Mathematics
Back To TopMathematics Courses
Back To TopFor Lower-Division Undergraduates
These courses are not open to graduate students except by special arrangement with the department chair. Credit earned in 22M:001 Basic Algebra I, 22M:002 Basic Algebra II, and 22M:003 Basic Geometry does not count toward degree requirements.
Although the sequences 22M:025 Calculus I and 22M:026 Calculus II, and 22M:031 Engineering Mathematics I: Single Variable Calculus and 22M:032 Engineering Mathematics II: Multivariable Calculus are similar, they cover the material in a different order and with different emphases. Students must consult with their advisor before taking the second semester of one sequence after taking the first semester of another. Students who consider taking 22M:026 Calculus II after 22M:016 Calculus for the Biological Sciences or 22M:017 Calculus and Matrix Algebra for Business must consult with their advisor.
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22M:001 Basic Algebra I | 3 s.h. | | Percents, ratio and proportion, algebraic expressions and operations, simple products, linear and quadratic equations, simultaneous equations, exponents and radicals; emphasis on verbal problems. | | |
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22M:002 Basic Algebra II | 3 s.h. | | Algebraic techniques, equations and inequalities, functions and graphs, exponential and logarithmic functions, systems of equations and inequalities. Prerequisite: 22M:001 or satisfactory score on math placement exam or one year of high school algebra. | | |
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22M:003 Basic Geometry | 3 s.h. | | Angles, triangles, polygons, areas, Pythagorean theorem, similar triangles, circles, loci, related topics. Offered spring semesters. Prerequisite: 22M:001 or satisfactory score on math placement exam or one year of high school algebra. | | |
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22M:005 Trigonometry | 3 s.h. | | Trigonometric functions, solutions of right and oblique triangles, complex numbers. Prerequisite: 22M:002, or satisfactory score on math placement exam, or two years of high school algebra and one year of high school geometry. | | |
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22M:006 Logic of Arithmetic | 3 s.h. | | Mathematical and conceptual foundations of the natural numbers used in elementary school arithmetic teaching; multiple algorithmic approaches to arithmetic and its mathematical and contextual relationships, extensions to integers, rational and irrational numbers, multiple representations. Prerequisite: 22M:001 or satisfactory score on math placement exam or equivalent or consent of instructor. GE: Quantitative or Formal Reasoning. | | |
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22M:009 Elementary Functions | 4 s.h. | | Functions, relations, coordinate systems; properties and graphs of algebraic, trigonometric, logarithmic, exponential functions; inverse trigonometric functions; properties of lines, conic sections. Prerequisite: 22M:005, or satisfactory score on math placement exam, or two years of high school algebra and one year of high school geometry. GE: Quantitative or Formal Reasoning. | | |
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22M:010 Finite Mathematics | 4 s.h. | | Introduction to logic, set theory, linear equations and inequalities, linear programming, matrix algebra, combinatorial probability. Prerequisite: 22M:002 or satisfactory score on math placement exam or two-and-a-half years of high school mathematics. GE: Quantitative or Formal Reasoning. | | |
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22M:012 Theory of Arithmetic | 3 s.h. | | Sets, cardinalities, reasoning in proofs, counterexamples, arithmetic with integers, rationals, irrationals, number theory, functions, algebraic expressions. Prerequisite: 22M:009 or a more advanced course or satisfactory score on math placement exam or equivalent or consent of instructor. GE: Quantitative or Formal Reasoning. | | |
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22M:013 Mathematics for Business | 4 s.h. | | Algebraic techniques, functions and functional models, exponential and logarithmic functions and models, linear programming, informal introduction to calculus; examples and applications from management, economic sciences, related areas. Prerequisites: 22M:002, or satisfactory score on math placement exam, or two years of high school algebra and one year of high school geometry. GE: Quantitative or Formal Reasoning. | | |
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22M:014 First-Year Seminar | 1 s.h. | | Small discussion class taught by a faculty member; topics chosen by instructor; may include outside activities (e.g., films, lectures, performances, readings, visits to research facilities). Prerequisite: first- or second-semester standing. | | |
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22M:015 Mathematics for the Biological Sciences | 4 s.h. | | Relations, functions, coordinate systems, graphing, polynomials, trigonometric functions, logarithmic and exponential functions; discrete mathematics, probability; examples and applications from biological sciences. Prerequisite: 22M:002 or satisfactory score on math placement exam or three years of high school mathematics. GE: Quantitative or Formal Reasoning. | | |
