Am I good enough to make it in grad school for Math?

[fk378]

So my story is that I changed my major halfway through undergrad. I'm a senior now but I'm staying at least one more semester until I graduate with a math degree. I'm taking my first proofs courses this year, Analysis, and Algebra. I really enjoy Algebra but most of the time I look at the questions on the homework and I'm totally clueless. I understand the proofs of theorems but when I have to answer homework problems I don't know how to connect all of the proofs together to get the answer. I feel like my mind hasn't molded into the abstract mindset that you need for Algebra. I wanted to go to grad school to get a phD in math, to do research afterwards, but after taking Algebra I don't even know if I'll be able to survive the math courses in grad school.

When going into grad school for math, should I be feeling like I'm really really prepared to tackle it or is it normal to wonder if I can even do it?
Also, since I changed my major so late, I have to take 6 more math classes within the next 2 semesters. This is including 2 other requirements I still have to fulfill. So is it best to spend whole 'nother year for undergrad? So instead of graduating May 09, I would be graduating May '10. This way I can take 3 classes per semester (spring 09 I would take my 2 requirements and Algebra II...fall 09 I would take 3 math classes, and spring '10 I would take 3 math classes--so I would end up with taking an extra math class for my undergrad degree) and just concentrate on math. Would that look bad to programs that I apply to?

Ahh, anyone else just starting out in grad school that felt the same way as me?

 

[mbisCool]

Three upper level math classes in a single semester would probably be a struggle for even the brightest of students. Not saying, you cannot do this; however, if you are having difficulty with taking one upper level math class you might be setting yourself up for failure.

What are your 2 "other" required courses? I would assume they are not on par with your upper level math classes so if possible i would at least spread those over 2 semesters so you are taking 2 math classes and another non math required course instead of 3 math classes at once when possible.

Also, don't let your first exposure to proofs be daunting as many people have difficulty in this area. Just practice, and seek extra help when/if needed. Have you tried getting another book to supplement your text? I have read a lot of recommendations on PF for cheap books on topics such as introduction to proofs and they seem to have helped many others in your situation regarding difficulty in first exposure to proofs. Another option would be to acquire another text on the subject matter. It can be very beneficial to learn the material from another viewpoint.

hope this helps

 

[fk378]

Well this semester I'm currently taking 4 courses--Analysis, Algebra, Physics, and Intermediate Spanish (required). So I feel like I can't spend as much time as I would like on my math classes. Next semester I'm planning on Algebra II+2 required courses, and if I take 3 math classes throughout the next 2 semesters after spring 09, they would just be electives or 2 electives+Analysis II for one of the semesters.

Also my two other required courses are not math-related, they are for the school. (a humanities course that requires a lot of reading, and Intermediate Spanish II which assigns homework for every class).

Would this look bad to grad schools that I apply to?

 

[quasar_4]

I'm applying to physics programs, so I'm not sure it's exactly the same for math, but I think it would be in your best interests to take the extra year, and I don't think it will look bad to grad schools (so long as you keep your grades up). I had a similar experience. I added math as a second major in the spring of my junior year and had to take an extra year to fit it all in - and worst of all has been this semester, because I had to take 6 courses (4 of which were upper level math and physics, one of them a grad class) and it's practically killed me, especially with the physics gre in the midst of it all. I think it is better to spread it out and learn more from each class, rather than to cram it all in and not get as much out of the courses.

As for learning to write proofs, don't worry, many of us struggled in the beginning. There's a common misconception floating around that you have to be some genius to do math, but that's not true - if you just spend enough time studying and working at it, you can do it. The extra time would give you a lot of time to work on it. One thing that might help is to try proving the theorems in your textbook, after you've read each section. Read through the book's proof the first time, then later try to prove them by yourself without looking at the book's proof. That helped me a lot in abstract algebra and group theory.