1. 2 concerns about globalization 3 manufacturing & technology
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Concerns About Globalization
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Manufacturing & Technology
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Financial, Retail & Housing Markets
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Innovation Required For Economic Growth
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Innovation Requires a Strong STEM Workforce
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Big Problem: Lack of Household Participation
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Government Stimulating Growth in STEM Fields
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Need New Models for Research & Education
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IMPACTInterdisciplinary Mentoring Program in Analysis,
Computation, and Theory
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PERSONNEL
• 9 Faculty Mentors
• 7 Graduate Students
• 21 Undergraduates
• 11 Alumni (9 Ph.D students, 1 Medical School, 1 Workforce)
• 14 Members on Advisory Board
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Intellectual Core
Analysis
Computation
Theory
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Program Vision
Attract & Retain students into the
mathematical sciences through:
•Interdisciplinary Research
•Modernized Curriculum
•Socialization and Team Building
•Industrial Cooperation
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Interdisciplinary Research
•Attracts students to the mathematical
sciences
•Connects us with faculty in other
disciplines
Mathematics
Statistics Computation
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Modernized Curriculum
•Cuts through jargon
•Reduces barriers across
disciplines.
•Reveals common themes.
•Centralizes mathematics as a core
subject.
•Reduces redundancy across
campus.
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Socialization and Team Building
•Horizontal Integration:
Exploring multiple disciplines
simultaneously.
•Vertical Integration
Brings together undergraduates,
graduate students, and faculty.
•Combination allows for everyone to
participate as teacher-scholars.
•Social activities form personal
bonds and trust.
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Industrial Cooperation
•Provides students with
opportunities for
•Internships
•Employment
•Entrepreneurship.
•Additional funding sources
•Interesting problems
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CSUMS Program Schedule
•Summer Program (Bootcamp)
•Research During the School
Year
•Spring Immersion
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Summer Program “Boot Camp”
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Boot Camp Schedule
7 Weeks:•MWF •Morning Classes 8am-12pm•Work on assignments noon-evening•TuTh•Morning Computer Labs 8am-12pm•Work on assignments noon-evening•Ultimate Frisbee/Soccer TuTh
evenings•Friday afternoon movie/pizza
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OptimizationConvex AnalysisOptimizationAdv. Least SquaresUnconstrained Opt.Constrained Opt.Optimal Control
Signals and SystemsSignal ProcessingDynamical SystemsControl Theory
Linear Algebra ReviewInner Product SpacesSpectral Theory
Summer Topics
Probability & StatisticsIntroduction to ProbMultivariate StatsBayesian StatisticsRegressionTime Series AnalysisHMM
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Recurring Themes
Linear AlgebraOrthogonality, Fourier Coefficients
Projections and Least SquaresSingular-Value Decomposition (SVD)The Contraction Mapping Principle
Newton’s Method and VariantsInverse and Implicit Function
TheoremsConvex Analysis
Jensen’s InequalityConvex Optimization
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•Principal Component Analysis•Factor Analysis•Latent Semantic Analysis•Conjoint Analysis•Hotelling Transforms•Empirical Mode Decomposition•Empirical Orthogonal Decomposition•Proper Orthogonal Decomposition•Karhunen-Loève Expansion•EigenfacesSVD FAMILY
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Newton’s Method and the Contraction
Mapping Principle
•Unconstrained Optimization•Interior-Point methods•Many Numerical Methods in Linear Algebra•Many Numerical Methods in Differential Equations•Proofs to Inverse and Implicit Function Theorems•Existence and Uniqueness of ODEs•Kalman filter; Recursive Least Squares•Many/Most Results in Nonlinear Analysis
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During the School Year
•Students work on research projects(weekly group meetings)•Each student works on two projects(one as lead, one as assistant)•Weekly IMPACT meetings(two 15-20 minute talks each week)•Social Activities(usually involve pizza or ice cream)•Reviews Each Semester(performance examined, goals set)
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Weekly Meetings
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Computation Seminar
•Advanced LaTeX & Beamer•Python•RegExp•C/C++, OOP Review•Fortran•Mex Interface for Matlab•MySQL & RDBMS Normalization•PHP, HTML, XML•OpenMP•MPI
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Spring Immersion
•Regional MAA Conference in
March
•7 Week Wrap Up (April-June)
•Plan for a paper, conference
presentation or a technical
report.
•Final Review
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2009-2010 Programs
• Actuarial, Investment, & Management Sciences
• Functional Data Analysis
• Mathematical Systems & Optimization
• Nonlinear Waves & Coherent Structures
• Computational Biology and Bioinformatics
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impact.byu.eduProject funded primarily by
the National Science Foundation
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