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!

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.

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

• 🎓 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.

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

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

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.

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.

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

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

Determine the student's average grade:

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

Note: S represents the set of semesters.

Defining success:

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

Capture the student's enrollment uncertainty:

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

Higher grades might tempt students to enroll abroad:

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

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

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