Advice for an Undergraduate Math Major (from an Undergraduate Math Major)

It's that time of year. Back to school ads are popping up. Pencils and calculators are being purchased. Syllabi are being sent out. Whether you're an incoming freshman or a senior with an eye out the door, each year brings all the stress of college life. There's no book on how to have a perfect college experience without some troubles, but there are a few things to try as you enter the new school year!

Do Practice Problems!
No one will be hovering over your shoulder making sure you understand all the math being taught to you. Lectures will cover the material, but there won't be a lot of examples assigned to you. The best way to learn the material will be to find problems to do. Sometimes professors will have graded homework, but many of them will expect you to do problems by yourselves. They will usually tell you which problems they want you to try so you can learn the material. There will be an occasion (or two, or three, or ... ) when you don't understand a problem or how to do the math. What should you do then?

Use your computer!
Sometimes, the best way to figure out a concept is to watch someone do the problem out step by step. Or to watch someone do as many problems as it takes until the concept makes sense. The easiest and most convenient place to find problems done out is, of course, the internet. Whether you want solutions to problems done out, or want a broad subject explained in depth, there are plenty of resources online. WCoM, for example, offers videos ranging from exploring the basics of different subjects within mathematics to doing out solutions of practice problems found in textbooks.                                                                                                                                                                                 
Go to Office Hours! 
Professors can seem intimidating. They have been studying mathematics for years and years, so it can be scary to approach them with a problem they've been teaching for a long time. However, every professor will at the very least give you the help necessary to understand the material, which is a very good minimum. The majority of math professors, however, will be able to offer much more. They can be references for job applications. They can offer research opportunities. And they are also a resource for any questions about math that you may have. Want to know about what kind of careers you can do with a math degree? Curious about a field of mathematics? There is no better resource for any sort of question you have about mathematics than office hours. And if you can't make office hours, many professors will be accommodating to your schedule and will be able to find time to meet with you.

Work with Friends!
Fortunately (or unfortunately, depending on your viewpoint) math is a subject with not a lot of group projects. This can make it easy to isolate yourself when doing your work. However, to quote a professor who told me this (during office hours!), math is a social activity, and should be treated as such. This isn't to say that you should copy your friend's work or offer your own work to be copied. Working together on a problem will ensure that both you and your friend understand the material and get the problem right. I've tried to take on many homework assignments by myself and ran into many hurdles along the way. Hours have been spent trying to figure out what I'm doing wrong. However, after 5 minutes with a friend, these hurdles are usually cleared. Two minds are better than one, and no where is that more true than on a math problem you can't seem to solve.

Take Breaks!

The college workload will be a lot, and there will be pressure to study all night and all day sometimes. However, there is a lot of value in taking a step away from work for a little bit. Taking a break to work out, take a walk outside, or spend time with friends is usually a good way to recover from all the work. After the break, problems that you've stared at for hours on end start to look a little more clear.

Get some sleep!
Everyone knows the stereotypical college student camped out in the library, cans of Red Bull scattered around them, pulling an all nighter studying. While that might seem like the best way to teach yourself multivariable calculus, you shouldn't ever sacrifice sleep in order to learn! The best way to go about learning something is to do a little at a time rather than all at once before a big test. I certainly can't say that I haven't crammed before, but the best test grades are those that come from taking time to learn the material and understand the concepts, while getting as much sleep as possible.

We hope this advice helps! And remember that the Center of Math website has plenty of resources for Math majors!