Math and Science Working Groups

Date:

Apr 15, 2025

Author:

Mark Galassi <mark@galassi.org>

Contents:

• 1. Introduction and notes for teachers
  • 1.1. Overall motivation and plan
  • 1.2. Prerequisites
  • 1.3. Notes for teachers
  • 1.4. A case to whet your appetite
• 2. Logistics for specific courses
  • 2.1. Winter/spring 2025 - math for research
  • 2.2. OLD: Fall/winter 2024 - visualizing algebra
  • 2.3. OLD: Winter/spring 2024 - math for research
  • 2.4. OLD: Fall/winter 2023 - visualizing algebra
  • 2.5. OLD: Winter/spring 2023 - math for research
  • 2.6. OLD: Winter 2022-2023

Part I -- Visualizing algebra

• 1. Visualizing algebra: motivation and review of prerequisites
• 2. Introducing symbolic algebra
• 3. Visualizing functions
• 4. The pantheon of functions
• 5. Tour of polynomial geometry
• 6. Solving difficult equations
• 7. Data visualization
• 8. Fitting
• 9. Appendix: visualizing algebra - sample lesson plans

Part II -- Math for research

• 1. Math for research: motivation and review of prerequisites
• 2. Approximating functions with series
• 3. Calculating Taylor coefficients
• 4. More taylor series
• 5. Taylor series – applications and intuition
• 6. Fourier series: the “bones” of a function
• 7. Fourier analysis on real data
• 8. Fourier analysis on sound and music
• 9. Approximating differential equations
• 10. Approximating areas and integrals
• 11. Monte Carlo methods
• 12. Finding roots of functions
• 13. Resources and further reading
• 14. Appendix: Math for research - sample lesson plans

Supplementary materials

• 1. Appendix: How to build this book
  • 1.1. Prerequisites for building the book
  • 1.2. Cloning from codeberg.org
  • 1.3. Building the book
• 2. Glossary Terms

Bibliography

[Abr21]

Jay Abramson. Algebra and Trigonometry 2e. OpenStax, Place of publication not identified, 2021. ISBN 9781938168376. URL: https://openstax.org/details/books/algebra-and-trigonometry-2e.

[Bac77]

J Backus. Musical note to frequency conversion chart. https://web.archive.org/web/20161020141910/http://www.audiology.org/sites/default/files/ChasinConversionChart.pdf, 1977. Accessed: 2016-10-20.

[Lin16]

Samuel J. Ling. University physics. volume 1. 2016.

[Sav14]

Ivan Savov. No bullshit guide to math and physics. Minireference Co., 2014.

[Wikipediacontributors25]

Wikipedia contributors. Piano key frequencies — Wikipedia, the free encyclopedia. 2025. [Online; accessed 15-April-2025]. URL: https://en.wikipedia.org/w/index.php?title=Piano_key_frequencies&oldid=1284580404.

Indices and tables

• Index

• Module Index

• Search Page