Final answer:
The student must create a Java program with a GUI that uses the Math class to perform mathematical operations, display results, and include comments for code clarity.
Step-by-step explanation:
The task described requires creating a program in Java that uses the Math class to perform various mathematical operations and display the results in a user interface. Designing a form in Java typically involves using a graphical user interface (GUI) toolkit like Swing or JavaFX. Each button in the form should be linked to an event handler that invokes the respective mathematical operation when clicked. You would use methods from the Java Math class such as Math.sqrt() for square root, Math.pow() for exponentiation, and others for different mathematical tasks. It is crucial to test the program thoroughly to ensure that all computations are accurate and that the UI behaves as expected.
Moreover, the program should follow best practices of coding by including comments that explain the purpose of various sections of the code. This is helpful not only for grading purposes but also for any future maintenance or expansion of the program. Mathematical principles and algebraic manipulation may be required to prepare the inputs and interpret the outputs from the methods used from the Math class.