git clone https://github.com/Dillettant/Athena

cd Athena

conda create -n athena python=3.10 -y

conda activate athena

pip install -r requirements.txt

export OPENAI_API_KEY=$YOUR_OPENAI_API_KEY

export OPENAI_API_KEY='sk...DAHY'

cd src/

python test.py

[DEBUG] Topics: 
1. "Analyzing the Impact and Efficiency of Different Voting Systems through Mathematical Modelling"
2. "A Comprehensive Study about the Probability and Statistical Implications in Casino Games"
3. "The Application and Effectiveness of Cryptography in Digital Security: A Mathematical Perspective"
select one of the topic.. 

Admin (to chat_manager):

Write an IB essay "Evaluating the Efficiency and Impact of Cryptographic Algorithms in Cybersecurity: A Mathematical Analysis" with 4000 words.

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subject_expert (to chat_manager):

[plan]
Title: Evaluating the Efficiency and Impact of Cryptographic Algorithms in Cybersecurity: A Mathematical Analysis

1. Introduction/Rationale (Word Count: 300)
- Purpose: To explore the significance of cryptographic algorithms in the digital age where cybersecurity threats are omnipresent, and to understand and evaluate their mathematical complexities and efficacies.
- Personal Motivation: Recount a scenario wherein the breach of personal data led to a growing concern over cybersecurity and a fascination with the cryptographic measures employed for protection. This intrigue fueled a deeper look into the underlying mathematics of these cryptographic systems.
- Research Objective: To quantitatively analyze and assess the efficiency and impact of various cryptographic algorithms, with a focus on their computational complexity, security level, and practical performance in cybersecurity applications.

2. Background Information (Word Count: 500)
...

Admin (to chat_manager):

Write the following paragraph:
 1.Introduction/Rationale
pose: To explore the significance of cryptographic algorithms in the digital age where cybersecurity threats are omnipresent, and to understand and evaluate their mathematical complexities and efficacies.
sonal Motivation: Recount a scenario wherein the breach of personal data led to a growing concern over cybersecurity and a fascination with the cryptographic measures employed for protection. This intrigue fueled a deeper look into the underlying mathematics of these cryptographic systems.
earch Objective: To quantitatively analyze and assess the efficiency and impact of various cryptographic algorithms, with a focus on their computational complexity, security level, and practical performance in cybersecurity applications. 
 total words:300
...
In the vibrant realm of casino games, understanding the dance of chance is paramount. At its core lies probability theory, a branch of mathematics that navigates through the potential outcomes in games of chance. It all begins with a well-defined set of possibilities, known as the sample space, and the events or outcomes that may occur within it. The probability of an event is simply the count of favorable outcomes divided by the total number of outcomes - a formula elegantly captured by \( P(E) = \frac{n(E)}{n(S)} \).

Random variables come into play when outcomes are numerical, such as the dots facing up after a dice toss. These variables allow us to calculate predicted results or 'expected values'. The expected value—what one might anticipate in the long run—is found by weighting each possible outcome by its corresponding probability and summing them up: \( E(X) = \sum (x_i \cdot P(x_i)) \).

Another vital tool is variance, which captures how much the outcomes spread out from the expected value. It's described mathematically by \( Var(X) = E((X - E(X))^2) \), offering a gauge of a game's risk level. The square root of variance, the standard deviation, is especially handy as it measures risk in the original units of the data.

Statistical independence is the notion that one event doesn't influence another, essential when dealing with sequential actions, such as separate draws from a deck of cards. Independence is central to correctly calculating combined event probabilities, a frequent aspect of gaming strategies.

The binomial distribution allows us to predict outcomes for a specific number of successes in a series of independent trials, such as betting on red in roulette several times. It's a model that exemplifies the predictability embedded within supposedly random events.

Probability distributions chart all the potential outcomes for a variable and their likelihoods, summing up to 1. These can be discrete or continuous, painting a picture of what to expect from a game on any given play.

Breaking down these foundational concepts, such as random variables, expected value, variance, statistical independence, and binomial distribution, and applying probability to sample spaces in games of chance, we can interpret the erratic nature of games into more measured elements. This treatment not only deepens our strategic understanding but creates a bridge from abstract math to the tangible decisions made at the tables and slot machines.
...