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MATH Mathematics( Computer, Mathematical and Physical Sciences) MATH003 Developmental Mathematics; (3 credits) Grade Method: S-F.Recommended: For students who plan to take MATH110, MATH111, MATH113, MATH115 or STAT100, but are not currently qualified to do so. MATH 003 is a review of Intermediate High School Algebra intended for students preparing for one of the credit bearing Fundamental Studies Math Courses. It is taught in special computer labs using a self-paced computer program. The curriculum will be geared toward the student's level of algebra skills and eventual goals. The course does not carry any credit toward any degree at the University. The course is repeatable. Topics will be chosen from exponents, polynomials, linear equations, quadratic equations as well as polynomial, rational, exponential and logarithm functions and elementary probability or statistics, depending on the student. For the Fall and Spring semesters, there is a special fee of $230 for the course in addition to the regular tuition charge. During the Winter term the $230 fee is assessed in addition to mandatory fees; in the Summer terms only the $230 fee is assessed.
MATH 010, MATH 011, MATH 013 and MATH 015 are preparation courses for MATH 110, MATH 111, MATH 113 and MATH 115 respectively, and meet only for the first 5 weeks of the semester. Special sections of MATH 110, MATH 111, MATH 113 and MATH 115 will begin at this point and the student will automatically be enrolled in the course, provided he/she passes the Placement Exam for that course at the end of the 5 week period. If the Placement Exam is not passed at this point, the student will be placed in MATH 003. There will be a fee for these courses, the same as for MATH003. For the students who move into MATH 003 from MATH 010, MATH 011, MATH 013 or MATH 015, no new fee will be charged.
MATH010
Algebra for MATH 110;
(3 credits)
Grade Method: REG/P-F/AUD.
MATH011 Algebra for MATH 111; (3 credits) Grade Method: REG/P-F/AUD. There is a special fee for this class in addition to the regular tuition charge. A review of Intermediate High School Algebra intended for students preparing for MATH 111. It is taught 5 days per week for the first 5 weeks, then leads directly into a special section of MATH 111, the same semester, which also meets 5 days per week. Continuation in MATH 111 is conditional on the student passing the MATHEMATICS PLACEMENT EXAM at the appropriate level. Topics include exponents, polynomials, linear equations, quadratic equations, as well as polynomial, rational, exponential and logarithm functions, Venn diagrams, permutations and combinations. MATH 011 does not carry any credit toward any degree at the University, nor is it graded. It leads directly to MATH 111 (or MATH 113 or MATH 110), or MATH 003, all of which are graded. MATH013 Algebra for MATH 113; (3 credits) Grade Method: REG/P-F/AUD. There is a special fee for this class in addition to the regular tuition charge. A review of Intermediate High School Algebra intended for students preparing for MATH 113. It is taught 5 days per week for the first 5 weeks, then leads directly into a special section of MATH 113, the same semester, which also meets 5 days per week. Continuation in MATH 113 is conditional on the student passing the MATHEMATICS PLACEMENT EXAM at the appropriate level. Topics include exponents, polynomials, linear equations, quadratic equations, as well as polynomial, rational, exponential and logarithm functions. MATH 013 does not carry any credit toward any degree at the University, nor is it graded. It leads directly to MATH 113 (or MATH 110), or MATH 003, all of which are graded. MATH015 Algebra for MATH 115; (3 credits) Grade Method: REG/P-F/AUD. There is a special fee for this class in addition to the regular tuition charge. A review of Intermediate High School Algebra intended for students preparing for MATH 115. It is taught 5 days per week for the first 5 weeks, then leads directly into a special section of MATH 115, the same semester, which also meets 5 days per week. Continuation in MATH 115 is conditional on the student passing the MATHEMATICS PLACEMENT EXAM at the appropriate level. Topics include exponents, polynomials, linear equations in one and two variables, quadratic equations, as well as polynomial, rational, exponential and logarithm functions. MATH 015 does not carry any credit toward any degree at the University, nor is it graded. It leads directly to MATH 115 (or MATH 111 or MATH 113 or MATH 110), or