In what way are you weak on proofs? Are there gaps in the logic? Are you unable to see how to prove something? Do you confuse sufficiency with necessity? Or...?Arnoldjavs3 said:I'm a CS student and I'm about to take discrete mathematics next two semesters. My proofs are very weak and I want to change this. (I'm told discrete math is a lot of proofs.)
Are there any books/courses/resources to help me work my way up? I have a summer to prepare for.
Not knowing where to begin. How to make proper use of information that they already give me.haruspex said:In what way are you weak on proofs? Are there gaps in the logic? Are you unable to see how to prove something? Do you confuse sufficiency with necessity? Or...?
Mark44 said:Here are a couple of books I have that might be helpful to you.
"How to Read and Do Proofs, 2nd Ed." -- Daniel Solow, ISBN 0-471-51004-1
"The Nuts and Bolts of Proofs" -- Antonella Cupillari, ISBN 0-534-10320-0
A method I often used to was to try to construct a counterexample, i.e. disprove the thing to be proved. It can shed light on why the given facts prevent such a counterexample.Arnoldjavs3 said:Not knowing where to begin. How to make proper use of information that they already give me.
Arnoldjavs3 said:My proofs are very weak and I want to change this. (I'm told discrete math is a lot of proofs.) Are there any books/courses/resources to help me work my way up?
UsableThought said:You haven't said what you've actually studied in this area. If you can be specific, that might help people give you more precise recommendations.
For example, I recently took a popular introductory-level MOOC on predicate logic & proofs, via Stanford University - Introduction to Mathematical Thinking - and enjoyed it. But I can't tell from what you've said so far if this would be appropriate for you, or whether it would be too elementary.
One strategy for understanding and comprehending proofs is to break the proof down into smaller, more manageable chunks. This can help you focus on each step and better understand the logic behind it. Additionally, it can be helpful to actively engage with the proof by asking yourself questions and trying to come up with counterexamples.
Improving your logical reasoning skills takes practice and patience. One way to do this is by regularly working on logic puzzles and problems. You can also try to explain mathematical concepts and proofs to others, as this can help you solidify your understanding and reasoning abilities.
There are many resources available to help you improve your ability to work with proofs. Some options include textbooks, online tutorials and videos, practice problems and exercises, and seeking help from a math tutor or professor. It can also be helpful to join a study group or attend a workshop on proofs.
Staying organized is key when working with proofs. One way to do this is by writing down all the given information and what you are trying to prove. Then, clearly outline the steps you need to take to reach the proof. It can also be helpful to use different colors or symbols to distinguish between different parts of the proof.
One common mistake when working with proofs is assuming that a statement is true without actually proving it. It is important to always back up your claims with solid reasoning and evidence. Another mistake is skipping steps or not clearly explaining each step in the proof. It is important to be thorough and precise when working with proofs.