geodesics parallel displacement Gauss Bonnet theorem Three lectures Prerequisites Math 20E with a grade of C or better and Math 20F with a grade of C or better or consent of instructor F 150B Calculus on Manifolds 4 Calculus of functions of several variables inverse function theorem Further topics may include exterior differential forms Stokes theorem manifolds Sard s theorem elements of differential topology singularities of maps catastrophes further topics in differential geometry topics in geometry of physics Prerequisites Math 150A or consent of instructor W 152 Applicable Mathematics and Computing 4 This course will give students experience in applying theory to real world applications such as Internet and wireless communication problems The course will incorporate talks by experts from industry and students will be helped to carry out independent projects Topics include graph visualization labelling and embeddings random graphs and randomized algorithms May be taken 3 times for credit Prerequisites Math 20D and either 20F or Math 31AH or consent of instructor 153 Geometry for Secondary Teachers 4 Two and three dimensional Euclidean geometry is developed from one set of axioms Pedagogical issues will emerge from the mathematics and be addressed using current research in teaching and learning geometry This course is designed for prospective secondary school mathematics teachers Prerequisites Math 109 or Math 31CH or consent of instructor 154 Discrete Mathematics and Graph Theory 4 Basic concepts in graph theory Combinatorial tools structures in graphs Hamiltonian cycles perfect matching Properties of graphics and applications in basic algorithmic problems planarity k colorability traveling salesman problem Prerequisites Math 109 or Math 31CH or consent of instructor 155A Geometric Computer Graphics 4 Bezier curves and control lines de Casteljau construction for subdivision elevation of degree control points of Hermite curves barycentric coordinates rational curves Programming knowledge recommended Students may not receive credit for both Math 155A and CSE 167 Prerequisites Math 20F or Math 31AH or consent of instructor F 160A Elementary Mathematical Logic I 4 An introduction to recursion theory set theory proof theory model theory Turing machines Undecidability of arithmetic and predicate logic Proof by induction and definition by recursion Cardinal and ordinal numbers Completeness and compactness theorems for propositional and predicate calculi Prerequisites Math 100A or Math 103A or Math 140A or consent of instructor 160B Elementary Mathematical Logic II 4 A continuation of recursion theory set theory proof theory model theory Turing machines Undecidability of arithmetic and predicate logic Proof by induction and definition by recursion Cardinal and ordinal numbers Completeness and compactness theorems for propositional and predicate calculi Prerequisites Math 160A or consent of instructor 163 History of Mathematics 4 Topics will vary from year to year in areas of mathematics and their development Topics may include the evolution of mathematics from the Babylonian period to the eighteenth century using original sources a history of the foundations of mathematics and the development of modern mathematics Prerequisites Math 20B or consent of instructor S 168A Topics in Applied Mathematics Computer Science 4 Topics to be chosen in areas of applied mathematics and mathematical aspects of computer science May be repeated once for credit with different topics Prerequisites Math 20F or Math 31AH or consent of instructor W S 170A Introduction to Numerical Analysis Linear Algebra 4 Analysis of numerical methods for linear algebraic systems and least squares problems Orthogonalization methods Ill conditioned problems Eigenvalue and singular value computations Three lectures one recitation Knowledge of programming recommended Prerequisites Math 20F F S 170B Introduction to Numerical Analysis Approximation and Nonlinear Equations 4 Rounding and discretization errors Calculation of roots of polynomials and nonlinear equations Interpolation Approximation of functions Three lectures one recitation Knowledge of programming recommended Prerequisites Math 170A W 170C Introduction to Numerical Analysis Ordinary Differential Equations 4 Numerical differentiation and integration Ordinary differential equations and their numerical solution Basic existence and stability theory Difference equations Boundary value problems Three lectures one recitation Prerequisites Math 20D or 21D and Math 170B or consent of instructor S 171A Introduction to Numerical Optimization Linear Programming 4 Linear optimization and applications Linear programming the simplex method duality Selected topics from integer programming network flows transportation problems inventory problems and other applications Three lectures one recitation Knowledge of programming recommended Credit not allowed for both Math 171A and Econ 172A Prerequisites Math 20F or consent of instructor 171B Introduction to Numerical Optimization Nonlinear Programming 4 Convergence of sequences in Rn multivariate Taylor series Bisection and related methods for nonlinear equations in one variable Newton s methods for nonlinear equations in one and many variables Unconstrained optimization and Newton s method Equality constrained optimization Kuhn Tucker theorem Inequality constrained optimization Three lectures one recitation Knowledge of programming recommended Credit not allowed for both Math 171B and Econ 172B Prerequisites Math 171A or consent of instructor 174 Numerical Methods for Physical Modeling 4 Conjoined with Math 274 Floating point arithmetic direct and iterative