Which mathematics courses should I take?

[Sunflower1217]

Hello everyone!
I am a high school junior with a great love for mathematics! I have been taking math courses at a nearby university since the end of sophomore year. So far I have taken Multivariable Calculus and Ordinary Differential Equations and received A's in both courses. I would love to take two math courses this summer, but I am at a loss for which ones I can take and succeed in. I know that I will definitely be taking Linear Algebra, but I can't decide on my second course! Here are my current options:

Calculus IV (which is like Introduction to Real Analysis...I think)
Complex Analysis
Partial Differential Equations

I greatly appreciate everyone's help with my question!
Thank you!
Sunflower1217

 

[jbmiller]

This doesn't really answer your question, but how long were both of the courses? And what high school courses have you taken?

 

[Sunflower1217]

Both my Multivariable Calculus and Differential Equations courses were a semester long at the university. Before taking these courses, I took AP Calculus BC and AP Statistics as a sophomore at my high school. I hope this additional information helps! Thank you!

 

[thrill3rnit3]

spend time with olympiad problems! They're more fun!

 

[micromass]

What do you want to go into later?

If you're planning to do physics or applied math, then take PDE.
If you're planning to go into pure math, then I think Calc IV would be most suitable right now (not that complex analysis or PDE is a bad option for a math major)

 

[Sunflower1217]

Micromass, thank you for your response! I had no idea that the different courses were more applicable to different fields! I'm not entirely sure if I want to go the applied or pure route yet. As far as difficulty, which of the courses is the most challenging and least challenging in your opinion? Thank you for all of your help!

Thrill3rnite3, that is good advice as well! Sometimes it is good to take a break and have some genuine math fun! :)

 

[bpatrick]

if it's offered, definitely take linear algebra. if it's not, you might enjoy the calc iv + complex analysis combo.

 

[Robert1986]

If I were you, I'd do the Calc 4 thing and here's why. If you decide to do Math, and Calc 4 is like an "Advanced Calc" class, then you can get your feet wet over the summer doing more proof based stuff (i.e. real math.) You'll also be doing a little of this in linear algebra. PDEs and Complex Analysis are good, but since it is the Summer, they will be done at a slightly faster pace than normal. This isn't all that bad with the Calc 4 since you will, presumably, be taking Analysis next semester.