Trouble in Discrete math will it affect my graduate school opportunities?

[Hercuflea]

Hello everyone,

I'm a first time poster and I just want to say this forum is great. Every time I have a question Physics Forums is the first site to answer it.

So lately I have been really struggling in my Discrete Mathematics I course at my university. This is one of the few times in college (127 credit hours - 3.8 GPA) that I have had trouble in a class because I legitimately did not understand it. The thing that is giving me the most trouble is, predictably, Proofs by Induction. It doesn't help that I have absolutely no idea what kind of problem my professor will throw at me on the quizzes or test. Today I failed a quiz because my mind just went absolutely blank on an induction proof.

One of the proof that stumped me went something like this:

Prove by math induction that P(n): 1+4+7+...+(3n-2) = (n(3n+1))/2Anyways, I am worried that I may get a B or even a C in this class, and I really want to be accepted into a Master's or Ph. D. program in nuclear engineering (preferably Ga Tech, maybe UMich-Ann Arbor). If worst comes to worst would I still have a chance at being accepted into a good PhD program in that field? I have made nearly perfect 100's in my Calc 1-3, chemistry, and Linear algebra, and I am doing satisfactory in differential equations.

Thanks

 

[Hercuflea]

Sorry, I forgot to add that I am a Math major - my school does not offer any physics or engineering degree programs, and I recently switched from Economics, so math was the best option for me.

 

[Hercuflea]

bump - an answer would be nice

and an update: I just got another 78 on a quiz on basic counting principles (pigeonhole, etc) I seriously thought I had a perfect 100 on it when I walked out of there. Now I feel like sh**

 

[xdrgnh]

I highly doubt it because discrete math isn't used in Nuclear engineering.

 

[Hercuflea]

Thanks, I just hate to think about what it might do to my gpa

 

[Dembadon]

...my school does not offer any physics or engineering degree programs...

If you're planning on pursuing graduate studies in engineering, the above is likely to be more of an issue than your grade in discrete math.

Regarding your struggles with writing proofs; a first course in proof writing is awkward for most students. If you need more practice with induction and the pigeonhole principle, then grab some resources and start reading proofs which use these concepts. However, do not simply read through them and move on when you feel like you understand them; you should verify each claim for yourself and try to prove things on your own. This is the only way to become proficient at proving things. I'll quote/paraphrase Hungerford's message to the student in his introductory abstract algebra text, which still applies to your discrete math course:

Read the text with pencil and paper in hand before looking at the exercises. When you read the statement of a theorem, be sure you know the meaning of all the terms in the statement of the theorem. For example, if it says "every finite integral domain is a field," review the definitions of "integral domain" and "field" -- if necessary, look up the definitions online or in another text.

Once you understand what the theorem claims is true, then turn to the proof. Remember, there is a big difference between understanding a proof in the text and constructing one yourself. ... Begin by skimming through the proof to get a general idea of its outline before worrying about the details in each step. It's easier to understand an argument if you know approximately where it's headed. Then go back to the beginning of the proof and read it carefully, line by line. If it says "such-and-such is true by theorem 5.18," go back and check to see just what Theorem 5.18 says and make sure you understand why it applies here. When you get stuck, take that part on faith and finish the proof. If you still get stuck after that, ask a professor.

The bold emphasis in the above quote was added by me because I believe it is extremely important to one's success as a mathematics major. Following Hungerford's advice with diligence and patience with yourself will work wonders. Everyone struggles at some point; how you respond is extremely important to your success, or failure. Best of luck to you!