solution of linear equations iterative solution of nonlinear equations optimization approximation theory interpolation quadrature numerical methods for initial and boundary value problems in ordinary differential equations Students may not receive credit for both Math 174 and PHYS 105 AMES 153 or 154 Students may not receive credit for Math 174 if Math 170A B or C has already been taken Graduate students will do an extra assignment exam Prerequisites Math 20D or Math 21D and either Math 20F or Math 31AH or consent of instructor 175 Numerical Methods for Partial Differential Equations 4 Conjoined with Math 275 Mathematical background for working with partial differential equations Survey of finite difference finite element and other numerical methods for the solution of elliptic parabolic and hyperbolic partial differential equations Formerly Math 172 Students may not receive credit for Math 175 275 and Math 172 Graduate students do an extra paper project or presentation per instructor Prerequisites Math 174 or Math 274 or consent of instructor 179 Projects in Computational and Applied Mathematics 4 Conjoined with Math 279 Mathematical models of physical systems arising in science and engineering good models and well posedness numerical and other approximation techniques solution algorithms for linear and nonlinear approximation problems scientific visualizations scientific software design and engineering project oriented Graduate students will do an extra paper project or presentation per instructor Prerequisites Math 174 or Math 274 or consent of instructor 180A Introduction to Probability 4 Probability spaces random variables independence conditional probability distribution expectation variance joint distributions central limit theorem Two units of credit offered for Math 180A if Econ 120A previously no credit offered if Econ 120A concurrently Prior or concurrent enrollment in Math 109 is highly recommended Prerequisites Math 20C or Math 31BH or consent of instructor F 180B Introduction to Stochastic Processes I 4 Random vectors multivariate densities covariance matrix multivariate normal distribution Random walk Poisson process Other topics if time permits Prerequisites Math 20D and either Math 20F or Math 31AH and Math 109 and Math 180A or consent of instructor W 180C Introduction to Stochastic Processes II 4 Markov chains in discrete and continuous time random walk recurrent events If time permits topics chosen from stationary normal processes branching processes queuing theory Three lectures Prerequisites Math 180B or consent of instructor S 181A Introduction to Mathematical Statistics I 4 Multivariate distribution functions of random variables distributions related to normal Parameter estimation method of moments maximum likelihood Estimator accuracy and confidence intervals Students completing Econ 120A instead of Math 180A must obtain consent of instructor to enroll Prior or concurrent enrollment in Math 109 is highly recommended Prerequisites Math 180A and Math 20F or Math 31AH or consent of instructor W 181B Introduction to Mathematical Statistics II 4 Hypothesis testing Linear models regression and analysis of variance Goodness of fit tests Nonparametric statistics Two units of credit offered for Math 181B if Econ 120B previously no credit offered if Econ 120B concurrently Prior enrollment in Math 109 is highly recommended Prerequisites Math 181A or consent of instructor S 181C Mathematical Statistics Nonparametric Statistics 4 Topics covered may include the following classical rank test rank correlations permutation tests distribution free testing efficiency confidence intervals nonparametric regression and density estimation resampling techniques bootstrap jackknife etc and cross validations Prior enrollment in Math 109 is highly recommended Prerequisites Math 181B or consent of instructor 181E Mathematical Statistics Time Series 4 Analysis of trends and seasonal effects autoregressive and moving averages models forecasting informal introduction to spectral analysis Prerequisites Math 181B or consent of instructor 183 Statistical Methods 4 Introduction to probability Discrete and continuous random variables binomial Poisson and Gaussian distributions Central limit theorem Data analysis and inferential statistics graphical techniques confidence intervals hypothesis tests curve fitting Credit not offered for Math 183 if Econ 120A ECE 109 Math 180A Math 181A or Math 186 previously or concurrently taken Prerequisites Math 20C 21C with a grade of C or better or consent of instructor F S 184A Combinatorics 4 Introduction to the theory and applications of combinatorics Enumeration of combinatorial structures Ranking and unranking Graph theory with applications and algorithms Recursive algorithms Inclusion exclusion Generating functions Polya theory Prerequisites Math 109 with a grade of C or better or consent of instructor W S 185 Introduction to Computational Statistics 4 Statistical analysis of data by means of package programs Regression analysis of variance discriminant analysis principal components Monte Carlo simulation and graphical methods Emphasis will be on understanding the connections between statistical theory numerical results and analysis of real data Recommended preparation exposure to computer programming such as CSE 5A CSE 7 or ECE 15 highly recommended Prerequisites Math 11 or Math 181A or Math 183 or Math 186 or MAE 108 or ECE 109 or Econ 120A and either Math 20F or Math 31AH or consent of instructor 186 Probability Statistics for Bioinformatics 4 This course will cover discrete and random variables data analysis and inferential statistics likelihood estimators and scoring