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22M:016 Calculus for the Biological Sciences | 4 s.h. | | Differential, integral calculus; differential equations, multivariable calculus; applications to life sciences. Prerequisite: 22M:015; or satisfactory score on math placement exam; or three and one-half years of high school mathematics, including trigonometry. GE: Quantitative or Formal Reasoning. | | |
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22M:017 Calculus and Matrix Algebra for Business | 4 s.h. | | Quantitative methods for treating problems arising in management, economic sciences, related areas; introduction to differential and integral calculus, systems of linear equations and matrix operations. Prerequisite: 22M:002 or 22M:013 or satisfactory score on math placement exam. GE: Quantitative or Formal Reasoning. | | |
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22M:025 Calculus I | 4 s.h. | | Fundamental concepts, methods, techniques of single-variable differential and integral calculus; differentiation, techniques of integration, series, applications. Prerequisite: 22M:009; or 22M:002 and 22M:005; or three and one-half years of high school mathematics, including analytic geometry and trigonometry. GE: Quantitative or Formal Reasoning. | | |
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22M:026 Calculus II | 4 s.h. | | Continuation of 22M:025. Prerequisite: 22M:025 or consent of advisor. | | |
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22M:027 Introduction to Linear Algebra | 4 s.h. | | Vector algebra and geometry of three-dimensional Euclidean space and extensions to n-space and vector spaces; lines and planes, matrices, linear transformations, systems of linear equations, reduction to row echelon form, dimension, rank, determinants, eigenvalues and eigenvectors. Prerequisite: 22M:025 or 22M:031 or consent of instructor. | | |
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22M:028 Calculus III | 4 s.h. | | Multivariable calculus; vector functions, line integrals, total differentials, gradient, implicit functions, coordinate systems, Taylor's expansion, extrema, multiple integrals, vector fields, surface integrals, Stokes' theorem. Prerequisite: 22M:026 or consent of instructor. | | |
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22M:031 Engineering Mathematics I: Single Variable Calculus | 4 s.h. | | Limits, derivatives, max/min, other applications, mean-value theorem, approximating functions, concavity, curve sketching, exponential models; Riemann sums, fundamental theorem; integration techniques, improper integrals, approximations. Prerequisite: 22M:005 or 22M:009; or three and one-half years of high school mathematics, including introduction to analytic geometry and trigonometry. GE: Quantitative or Formal Reasoning. | | |
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22M:032 Engineering Mathematics II: Multivariable Calculus | 4 s.h. | | Vector geometry; functions of several variables; polar coordinates; partial derivatives, gradients, directional derivatives; tangent lines and planes; max/min/parametric curves, curvilinear motion; multiple integrals; vector fields, flows; integration on curves, work; divergence, flux, Green's theorem. Prerequisite: 22M:031, or score of 4 or higher on AP Calc (AB) exam, or score of 3 or higher on AP Calc (BC) exam, or consent of instructor. | | |
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22M:033 Engineering Mathematics III: Matrix Algebra | 2 s.h. | | Applications, computers for matrix calculations; matrix, vector arithmetic; linear independence, basis, subspace (in R2, R3); systems of equations, matrix reduction; rank, dimension; determinants, applications; eigenvalues, eigenvectors; diagonalization, principal axis theorem. Prerequisites: 22M:031, and engineering major or consent of department chair. | | |
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22M:034 Engineering Mathematics IV: Differential Equations | 3 s.h. | | Ordinary differential equations and applications, with integrated use of computing, student projects; first-order equations; higher order linear equations; systems of linear equations, Laplace transforms; introduction to nonlinear equations and systems, phase plane, stability. Prerequisites: 22M:032, 22M:033, and engineering major or consent of department chair. | | |
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22M:037 Engineering Mathematics V: Vector Calculus | 3 s.h. | | Partial derivatives, max-min problems, integrals along curves, surfaces and solids, vector fields and conservation of energy; curl, divergence, Stokes' theorem and the divergence theorem; the classical partial differential equations and qualitative behavior of their solutions. Prerequisites: 22M:034 or consent of instructor, and engineering major or consent of department chair. | | |
Back To TopElementary Topics of General Interest
These courses are not open to graduate students except by special arrangement with the department chair.
