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Schedule, Notes/Handouts & Videos

Computer Assisted Proofs in Applied Mathematics (SLMath) July 07, 2025 - July 18, 2025

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Jul 07, 2025
Monday
09:00 AM - 09:15 AM
  Introduction to SLMath
09:15 AM - 10:15 AM
  Morning Session 1: Introduction to Computer Assisted Proofs in Applied Math
Jonathan Jaquette (New Jersey Institute of Technology)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Morning Session 2: Software Installation, Interval Arithmetic
Evelyn Sander (George Mason University)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Afternoon Session 1: Getting Familiar with Matlab and Intlab, Riemann Integration
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 05:00 PM
  Afternoon Session 2: Intro to CAP Challenge Problems
Jonathan Jaquette (New Jersey Institute of Technology), Evelyn Sander (George Mason University)
Jul 08, 2025
Tuesday
09:00 AM - 10:15 AM
  Morning Session 1: Matrices, Norms, Projections, Gershgorin Circles
Evelyn Sander (George Mason University)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Morning Session 2: CAP Challenge Matrix Problem
Evelyn Sander (George Mason University)
12:00 PM - 01:45 PM
  Lunch
01:45 PM - 03:00 PM
  Afternoon Session 1: Branch and Bound and Higher Order Integration Methods
Jonathan Jaquette (New Jersey Institute of Technology)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 05:00 PM
  Afternoon Session 2: CAP Challenge 1D Integral Problem
Jonathan Jaquette (New Jersey Institute of Technology)
Jul 09, 2025
Wednesday
09:00 AM - 10:15 AM
  Morning Session 1: Interval Newton's Method
Evelyn Sander (George Mason University)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Morning Session 2: Period 3 Implies Chaos
Evelyn Sander (George Mason University)
12:00 PM - 02:00 PM
  Lunch Activity
02:00 PM - 03:00 PM
  Afternoon Session 1: Newton-Kantorovich Methods, Branch and Bound in Two Dimensions
Jonathan Jaquette (New Jersey Institute of Technology)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 05:00 PM
  Afternoon Session 2: CAP Challenge 2D Minimum Problem
Jonathan Jaquette (New Jersey Institute of Technology)
Jul 10, 2025
Thursday
09:00 AM - 10:15 AM
  Morning Session 1: Solving Ordinary Differential Equations Using Infinite Series
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Morning Session 2: Numerical Methods Using Taylor and Fourier Series
Jonathan Jaquette (New Jersey Institute of Technology)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Afternoon Session 1: CAP Challenge Galactic Escape in the Henon Heiles Equation
03:00 PM - 03:10 PM
  Group Photo
03:10 PM - 03:40 PM
  Afternoon Tea
03:40 PM - 05:00 PM
  Afternoon Session 2: Presentation of the Group Projects and Voting Opens
Jonathan Jaquette (New Jersey Institute of Technology), Evelyn Sander (George Mason University)
Jul 11, 2025
Friday
09:00 AM - 10:15 AM
  Morning Session 1: Periodic Orbit for Ordinary Differential Equations
Jonathan Jaquette (New Jersey Institute of Technology)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Morning Session 2: Improved Estimates on CAP Challenge 1D Integral Problem
Jonathan Jaquette (New Jersey Institute of Technology)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Afternoon Session 1: Fast Spectral Methods in Theory and Practice (FFT)
Evelyn Sander (George Mason University)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:45 PM
  Afternoon Session 2: CAP Challenge Periodic Orbits in the Henon Heiles Equation
Evelyn Sander (George Mason University)
04:45 PM - 05:00 PM
  Project Groups Assigned
Jul 14, 2025
Monday
09:00 AM - 10:15 AM
  Morning Session 1: Continuation with Respect to a Variable
Evelyn Sander (George Mason University)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Morning Session 2: Validated Continuation
Evelyn Sander (George Mason University)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Afternoon Session 1: Bifurcation
Jonathan Jaquette (New Jersey Institute of Technology)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Afternoon Session 2: Group Work on Long Term Projects
Alanna Haslam-Hyde (Boston University), Michael Storm (New Jersey Institute of Technology)
Jul 15, 2025
Tuesday
09:00 AM - 10:15 AM
  Morning Session 1: Tail Bounds: Completing the Proof of the Integration Estimates
Jonathan Jaquette (New Jersey Institute of Technology)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Morning Session 2: Validate Galactic Escape in Henon Heiles
Jonathan Jaquette (New Jersey Institute of Technology)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:00 PM
  Afternoon Session 1: Boundary Value Problems
Evelyn Sander (George Mason University)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Afternoon Session 2: Group Work on Long Term Projects
Alanna Haslam-Hyde (Boston University), Michael Storm (New Jersey Institute of Technology)
Jul 16, 2025
Wednesday
09:00 AM - 10:15 AM
  Morning Session 1: Validation of Periodic Orbit in Henon Heiles
Jonathan Jaquette (New Jersey Institute of Technology)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Morning Session 2: Group Work on Long Term Projects
Alanna Haslam-Hyde (Boston University), Michael Storm (New Jersey Institute of Technology)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Afternoon Session 1: Validation for a Boundary Value Problem
Evelyn Sander (George Mason University)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 05:00 PM
  Afternoon Session 2: Group Work on Long Term Projects
Alanna Haslam-Hyde (Boston University), Michael Storm (New Jersey Institute of Technology)
Jul 17, 2025
Thursday
09:00 AM - 10:15 AM
  Morning Session 1: Higher Dimensional Problems
Evelyn Sander (George Mason University)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 12:00 PM
  Morning Session 2: Group Work on Long Term Projects
Alanna Haslam-Hyde (Boston University), Michael Storm (New Jersey Institute of Technology)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Afternoon Session 1: Chebyshev and Other Bases
Jonathan Jaquette (New Jersey Institute of Technology)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 05:00 PM
  Afternoon Session 2: Group Work on Long Term Projects
Alanna Haslam-Hyde (Boston University), Michael Storm (New Jersey Institute of Technology)
Jul 18, 2025
Friday
09:00 AM - 10:15 AM
  Morning Session 1: Looking Forward: Current Trends in the Field
Jonathan Jaquette (New Jersey Institute of Technology), Evelyn Sander (George Mason University)
10:15 AM - 10:30 AM
  Morning Break
10:30 AM - 11:30 AM
  Morning Session 2: Group Work on Long Term Projects
Alanna Haslam-Hyde (Boston University), Michael Storm (New Jersey Institute of Technology)
11:30 AM - 12:00 PM
  Participant Survey
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Afternoon Session 1: Group Work on Long Term Projects
Alanna Haslam-Hyde (Boston University), Michael Storm (New Jersey Institute of Technology)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 05:00 PM
  Afternoon Session 2: Presentation of Long Term Projects and Wrap Up
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