Students should have substantial experience with theorem-proof mathematics; the listed pre- requisites are minimal and stronger preparation is recommended. This course introduces students to mathematical modeling and quantitative techniques used to investigate neural systems at many different scales, from single neuron activity to the dynamics of large neuronal networks. 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 451 and one of Math 420 or 494, or permission of instructor. The prerequisites include linear algebra, advanced calculus, and complex variables. Quantifying the financial impact of uncertain events is the central challenge of actuarial mathematics. 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. Please check your bulk mail or spam folder first. Math 565 and 566 introduce the basic notions and techniques of combinatorics and graph theory at the beginning graduate level. Mathematical techniques introduced in this course include 1) the method of averaging, 2) harmonic balance, 3) Fourier techniques, 4) entrainment and coupling of oscillators, 4) phase plane analysis, and 5) various techniques from the theory of dynamical systems. The first 2-3 weeks of the course will be devoted to general topology, and the remainder of the course will be devoted to differential topology. This course is an introduction to numerical linear algebra, a core subject in scientific computing. The course will start with classical differential equation and game theory approaches. Fundamental concepts and methods of analysis are emphasized. This course covers topics in Biological Sequence Analysis. This is one of the basic courses for students beginning study towards the Ph.D. degree in mathematics. Algorithms for sequence alignment, statistical analysis of similarity scores, hidden markov models, neural networks, training, gene finding, protein family profiles, multiple sequence alignment, sequence comparison, and structure prediction. Emphasis will be placed on primary sources (papers from the literature) particularly those in the biological sciences. Topic will vary according to the instructor. The prerequisites for this course are a basic knowledge of analysis, algebra, and topology. The sample description below is for a course in biological oscillators from Winter 2006. The development of Set Theory will be largely axiomatic with the emphasis on proving the main results from the axioms. Recent examples have been: Nonlinear Waves, Mathematical Ecology, and Computational Neuroscience. No course in mathematical logic is presupposed. Please enter the umich.edu email address to which you would like to add your classes. The prerequisites include linear algebra, advanced calculus, and complex variables. MATH 463: Introduction to Mathematical Biology MWF 01:10 - 2:00, 3088 EH. The course starts with the general Theory of Asset Pricing and Hedging in continuous time and then proceeds to specific problems of Mathematical Modeling in Continuous- time Finance. This information may not, under any circumstances, be copied, modified, reused, or incorporated into any derivative works or compilations, without the prior written approval of Koofers, Inc. university-of-michigan-ann-arbor-umich/math/526-disc-stoc-proc/. This course is an introduction to the theory of smooth manifolds. Math 465 or equivalent experience with abstract mathematics. Piazza is designed to simulate real class discussion. This is a first course in number theory. A recent survey showed that most Fortune 500 companies regularly use linear programming in their decision making. In addition, this course discusses Optimal Investment in Continuous time (Merton’s problem), Highfrequency Trading (Optimal Execution), and Risk Management (e.g. Summer 2020 This course extends the single decrement and single life ideas of Math 520 to multi-decrement and multiple-life applications directly related to life insurance.

Math 556 is not a prerequisite. We strive to recreate that communal atmosphere among students and instructors. Graduate students from engineering and science departments and strong undergraduates are also welcome. This is an introduction to methods of applied analysis with emphasis on Fourier analysis and partial differential equations. Selected Term: Instructors can also answer questions, endorse student answers, and edit or delete any posted content. Math 450 or 451. Students should have a basic knowledge of common probability distributions (Poisson, exponential, gamma, binomial, etc.) Survey of continuous optimization problems. 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. This course is the first half of the Math/Stats 525-526 sequence. It is a second course in probability which should be of interest to students of mathematics and statistics as well as students from other disciplines in which stochastic processes have found significant applications. This course is an introduction to Ordinary Differential Equations and Dynamical Systems with emphasis on qualitative analysis. The purpose of this course is to introduce basic concepts of topology. We will also cover a bit of algebraic topology (e.g., fundamental groups) as time permits. Check your inbox for your confirmation email. The prerequisite of a course in advanced calculus is essential. Probabilistic models of proteins and nucleic acids. Math 565 emphasizes the aspects of combinatorics connected with computer science, geometry, and topology. Topics include group theory, permutation representations, simplicity of alternating groups for n>4, Sylow theorems, series in groups, solvable and nilpo- tent groups, Jordan-Hölder Theorem for groups with operators, free groups and presentations, fields and field extensions, norm and trace, algebraic closure, Galois theory, and transcendence degree. Mathematical modeling and analysis are needed to understand what causes these oscillations to emerge, properties of their period and amplitude, and how they synchronize to signals from other oscillators or from the external world. ), bounds for codes, and more. Math 217, 417, 419, or permission of instructor. Each such problem has as its goal the maximization of some positive objective such as investment return or the minimization of some negative objective such as cost or risk. This is one of the basic courses for students beginning study towards the Ph.D. degree in mathematics. The approach is theoretical and rigorous and emphasizes abstract concepts and proofs. Students are expected to master both the proofs and applications of major results. It will then focus on the theory and application of particular models of adaptive systems such as models of neural systems, genetic algorithms, classifier systems, and cellular automata. It is intended for students with interests in mathematical, computational, and/or modeling aspects of interdisciplinary science, and the course will develop the intuitions of the field of application as well as the mathematical concepts. Finally, the continuous time version of the proposed methods is presented, culminating with the BlackScholes model.

These models are “agent-based” or “bottom-up” in that the structure is placed at the level of the individuals as basic components; they are “adaptive” in that individuals often adapt to their environment through evolution or learning. This course develops the mathematical models for pre-funded retirement benefit plans. This is a continuation of Math 573. This is one of the basic courses for students beginning the PhD program in mathematics. 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. Don't miss the Math Career Fair on Nov 6!! Risk management is of major concern to all financial institutions, especially casualty insurance companies. Instructors can also answer questions, endorse student answers, and edit or delete any posted content. The structure theory of modules over a PID will be an important topic, with applications to the classification of finite abelian groups and to Jordan and rational canonical forms of matrices. This course is a survey of the basic techniques and results of elementary number theory. This course emphasizes the application of mathematical methods to the relevant problems of financial industry and focuses mainly on developing skills of model building.

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