MATH 003, all of which are graded. MATH110 Elementary Mathematical Models; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: permission of department based on satisfactory score on the MATHEMATICS PLACEMENT EXAM, or satisfactory completion of MATH003 with the appropriate eligibility. Not open to students majoring in mathematics, engineering, business, life sciences, and the physical sciences. Not open to students who have completed MATH 140, MATH 220, or any MATH or STAT course for which MATH 140 or MATH 220 is a prerequisite. Credit will be granted for only one of the following: MATH110, MATH112, or MATH113. Topics include simple and compound interest; recursion for computing balances; installment loans and amortization; approximating data by linear models; analysis of applications to real-world collections of data; probability; conditional probability; independence; expected value; graphing and analysis of systems of inequalities; linear programming and applications. All sections will require the use of a TI graphics calculator. Instructor will use a TI83 or TI83+ calculator. MATH111 Introduction to Probability; (3 credits) Grade Method: REG/P-F/AUD. CORE Mathematics or Formal Reasoning (MS) Course. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisite: permission of department based on satisfactory score on the MATHEMATICS PLACEMENT EXAM, or satisfactory completion of MATH 003 with the appropriate eligibility or MATH110. Not open to students majoring in mathematics, engineering or the physical sciences. Not open to students who have completed STAT100 or any MATH or STAT course with a prerequisite of MATH141. Credit will be granted for only one of the following: MATH111 or STAT100. Logic, Boolean algebra, counting, probability, random variables, expectation applications of the normal probability distribution. MATH112 College Algebra with Applications and Trigonometry; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: permission of department, based on math placement exam or MATH003 performance. Not open to students who have completed MATH140 or MATH220 or any course for which MATH140 or MATH220 is a p rerequisite. Credit will be granted for only one of the following: (i) MATH112, or (ii) MATH113, or (iii) (MATH110 and MATH115). Graphs and applications of elementary functions, including polynomial, rational, exponential and logarithmic functions. Systems of equations. Triangle trigonometry. The course differs from MATH 113 only in that it covers a substantial amount of trigonometry in place of material on matrices, linear programming, sequences and series. MATH 112 is strongly recommended for students in Architecture, Landscape Architecture, Life Sciences, and those needing PHYS 141. MATH113 College Algebra with Applications; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: permission of department based on satisfactory score on the MATHEMATICS PLACEMENT EXAM, or satisfactory completion of MATH003 with the appropriate eligibility or MATH110. Not open to students who have completed MATH140, MATH220, or any course for which MATH140 or MATH220 is a prerequisite. Credit will be granted for only one of the following: MATH112; or MATH113; or (MATH110 and MATH115). Preparation for MATH220. Graphs and applications of elementary functions including: polynomial, rational, exponential and logarithmic functions. Systems of linear equations and linear inequalities used to solve representative problems in linear programming. Matrices and matrix operations including inverse. Sequences. All sections will require the use of a TI graphics calculator. Instructor will use a TI-83 or a TI-83+ calculator. MATH115 Precalculus; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: permission of department based on satisfactory score on the MATHEMATICS PLACEMENT EXAM, or satisfactory completion of MATH003 with the appropriate eligibility, or MATH113. Not open to students who have completed MATH140 or any MATH or STAT course for which MATH140 is a prerequisite. Credit will be granted for only one of the following: MATH113 or MATH115. Preparation for MATH 220 or MATH 140. Elementary functions and graphs: polynomials, rational functions, exponential and logarithmic functions, trigonometric functions. Algebraic techniques preparatory for calculus. Preparation for MATH220 or MATH140. All sections will require the use of a TI graphics calculator. Instructor will use a TI-83 or a TI-83+ calculator. If purchasing used books additional software may be required. This can be purchased on the web and the cost is under $10.00. MATH140 Calculus I; (4 credits) Grade Method: REG/P-F/AUD. CORE Mathematics or Formal Reasoning (MS) Course. