Prototypes in Javascript to Typescript Syntax

In typescript you use classes, the compiler will do the prototype work for you.
You code is equivalent to:

class Module {
    public name: string;

    constructor(name: string) {
        this.name = name;
    }

    toString(): string {
        return this.name;
    }
}

class Student {
    public name: string;
    public studentNumber: number;
    public bookedModules: Module[];

    constructor(name: string, studentNumber: number) {
        this.name = name;
        this.bookedModules = [];
        this.studentNumber = studentNumber;
    }

    bookModule(book: Module): void {
        this.bookedModules.push(book);
    }

    bookedModuleNames(): string[] {
        return this.bookedModules.map(book => book.name);
    }
}

(code in playground)

Which compiles into:

var Module = (function () {
    function Module(name) {
        this.name = name;
    }
    Module.prototype.toString = function () {
        return this.name;
    };
    return Module;
}());
var Student = (function () {
    function Student(name, studentNumber) {
        this.name = name;
        this.bookedModules = [];
        this.studentNumber = studentNumber;
    }
    Student.prototype.bookModule = function (book) {
        this.bookedModules.push(book);
    };
    Student.prototype.bookedModuleNames = function () {
        return this.bookedModules.map(function (book) { return book.name; });
    };
    return Student;
}());

Use classes - typescript will generate this code for you:

class Module {
    constructor(public name) {
    }

    toString() {
        return this.name;
    }
}

class Student {
    bookedModules: Module[];   

    constructor(public name, public studentNumber) {
        this.bookedModules = [];
    }

    bookModule(bookedModule: Module) {
        this.bookedModules.push(bookedModule);
    } 

    //...
}