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22M:050 Introduction to Abstract Algebra I | 3 s.h. | | Basic logic, proof methods, sets, functions, relations, mathematical induction; gradual transition from familiar number systems to abstract structures--division algorithm, unique factorization theorems; groups, subgroups, quotient groups, homomorphisms. Prerequisite: 22M:027. Corequisite: second-semester calculus or consent of instructor. | | |
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22M:055 Fundamental Properties of Spaces and Functions I | 3 s.h. | | Elementary topological and analytic properties of real numbers; emphasis on ability to handle definitions, theorems, proofs. Prerequisite: second-semester calculus. Corequisite: 22M:027 or consent of instructor. | | |
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22M:056 Fundamental Properties of Spaces and Functions II | 4 s.h. | | Multivariable analysis; Bolzano-Weierstrass theorem in three-dimensional Euclidean space, differential calculus, inverse and implicit function theorems, multiple integrals, surface and line integrals, differential forms and Stokes' theorem in n-dimensional Euclidean space. Prerequisites: 22M:055; closed to students who have taken 22M:028. | | |
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22M:070 Foundations of Geometry | 3 s.h. | | Axiomatic development of common foundation for Euclidean, non-Euclidean geometry; constructions of non-Euclidean models, independence of parallel postulate. Prerequisite: 22M:026 or equivalent. | | |
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22M:072 Elementary Numerical Analysis | 3 s.h. | | Computer arithmetic, root finding, polynomial approximation, numerical integration, systems of linear equations, ordinary differential equations; use of higher-level computer language such as Matlab, Maple, Mathematica. Prerequisite: grade of C- or higher in 22M:026 or 22M:032. Same as 22C:072. | | |
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22M:081 Geometry for Elementary Teachers | 3 s.h. | | Points, lines, planes; measurement, two- and three-dimensional coordinate geometry, transformational geometry and vectors; applications of geometry to solve real-world problems. Offered spring semesters. Prerequisites: 22M:001 or equivalent, and elementary teacher certificate candidacy or certification. | | |
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22M:095 Introduction to Research Opportunities | 1 s.h. | | Modern mathematics research areas and activities; seminar. Prerequisite: 22M:027 or consent of instructor. | | |
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22M:096 Introduction to Mathematics Research | 3 s.h. | | Research experience; students study an elementary topic of active research, then work in groups under faculty supervision. Prerequisites: 22M:026 and 22M:027, or consent of instructor. | | |
Back To TopFor Upper-Division Undergraduates
Graduate students in mathematics may not receive credit for 22M:100 Introduction to Ordinary Differential Equations, 22M:104 Introduction to Matrix Theory, 22M:105 Basic Analysis, or 22M:109 Classical Analysis.
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22M:100 Introduction to Ordinary Differential Equations | 2-3 s.h. | | First-order ordinary differential equations; second-order linear differential equations; series solutions; higher-order linear and matrix differential equations; existence and uniqueness theorems. Prerequisites: 22M:027 and 22M:028, or 22M:056 or equivalent; or consent of instructor. | | |
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22M:104 Introduction to Matrix Theory | 3 s.h. | | Vector algebra and geometry of three-dimensional Euclidean space and extensions to n-space and vector spaces; lines and planes, matrices, linear transformations, systems of linear equations, reduction to row-echelon form, dimension, rank, determinants, eigenvalues, eigenvectors. Prerequisite: graduate standing. | | |
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22M:105 Basic Analysis | 3 s.h. | | Elementary topological and analytical properties of real numbers; emphasis on ability to handle definitions, theorems, proofs; same material as 22M:055 for non-mathematics graduate students. Prerequisites: graduate standing, one year of calculus, and one semester of linear algebra. | | |
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22M:107 History of Mathematics | 3 s.h. | | May include numerical systems; Babylonian, Egyptian, and Greek mathematics; mathematics of other cultures; calculus; 19th- and 20th-century mathematics. Prerequisites: two semesters of calculus and one semester of linear algebra, or consent of instructor. | | |
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22M:108 Philosophy of Mathematics | 3 s.h. | | Role of formalism, intuitionism, logicism, Platonism in shaping foundations of mathematics; nature of mathematical existence and truth; Godel's incompleteness theorems; axiom of choice; philosophical differences between various set theories (e.g., Zermelo-Fraenkel, Godel-von Neumann), category theory, other viable foundations of mathematics; relationship between mathematics, science. Prerequisites: two semesters of calculus, and 22M:027 or equivalent; or consent of instructor. | | |