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisite: permission of department based on 3 1/2 years of college preparatory mathematics (including trigonometry) and a satisfactory score on the MATHEMATICS PLACEMENT EXAM, or MATH115 with a grade of C or better. Credit will be granted for only one of the following: MATH140 or MATH220. Introduction to calculus, including functions, limits, continuity, derivatives and applications of the derivative, sketching of graphs of functions, definite and indefinite integrals, and calculation of area. The course is especially recommended for science, engineering and mathematics majors. All sections will require the use of a TI graphics calculator. Instructor will use a TI-83, TI-83+, or TI-86 calculator. Emphasis on student interaction in groups, including team approach to solving calculus based problems. There will be 3 one-hour lectures and 2 eighty-minute workshops each week with enhanced assistance and support for students. If purchasing used books additional software may be required. This can be purchased on the web and the cost is under $10.00. MATH140H Calculus I; (4 credits) Grade Method: REG/P-F/AUD. CORE Mathematics or Formal Reasoning (MS) Course. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisite: permission of department based on 3 1/2 years of college preparatory mathematics (including trigonometry) and a satisfactory score on the MATHEMATICS PLACEMENT EXAM, or MATH115 with a grade of C or better. Credit will be granted for only one of the following: MATH140 or MATH220. For general honors students only. Offered fall only. All sections will require the use of a TI graphics calculator. Instructor will use a TI-83 TI-83+, or TI-86 calculator. MATH141 Calculus II; (4 credits) Grade Method: REG/P-F/AUD. CORE Mathematics or Formal Reasoning (MS) Course. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisite: A grade of C or better in MATH140 or equivalent. Credit will be granted for only one of the following: MATH141 or MATH221. Continuation of MATH 140, including techniques of integration, improper integrals, applications of integration (such as volumes, work, arc length, moments), inverse functions, exponential and logarithmic functions, sequences and series. All sections will require the use of a TI graphics calculator. Instructor will use a TI-83, TI-83+, or TI-86 calculator. If purchasing used books additional software may be required. This can be purchased on the web and the cost is under $10.00. MATH141H Calculus II; (4 credits) Grade Method: REG/P-F/AUD. CORE Mathematics or Formal Reasoning (MS) Course. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisite: A grade of C or better in MATH140 or equivalent. Credit will be granted for only one of the following: MATH141 or MATH221. For general honors students only. TI graphics calculator required. Instructor will use a TI-83, TI-83+, or TI-86 calculator. MATH212 Elements of Numbers and Operations; (3 credits) Grade Method: REG/AUD. Prerequisite: One year of college preparatory algebra. Restricted to elementary, early childhood, and special education majors. Not open to students who have completed MATH210 with a grade of C- or better. Credit will be granted for only one of the following: MATH210 or MATH212. Topics from algebra and number theory designed to provide insight into arithmetic: sets, functions, number systems, number theory; operations with natural numbers, integers, rational numbers; linear equations. MATH213 Elements of Geometry and Measurement; (3 credits) Grade Method: REG/AUD. Prerequisite: MATH212. Restricted to elementary and early childhood education majors. Not open to students who have completed MATH211 with a grade of C- or better. Credit will be granted for only one of the following: MATH211 or MATH213. Properties of geometric objects in two and three dimensions; parallel lines, curves and polygons; ratio, proportion, similarity; transformational geometry and measurement, constructions, justifications and proofs. MATH214 Elements of Probability and Statistics; (3 credits) Grade Method: REG/AUD. Prerequisite: MATH212. Restricted to elementary and early childhood education majors. Not open to students who have completed MATH 211 with a grade of C or better. Credit will be granted for only one of the following: MATH211 or MATH214. Permutations and combinations; probability; collecting and representing data; using statistics to analyze and interpret data. MATH220 Elementary Calculus I; (3 credits) Grade Method: REG/P-F/AUD. CORE Mathematics or Formal Reasoning (MS) Course. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisite: permission of department based on 3 1/2 years of college preparatory mathematics (including trigonometry) and satisfactory performance on the MATHEMATICS PLACEMENT EXAM, or MATH113, or MATH115. Not open to students majoring in mathematics, engineering or the physical sciences. Credit will be granted for only one of the following: MATH140 or MATH220. Basic ideas of differential and integral calculus, with emphasis on elementary techniques of differentiation and applications. MATH221 Elementary Calculus II; (3 credits) Grade Method: REG/P-F/AUD. CORE Mathematics or Formal Reasoning (MS) Course. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisite: MATH220, or MATH140, or equivalent. Not open to students majoring in mathematics, engineering or the physical sciences. Credit will be granted for only one of the following: MATH141 or MATH221. Differential and integral calculus, with emphasis on elementary techniques of integration and applications. MATH240 Introduction to Linear Algebra; (4 credits) Grade Method: REG/P-F/AUD. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisite: MATH141 or equivalent. Credit will be granted for only one of the following: MATH240, MATH341, MATH400, or MATH461. Basic concepts of linear algebra: vector spaces, applications to line and plane geometry, linear equations and matrices, similar matrices, linear transformations, eigenvalues, determinants and quadratic forms. MATH241 Calculus III; (4 credits) Grade Method: REG/P-F/AUD. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisites: MATH141. Credit will be granted for only one of the following: MATH241 or MATH340. Introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss. All sections will use MATLAB. MATH241H Calculus III; (4 credits) Grade Method: REG/P-F/AUD. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisites: MATH141. Credit will be granted for only one of the following: MATH241 or MATH340. For general honors students only. MATH242 Numerical Techniques in Engineering; (3 credits) Grade Method: REG. Prerequisite: MATH141; and ENEE114 or CMSC106 or CMSC131 or equivalent. Restricted to Engineering, Math, and Physics majors only. Also offered as ENEE241. Credit will be granted for only one of the following: ENES240 or ENEE241 or MATH242. Introduction to error analysis, conditioning and stability of algorithms. Numerical solution of nonlinear equations. Vector spaces and linear transformations. Matrix algebra. Gaussian elimination. LU factorization, matrix inversion. Similarity transformations and diagonalization. Iterative computation of eigenvalues. Interpolation; splines; data fitting. Numerical integration. MATH246 Differential Equations for Scientists and Engineers; (3 credits) Grade Method: REG/P-F/AUD. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisite: MATH141; and any one of the following: MATH240 or ENES102 or PHYS161 or PHYS171. Credit will be granted for only one of the following: MATH246 or MATH341. An introduction to the basic methods of solving ordinary differential equations. Equations of first and second order, linear differential equations, Laplace transforms, numerical methods and the qualitative theory of differential equations. All sections will use MATLAB. MATH246H Differential Equations for Scientists and Engineers; (3 credits) Grade Method: REG/P-F/AUD. USP Distributive Studies Area B: Natural Sciences and Mathematics Course. Prerequisite: MATH141; and any one of the following: MATH240 or ENES102 or PHYS161 or PHYS171. Credit will be granted for only one of the following: MATH246 or MATH341. MATH299A (PermReq) Selected Topics in Mathematics; (1-3 credits) Grade Method: REG/P-F/AUD. Individual Instruction course: contact department or instructor to obtain section number. MATH299B Selected Topics in Mathematics: Putnam Express; (1 credit) Grade Method: REG/P-F/AUD. MATH310 Introduction to Analysis; (3 credits) Grade Method: REG. Prerequisite: MATH141. Corequisite: MATH241. Math majors may not use this course to satisfy an upper-level requirement. For MATH majors only. To prepare students for MATH 410 Advanced Calculus. To develop the students' ability to construct a rigorous proof of a mathematical claim. Students will also be made aware of mathematical results that are of interest to those wishing to analyze a particular mathematical model. Topics will be drawn from