UTK - Math 518 - Fall 2024
Mathematics in Industry
TR 5:40-6:55, Ayres 121
Qualifies for the Interdisciplinary Graduate Minor in Computational Science (IGMCS) program
  •   Course Announcement   (printable PDF)   ( comments from former students)
  •   Course Syllabus

  •   Term/Team Project
  •   Guide for preparing Project Reports
  •   Guide for preparing a proposal

  • Math Modeling: Computing and Communicating
  • MathModels.org
  • PICmath case studies
  • NASA Computational Case Studies
  • Mathematics for Planet Earth
    The ASSIGNMENTS are here
    Ten Commandments of Computer Ethics
    "The nice thing about computers is that they will do exactly what you tell them to do.
    Unfortunately, they will do it exactly, so you need to get your instructions exactly right."
                      --David J. Eck, The Most Complex Machine, p.173         		"A computer lets you make more mistakes faster than any invention in human history,
    with the possible exception of handguns and tequila."
                      -- Mitch Ratliffe, Technology Review, Apr. 1992
  • POSEIDON: Efficient Foundation Models for PDEs May 2024, amazing what it can do!!! ← NEW
  • AI and Mathematics Terence Tao lecture at IMO, Aug.2024 ← NEW
  • AI Hype, NPR Planet Money, Aug.2024 (a more sober view on why AI may be overrated...) ← NEW
  • Hybrid modeling design patterns J.Math.Industry 14:3, Mar.2024 excellent ← NEW
  • NeuralUQ SIAM Review 66, Mar.2024 ← NEW
  • AI for Science Weinan E, SIAM News, Dec.2023 (superb! grand synthesis of ideas) ← NEW
  • Data Scientists in High Demand in AI Job Market Nov.2023 need statistics, math, coding, strong communication/project mgmt skills
  • The Universal Approximation Theorem, DeepMind Blog, Mar.2023 (detailed explanation, and of how Neural Nets work)
  • Hybrid modeling: towards the next level of scientific computing in engineering J.Math.Industry, 2022
  • Ten computer codes that transformed science, Nature Feb.2021: Fortran compiler #1!
  • Machine Learning and Computational Mathematics Weinan E, Commun. Comput. Phys., 28:1639-1670, 2020
  • Deep Learning: An Introduction for Applied Mathematicians SIAM Review 2019, excellent
  • How-To Essentials (unix,vi,zip,Xwindows,gnuplot,f77,WWW)   PDF for printing
  • gnuplot basics ,   a short intro ,   gnuplot FAQ,   the gnuplot site   and   gnuplot for win32
      gnuplot - How to print ,    gnuplot - On the fly (on unix/Linux)  and  template (for win or linux)

  • WSL_ubuntu (setup instructions) simplest way to have Linux on Windows10/11  
  • VirtualBox next best way to have Linux on Mac or Win   instructions and set up shared folder
  • Linux cheat sheet , very extensive, more than you really need...
  • tcsh shell in Linux: setup-tcsh
  • zip archive/compress for win32/64 (zip/unzip entire folders): 7-Zip   (free!)
  • VI editor vim ,   most powerful editor, available for all platforms (free!)   vi_QuickGuide.pdf
  • Remote login tools for win: PuTTY and PSCP   or:   openSSH   or:   SSH Tunnel   (free!)
  • X Windows on your PC:   Xming   or   NX Free   ...but best is   WSL for Win10/11   or VirtualBox
  • LaTeX help 1.1
  • UTK computer and email accounts , in particular Linux/Volweb accounts
  • UTK-ORNL Joint Institute for Computational Sciences (JICS)
  • Interdisciplinary Graduate Minor in Computational Science (IGMCS)
    Computational Resources    
  • on UNIX/Linux and VI editor         • on FORTRAN and C                 • on Matlab and Maple
  • on Computational Science           • on Internet - WWW - HTML           • Examples - Simulations
  • Modeling Books                    • Think Python good for self-study
  • Pitfalls in Computation SIAM News, Dec.2019     The Perils of Floating Point Lahey 1996, examples of machine arithmetic pitfalls
  • Research and Education in Computational Science and Engineering SIAM Review, Sep 2018 (excellent overview of the field)
  • Thoughts about Mathematical Modeling(.pdf) by A. Neumaier,   and a nice overview of Numerical Analysis(.pdf) by A. Iserles
  • Some useful shell scripts, in particular tcsh setup
  • Some useful aliases and how to set them up
    About Mathematics
  • AI for Science Weinan E, SIAM News, Dec.2023   (superb! grand synthesis of ideas) ← NEW
  • Data Scientists in High Demand as AI Job Market Grows Nov.2023 need statistics, math, coding, strong communication, project mgmt skills ← NEW
  • In AI, is bigger always better? Nature, Mar.2023, profound issues about Generative AI, LLMs ← NEW
  • Big Data / Data Science: Data Science Programs Guide for Students
  • DeepXDE: A Deep LearningLibrary for Solving Differential Equations, by Lu-Meng-Mao-Karniadakis, SIAM Review 63(1):208-228, 2021
  • The $25,000,000,000 Eigenvector: The Linear Algebra behind Google ( SIAM Review 48(3):569-581, 2006)
  • Making Do with Less: An Introduction to Compressed Sensing ( SIAM Review 55(3):547-566, Sep.2013)   central ideas
  • Illustrating the Impact of the Mathematical Sciences nice! ← NEW
  • How Imaginary Numbers Were Invented, Veritasium, excellent video, very revealing history and story, Nov.2021
  • A New IEEE 754 Standard for Floating-Point Arithmetic in an Ever-Changing World SIAM News, July 2021
  • The role of applied math in real-time pandemic response, excellent talk by Nina Fefferman (UTK), Apr.2020
  • DEs, a tourist guide   But what is a PDE?   But what is a Neural Network?   excellent videos by Grant Sanderson, of many at 3Blue1Brown
  • Timeline of Mathematics from 500BC to today, nice infographic
  • Pros and Cons of the Algorithm Age, Pew Research, Feb.2017   profound questions about the future...
  • The Map of Computer Science   and   The Map of Mathematics , by Dominic Walliman, 2017 (excellent videos!)
  • SIAM:   Math Matters, Apply It!   Math in Our Lives Video Series
  • Mathematics - The Science of Patterns and Algorithms by Ingrid Debauchies
  • Mathematicians of the Day     and     Famous Scientists chronology (from Kai Lai Chung: Green, Brown, and Probability,1995)
  • Jobs in the New U.S. Economy 2016-2026 : mathematician ranks very high, 33% growth projected
  • Cheer up, Math/CS/Engineering are most Lucrative College Majors:   Economic Value of College Majors
  • SIAM Career Center and Careers in Applied Mathematics (SIAM brochure)   . . .   and some funny occupational descriptions
  • Rankings of Mathematics Graduate Programs   (according to YOUR criteria)
  • Worldwide Job Market for Mathematicians
  • STEM Links (excellent, includes Career Resources)
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