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22M:109 Classical Analysis | 3 s.h. | | Multivariable calculus, vector functions, line integral, total differentials, gradient, implicit functions, coordinate systems, Taylor's expansion, extrema, multiple integrals, vector fields, surface integrals, Stoke's theorem. Prerequisites: graduate standing, and one year of calculus or consent of instructor. | | |
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22M:115 Introduction to Analysis I | 3 s.h. | | Real numbers, fundamentals of limits and continuity in the context of metric spaces; Lebesque theory of functions of one real variable. Prerequisite: 22M:055 or graduate standing or consent of instructor. | | |
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22M:116 Introduction to Analysis II | 3 s.h. | | Local theory of analytic functions of one complex variable, power series, classical transcendental functions; spaces of functions. Prerequisite: 22M:115 or consent of instructor. | | |
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22M:118 Complex Variables | 3 s.h. | | Geometry of complex plane, analytic functions; Cauchy-Goursat theorem, applications; Laurent series, residues, elementary conformal mapping. Prerequisite: 22M:028 or 22M:056 or 22M:109 or equivalent or consent of instructor. | | |
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22M:120 Abstract Algebra I | 3 s.h. | | Groups and homomorphisms, Sylow Theorems, rings, finitely generated modules over a PID, Galois theory, vector spaces, linear transformations and matrices, canonical forms. Prerequisite: 22M:050 or equivalent or consent of instructor. | | |
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22M:121 Abstract Algebra II | 3 s.h. | | Continuation of 22M:120. Prerequisite: 22M:120. | | |
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22M:123 Foundations of Set Theory | 3 s.h. | | Set theory as used in abstract mathematics; equivalent forms of axiom of choice, cardinal numbers and their arithmetic, ordinal numbers and transfinite induction. Prerequisite: 22M:050 or 22M:055 or graduate standing or consent of instructor. | | |
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22M:124 Foundations of Logic | 3 s.h. | | Propositional calculus, Boolean algebras, introduction to axiomatic theories. Prerequisite: 22M:050 or 22M:055 or graduate standing or consent of instructor. | | |
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22M:125 Master's Comprehensive Exam Preparation Seminars | 0 s.h. | | Exam preparation in pure and applied mathematics. Prerequisite: consent of instructor. | | |
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22M:126 Elementary Theory of Numbers | 2-3 s.h. | | Factorization, congruence, Diophantine equations, law of quadratic reciprocity. Prerequisite: 22M:050 or equivalent or consent of instructor. | | |
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22M:127 Matrix Theory | 3 s.h. | | Vector spaces, linear transformations, matrices, equivalence of matrices, eigenvalues and eigenvectors, canonical forms, similarity, orthogonal transformations, bilinear and quadratic forms. Prerequisite: 22M:027 or 22M:104 or equivalent or consent of instructor. | | |
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22M:132 General Topology | 3 s.h. | | Basic concepts of general topological spaces and continuous functions: countability of sets, topological space, comparing topologies; subspace, order, and product topologies; closed sets and limit points, continuous functions, metric topology, quotient topology (including projective spaces and gluing cells), connectedness in the real line and in general spaces, components and local connectedness, compactness in Euclidean and general spaces, limit point compactness, local compactness, countability axioms, separation axioms, normal spaces and Urysohn's Lemma, complete metric spaces, convergence in function spaces. Prerequisite: 22M:055 or consent of instructor. | | |
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22M:133 Introduction to Smooth Manifolds | 3 s.h. | | Calculus on smooth manifolds; smooth functions, mean value theorem, chain rule, smooth manifolds, tangent vectors, tangent spaces, inverse and implicit functions theorems, submersions and immersions, vectorfields, flows, multilinear algebra, differential forms, Stokes theorem. Prerequisites: 22M:027, 22M:055, and 22M:028 or 22M:056 or consent of instructor. | | |
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22M:140 Continuous Mathematical Models | 3 s.h. | | Building and analyzing mathematical models involving differential equations for specific problems from engineering and the sciences; modeling project. Prerequisite: 22M:100 or equivalent or consent of instructor. | | |
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22M:142 Nonlinear Dynamics with Numerical Methods | 3 s.h. | | Nonlinear differential equations, one- and two-dimensional flows, stability, phase plane analysis, limit cycles, bifurcations, chaos, fractals; Euler's, multistep, and Runge-Kutta numerical methods. Prerequisites: 22M:055 and 22M:100, or consent of instructor. | | |