matrices with applications to biological problems Introduction to Binomial Poisson and Gaussian distributions central limit theorem applications to sequence and functional analysis of genomes and genetic epidemiology Credit not offered for Math 186 if Econ 120A ECE 109 Math 180A Math 181A or Math 183 previously or concurrently Prerequisites Math 20C 21C with a grade of C or better or consent of instructor 187 Introduction to Cryptography 4 An introduction to the basic concepts and techniques of modern cryptography Classical cryptanalysis Probabilistic models of plaintext Monalphabetic and polyalphabetic substitution The one time system Caesar Vigenere Playfair Hill substitutions The Enigma Modern day developments The Data Encryption Standard Public key systems Security aspects of computer networks Data protection Electronic mail Three lectures one recitation Prerequisites programming experience S 189 Exploratory Data Analysis and Inference 4 An introduction to various quantitative methods and statistical techniques for analyzing data in particular big data Quick review of probability continuing to topics of how to process analyze and visualize data using statistical language R Further topics include basic inference sampling hypothesis testing bootstrap methods and regression and diagnostics Offers conceptual explanation of techniques along with opportunities to examine implement and practice them in real and simulated data Prerequisites Math 20F or Math 31AH and Math 180A Students who have not completed listed prerequisites may enroll with consent of instructor 190 Introduction to Topology 4 Topological spaces subspaces products sums and quotient spaces Compactness connectedness separation axioms Prerequisites Math 31CH or Math 140A Students who have not completed prerequisites may enroll with consent of instructor 191 Topics in Topology 4 Topics to be chosen by the instructor from the fields of differential algebraic geometric and general topology Three lectures Prerequisites Math 190 or consent of instructor S 192 Senior Seminar in Mathematics 1 The Senior Seminar Program is designed to allow senior undergraduates to meet with faculty members in a small group setting to explore an intellectual topic in mathematics at the upper division level Topics will vary from quarter to quarter Senior Seminars may be taken for credit up to four times with a change in topic and permission of the department Enrollment is limited to twenty students with preference given to seniors Prerequisites department stamp and or consent of instructor 193A Actuarial Mathematics I 4 Probabilistic Foundations of Insurance Short term risk models Survival distributions and life tables Introduction to life insurance Prerequisites Math 180A or Math 183 or consent of instructor 193B Actuarial Mathematics II 4 Life Insurance and Annuities Analysis of premiums and premium reserves Introduction to multiple life functions and decrement models as time permits Prerequisites Math 193A or consent of instructor 194 The Mathematics of Finance 4 Introduction to the mathematics of financial models Basic probabilistic models and associated mathematical machinery will be discussed with emphasis on discrete time models Concepts covered will include conditional expectation martingales optimal stopping arbitrage pricing hedging European and American options Prerequisites Math 20D and either Math 20F or Math 31AH and Math 180A or consent of instructor 195 Introduction to Teaching in Mathematics 4 Students will be responsible for and teach a class section of a lower division mathematics course They will also attend a weekly meeting on teaching methods Does not count towards a minor or major Five lectures one recitation Prerequisites consent of instructor F W S 196 Student Colloquium 1 A variety of topics and current research results in mathematics will be presented by guest lecturers and students under faculty direction May be taken for P NP grade only Prerequisites upper division status 197 Mathematics Internship 2 or 4 An enrichment program which provides work experience with public private sector employers Subject to the availability of positions students will work in a local company under the supervision of a faculty member and site supervisor Units may not be applied towards major graduation requirements Prerequisites completion of ninety units two upper division mathematics courses an overall 2 5 UC San Diego GPA consent of mathematics faculty coordinator and submission of written contract Department stamp required 199 Independent Study for Undergraduates 2 or 4 Independent reading in advanced mathematics by individual students Three periods P NP grades only Prerequisites permission of department F W S 199H Honors Thesis Research for Undergraduates 2 4 Honors thesis research for seniors participating in the Honors Program Research is conducted under the supervision of a mathematics faculty member Prerequisites admission to the Honors Program in mathematics department stamp Graduate 200A B C Algebra 4 4 4 Group actions factor groups polynomial rings linear algebra rational and Jordan canonical forms unitary and Hermitian matrices Sylow theorems finitely generated abelian groups unique factorization Galois theory solvability by radicals Hilbert Basis Theorem Hilbert Nullstellensatz Jacobson radical semisimple Artinian rings Prerequisites consent of instructor 201A Basic Topics in Algebra I 4 Recommended for all students specializing in algebra Basic topics include categorical algebra commutative algebra group representations homological algebra nonassociative algebra ring theory May be taken for credit six times with consent of adviser as topics