Mathematics

This mathematics section of Holistic Home Office is designed for me to learn math, as much as it is for teaching anyone else math. A lot of the content is a result of asking ChatGPT and other sources questions, and writing these stories using the ChatGPT responses as a primer. And then, continuing to study math from a variety of sources and editing and polishing and updating these stories as I continue learning.

The main reason this is an important subject for Holistic Home Office is to learn math for business and computer science. Math is very commonly used in both of those disciplines. Of course, you will be able to use the math to understand any subject you are interested in.

I’ve been thinking about studying mathematics for a while now. I have even bought some pretty big textbooks about algebra, analytical geometry, precalculus and advanced calculus. They have been sitting in my book case for a while now, unread.

The math books I have are.

I already read a tour of the calculus many years ago. It is the one book that is written as a story that you can speed read. The others are like a dictionary, full of mathematical formulas that I do not understand. You have to learn the Greek alphabet and a whole bunch of math symbols. It’s just like learning a new language, which is another not very interesting subject for me.

One of my friends says that you have to do the problems to learn math. Well, I’m kind of in a hurry. I have a ton of research material to read and solving math problems is not very interesting, in my opinion.

I want to understand the principles. What do those numbers, Greek letters and mathematical symbols and formulas mean? What are the patterns I need to recognize and understand.

Recently, I bought a copy of The Authoritative Translation of Isaac Newton’s, The Principia, Mathematical Principles of Natural Philosophy, by I Bernard Cohen, Anne Whitman and Julia Budenz. Isaac basically invents Calculus in the book. I figure that if anyone can teach me mathematics, it’s Isaac Newton.

I read most of the Principia and still don’t understand calculus. Most of it was incomprehensible. Book 1, which I presume is were Isaac first described calculus, was incomprehensible. Book 3 was a little more understandable. I could understand planets orbiting the sun and influencing each other. I still did not really understand the math.

Reading the books and writing these stories will help me understand the math. I’m probably going to have to do some math problems. I asked ChatGPT a bunch of questions and have made several stories based on the answers. I’ll learn a lot about math by editing and polishing the stories.

Part of the problem is knowing what questions to ask. Were do I start? What are the important questions? I’ve studied math quite a bit over the years. I’ve got to figure out what story the numbers are telling. Stories are interesting.

I talk and write a lot about the rule of law in the stories on this website. Freedom is lawful. Language is the most primal rule of law in human consciousness. There is natural law and the divine rule of law. Natural law is a subset of the divine rule of law. Mathematics is a very important dimension of the rule of law governing natural history.

Mathematics will help you understand the finances of your free enterprise. It will help you understand the computer science. Math is feature of the rule of law underlying natural history. Understanding the principles of mathematics will help you understand the natural laws governing all natural history. I will work on making this section a selection of stories that make it as easy as possible to learn math.

There is a lot of repetition in the section, which is a good thing. Just read through all the stories and let the results be what they are. Pay attention to the patterns. There is a mathematical structure in natural history.

Get familiar with that structure, to improve your understanding of the intellectual landscape we are all living and working in. Other than your faith, understanding mathematics is about as close to perceiving objective reality as you can get. 2 + 2 = 4, no matter what your subjective perspective is.

A Mathematical Alphabet

Here’s a list of the Greek alphabet, including both uppercase and lowercase letters, along with their English transliterations:

• Α α alpha a father
• Β β beta b
• Γ γ gamma g
• Δ δ delta d
• Ε ε epsilon e end
• Ζ ζ zêta z
• Η η êta ê hey
• Θ θ thêta th thick
• Ι ι iota i it
• Κ κ kappa k
• Λ λ lambda l
• Μ μ mu m
• Ν ν nu n
• Ξ ξ xi ks box
• Ο ο omikron o off
• Π π pi p
• Ρ ρ rho r
• Σ σ, ς sigma s say
• Τ τ tau t
• Υ υ upsilon u put
• Φ φ phi f
• Χ χ chi ch Bach
• Ψ ψ psi ps
• Ω ω omega ô grow

https://web.mit.edu/jmorzins/www/greek-alphabet.html

The Greek alphabet has been used since the late 9th or early 8th century BC and is the ancestor of many other alphabets, including Latin and Cyrillic. It’s used in many fields today, such as mathematics, science, engineering and fraternity and sorority names.