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22M:144 Partial Differential Equations with Numerical Methods | 3 s.h. | | Conservation laws, weak solutions, diffusion equation, Laplace's equation, finite difference methods, variational methods, finite element method. Prerequisite: 22M:028, 22M:055, and 22M:100 or consent of instructor. | | |
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22M:150 Introduction to Discrete Mathematics | 3 s.h. | | Basic methods of enumerative combinatorics, inclusion-exclusion and generating functions, applications of group theory (Polya-Burnside theorem). Offered fall semesters. Prerequisite: 22M:050 or equivalent or consent of instructor. | | |
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22M:151 Discrete Mathematical Models | 3 s.h. | | Case history approach to discrete models from various fields (e.g., genetics, psychology, health care, scheduling); construction, interpretation, analysis, simulation, testing of models; development of discrete mathematics. Prerequisite: 22M:027 or equivalent or consent of instructor. | | |
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22M:152 Theory of Graphs | 3 s.h. | | Connectivity properties, including Euler, Hamilton cycle problems; graph colorings, matchings; characterization of families of graphs such as trees, planar graphs, networks; graph algorithms, their applications. Prerequisite: 22M:050 or equivalent or consent of instructor. Same as 22C:137. | | |
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22M:160 Introduction to Differential Geometry I | 3 s.h. | | Space curves, differentiable manifolds, vector and tensor fields, integration of forms, covariant differentiation, intrinsic geometry of surfaces. Prerequisites: 22M:028 and 22M:055, or 22M:056 or 22M:100 or equivalent or consent of instructor. | | |
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22M:161 Introduction to Differential Geometry II | 3 s.h. | | May include Riemannian geometry, rigidity theorems, minimal surfaces, connections, elementary Lie groups, relativity. Prerequisite: 22M:160 or equivalent or consent of instructor. | | |
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22M:170 Numerical Analysis: Nonlinear Equations and Approximation Theory | 3 s.h. | | Root finding for nonlinear equations; polynomial interpolation; polynomial approximation of functions; numerical integration. Prerequisites: 22M:027 and 22M:028, or 22M:037 or 22M:056 or equivalent or consent of instructor; and knowledge of computer programming. Same as 22C:170. | | |
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22M:171 Numerical Analysis: Differential Equations and Linear Algebra | 3 s.h. | | Numerical methods for initial value problems for ordinary differential equations; direct and iterative methods for linear systems of equations; eigenvalue problems for matrices. Prerequisites: 22M:027 and 22M:028; or 22M:037 or 22M:056 or equivalent or consent of instructor; knowledge of computer programming; and 22M:100. Same as 22C:171. | | |
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22M:174 Optimization Techniques | 3 s.h. | | Basic theory of optimization, use of numerical algorithms in solution of optimization problems; linear and nonlinear programming, sensitivity analysis, convexity, optimal control theory, dynamic programming, calculus of variations. Prerequisites: 22M:027, 22M:028 or 22M:056, and 22M:072 or equivalent; or consent of instructor. Same as 22C:174. | | |
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22M:178 High Performance and Parallel Computing | 3 s.h. | | Parallel scientific computing methods such as parallel algorithms for dense and sparse matrices; implementation using libraries such as MPI; current topics such as grid computing. Prerequisites: a linear algebra course or a numerical analysis course, and a programming language. Same as 22C:177. | | |
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22M:191 Topics in Technology Uses in Mathematics | 2 s.h. | | Prerequisite: consent of instructor. | | |
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22M:195 Current Issues in Mathematics Education | 1-3 s.h. | | Recent curriculum developments, experimental programs, research relevant to classroom instruction, trends in education that may have a significant impact on mathematics programs. Same as 07E:235, 07S:235. | | |
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22M:196 Topics in Mathematics | arr. | | Prerequisite: consent of instructor. | | |
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22M:197 Individual Study and Honors in Mathematics | arr. | | Prerequisite: consent of advisor. | | |
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22M:199 Readings in Mathematics | arr. | | Prerequisite: consent of instructor. | | |
Back To TopCore Graduate Courses