vary Prerequisites Math 200C Students who have not taken Math 200C may enroll with consent of instructor 201B Basic Topics in Algebra II 4 Continued development of a basic topic in algebra Topics include categorical algebra commutative algebra group representations homological algebra nonassociative algebra ring theory May be taken for credit three times with consent of adviser as topics vary Prerequisites Math 201A Students who have not taken Math 201A may enroll with consent of instructor 202A Applied Algebra I 4 Introduction to algebra from a computational perspective Groups rings linear algebra rational and Jordan forms unitary and Hermitian matrices matrix decompositions perturbation of eigenvalues group representations symmetric functions fast Fourier transform commutative algebra Grobner basis finite fields Prerequisites graduate standing or consent of instructor 202B Applied Algebra II 4 Second course in algebra from a computational perspective Groups rings linear algebra rational and Jordan forms unitary and Hermitian matrices matrix decompositions perturbation of eigenvalues group representations symmetric functions fast Fourier transform commutative algebra Grobner basis finite fields Prerequisites Math 202A or consent of instructor 202C Applied Algebra III 4 Third course in algebra from a computational perspective Groups rings linear algebra rational and Jordan forms unitary and Hermitian matrices matrix decompositions perturbation of eigenvalues group representations symmetric functions fast Fourier transform commutative algebra Grobner basis finite fields Prerequisites Math 202B or consent of instructor 203A B C Algebraic Geometry 4 4 4 Places Hilbert Nullstellensatz varieties product of varieties correspondences normal varieties Divisors and linear systems Riemann Roch theorem resolution of singularities of curves Grothendieck schemes cohomology Hilbert schemes Picard schemes Prerequisites Math 200A B C F W S 204A Number Theory I 4 First course in graduate level number theory Local fields valuations and metrics on fields discrete valuation rings and Dedekind domains completions ramification theory main statements of local class field theory Prerequisites Math 200C Students who have not taken Math 200C may enroll with consent of instructor 204B Number Theory II 4 Second course in graduate level number theory Global fields arithmetic properties and relation to local fields ideal class groups groups of units ramification theory adèles and idèles main statements of global class field theory Prerequisites Math 204A Students who have not taken Math 204A may enroll with consent of instructor 204C Number Theory III 4 Third course in graduate level number theory Zeta and L functions Dedekind zeta functions Artin L functions the class number formula and generalizations density theorems Prerequisites Math 204B Students who have not taken Math 204B may enroll with consent of instructor 205 Topics in Number Theory 4 Topics in algebraic and analytic number theory such as L functions sieve methods modular forms class field theory p adic L functions and Iwasawa theory elliptic curves and higher dimensional abelian varieties Galois representations and the Langlands program p adic cohomology theories Berkovich spaces etc May be taken for credit nine times Prerequisites graduate standing 207A Topics in Algebra 4 Introduction to varied topics in algebra In recent years topics have included number theory commutative algebra noncommutative rings homological algebra and Lie groups May be taken for credit six times with consent of adviser as topics vary Prerequisites graduate standing Nongraduate students may enroll with consent of instructor 207B Further Topics in Algebra 4 Introduction to varied topics in algebra In recent years topics have included number theory commutative algebra noncommutative rings homological algebra and Lie groups May be taken for credit three times with consent of adviser as topics vary Prerequisites Math 207A Students who have not completed Math 207A may enroll with consent of instructor 209 Seminar in Number Theory 1 Various topics in number theory Prerequisites graduate standing or consent of instructor S U grade only 210A Mathematical Methods in Physics and Engineering 4 Complex variables with applications Analytic functions Cauchy s theorem Taylor and Laurent series residue theorem and contour integration techniques analytic continuation argument principle conformal mapping potential theory asymptotic expansions method of steepest descent Prerequisites Math 20DEF 140A 142A or consent of instructor 210B Mathematical Methods in Physics and Engineering 4 Linear algebra and functional analysis Vector spaces orthonormal bases linear operators and matrices eigenvalues and diagonalization least squares approximation infinite dimensional spaces completeness integral equations spectral theory Green s functions distributions Fourier transform Prerequisites Math 210A or consent of instructor W 210C Mathematical Methods in Physics and Engineering 4 Calculus of variations Euler Lagrange equations Noether s theorem Fourier analysis of functions and distributions in several variables Partial differential equations Laplace wave and heat equations fundamental solutions Green s functions well posed problems Prerequisites Math 210B or consent of instructor S 217 Topics in Applied Mathematics 4 In recent years topics have included applied complex analysis special functions and asymptotic methods May be repeated for credit with consent of adviser as topics vary Prerequisites graduate standing Nongraduate students may enroll with consent of instructor 220A B C Complex Analysis 4 4 4 Complex numbers