Hodie intrāmus villam Caeciliī.
Ambulāmus per ātrium, culīnam, hortum, et triclinium.
Personae nostrae: Caecilius, Metella, Quīntus, Grumiō, Clēmēns, ancilla, amīcus, mercātor, canis.

Parātus es?
Age, incipiāmus.

We will begin our journey by working through the Cambridge Latin Course Book 1.

This episode will help you with listening comprehension and increasing your active vocabulary for chapter 1.

In this short excursion I discuss the definition of Kolmogorov Complexity and work through a few examples.

In this episode I jump into abstract algebra.

I discuss the following topics:

1. Binary Operators

2. Closure Property

3. Commutativity

4. Associativity

5. Identity Elements

6. Inverse Elements

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:

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

Main Points:

1. Difficulty of establishing the actual (realworld) truth value is unimportant
2. 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:

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

Main Points:

1. Interrogative statements are neither T nor F.
2. #2 may be T or F depending on the value assigned to x.
3. 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.