The Mathematical Universe John Faucett

In this episode, I ramble on a bit about some of the parts of neural network mathematics, particularly activation functions and bias.



1. Activation Functions: https://en.wikipedia.org/wiki/Activation_function



I also talk about a book by Jeff Heaton, Introduction to the Math of Neural Networks. It's very short and simple but a nice fast read for a quick introduction to the topic. Check it out if you're interested: https://www.amazon.de/-/en/Jeff-Heaton-ebook/dp/B00845UQL6

In this episode we discuss the conditional proposition or the conditional sentence

Topics:

1. What is If P, then Q. (conditional)

2. If P, then Q (definition, antecedent, consequent)

3. Truth Table for if P, then Q.

4. Thinking about and conceptualizing the conditional in terms of promises.

5. True & False Examples

6. The Converse

7. The Contrapositive

8. The Equivalence of if P, then Q ~Q, then ~P.

In this episode I talk about



1. Logical Connectives: Conjunction, Disjunction, Negation.

2. Truth Tables

3. Examples of True and False well-formed formulas using conjunction, disjunction and negation.

4. Propositional forms.

What is a Proposition?

A statement that can be true of false.



Examples:


sqrt(2) is irrational.
1+1=5
The tiger will become extinct before the Gorilla on the planet Earth.
Socrates was left handed.



Main Points:


Difficulty of establishing the actual (realworld) truth value is unimportant
Some values can be immediately computed as T or F #1 or #2, others may take many years #3 or we may never know #4.



Non-Proposition Examples:


Can you please pass me the Ketchup?
x^2 = 49
This sentence is false.

Main Points:


Interrogative statements are neither T nor F.
#2 may be T or F depending on the value assigned to x.
Neither T nor F - a paradox.

Atomic Propositions - do not contain any other propositions - ex: It is raining. 

Compound Propositions - are formed by combining logical connectives with atomic (simple) propositions - ex: I am drinking coffee and its raining outside.