and functions Cauchy theorem and its applications calculus of residues expansions of analytic functions analytic continuation conformal mapping and Riemann mapping theorem harmonic functions Dirichlet principle Riemann surfaces Prerequisites Math 140A B or consent of instructor F W S 221A Topics in Several Complex Variables 4 Introduction to varied topics in several complex variables In recent years topics have included formal and convergent power series Weierstrass preparation theorem Cartan Ruckert theorem analytic sets mapping theorems domains of holomorphy proper holomorphic mappings complex manifolds and modifications May be taken for credit six times with consent of adviser as topics vary Prerequisites Math 200A and 220C Students who have not completed Math 200A and 220C may enroll with consent of instructor 221B Further Topics in Several Complex Variables 4 Continued development of a topic in several complex variables Topics include formal and convergent power series Weierstrass preparation theorem Cartan Ruckert theorem analytic sets mapping theorems domains of holomorphy proper holomorphic mappings complex manifolds and modifications May be taken for credit three times with consent of adviser as topics vary Prerequisites Math 221A Students who have not completed Math 221A may enroll with consent of instructor 231A B C Partial Differential Equations 4 4 4 Existence and uniqueness theorems Cauchy Kowalewski theorem first order systems Hamilton Jacobi theory initial value problems for hyperbolic and parabolic systems boundary value problems for elliptic systems Green s function eigenvalue problems perturbation theory Prerequisites Math 210A B or 240A B C or consent of instructor 237A Topics in Differential Equations 4 Introduction to varied topics in differential equations In recent years topics have included Riemannian geometry Ricci flow and geometric evolution May be taken for credit six times with consent of adviser as topics vary Prerequisites graduate standing Nongraduate students may enroll with consent of instructor 237B Further Topics in Differential Equations 4 Continued development of a topic in differential equations Topics include Riemannian geometry Ricci flow and geometric evolution May be taken for credit three times with consent of adviser as topics vary Prerequisites Math 237A Students who have not completed Math 237A may enroll with consent of instructor 240A B C Real Analysis 4 4 4 Lebesgue integral and Lebesgue measure Fubini theorems functions of bounded variations Stieltjes integral derivatives and indefinite integrals the spaces L and C equi continuous families continuous linear functionals general measures and integrations Prerequisites Math 140A B C F W S 241A B Functional Analysis 4 4 Metric spaces and contraction mapping theorem closed graph theorem uniform boundedness principle Hahn Banach theorem representation of continuous linear functionals conjugate space weak topologies extreme points Krein Milman theorem fixed point theorems Riesz convexity theorem Banach algebras Prerequisites Math 240A B C or consent of instructor 242 Topics in Fourier Analysis 4 In recent years topics have included Fourier analysis in Euclidean spaces groups and symmetric spaces May be repeated for credit with consent of adviser as topics vary Prerequisites Math 240C students who have not completed Math 240C may enroll with consent of instructor 243 Seminar in Operator Algebras 1 Various topics in operator algebras May be taken for credit nine times Prerequisites graduate standing or consent of instructor S U grades only 245A Convex Analysis and Optimization I 4 Convex sets and functions convex and affine hulls relative interior closure and continuity recession and existence of optimal solutions saddle point and min max theory subgradients and subdifferentials Prerequisites Math 20F and Math 142A or graduate standing or consent of instructor 245B Convex Analysis and Optimization II 4 Optimality conditions strong duality and the primal function conjugate functions Fenchel duality theorems dual derivatives and subgradients subgradient methods cutting plane methods Prerequisites Math 245A or consent of instructor 245C Convex Analysis and Optimization III 4 Convex optimization problems linear matrix inequalities second order cone programming semidefinite programming sum of squares of polynomials positive polynomials distance geometry Prerequisites Math 245B or consent of instructor 247A Topics in Real Analysis 4 Introduction to varied topics in real analysis In recent years topics have included Fourier analysis distribution theory martingale theory operator theory May be taken for credit six times with consent of adviser Prerequisites graduate standing Nongraduate students may enroll with consent of instructor 247B Further Topics in Real Analysis 4 Continued development of a topic in real analysis Topics include Fourier analysis distribution theory martingale theory operator theory May be taken for credit three times with consent of adviser as topics vary Prerequisites Math 247A Students who have not completed Math 247A may enroll with consent of instructor 248 Seminar in Real Analysis 1 Various topics in real analysis Prerequisites graduate standing or consent of instructor S U grade only 250A B C Differential Geometry 4 4 4 Differential manifolds Sard theorem tensor bundles Lie derivatives DeRham theorem connections geodesics Riemannian metrics curvature tensor and sectional curvature completeness characteristic classes Differential manifolds immersed in Euclidean space Prerequisites consent of instructor F W S 251A B C Lie Groups 4 4 4 Lie groups Lie algebras exponential map subgroup subalgebra