One of the great discoveries of modern mathematics was that essentially every mathematical concept may be defined in terms of sets and membership. Le programme Mathématique 526 transitoire s’adresse aux élèves de cinquième secondaire qui souhaitent poursuivre leurs études postsecondaires notamment en sciences humaines, en administration ou en formation technique et qui ont réussi le programme Mathématique 426 transitoire. © Copyright 2020 , Koofers, Inc. All rights reserved. The main topics covered are set algebra (union, intersection), relations and functions, orderings (partial, linear, well), the natural numbers, finite and denumerable sets, the Axiom of Choice, and ordinal and cardinal numbers. This is a core course for the quantitative finance and risk management Masters program and introduces students to the main concepts of Financial Mathematics. This is a core course sequence for the Applied and Interdisciplinary Mathematics graduate pro- gram.

Topics covered include divisibility and prime numbers, congruences, quadratic reciprocity, quadratic forms, arithmetic functions, and Diophantine equations. Topics include: Product and quotient topology, CW-complexes, group actions, topological groups, topological manifolds, smooth manifolds, manifolds with boundary, smooth maps, partitions of unity, tangent vectors and differentials, the tangent bundle, submersions, immersions and embeddings, smooth submanifolds, Sard's Theorem, the Whitney embedding theorem, transversality, Lie groups, vector fields, Lie brackets, Lie algebra, multilinear algebra, vector bundles, differential forms, exterior derivatives, orientation, De Rham cohomology groups, homotopy invariance, degree theory. Proofs are emphasized, but they are often pleasantly short.

Analysis of DNA/RNA and protein sequence data. Credit Value Adjustment). This theory is applied to problems of Pricing and Hedging of simple Financial Derivatives. ), bounds for codes, and more. Unconstrained optimization problems: unidirectional search techniques, gradient, conjugate direction, quasi-Newtonian methods; introduction to constrained optimization using techniques of unconstrained optimization through penalty transformation, augmented Lagrangians, and others; discussion of computer programs for various algorithms. This course focuses on discovering the way in which spatial variation influences the motion, dispersion, and persistence of species. However, the subject also has deep connections with higher-dimensional convex geometry. Guest lecturers from the industry will provide some of the instruction. Enter the validation code below so you can access your classes! We will send an email to this address with a link to validate your new email address. Many of the results of algebra and analysis were invented to solve problems in number theory. This course centers on the construction and use of agent-based adaptive models to study phenomena which are prototypical in the social, biological, and decision sciences. Winter 2020 Students can post questions and collaborate to edit responses to these questions. Don't miss the Math Career Fair on Nov 6!! Select a Term There is some coverage of how accounting theory and practice can be explained by these models and of the U.S. laws and regulations that give rise to the models used in practice. All LSA students should regularly use the LSA Degree Audit Checklist to make sure they are meeting degree requirements and to help with course scheduling decisions. Winter (Senior Year) Math 472, Elective. Topics in functional analysis that are used in the analysis of ordinary and partial differential equations. The course will also cover tensor, symmetric, and exterior algebras, and the classification of bilinear forms with some emphasis on the field case. The basic results on qualitative behavior, centered on themes of stability and phase plane analysis will be presented in a context that includes applications to a variety of classic examples. al. One of the goals of this course is to develop some understanding of how Set Theory plays this role. Historically the Actuarial Program has emphasized life, health, and pension topics. Summer 2020 The goal of this course is to teach the basic actuarial theory of mathematical models for financial uncertainties, mainly the time of death. Students can post questions and collaborate to edit responses to these questions. Models will typically use ordinary differential equations. Upon perusal, if you have any questions, please email us at math-grad-office@umich.edu. It will also look at how claims are settled, since this determines losses which are key components for insurance ratemaking and reserving. The main topics are the development of (1) probability distributions for the future lifetime random variable; (2) probabilistic methods for financial payments on death or survival; and (3) mathematical models of actuarial reserving. Math 214, 217, 417, 419, or 420 and one of Math 450, 451, or 454; or permission of instructor. Development of the simplex algorithm; duality theory and economic interpretations. This course develops the mathematical models for pre-funded retirement benefit plans. This is an advanced topics course intended for students with strong interests in the intersection of mathematics and the sciences, but not necessarily experience with both applied mathematics and the application field. In practice, such problems involve thousands of decision variables and constraints, so a primary focus is the development and implementation of efficient algorithms. The goal of these models is to understand how the structure at the individual or micro level leads to emergent behavior at the aggregate or macro level. Math 412 or 451 or equivalent experience with abstract mathematics.

This course starts with the basic version of Mathematical Theory of Asset Pricing and Hedging (Fundamental Theorem of Asset Pricing in discrete time and discrete space). Introduction to transportation and assignment problems; special purpose algorithms and advanced computational techniques. Flexible.

Math 451 (strongly recommended). Math 451 and one of Math 420 or 494, or permission of instructor. This course is centered on modeling in three major areas i) Models of Motion: Diffusion, Convection, Chemotaxis, and Haptotaxis; ii) Biological Pattern Formation; and iii) Delay-differential Equations and Age-structured Models. Metric and normed linear spaces, Banach spaces and the contraction mapping theorem, Hilbert spaces and spectral theory of compact operators, distributions and Fourier transforms, Sobolev spaces and applications to elliptic PDEs.

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