The topic you attempt to discuss is vast, I post some introductory thoughs for you to pick what you need and I can provide further details. Please note that my studies on Plato are related with the Morality of the Aesthetics and not with the topics you are interested in.
The question of what is ethical holds a central role in the Platonic Work. Plato started exploring the question since the period he composed "Gorgias" where he tries to examine where ethics spring from.
Being strongly influenced by the Hippocratic Doctors and the Pythagorean philosophers , Plato defines virtue as order, harmony and balance while order is composed by Justice and Prudency.
Those basic platonic thoughts regarding ethics are introduced in the "Republic" and they are connected ( again) with the trisection of the soul - a vast topic that is not of our interest in the present discussion but I can discuss later if you wish.
Having defined virtue as order, harmony and balance, Plato concludes that virtue is a characteristic of a healthy and beautiful soul. The opposite of virtue is Injustice that divides the soul and creates the inner chaos that he relates to the bad “karma” ( kakodaimonia is the word that Plato uses and that I grossly translate as "bad karma").
To elaborate this idea Plato sketches the profile of the tyrant, a passage that is a classic in the history of ideas and I am expecting that you will discuss in your courses since they are focused in leadership as well.
Now how ethics are related to mathematics?
The order and the harmony of the soul , two identities with which Plato defines virtue find ( according to Plato) their parallel to the order and the harmony of the physical word. In his famous "Timaeus" Plato discusses exactly that; the importance of numbers, symmetry, harmony, order and cosmic balance. In "Timaeus" Plato explores the philosophical image of the nature. For example, he says that the starts are living beings( empsyxa= with a soul) and the perfection of their soul is expressed where ?
In Mathematics of course!
The humans and their soul constitute—according to Plato- a microcosm, the essence of their soul is based on the circular movements that can be described by mathematic equations. Thus the connection with the maths.