correspondence adjoint group universal enveloping algebra Structure theory of semi simple Lie groups global decompositions Weyl group Geometry and analysis on symmetric spaces Prerequisites Math 200 and 250 or consent of instructor F W S 256 Seminar in Lie Groups and Lie Algebras 1 Various topics in Lie groups and Lie algebras including structure theory representation theory and applications Prerequisites graduate standing or consent of instructor S U grade only F W S 257A Topics in Differential Geometry 4 Introduction to varied topics in differential geometry In recent years topics have included Morse theory and general relativity May be taken for credit six times with consent of adviser Prerequisites graduate standing Nongraduate students may enroll with consent of instructor 257B Further Topics in Differential Geometry 4 Continued development of a topic in differential geometry Topics include Morse theory and general relativity May be taken for credit three times with consent of adviser Prerequisites Math 257A Students who have not completed Math 257A may enroll with consent of instructor 258 Seminar in Differential Geometry 1 Various topics in differential geometry May be taken for credit nine times Prerequisites graduate standing or consent of instructor S U grade only 259A B C Geometrical Physics 4 4 4 Manifolds differential forms homology deRham s theorem Riemannian geometry harmonic forms Lie groups and algebras connections in bundles homotopy sequence of a bundle Chern classes Applications selected from Hamiltonian and continuum mechanics electromagnetism thermodynamics special and general relativity Yang Mills fields Prerequisites graduate standing in mathematics physics or engineering or consent of instructor 260A Mathematical Logic I 4 Propositional calculus and first order logic Theorem proving Model theory soundness completeness and compactness Herbrand s theorem Skolem Lowenheim theorems Craig interpolation Prerequisites graduate standing or consent of instructor 260B Mathematical Logic II 4 Theory of computation and recursive function theory Church s thesis computability and undecidability Feasible computability and complexity Peano arithmetic and the incompleteness theorems nonstandard models Prerequisites Math 260A or consent of instructor 261A Probabilistic Combinatorics and Algorithms 4 Introduction to the probabilistic method Combinatorial applications of the linearity of expectation second moment method Markov Chebyschev and Azuma inequalities and the local limit lemma Introduction to the theory of random graphs Prerequisites graduate standing or consent of instructor 261B Probabilistic Combinatorics and Algorithms II 4 Introduction to probabilistic algorithms Game theoretic techniques Applications of the probabilistic method to algorithm analysis Markov Chains and Random walks Applications to approximation algorithms distributed algorithms online and parallel algorithms Math 261A must be taken before Math 261B Prerequisites Math 261A 261C Probabilistic Combinatorics and Algorithms III 4 Advanced topics in the probabilistic combinatorics and probabilistics algorithms Random graphs Spectral Methods Network algorithms and optimization Statistical learning Math 261B must be taken before Math 261C Prerequisites Math 261B 262A Topics in Combinatorial Mathematics 4 Introduction to varied topics in combinatorial mathematics In recent years topics have included problems of enumeration existence construction and optimization with regard to finite sets Recommended preparation some familiarity with computer programming desirable but not required May be taken for credit six times with consent of adviser as topics vary Prerequisites graduate standing Nongraduate students may enroll with consent of instructor 262B Further Topics in Combinatorial Mathematics 4 Continued development of a topic in combinatorial mathematics Topics include problems of enumeration existence construction and optimization with regard to finite sets Recommended preparation some familiarity with computer programming desirable but not required May be taken for credit three times with consent of adviser as topics vary Prerequisites Math 262A Students who have not completed Math 262A may enroll with consent of instructor 264A B C Combinatorics 4 4 4 Topics from partially ordered sets Mobius functions simplicial complexes and shell ability Enumeration formal power series and formal languages generating functions partitions Lagrange inversion exponential structures combinatorial species Finite operator methods q analogues Polya theory Ramsey theory Representation theory of the symmetric group symmetric functions and operations with Schur functions F W S 267A Topics in Mathematical Logic 4 Introduction to varied topics in mathematical logic Topics chosen from recursion theory model theory and set theory May be taken for credit six times with consent of adviser as topics vary Prerequisites graduate standing or consent of instructor Nongraduate students may enroll with consent of instructor 267B Further Topics in Mathematical Logic 4 Continued development of a topic in mathematical logic Topics chosen from recursion theory model theory and set theory May be taken for credit three times with consent of adviser as topics vary Prerequisites Math 267A or consent of instructor Students who have not completed Math 267A may enroll with consent of instructor 268 Seminar in Logic 1 Various topics in logic Prerequisites graduate standing or consent of instructor S U grade only 269 Seminar in Combinatorics 1 Various topics in combinatorics Prerequisites graduate standing or consent of instructor S U grade only 270A Numerical Linear