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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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