How do you solve hard math problems?

refamiliarize yourself with all of the notation and definitions in the statement of the problem. Great tools for this are the textbook, your notes, or the internet.

Determine exactly what the problem is requiring you to find.

Write down all the given information.

Try Reflecting on Success: look through your notes and the book. Have you or the text solved similar problems to this one?

Try Working Backwards: Instead of starting from what you know and working towards what you want, start from what you want, and ask yourself what you need to get there.

Try Simplifying the Problem: set your sights a little lower, then raise them once you tackle the simpler problem.

Try Letting the Natural Cycle of problem-solving take its course: start early, try, then take a break, then try again with a friend, then take another break, then ask for help, then take a break, and try again ... very few problems worth solving can be figured out in one sitting.

Ask yourself: Does my answer make sense? Did I accomplish what the problem asked of me?

Compare answers with a friend. If your answers don’t agree, justify your reasoning to each other.