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Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.
Note: For listings of related courses, see Actuarial Science, Mathematics, Pure Mathematics and Statistics.
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Applied Mathematics
311
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Differential Equations I
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Classification of ordinary differential equations, first and second order equations with applications, series solutions about regular points and singular points, special functions, Laplace transform.
Course Hours:
3 units; H(3-1T)
Prerequisite(s):
Mathematics 253 or 267 or 277 or 283 or Applied Mathematics 219.
Antirequisite(s):
Credit for Applied Mathematics 311 and either Mathematics 375 or Applied Mathematics 307 will not be allowed.
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Applied Mathematics
411
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Differential Equations II
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Existence and uniqueness theorems, comparison and oscillation theorems, Green's functions, Sturm-Liouville problems, systems of equations, phase portraits, stability.
Course Hours:
3 units; H(3-1T)
Prerequisite(s):
One of Mathematics 375, Applied Mathematics 311 or 307; and one of Mathematics 331, 353, 367, 377, 381, or Applied Mathematics 309.
Notes:
It is recommended that students complete Mathematics 335 or 355 or Pure Mathematics 435 or 455 before taking this course.
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Applied Mathematics
413
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Introduction to Partial Differential Equations
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First order partial differential equations, Sturm-Liouville systems, Fourier series, Double Fourier series, Fourier integrals, Applications to boundary value problems in bounded and unbounded domains, Bessel function with applications.
Course Hours:
3 units; H(3-1T)
Prerequisite(s):
Mathematics 375 or 331; or one of: Mathematics 353 or 367 or 381 or Applied Mathematics 309 and one of: Applied Mathematics 307 or 311.
Antirequisite(s):
Credit for Applied Mathematics 413 and 415 will not be allowed in the Actuarial Science, Applied Mathematics, General Mathematics, Pure Mathematics, Statistics programs, and the Natural Sciences program with a Concentration in General Mathematics.
Notes:
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Applied Mathematics
415
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Mathematical Methods
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Mathematical analysis of linear systems. Fourier and Laplace transforms, applications and numerical methods. Functions of a complex variable and applications.
Course Hours:
3 units; H(3-1T)
Prerequisite(s):
One of Applied Mathematics 311, 307, Mathematics 331, 353, 367, 375, 381, or Applied Mathematics 309.
Antirequisite(s):
Credit for Applied Mathematics 415 and 413 in the Actuarial Science, Applied Mathematics, General Mathematics, Pure Mathematics, Statistics, and the Natural Sciences program with a Concentration in General Mathematics will be not be allowed.
Notes:
Credit in an introductory Computer Science course is highly recommended as a prerequisite.
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Applied Mathematics
425
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Introduction to Optimization
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Examples of optimization problems. Quadratic forms, minimum energy and distance. Least squares, generalized inverse. Location and classification of critical points. Variational treatment of eigenvalues. Lagrange multipliers. Linear programming.
Course Hours:
3 units; H(3-1T)
Prerequisite(s):
Mathematics 311 or 313; and one of Mathematics 331 or 353 or 367 or 377 or 381 or Applied Mathematics 309.
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Applied Mathematics
433
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Mathematical Methods in Physics
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Fourier analysis. Laplace Transforms. Partial differential equations. Complex analysis. Residue integrals. Extensive physical applications.
Course Hours:
3 units; H(3-1T)
Prerequisite(s):
Mathematics 211 or 213; and one of Applied Mathematics 307 or 311 or Mathematics 375; and one of Applied Mathematics 309 or Mathematics 353 or 367 or 377 or 381 or 331.
Antirequisite(s):
Credit for Applied Mathematics 433 in the Actuarial Science, Applied Mathematics, General Mathematics, Pure Mathematics, Statistics programs, and the Natural Sciences program with a Concentration in General Mathematics will be not be allowed.
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Applied Mathematics
481
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Introduction to Mathematical Finance
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An introduction to the fundamental concepts of mathematical finance in an elementary setting. Topics include: risk, return, no arbitrage principle; basic financial derivatives: options, forwards and future contracts; risk free assets, time value of money, zero coupon bonds; risky assets, binomial tree model, fundamental theorem of asset pricing; portfolio management and capital asset pricing model; no arbitrage pricing of financial derivatives; hedging.
Course Hours:
3 units; H(3-1T)
Prerequisite(s):
Statistics 321.
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Applied Mathematics
491
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Numerical Analysis I
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Interpolation and approximation, numerical integration, numerical methods for the solution of non-linear equations, systems of linear equations and the eigenvalue problem.
Course Hours:
3 units; H(3-1T)
Prerequisite(s):
Computer Science 231 or 217; and Mathematics 311 or 313; and one of Mathematics 381 or 367 or 377 or 349 and 353 or Applied Mathematics 309.
Antirequisite(s):
Credit for Applied Mathematics 491 and Computer Science 491 will not be allowed.
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Applied Mathematics
501
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Seminar in Applied Mathematics
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Topics will be chosen according to the interests of instructors and students and could include analysis of optimization algorithms, approximation theory, control theory, differential equations, mathematical physics.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Consent of the Department.
MAY BE REPEATED FOR CREDIT
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Applied Mathematics
503
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The Mathematics of Wavelets, Signal and Image Processing
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Continuous and discrete Fourier transforms, the Fast Fourier Transform, wavelet transforms, multiresolution analysis and orthogonal wavelet bases, and applications.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Applied Mathematics 491 or Computer Science 491.
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Applied Mathematics
505
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Calculus on Manifolds
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Integral and differential calculus on manifolds including tensor fields, covariant differentiation, Lie differentiation, differential forms, Frobenius' theorem, Stokes' theorem, flows of vector fields.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Pure Mathematics 445 or 545; and one of Mathematics 375 or Applied Mathematics 311 or 307.
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Applied Mathematics
581
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Stochastic Calculus for Finance
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Martingales in discrete and continuous time, risk-neutral valuations, discrete- and continuous-time (B,S)-security markets, Cox-Ross-Rubinstein formula, Wiener and Poisson processes, Ito formula, stochastic differential equations, Girsanov’s theorem, Black-Scholes and Merton formulas, stopping times and American options, stochastic interest rates and their derivatives, energy and commodity models and derivatives, value-at-risk and risk management.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Applied Mathematics 481.
Antirequisite(s):
Credit for Applied Mathematics 581 and 681 will not be allowed.
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Applied Mathematics
583
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Computational Finance
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Review of financial asset price and option valuation models; model calibration; tree-based methods; finite-difference methods; Monte Carlo simulation; Fourier methods.
Course Hours:
3 units; H(3-0)
Prerequisite(s):
Applied Mathematics 481 and 491.
Antirequisite(s):
Credit for Applied Mathematics 583 and 683 will not be allowed.
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COURSES OF INSTRUCTION