logic, set theory, structure of the number line, elementary topology, metric spaces, functions, sequences and continuity. MATH340 Multivariable Calculus, Linear Algebra and Differential Equations I (Honors); (4 credits) Grade Method: REG/P-F/AUD. Prerequisite: MATH140; MATH141; and permission of department. Credit will be granted for only one of the following: MATH241 or MATH340. First semester of the MATH 340-341 sequence which gives a unified and enriched treatment of multivariable calculus, linear algebra and ordinary differential equations, with supplementary material from subjects such as differential geometry, Fourier series and calculus of variations. Students completing MATH 340-341 will have covered the material of MATH 240, MATH 241, and MATH 246, and may not also receive credit for MATH 240, MATH 241 or MATH 246. MATH386 (PermReq) Experiential Learning; (3-6 credits) Grade Method: REG/P-F. Individual Instruction course: contact department or instructor to obtain section number. Prerequisite: Learning Proposal approved by the Office of Experiential Learning Programs, faculty sponsor and student's internship sponsor. Junior standing. MATH401 Applications of Linear Algebra; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: MATH 240 or MATH 461. Various applications of linear algebra: theory of finite games, linear programming, matrix methods as applied to finite Markov chains, random walk, incidence matrices, graphs and directed graphs, networks and transportation problems. MATH402 Algebraic Structures; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: MATH240 or equivalent. Not open to mathematics graduate students. Credit will be granted for only one of the following: MATH402 or MATH403. For students having only limited experience with rigorous mathematical proofs. Parallels MATH 403. Students planning graduate work in mathematics should take MATH 403. Groups, rings, integral domains and fields, detailed study of several groups; properties of integers and polynomials. Emphasis is on the origin of the mathematical ideas studied and the logical structure of the subject. Students planning graduate work in mathematics should take MATH 403. MATH403 Introduction to Abstract Algebra; (3 credits) Grade Method: REG/P-F/AUD. Prerequisites: MATH240; and MATH241; or equivalent. Credit will be granted for only one of the following: MATH402 or MATH403. Integers; groups, rings, integral domains, fields. MATH405 Linear Algebra; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: MATH240 or MATH461. An abstract treatment of finite dimensional vector spaces. Linear transformations and their invariants. MATH406 Introduction to Number Theory; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: MATH141 or permission of department. Integers, divisibility, prime numbers, unique factorization, congruences, quadratic reciprocity, Diophantine equations and arithmetic functions. MATH410 (PermReq) Advanced Calculus I; (3 credits) Grade Method: REG/P-F/AUD. Prerequisites: MATH240 and MATH241, with grade of C or better; and permission of department. First semester of a year course. Subjects covered during the year are: sequences and series of numbers, continuity and differentiability of real valued functions of one variable, the Riemann integral, sequences of functions and power series. Functions of several variables including partial derivatives, multiple integrals, line and surface integrals. The implicit function theorem. MATH411 (PermReq) Advanced Calculus II; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: MATH410 and permission of department. Credit will be granted for only one of the following: MATH411 or MATH412. Continuation of MATH 410. MATH414 Differential Equations; (3 credits) Grade Method: REG/P-F/AUD. Prerequisites: MATH410; and MATH240; or equivalent. Existence and uniqueness theorems for initial value problems. Linear theory: fundamental matrix solutions, variation of constants formula, Floquet theory for periodic linear systems. Asymptotic orbital and Lyapunov stability with phase plane diagrams. Boundary value theory and series solutions. MATH424 (PermReq) Introduction to the Mathematics of Finance; (3 credits) Grade Method: REG/P-F/AUD. Prerequisites: MATH141; and either STAT400 or BMGT231 and permission of department. Corequisite: BMGT343. Recommended: MATH240, MATH241 or MATH246. Credit will be granted for only one of the following: BMGT444, MATH424 or MATH498F. Formerly MATH 498F. Introduction to the mathematical models used in finance and economics with emphasis on