Why am I struggling with abstract math and how can I improve?

[chimath35]

guidance on math "failure"

Can someone please give me some feedback on why I am having such a hard time with abstract

math? I went went from almost straight a's to barely being able to solve a problem in number

theory. I had someone tell me that it is like I have storage spots in my brain but they are already

filled up. My last two exams scores were 98 and 99 in calc. 3. Now I cannot seem to solve even one

problem out of my homework in number theory.

 

[Vahsek]

chimath35,

I've already read some of your previous posts before, and I'd say that you are having trouble with abstract math simply because you've never been exposed to proofs before. That being said, I remember that you were saying something about taking up an intro to proofs course next semester, so maybe after that course you'll be alright. Plus, you could also pick up some books on intro to proofs and work through them.

 

[chimath35]

Thanks Vahsek, I guess my professor just doesn't encourage me a whole lot; maybe even discourages me.

 

[Vahsek]

Thanks Vahsek, I guess my professor just doesn't encourage me a whole lot; maybe even discourages me.

Haha. I'd say most professors don't care a whole lot about undergrad students. But don't worry; as I said before, you'll be just fine after knowing how to write proofs. In fact, I guarantee that you will even get addicted to reading/writing proofs for a while... (I found proofs addictive for a while, but then most proofs started to look obvious and boring )

 

[chimath35]

Thanks, I just have a hard time following and understanding a lot of the pieces even in proofs. I can't seem to grasp many pieces maybe because of abstractness. Not seeing numbers and just seeing letters seems to be causing me problems. I can't seem to wrap my head around just all these letters.

 

[Vahsek]

Thanks, I just have a hard time following and understanding a lot of the pieces even in proofs. I can't seem to grasp many pieces maybe because of abstractness. Not seeing numbers and just seeing letters seems to be causing me problems. I can't seem to wrap my head around just all these letters.

https://www.amazon.com/dp/0521675995/?tag=pfamazon01-20

Get the above book, whether or not you are taking/going to take an intro to proofs course. Work through chapters 1,2,3 and 5. You'll have virtually no problems at all with proofs after that. Basically, you'll learn about basic logic and the main methods of proofs:
1. Direct proof
2. Proof by contrapositive
3. Existence proofs
4. Proof by contradiction
5. Proof by induction
6. Uniqueness proofs

Dude, seriously, I'm telling you: get that book asap. It's a life-saver! (Well, you won't get better at proofs in just 2 or 3 days... It's going to take you like 2-3 months, but who cares?? You'll have the summer holidays!)

 

[chimath35]

Lol, thanks; I started a whole thread having people help me understand the first proof in this book.

 

[Vahsek]

Lol, thanks; I started a whole thread having people help me understand the first proof in this book.

Oh yeah, right! Lol, I saw that thread. Although, frankly he clearly stated not to worry if you don't really understand the proof. You'll understand every aspect of it after you're done learning the techniques of proofs in the later chapters. Personally, I did not even try to understand that whole proof in the first chapter; I just moved on to the second chapter and then to third one, where he takes up that exact same proof again.

 

[lauraofrohan]

I'm surprised that you are taking number theory without a prereq in basic proofs course. I've TA'd/graded for a basic proof course at my school, and I do know of a few good books that might help you get the basics down.

This book is simple, but effective in teaching how to approach problems.

This is the book that I used when I took the course my first semester of college. I really liked it, because it explained the concepts at a very basic level. But if you are already in Number Theory, you might want to look at a different book.

I really like this book. If your schools has a subscription to Springer (which a lot of schools do), it will be free. This is a fun textbook - well-written and more challenging (in my opinion).