Algebra 4 Error analysis of the numerical solution of linear equations and least squares problems for the full rank and rank deficient cases Error analysis of numerical methods for eigenvalue problems and singular value problems Iterative methods for large sparse systems of linear equations Prerequisites graduate standing or consent of instructor 270B Numerical Approximation and Nonlinear Equations 4 Iterative methods for nonlinear systems of equations Newton s method Unconstrained and constrained optimization The Weierstrass theorem best uniform approximation least squares approximation orthogonal polynomials Polynomial interpolation piecewise polynomial interpolation piecewise uniform approximation Numerical differentiation divided differences degree of precision Numerical quadrature interpolature quadrature Richardson extrapolation Romberg Integration Gaussian quadrature singular integrals adaptive quadrature Prerequisites Math 270A or consent of instructor 270C Numerical Ordinary Differential Equations 4 Initial value problems IVP and boundary value problems BVP in ordinary differential equations Linear methods for IVP one and multistep methods local truncation error stability convergence global error accumulation Runge Kutta RK Methods for IVP RK methods predictor corrector methods stiff systems error indicators adaptive time stepping Finite difference finite volume collocation spectral and finite element methods for BVP a priori and a posteriori error analysis stability convergence adaptivity Prerequisites Math 270B or consent of instructor 271A B C Numerical Optimization 4 4 4 Formulation and analysis of algorithms for constrained optimization Optimality conditions linear and quadratic programming interior methods penalty and barrier function methods sequential quadratic programming methods Prerequisites consent of instructor F W S 272A Numerical Partial Differential Equations I 4 Survey of discretization techniques for elliptic partial differential equations including finite difference finite element and finite volume methods Lax Milgram Theorem and LBB stability A priori error estimates Mixed methods Convection diffusion equations Systems of elliptic PDEs Prerequisites graduate standing or consent of instructor 272B Numerical Partial Differential Equations II 4 Survey of solution techniques for partial differential equations Basic iterative methods Preconditioned conjugate gradients Multigrid methods Hierarchical basis methods Domain decomposition Nonlinear PDEs Sparse direct methods Prerequisites Math 272A or consent of

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  • Mathematics Faculty
    PhD Emeritus Philip E Gill PhD Fan Chung Graham PhD Paul Erdos Professor of Combinatorics Leonard R Haff PhD Emeritus Hubert Halkin PhD Emeritus Guershon Harel PhD J William Helton PhD Michael J Holst PhD Chancellor s Associates Professor of Mathematics Adrian Ioana PhD Elham Izadi PhD Kiran Kedlaya PhD Stefan E Warschawski Professor of Mathematics Melvin Leok PhD Bo Li PhD James P Lin PhD Emeritus Alfred B Manaster PhD Emeritus James McKernan PhD Charles Lee Powell Professor of Mathematics David A Meyer PhD Lei Ni PhD John O Quigley PhD Emeritus Dimitris Politis PhD Cristian Popescu PhD Jeffrey M Rabin PhD Academic Senate Distinguished Teaching Award Jeffrey B Remmel PhD Associate Dean Division of Physical Sciences Yosef Rinott PhD Emeritus Burton Rodin PhD Emeritus Daniel S Rogalski PhD Helmut Rohrl PhD Emeritus Murray Rosenblatt PhD Emeritus Linda P Rothschild PhD Emerita Jason Schweinsberg PhD Michael J Sharpe PhD Emeritus Lance W Small PhD Emeritus Donald R Smith PhD Emeritus Harold M Stark PhD Emeritus Audrey A Terras PhD Emerita Jacques Verstraete PhD Adrian R Wadsworth PhD Emeritus Nolan R Wallach PhD Emeritus Hans G Wenzl PhD Vice Chair Ruth J Williams PhD Charles Lee Powell Professor of Mathematics

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  • Mathematics and Science Education
    UC San Diego MSED 290 Mathematics education students must select two of the following additional courses SDSU MTHED 600 601 604 605 606 and 607 Three courses on quantitative and qualitative research methods SDSU MSE 810 or MTHED 810 and one of the following sequences UC San Diego PSYC 201A 201B or UC San Diego MATH 282A 282B or SDSU PSY 670A 670B Two courses in cognitive science at UC San Diego selected from COGS 102A or 234 COGS 102B 200 260 or one of COGS 101A 101B 101C One teaching practicum SDSU MSE 805 806 or 807 or UC San Diego EDS 129A 139 or Discipline 500 Two courses from different categories are selected with advisers according to the student s needs and background Philosophy and History UC San Diego PHIL 145 146 147 209A HISC 106 107 108 109 160 260 163 263 164 264 or 165 265 Sociology UC San Diego Soc G 270 SOCI 117 EDS 117 or SOCI 126 EDS 126 Mathematics and Science Graduate level courses in biology chemistry mathematics or physics Teaching Experience An option for students who have not yet had teaching experiences at both the K 12 and collegiate levels is to take a second teaching practicum Other Other types of courses at the graduate or upper division undergraduate level can be approved by the advisers if they contribute to a coherent program Two doctoral research courses SDSU MSE 830 or MTHED 830 and either SDSU MSE 899 or UC San Diego MSED 299 Beyond these requirements no specified number of courses is required for the doctoral degree It is expected however that all the doctoral students will supplement the requirements with electives that contribute to individual career objectives Additional Requirements for Students Entering with a Master s Degree in Mathematics Education Students