pricing derivative instruments. Designed for students in mathematics, computer science, engineering, finance and physics. Financial markets and instruments; elements from basic probability theory; interest rates and present value analysis; normal distribution of stock returns; option pricing; arbitrage pricing theory; the multiperiod binomial model; the Black-Scholes option pricing formula; proof of the Black-Scholes option pricing formula and applications; trading and hedging of options; Delta hedging; utility functions and portfolio theory; elementary stochastic calculus; Ito's Lemma; the Black-Scholes equation and its conversion to the heat equation. MATH430 Euclidean and Non-Euclidean Geometries; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: MATH141. Hilbert's axioms for Euclidean geometry. Neutral geometry: the consistency of the hyperbolic parallel postulate and the inconsistency of the elliptic parallel postulate with neutral geometry. Models of hyerbolic geometry. Existence and properties of isometries. MATH432 Introduction to Topology; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: MATH410 or equivalent. Metric spaces, topological spaces, connectedness, compactness (including Heine-Borel and Bolzano-Weierstrass theorems), Cantor sets, continuous maps and homeomorphisms, fundamental group (homotopy, covering spaces, the fundamental theorem of algebra, Brouwer fixed point theorem), surfaces (e.g., Euler characteristic, the index of a vector field, hairy sphere theorem), elements of combinatorial topology (graphs and trees, planarity, coloring problems). MATH436 Differential Geometry of Curves and Surfaces I; (3 credits) Grade Method: REG/P-F/AUD. Prerequisites: MATH241; and either MATH240 or MATH461; and two 400-level MATH courses (not including MATH400, 461 and 478). Curves in the plane and Euclidean space, moving frames, surfaces in Euclidean space, orientability of surfaces; Gaussian and mean curvatures; surfaces of revolution, ruled surfaces, minimal surfaces, special curves on surfaces, "Theorema Egregium"; the intrinsic geometry of surfaces. MATH450 (PermReq) Logic for Computer Science; (3 credits) Grade Method: REG/P-F/AUD. Prerequisites: CMSC251 and MATH141, with grade of C or better and permission of department. Also offered as CMSC450. Credit will be granted for only one of the following: MATH445 or MATH450/CMSC450. Elementary development of propositional and first-order logic accessible to the advanced undergraduate computer science student, including the resolution method in propositional logic and Herbrand's Unsatisfiability Theorem in first-order logic. Included are the concepts of truth, interpretation, validity, provability, soundness, completeness, incompleteness, decidability and semi-decidability. MATH452 Introduction to Dynamics and Chaos; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: MATH240 and MATH246. Also offered as AMSC452. Credit will be granted for only one of the following: AMSC452, MAPL452 or MATH452. An introduction to mathematical dynamics and chaos. Orbits, bifurcations, Cantor sets and horseshoes, symbolic dynamics, fractal dimension, notions of stability, flows and chaos. Includes motivation and historical perspectives, as well as examples of fundamental maps studied in dynamics and applications of dynamics. MATH456 (PermReq) Cryptology; (3 credits) Grade Method: REG/P-F/AUD. Prerequisites: Any two 400-level MATH courses; OR CMSC330 and CMSC351 and permission of department. Also offered as CMSC456. Credit will be granted for only one of the following: MATH456 or CMSC456. Importance in protecting data in communications between computers. The subject lies on the border between mathematics and computer science. Mathematical topics include number theory and probability. Computer science topics include complexity theory. MATH461 Linear Algebra for Scientists and Engineers; (3 credits) Grade Method: REG/P-F/AUD. Prerequisites: MATH141 and one MATH/STAT course for which MATH141 is a prerequisite. This course cannot be used toward the upper level math requirements for MATH/STAT majors. Credit will be granted for only one of the following: MATH240, MATH341, MATH400 or MATH461. Basic concepts of linear algebra. This course is similar to MATH 240, but with more extensive coverage of the topics needed in applied linear algebra: change of basis, complex eigenvalues, diagonalization, the Jordan canonical form. MATH462 Partial Differential Equations for Scientists and Engineers; (3 credits) Grade Method: REG/P-F/AUD. Prerequisites: MATH241 and