What resources can help me succeed in honors calculus?

In summary, a student is struggling with their Analysis course, which is primarily focused on proofs. They come from a high school where they did not have much experience with proofs and are finding the course very challenging. They are already working late into the night on the problem sets and are wondering if they should drop the course. Some suggest getting tutoring or switching to an easier proof course. Others recommend forming a study group and getting a proof writing book. The student is considering dropping the course or switching to a regular calculus class. It is suggested that they continue to work hard and see how they do on the first term test before making a decision.
  • #1
plutonium11
3
0
Hey everyone,

This is my third day at university. I'm taking an Analysis course and I'm getting owned!

I came from a relatively small high school in a small town and we hardly did any proofs at all except for proving trig identities. Now this course is all proofs; I thought I can handle it but it's so hard for me. I am typing this at 11:00pm now, I've been working on the problem sets since 3:00pm today. I managed to finish about 3 questions out of the 13. I haven't even looked at my other courses yet. I feel like I'm so far behind...everyone else has fancy AP credit and stuff and I am struggling. I don't know what to do. I might be able to do well in this course but at the expense of my other 4 courses. Is this the end to my dreams of becoming a physics or math professor? Anyone have any advice for me or words of wisdom?

Sorry about rambling.
 
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  • #2
What textbook is assigned for your analysis course ?(Im simply curious)
 
  • #3
Calculus by Spivak
 
  • #4
Does your university have any courses geared towards introducing students to proof writing?
 
  • #5
no...I plan to look for a book like 'Math Proofs demystified' or something...I really hope it helps.
 
  • #6
Can you get some tutoring?
 
  • #7
Math Is Hard said:
Can you get some tutoring?

I agree with MIH - grt into tutoring, sooner rather than later.

Good luck!
 
  • #8
drop the class. freshmen shouldn't take real analysis. its just too much for the non mathematically mature. Take an easier proof course like linear algebra first.
 
  • #9
torquerotates said:
drop the class. freshmen shouldn't take real analysis. its just too much for the non mathematically mature. Take an easier proof course like linear algebra first.

I agree, get out now while you still can!

Take the book with you and study on your own pace that way you'll better prepare yourself for the next go around coming Spring Semester.
 
  • #10
How come freshmen are allowed to do analysis in their first semester? Isn't there a course pre-req for that?
 
  • #11
Oh boy, I remember my first year by reading this. I took linear algebra with a proof-oriented professor right after I took AP Calculus (= just a bunch of silly computations), and that was the first time I ever thought math was hard. Fortunately, the class was on curve, and I still managed to get an A, but at least I realized I needed some practice on proofs before I take higher-level math courses.

Now that I've taken number theory and elementary analysis, I'm relatively confident with writing proofs. But the truth is, proofs are difficult to manage at the beginning, and you need some practice with it. Have you ever studied logics (truth table, if-then statement, etc)? You'll definitely need to know a fair amount of those if you're trying to prove something.

Now, I don't know what you should do about your analysis course. A course you might want to consider taking is discrete mathematics--this course is usually required for computer science majors (and usually not required for math majors), but the course covers proof-oriented math at more elementary level than analysis (e.g. set theory, number theory, logics, inductions, etc). I'm also confused about the level of your analysis course--I know nothing about textbooks, but I thought Spivak's Calculus was more of a proof-oriented calculus textbook rather than the hard-core advanced analysis course that uses Rudin's. If that's the case, I think the level of your analysis course is just right, and it is possible that there are people in the class who think the material is difficult.

One last thing: Form a study group. This helped me a lot when I was doing homework for elementary analysis. It's also a good practice to explain your thoughts to other people in the group.

Good luck!
 
  • #12
that seems like more of an honors calc class rather than real analysis. I would consider switching to a regular calc class. As the previous poster said, getting a proof writing book( I personally like Gary Chartrand's book and Sallow's is also nice) would be ideal. Better to make a decision while switching and dropping are still options.
 
  • #13
ytoruno said:
that seems like more of an honors calc class rather than real analysis. I would consider switching to a regular calc class. As the previous poster said, getting a proof writing book( I personally like Gary Chartrand's book and Sallow's is also nice) would be ideal. Better to make a decision while switching and dropping are still options.

Yeah, he isn't doing real analysis... more like calculus on crack. Have any of you actually read Spivak?

OP, you are enrolled in an honors calculus class that is intended for pure mathematicians. It is very difficult mainly because most students are not trained in rigorous math, only computation. Since you didn't prepare ahead of time, and are on a full course load, you will have great difficulty for at the very least the first two months. Its a tough call because if you drop it, you will not be able to continue your pure math stream in upper years. If you hold on you risk getting weaker grades in other courses.

My advice is continue to work hard at it until the first term test. See what sort of grade you get relative to others and if its horrible drop down to easier calculus. Also, if you see you are not able to keep up consider changing before hand too.

Lastly, consider getting the answer book for Spivak. Full solutions will help you see how a proof ought to be.
 

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