who are admitted into the doctoral program with a master s degree in mathematics education will increase the breadth and depth of their mathematical knowledge by fulfilling the requirements specified for Option A or Option B Option A UC San Diego Math 240A 240B 240C and Pass the UC San Diego comprehensive examination on analysis at the master s level and One graduate algebra course UC San Diego Math 200A or SDSU MATH 627A or 623 MATH 623 can only be selected if the student has already taken a graduate level abstract algebra course Option B Select two of SDSU MATH 627A 627B 623 and Pass the SDSU comprehensive examination on algebra at the master s level and UC San Diego Math 240A Whether the student selects Option A or Option B the yearlong sequence in algebra or analysis must be taken in Year 1 of the doctoral program All of the requirements for Option A or Option B must be completed prior to the second year examination however students are strongly encouraged to fulfill all of the requirements in Year 1 A grade of B or better must be earned in each course Examinations Students in the

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  • Mathematics and Science Education Courses
    graduate student will teach or assist a teacher in a K 12 setting The graduate student will have the mentorship of the classroom teacher as well as the supervision of an MSED faculty member Prerequisites admission to the Joint Doctoral Program in Mathematics and Science Education S U grades only MSED 295 MSED Orientation Practicum 1 3 Each practicum lasts five weeks and is designed to inform students about a faculty member s research program Assignment as a research assistant may be used as one practicum This course should be taken during the first year May be taken for credit three times Prerequisites admission to MSED Joint Doctoral Program S U grades only MSED 296A Theories and Applications of Mathematics and Science Education 4 The course is designed to cover several major themes in mathematics and science education It will address theories and applications of cognition teaching and learning and curriculum with particular emphasis on international perspectives This is a three quarter sequence Prerequisites admission to the Joint Doctoral Program in Mathematics and Science Education or a master s degree in biology chemistry biochemistry mathematics or physics with consent of instructor MSED 296B Theories and Applications of Mathematics and Science Education 4 The course is designed to cover several major themes in mathematics and science education It will address theories and applications of cognition teaching and learning and curriculum with particular emphasis on international perspectives This is a three quarter sequence Prerequisites admission to the Joint Doctoral Program in Mathematics and Science Education or a master s degree in biology chemistry biochemistry mathematics or physics with consent of instructor MSED 296A must be taken before MSED 296B MSED 296C Theories and Applications of Mathematics and Science Education 4 The course is designed to cover several major themes in mathematics and

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  • Mathematics and Science Education Faculty
    Academic Senate website http senate ucsd edu catalog copy approved updates Professors Mark I Appelbaum Psychology Paul M Churchland Philosophy Michael Cole Communication Guershon Harel Mathematics Barbara Jones Emerita Physics Douglas Magde Chemistry and Biochemistry Hugh B Mehan Sociology Jeffrey Rabin Mathematics Jeffrey Remmel Mathematics Douglas W Smith Emeritus Biological Sciences Senior Lecturers with Security of Employment Barbara A Sawrey Chemistry and Biochemistry Randall J Souviney Emeritus Education Studies Program

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  • Middle East Studies
    ancient medieval or modern Middle East or a three quarter minimum 12 credits sequence of a Middle Eastern language in which case only four of the seven courses need to be upper division Ordinarily all seven courses must be taken for a letter grade The courses that make up the minor must be approved by the student s college and by the Middle East Studies Program Approved courses taken at other universities or through participation in the Education Abroad Program can be included as part of the minor by petition Courses For course descriptions not found in the UC San Diego General Catalog 2014 15 please contact the department for more information Core Courses ANTH 199 Independent Study Middle East Anthropology ANSC 133 Peoples and Culture of the Middle East HINE 108 The Middle East before Islam HINE 114 History of the Islamic Middle East HINE 116 The Middle East in the Age of European Empires HINE 118 The Middle East in the Twentieth Century HINE 119 United States Mideast Policy HINE 126 Iranian Revolution in Historical Perspective HINE 127 History of Modern Turkey HINE 166 Nationalism in the Middle East HINE 186 Special Topics in Middle Eastern History HINE 199 Independent Study in Near Eastern History HITO 105 Jews and Judaism in the Modern World LTWL 141 Islam and Modernity LTWL 160 Women in Literature Arabic Women in Literature and Society POLI 121 Government and Politics of the Middle East POLI 138D Special Topics Comparative Polities The Arab Israeli Conflict SOCI 158 Islam in the Modern World SOCI 188F Modern Jewish Societies and Israeli Society SOCI 199 Independent Study Middle East Sociology TWS 25 Middle Eastern Literatures Supporting Courses ANAR 140 Foundations Social Complex Near East ANAR 141 Prehistory of the Holy Land JUDA 1 Beginning Hebrew JUDA 2

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