MATH246. Linear spaces and operators, orthogonality, Sturm-Liouville problems and eigenfunction expansions for ordinary differential equations. Introduction to partial differential equations, including the heat equation, wave equation and Laplace's equation. Boundary value problems, initial value problems and initial-boundary value problems. MATH463 Complex Variables for Scientists and Engineers; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: MATH241 or equivalent. The algebra of complex numbers, analytic functions, mapping properties of the elementary functions. Cauchy integral formula. Theory of residues and application to evaluation of integrals. Conformal mapping. MATH464 Transform Methods for Scientists and Engineers; (3 credits) Grade Method: REG/P-F/AUD. Prerequisite: MATH246. Fourier series, Fourier and Laplace transforms. Evaluation of the complex inversion integral by the theory of residues. Applications to ordinary and partial differential equations of mathematical physics: solutions using transforms and separation of variables. Additional topics such as Bessel functions and calculus of variations. MATH478A (PermReq) Selected Topics For Teachers of Mathematics; (1-3 credits) Grade Method: REG/P-F/AUD. Individual Instruction course: contact department or instructor to obtain section number. MATH489 (PermReq) Research Interactions in Mathematics; (1-3 credits) Grade Method: REG/P-F/AUD. Individual Instruction course: contact department or instructor to obtain section number. MATH498A (PermReq) Selected Topics in Mathematics; (1-9 credits) Grade Method: REG/P-F/AUD. Individual Instruction course: contact department or instructor to obtain section number. MATH498E (PermReq) Selected Topics in Mathematics: Mathematics for Secondary Education; (3 credits) Grade Method: REG/P-F/AUD. Click here for information. MATH600 Abstract Algebra I; (3 credits) Grade Method: REG/AUD. Prerequisite: MATH 403 and MATH405; or equivalent. Groups with operators, homomorphism and isomorphism theorems, normal series, Sylow theorems, free groups, Abelian groups, rings, integral domains, fields, modules. Topics may include HOM (A,B), Tensor products, exterior algebra. Offered fall only. MATH603 Commutative Algebra; (3 credits) Grade Method: REG/AUD. Prerequisite: MATH 600. Ideal theory of Noetherian rings, valuations, localizations, complete local rings, Dedekind domains. MATH608A Selected Topics in Algebra; (1-3 credits) Grade Method: REG/AUD. Individual Instruction course: contact department or instructor to obtain section number. MATH608F Selected Topics in Algebra: Automorphic Forms on GL(2); (3 credits) Grade Method: REG/AUD. MATH608K Selected Topics in Algebra: Algebraic K-Theory; (3 credits) Grade Method: REG/AUD. MATH630 Real Analysis I; (3 credits) Grade Method: REG/AUD. Prerequisite: MATH 411 or equivalent. Lebesgue measure and the Lebesgue integral on R, differentiation of functions of bounded variation, absolute continuity and fundamental theorem of calculus, Lp spaces on R, Riesz-Fischer theorem, bounded linear functionals on Lp, measure and outer measure, Fubini's theorem. MATH634 Harmonic Analysis; (3 credits) Grade Method: REG/AUD. Prerequisite: MATH 631. L1 theory: Fejer theorem, inversion theorem, ideal structure, Tauberian theorem. L2 theory: Plancherel-Parseval theorems, Paley-Wiener theorem. Lp theory: Hausdorff-Young theorem. Distribution theory: Bochner's theorem, Wiener continuous measures theorem, Malliavin theorem, Schwartz theory, almost periodic functions. MATH642 Dynamical Systems I; (3 credits) Grade Method: REG/AUD. Prerequisites: MATH 432; and MATH 630 or equivalent. Foundations of topological dynamics, homeomorphisms, flows, periodic and recurrent points, transitivity and minimality, symbolic dynamics. Elements of ergodic theory, invariant measures and sets, ergodicity, ergodic theorems, mixing, spectral theory, flows and sections. Applications of dynamical systems to number theory, the Weyl theorem, the distribution of values of polynomials, Vander Waerden's theorem on arithmetic progressions. Offered fall only. MATH648A Selected Topics in Analysis; (1-3 credits) Grade Method: REG/AUD. Individual Instruction course: contact department or instructor to obtain section number. MATH648C Selected Topics in Analysis: Calculus of Variations; (3 credits) Grade Method: REG/AUD. MATH660 Complex Analysis I; (3 credits) Grade Method: REG/AUD. Prerequisite: MATH 410 or equivalent. Linear transformations, analytic functions, conformal mappings, Cauchy's theorem and applications, power