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22M:200 Introduction to Differential Topology | 3 s.h. | | Manifolds, functions: tangent bundle, Morse-Sard theorem, transversality, submanifolds, tubular neighborhoods, normal bundles, vector fields, degree and intersection theory, fixed-point theory, Morse theory. Prerequisite: 22M:133 or equivalent or consent of instructor. | | |
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22M:201 Introduction to Algebraic Topology | 3 s.h. | | Homotopy, fundamental group and covering spaces, CW and simplicial complexes, simplicial homology, Euler characteristic. Prerequisite: 22M:132 or equivalent or consent of instructor. | | |
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22M:203 Topology of Manifolds | 3 s.h. | | Embedding, knotting, immersions; isotopy, homotopy, regular neighborhoods, engulfing, surgery, cobardism; three-, four-, and higher dimensional manifolds. Prerequisites: 22M:200 and 22M:201, or equivalents or consent of instructor. | | |
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22M:205 Introduction to Algebra I | 3 s.h. | | Abstract algebra: semigroups, groups, rings, integral domains, polynomial rings, division rings, fields, vector spaces, matrices, modules over rings, lattices, categories. Prerequisite: 22M:120 or equivalent or consent of instructor. | | |
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22M:206 Introduction to Algebra II | 3 s.h. | | Continuation of 22M:205. Prerequisite: 22M:205 or equivalent or consent of instructor. | | |
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22M:210 Analysis I | 3 s.h. | | Lebesque measure and integral, fundamental theorem of calculus, abstract measures and integration, Fubini's theorem, Radon-Nikodym theorem, Riesz representation theorem, L-p spaces. Prerequisite: 22M:116 or equivalent or consent of instructor. | | |
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22M:211 Analysis II | 3 s.h. | | Hilbert space, Banach space techniques; Hahn-Banach theorem, open mapping theorem, principle of uniform boundedness; reflexivity, H-p spaces, Paley-Wiener theorem, space of functions analytic on the open unit disk. Prerequisites: 22M:118 and 22M:210, or equivalents or consent of instructor. | | |
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22M:213 Ordinary Differential Equations I | 3 s.h. | | Existence, uniqueness, continuous dependence of solutions to initial value problems, autonomous systems; Poincare-Bendixon theory, linear systems and linearizations, perturbation, stability, periodic solutions, bifurcation, comparison and oscillation theorems, boundary value problems. Prerequisite: 22M:116 or equivalent or consent of instructor. | | |
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22M:214 Ordinary Differential Equations II | 3 s.h. | | Continuation of 22M:213. Prerequisite: 22M:213 or equivalent or consent of instructor. | | |
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22M:216 Partial Differential Equations I | 3 s.h. | | Eliptic equations; potential theory, maximum principle, a priori estimate, Dirichlet problem; initial value problem for parabolic equations; hyperbolic equations; Duhamel's principle, Cauchy problem; nonlinear equations, characteristics, canonical form, first-order systems. Prerequisite: 22M:116 or equivalent or consent of instructor. | | |
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22M:217 Partial Differential Equations II | 3 s.h. | | Continuation of 22M:216. Prerequisite: 22M:216 or equivalent or consent of instructor. | | |
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22M:220 Introduction to Mathematical Logic I | 3 s.h. | | Propositional calculus, first-order predicate calculus, GWdel completeness theorem, formal elementary number theory, GWdel incompleteness theorem. Prerequisite: graduate standing or consent of instructor. | | |
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22M:221 Introduction to Mathematical Logic II | 3 s.h. | | Formal number theory, arithmetic hierarchy, Post theorem, formal recursive functions, Turing machines, Thu systems, world problems. Prerequisite: 22M:220 or equivalent or consent of instructor. | | |
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22M:224 First-Year Graduate Seminar | 1 s.h. | | Introduction to mathematics graduate program. Prerequisite: first-year math graduate student. | | |
Back To TopPrimarily for Graduate Students
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22M:260 Differential Geometry I | 3 s.h. | | Differential manifolds and functions, form, connections, curvature, related topics. Prerequisite: consent of instructor. | | |
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22M:261 Differential Geometry II | 3 s.h. | | Continuation of 22M:260. Prerequisite: 22M:260 or equivalent or consent of instructor. | | |
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22M:270 Theoretical Numerical Analysis I | 3 s.h. | | Theoretical foundations of numerical analysis, within framework of functional analysis; application areas including approximation theory, numerical methods for partial differential equations, integral equations; introduction to functional analysis. Prerequisites: 22M:115, 22M:116, 22M:170, and 22M:171; or equivalents; or consent of instructor. | | |