Mathematical formulas use a wide range of symbols to represent operations, relations, and other concepts. Here’s a list of common mathematical symbols and their meanings:

1. + (Plus Sign) – Addition
2. – (Minus Sign) – Subtraction or Negative
3. ×, * (Multiplication Sign) – Multiplication
4. ÷, / (Division Sign) – Division
5. = (Equal Sign) – Equality
6. ≠ (Not Equal Sign) – Inequality
7. < (Less Than Sign) – Less than
8. > (Greater Than Sign) – Greater than
9. ≤ (Less Than or Equal To) – Less than or equal to
10. ≥ (Greater Than or Equal To) – Greater than or equal to
11. ( ) (Parentheses) – Grouping of terms or operations
12. [ ] – Grouping of terms or operations, often used within parentheses
13. { } (Braces) – Set notation or grouping in more complex expressions
14. √ (Square Root Sign) – Square root
15. | | (Absolute Value Sign) – Absolute value
16. ∑ (Sigma) – Summation
17. ∏ (Pi) – Product notation
18. ∫ (Integral Sign) – Integral
19. d/dx (Derivative Sign) – Derivative with respect to x
20. ∂ (Partial Derivative Sign) – Partial derivative
21. ∞ (Infinity Sign) – Infinity
22. ∈ (Element Of) – Element of a set
23. ∉ (Not an Element Of) – Not an element of a set
24. ⊂ (Subset Of) – Subset
25. ⊄ (Not a Subset Of) – Not a subset
26. ∪ (Union) – Union of sets
27. ∩ (Intersection) – Intersection of sets
28. ∃ (There Exists) – Existential quantifier
29. ∀ (For All) – Universal quantifier
30. ⇒ (Implies) – Implication
31. ⇔ (If and Only If) – Bi-conditional
32. ∇ (Nabla/Del) – Gradient or del operator
33. ℝ (Real Numbers) – Set of real numbers
34. ℤ (Integers) – Set of integers
35. ℚ (Rational Numbers) – Set of rational numbers
36. ℕ (Natural Numbers) – Set of natural numbers
37. ℂ (Complex Numbers) – Set of complex numbers

Algebra Symbols
Variables and Constants:
x (variable) – unknown value to find
≡ (equivalence) – identical to
≜ (equal by definition) – equal by definition
:= (equal by definition) – equal by definition
~ (approximately equal) – weak approximation
∝ (proportional to) – proportional to

Functions:
f (function of x) – maps values of x to f
(f ∘ g) (function composition) – composition of functions

Logic Symbols:
⋅ (and) – and
^ (caret) – and
& (ampersand) – and
⇔ (equivalent) – if and only if
↔ (equivalent) – if and only if
∀ (for all) – for all

Geometry and Trigonometry Symbols
Points and Lines:
AB (line segment) – line from point A to point B
≅ (congruent to) – equivalence of geometric shapes and size
|x-y| (distance) – distance between points x and y

Angles and Shapes:
π (pi constant) – ratio between circumference and diameter of a circle
rad (radians) – angle unit
grad (gradians) – angle unit

Calculus and Analysis Symbols
Limits and Derivatives:
lim (limit) – limit value of a function
y” (second derivative) – derivative of derivative
∫ (integral) – opposite to derivation
∫∫ (double integral) – integration of function of 2 variables
∫∫∫ (triple integral) – integration of function of 3 variables

Complex Numbers:
Re (real part) – real part of a complex number
Im (imaginary part) – imaginary part of a complex number
|z| (absolute value) – absolute value of a complex number
arg (argument) – argument of a complex number

Statistics and Probability Symbols
Descriptive Statistics:
∑ (summation) – sum of all values in range of series
∏ (product) – product of all values in range of series

Inferential Statistics:
e (e constant) – base of natural logarithm
γ (Euler-Mascheroni constant) – constant in mathematics
φ (golden ratio) – golden ratio constant
π (pi constant) – ratio between circumference and diameter of a circle

Brave Leo

These symbols are the building blocks of mathematical notation, allowing for the concise expression of mathematical concepts and operations.

Sources:

ChatGPT
Brave Leo