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# MFA501 Mathematical Foundations of AI- Domain And Range

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### Summary

In this assessment, you will be given a wide range of programming exercises to complete, which require using and applying mathematical concepts. These will be submitted in Module 6 (20%) and in Module 10 (20%). This assessment is to be completed individually and you are to submit a zip file including source code, debug, and release build and supporting documents for each problem set.

### Context

This assessment activity assesses your skills in employing AI mathematical foundation to solve realworld problems and scenarios. The assessment is made of two parts due in modules 6 and 10 over the course of trimester.

### 1. Choose two of these programming exercises:

• Write a program to find the Eigenvalues of a n-by-n matrix. (bonus mark for the case that you can make it work for any nϵN; if you can’t simplify it for n=2,3,4)
• Write a program to calculate Integral of a function. (bonus mark for the case that you can make it work for most functions; if you can’t simplify the function to be polynomial)
• Write a program that gets two sets and draws Venn diagram of those sets (their intersection and union).
• Write a program to decide if a relation is a function or not and if it is a function, find its domain and range.

### 2. Choose two of these programming exercises:

Refer to this paper: https://research.ijcaonline.org/volume92/number3/pxc389495 5.pdf

And write a program that calculates the gradient for RRBF_type1 or RRBF_type2 (choose the one which you prefer).

Write a program to determine if a set of randomly produced data has a normal distribution or not (You can produce 1000 data points randomly and run your code on it).

Write a program that displays the behaviour of these two functions in the interval of [-1,1] (analyse their behaviour as x and y approach zero);

Write a programme based on a recursive function to calculate the determinant of an nxn matrix

### Answer in Detail

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