series, partial fractions and factorization, elementary Riemann surfaces, Riemann's mapping theorem. MATH668A (PermReq) Selected Topics in Complex Analysis; (1-3 credits) Grade Method: REG/AUD. Individual Instruction course: contact department or instructor to obtain section number. MATH670 Ordinary Differential Equations I; (3 credits) Grade Method: REG/AUD. Prerequisites: MATH 405; and MATH 410 or the equivalent. Also offered as AMSC 670. Credit will be granted for only one of the following: AMSC 670, MAPL 670 OR MATH 670. Existence and uniqueness, linear systems usually with Floquet theory for periodic systems, linearization and stability, planar systems usually with Poincare-Bendixson theorem. Offered fall only. MATH673 Partial Differential Equations I; (3 credits) Grade Method: REG/AUD. Prerequisite: MATH 411 or equivalent. Also offered as AMSC 673. Credit will be granted for only one of the following: AMSC 673, MAPL 673 or MATH 673. Analysis of boundary value problems for Laplace's equation, initial value problems for the heat and wave equations. Fundamental solutions, maximum principles, energy methods. First order nonlinear PDE, conservation laws. Characteristics, shock formation, weak solutions. Distributions, Fourier transform. Offered fall only. MATH687 Minicourse Series in the Mathematical Sciences; (1 credit) Grade Method: REG/AUD. Also offered as AMSC 687 and STAT 687. Credit will be granted for only one of the following: AMSC 687, MATH 687 or STAT 687. This series will consist of up to sixteen 3-lecture presentations covering a broad rnage of topics in the mathematical sciences. Each minicourse is intended to be self-contained and accessible to first year graduate students and advanced undergraduates. The goal of each minicourse is to present an active research area or significant result and the necessary vocabulary and perspective for students to appreciate it. The goal of the Minicourse Series is to broaden a student's awareness of the mathematical sciences and to inform them of research directions. MATH689 (PermReq) Research Interactions in Mathematics; (1-3 credits) Grade Method: REG/AUD. Individual Instruction course: contact department or instructor to obtain section number. MATH695 Teaching Seminar; (1 credit) Grade Method: REG. For MATH majors only. A course intended for first year teaching assistants. Topics include: everyday mechanics of teaching; teaching methods and styles; technology; course enrichment, diversity in the classroom; sexual harassment; teacher-student interactions; presentations by students. MATH712 Mathematical Logic I; (3 credits) Grade Method: REG/AUD. Sentential logic, first-order languages, models and formal deductions. Basic model theory including completeness and compactness theorems, other methods of constructing models, and applications such as non-standard analysis. Offered fall only. MATH718A Selected Topics in Mathematical Logic; (1-3 credits) Grade Method: REG/AUD. Individual Instruction course: contact department or instructor to obtain section number. MATH718M Selected Topics in Mathematical Logic: Model Theory; (3 credits) Grade Method: REG/AUD. MATH730 Fundamental Concepts of Topology; (3 credits) Grade Method: REG/AUD. Prerequisites: MATH 410, and MATH 411, and MATH 403; or equivalent. Survey of basic point set topology, fundamental group, covering spaces, Van Kampen's theorem, simplicial complexes, simplicial homology, Euler characteristics and classification of surfaces. MATH744 Lie Groups I; (3 credits) Grade Method: REG/AUD. Prerequisite: MATH 403, MATH 405, MATH 411 and MATH 432; or equivalent. An introduction to the fundamentals of Lie groups, including some material on groups of matrices and Lie algebras. MATH748A Selected Topics in Geometry and Topology; (1-3 credits) Grade Method: REG/AUD. Individual Instruction course: contact department or instructor to obtain section number. MATH748K Selected Topics in Geometry and Topology: Knots, Braids, and Yang-Baxter; (3 credits) Grade Method: REG/AUD. MATH799 Master's Thesis Research; (1-6 credits) Grade Method: REG/S-F. Individual Instruction course: contact department or instructor to obtain section number. MATH898 Pre-Candidacy Research; (1-8 credits) Grade Method: REG/S-F. Individual Instruction course: contact department or instructor to obtain section number. MATH899 Doctoral Dissertation Research; (6 credits) Grade Method: REG/S-F. Individual Instruction course: contact department or instructor to obtain section number.
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