Model of Enrollment 🎓 📊

A detailed model to understand and predict student enrollment for postgraduate programs based on various factors. Dive in to explore how different parameters affect the enrollment decisions of students!

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🌟 Overview

We're aiming to craft a mathematical model that's rooted in real-world conditions but also accounts for hypothetical scenarios, providing a comprehensive understanding of the enrollment landscape.

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🎯 Preconditions:

• 🪑 100 slots available for the master's program.
• 💰 15 of those slots are funded (budgeted).

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🤔 Assumptions:

• 🎓 The number of students applying for the master's program is estimated to be between 1/3 and 1/4 of those who obtain a bachelor's degree.
• 📈 Predominantly, those who were in the upper part of the ranking will enroll in the master's program. Expected ratio is approximately 80/20.

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🎯 Target:

• 🖥️ To create a mathematical model for the enrollment of the IT Software Development stream, which can be later verified.

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📜 Parameters (Hypothetically Based):

• 📌 Initially, we will consider the model as a linear combination of elementary functions.
• ➡️ We will transition to more complex variants later.

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🛠 Model:

1. Desire to Join Masters 🎓❤️:

Let the "desire" to join the master's be represented as: $$w=\sum_{i\in S} \log{f(i)}$$

Where f(i) denotes the success metric in the i-th semester.

If w ≤ 0, the student does not go to the master's.

2. Group Equalization Coefficient 🧮:

Given the uneven distribution of groups, we introduce an equalization coefficient. For instance, groups 5-10 have a weight of c = 0.9 during enrollment.

3. Average Rating Position 🌟:

Extract insights from historical data to compute an average ranking position:

$$P = \sum_{i\in S}\frac{S[i]}{|S|}$$

4. Average Grade Calculation 📚:

Determine the student's average grade:

$$X = \sum_{i\in S}\frac{R[i]}{|S|}$$

Note: S represents the set of semesters.

5. Success Metric 🏆:

Defining success:

$$J = e^{\frac{f(i)}{X}}$$

6. Random Variable 🎲:

Capture the student's enrollment uncertainty:

$$ u=-tR\pi e^{\pi}, 0 \le R \le 1 $$

7. Foreign University Enrollment Temptation ✈️:

Higher grades might tempt students to enroll abroad:

$$ M = -\frac{2^{\frac{X}{tP}}}{P} $$

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📝 Resulting Equation:

$$A = w u + J + M$$

Here, A represents the final enrollment decision based on all the factors discussed above.

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