Four Dimensional Maths: Things to See and Hear in the Fourth Dimension - with Matt Parker

Entertaining & Interesting...

Quantum Magazine: The Peculiar Math That Could Underlie the Laws of Nature

https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

"In 2014, a graduate student at the University of Waterloo, Canada, named Cohl Furey rented a car and drove six hours south to Pennsylvania State University, eager to talk to a physics professor there named Murat Günaydin. Furey had figured out how to build on a finding of Günaydin’s from 40 years earlier — a largely forgotten result that supported a powerful suspicion about fundamental physics and its relationship to pure math."

"The suspicion, harbored by many physicists and mathematicians over the decades but rarely actively pursued, is that the peculiar panoply of forces and particles that comprise reality spring logically from the properties of eight-dimensional numbers called 'octonions.'" 

https://www.furey.space/

Cohl Furey's YouTube Channel:

• https://www.youtube.com/channel/UCvsmxUuD5ZdOGittaeosXMA/videos
• 14 videos: Division algebras and the standard model
• https://www.youtube.com/playlist?list=PLNxhIPHaOTRZMO1VjJcs7_3dgyJ2qU1yZ

Interesting Mathematician: Isaac Namioka

https://en.wikipedia.org/wiki/Isaac_Namioka

Online Calculators

This posting is intended as a placeholder for useful online calculators that I find:

1. https://getcalc.com/
2. https://www.wolframalpha.com/
• https://www.wolframalpha.com/examples/mathematics/

What's so special about the Mandelbrot Set? - Numberphile

Videos: Perspectives on the Riemann Hypothesis, Bristol 2018

Perspectives on the Riemann Hypothesis, Bristol 2018
https://vimeo.com/album/5303404
Heilbronn Institute for Mathematical Research

March 2018 (Vol.. 73) - The American Statistician: Statistical Inference in the 21st Century: A World Beyond p < 0.05

A selection of interesting article titles in the current list of articles for current edition of The American Statistician.

https://amstat.tandfonline.com/toc/utas20/73/sup1?nav=tocList
Statistical Inference in the 21st Century: A World Beyond p < 0.05

• Moving to a World Beyond “p < 0.05”
• What Have We (Not) Learnt from Millions of Scientific Papers with P Values?
• Why is Getting Rid of P-Values So Hard? Musings on Science and Statistics
• Will the ASA's Efforts to Improve Statistical Practice be Successful? Some Evidence to the Contrary
• Correcting Corrupt Research: Recommendations for the Profession to Stop Misuse of p-Values
• Quality Control for Scientific Research: Addressing Reproducibility, Responsiveness, and Relevance
• The Role of Expert Judgment in Statistical Inference and Evidence-Based Decision-Making
• Expert Knowledge Elicitation: Subjective but Scientific
• Before p < 0.05 to Beyond p < 0.05: Using History to Contextualize p-Values and Significance Testing
• The Limited Role of Formal Statistical Inference in Scientific Inference
• Large-Scale Replication Projects in Contemporary Psychological Research
• Valid P-Values Behave Exactly as They Should: Some Misleading Criticisms of P-Values and Their Resolution With S-Values
• The p-Value Requires Context, Not a Threshold
• Assessing Statistical Results: Magnitude, Precision, and Model Uncertainty
• Putting the P-Value in its Place
• Evidence From Marginally Significant t Statistics
• The p-value Function and Statistical Inference
  
• p-Values, Bayes Factors, and Sufficiency
• Limitations of P-Values and R-squared for Stepwise Regression Building: A Fairness Demonstration in Health Policy Risk Adjustment
• An Introduction to Second-Generation p-Values
• A Proposed Hybrid Effect Size Plus p-Value Criterion: Empirical Evidence Supporting its Use
• Three Recommendations for Improving the Use of p-Values
• The False Positive Risk: A Proposal Concerning What to Do About p-Values
• Moving Towards the Post p < 0.05 Era via the Analysis of Credibility
• Blending Bayesian and Classical Tools to Define Optimal Sample-Size-Dependent Significance Levels
• How Effect Size (Practical Significance) Misleads Clinical Practice: The Case for Switching to Practical Benefit to Assess Applied Research Findings
• Abandon Statistical Significance
  