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22M:271 Theoretical Numerical Analysis II | 3 s.h. | | Continuation of 22M:270. Prerequisite: 22M:270 or equivalent or consent of instructor. | | |
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22M:280 Introduction to Financial Mathematics | 2-3 s.h. | | Financial mathematics; option pricing and portfolio optimization, stochastic integration, methods due to Ito and Feynman-Kac, Monte-Carlo simulation. Prerequisite: 22M:210 or equivalent or consent of instructor. | | |
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22M:303 Topics in Analysis | 2-3 s.h. | | Measure theory, integration, general topology. Repeatable. Prerequisite: consent of instructor. | | |
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22M:305 Topics in Topology | 2-3 s.h. | | May include homotopy theory, topology of 3-manifolds, 4-manifolds, or higher-dimensional manifolds, knotting and embedding problems, fiber bundles and characteristic classes, K-theory, PL manifolds, infinite-dimensional manifolds. Repeatable. Prerequisite: consent of instructor. | | |
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22M:313 Functional Analysis I | 2-3 s.h. | | Locally convex topological vector spaces, duality, tensor products and nuclear spaces; Krein-Millman theorem, Choquet's theory; geometry of Banach spaces, nonlinear functional analysis; operators on Hilbert spaces, spectral theorem, algebras of operators. Prerequisite: 22M:211 or equivalent or consent of instructor. | | |
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22M:314 Functional Analysis II | 2-3 s.h. | | Continuation of 22M:313. Prerequisite: 22M:313 or equivalent or consent of instructor. | | |
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22M:321 Topics in Applied Mathematics | arr. | | Application of mathematics to other disciplines. Repeatable. Prerequisite: consent of instructor. | | |
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22M:324 Topics in Partial Differential Equations | 2-3 s.h. | | Regularity theory, nonlinear analysis in partial differential equations, fluid dynamics, harmonic analysis, conservation laws, other topics. Repeatable. Prerequisite: consent of instructor. | | |
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22M:328 Topics in Logic | 2-3 s.h. | | Theory of models, recursive functions, sets, deductions. Repeatable. Prerequisite: 22M:221 or equivalent or consent of instructor. | | |
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22M:330 Topics in Algebra | 2-3 s.h. | | May include algebraic number theory, groups, representation theory, algebras, ideal theory, lattice theory. Repeatable. Prerequisite: 22M:206 or equivalent or consent of instructor. | | |
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22M:340 Homological Algebra | 2-3 s.h. | | Modules, tensor products, groups of homomorphisms, categories, functors, homology functors, projective and injective modules, derived functors, torsion and extension functors, homological dimension. Prerequisite: 22M:206 or equivalent or consent of instructor. | | |
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22M:360 Topics in Mathematical Biology | 2-3 s.h. | | Application of mathematics to biology. Prerequisite: consent of instructor. | | |
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22M:383 Seminar: Commutative Ring Theory | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:384 Seminar: Fourier Analysis | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:385 Seminar: Representation Theory | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:386 Seminar in Undergraduate Mathematics Education | arr. | | Varied topics in teaching, learning, curriculum; philosophy, objectives, strategies, methods; use of technology, group learning, projects, discovery method, multiple approaches, other current issues. Repeatable. Prerequisite: consent of instructor. | | |
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22M:387 Seminar: Differential Geometry | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:389 Seminar: Algebra | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:390 Seminar: Operator Theory | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:391 Seminar: Logic and Foundations of Mathematics | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:392 Seminar: Topology | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:393 Seminar: Mathematical Physics | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:394 Seminar: Mathematical Biology | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:395 Seminar: Analysis | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:396 Seminar: Functional Analysis | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:397 Seminar: Partial Differential Equations | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:398 Seminar: Numerical Analysis | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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22M:399 Reading Research | arr. | | Repeatable. Prerequisite: consent of instructor. | | |
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