• Statistical Inference Enables Bad Science; Statistical Thinking Enables Good Science
• Inferential Statistics as Descriptive Statistics: There Is No Replication Crisis if We Don’t Expect Replication
• The New Statistics for Better Science: Ask How Much, How Uncertain, and What Else Is Known
• How Large Are Your G-Values? Try Gosset’s Guinnessometrics When a Little “p” Is Not Enough
• Predictive Inference and Scientific Reproducibility
• Treatment Choice With Trial Data: Statistical Decision Theory Should Supplant Hypothesis Testing
• Multiple Perspectives on Inference for Two Simple Statistical Scenarios
• Coup de Grâce for a Tough Old Bull: “Statistically Significant” Expires
• The World of Research Has Gone Berserk: Modeling the Consequences of Requiring “Greater Statistical Stringency” for Scientific Publication
• Assessing the Statistical Analyses Used in Basic and Applied Social Psychology After Their p-Value Ban

Essence of Linear Algebra (15 videos) by 3Blue1Brown

Animated Math
https://www.3blue1brown.com/
https://www.youtube.com/c/3blue1brown

Essence of Linear Algebra (15 Video Chapters)

• https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

"3blue1brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective."

Useful References for Mathematical Notations, Symbols, and Constants

https://en.wikipedia.org/wiki/Mathematical_notation

https://en.wikipedia.org/wiki/List_of_mathematical_symbols

https://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering

https://en.wikipedia.org/wiki/List_of_letters_used_in_mathematics_and_science

https://en.wikipedia.org/wiki/ISO_31-11

https://en.wikipedia.org/wiki/Latin_letters_used_in_mathematics

https://en.wikipedia.org/wiki/List_of_mathematical_abbreviations

https://en.wikipedia.org/wiki/List_of_mathematical_symbols_by_subject

https://en.wikipedia.org/wiki/List_of_mathematical_constants

https://en.wikipedia.org/wiki/Notation_in_probability_and_statistics

https://en.wikipedia.org/wiki/Mathematical_operators_and_symbols_in_Unicode

https://en.wikipedia.org/wiki/Physical_constant

https://en.wikipedia.org/wiki/List_of_logic_symbols

https://en.wikipedia.org/wiki/Typographical_conventions_in_mathematical_formulae

http://functions.wolfram.com/Notations/
http://functions.wolfram.com/PDF/Notations.pdf

HOW TO WRITE MATHEMATICS, by P.R. Halmos

https://en.wikipedia.org/wiki/Paul_Halmos

"Paul Richard Halmos (Hungarian: Halmos Pál; March 3, 1916 – October 2, 2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor."

• https://entropiesschool.sciencesconf.org/data/How_to_Write_Mathematics.pdf
• https://www.math.uh.edu/~tomforde/Books/Halmos-How-To-Write.pdf
• http://www.stat.columbia.edu/~liam/teaching/HalmosWrite.pdf

One of "The Martians"

What Happens When Maths Goes Wrong? - with Matt Parker

Article: Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations

A very useful article to review before embarking on any experimental research efforts:

Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4877414/
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4877414/pdf/10654_2016_Article_149.pdf

Tai-Danae Bradley's Math3ma blog

A tip of the hat to my friend Dean Wampler, PhD - who mentioned this blog in a tweet.
https://www.math3ma.com/

She also wrote "What is Applied Category Theory?"

Steven Strogatz Books

I'm interested in reading the two books, in particular:

Infinite Powers: How Calculus Reveals the Secrets of the Universe
https://www.amazon.com/Infinite-Powers-Calculus-Reveals-Universe/dp/1328879984

The Joy of x: A Guided Tour of Math, from One to Infinity
https://www.amazon.com/Joy-Guided-Tour-Math-Infinity/dp/0544105850/

https://www.amazon.com/Steven-H.-Strogatz/e/B001KHB290

"Steven Strogatz is the Schurman Professor of applied mathematics at Cornell University. A renowned teacher and one of the world's most highly cited mathematicians, he has been a frequent guest on National Public Radio's Radiolab. Among his honors are MIT's highest teaching prize, membership in the American Academy of Arts and Sciences, and a lifetime achievement award for communication of math to the general public, awarded by the four major American mathematical societies. He also wrote a popular New York Times online column, "The Elements of Math," which formed the basis for his new book, The Joy of x. He lives in Ithaca, New York with his wife and two daughters."

http://www.stevenstrogatz.com/
https://twitter.com/stevenstrogatz