<p>or anyone capable of answering,</p>
<p>some professors and friends alike cautiously warn that
upper division proof-based theory mathematics is somewhat
like either you get it or you don't. even the berkeley math
department website warns prospective student applying for
the math major about this drastically different nature of
upper div math.</p>
<p>sure if you try really hard, you may run away with a B or C but
i heard getting an A in these classes really requires you to have
the type of brain suited for this kind of math as opposed to just
computation.</p>
<p>so how much of this is really true?</p>
<p>i'm probably taking math 55 next semester but i just want to know how true
the rumors are.</p>
<p>ya… good question. I want to know this too. I’ve found Math 1A/B to be pretty easy so far. Except for delta/epsilon proofs which i still haven’t understood despite trying really hard. I just don’t get the hang of it. Are upper division proofs in any way similiar to these?</p>
<p>Well, here’s the deal. What is the purpose of these fundamental upper divisions? To understand this, we should say something about what math is about in general. The subject is not fundamental about making things amenable to calculation, building something, etc – it’s about classifying natural objects. What you see in the upper division are books in which the works of several mathematicians on fundamental classical problems are presented, so that you know the state of affairs in the current day and age. They’re presenting a refined theory that’s meant to change how you look at certain objects. For instance, complex analysis should change how you view functions on the complex plane dramatically, because it really tells you that things can’t behave as scarily as you might expect – there’s a lot of restriction on what things can do, that makes the objects nice to work with for those who need to use them.</p>
<p>So to answer CCnewbie, epsilon-delta proofs are just using the definition to determine that a limit exists. In the higher levels, it’s closer to tossing around abstract perspectives on how certain things behave to determine some nontrivial conclusion. </p>
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<p>Nobody has the brain already developed, but some have the potential to do it. I.e. some have the potential to change their way of thinking drastically and are already strong logical thinkers, and thus succeed. I think a lot of bright people have trouble because they aren’t able to change their thought process to match the mathematician’s. The only way to figure out if you can do it really is to test yourself out and see how you like it. Maybe it’s for you or maybe you prefer to use the tools of mathematicians to do involved applications, who knows. All about finding where you fit in.</p>
<p>Hey mathboy, a few questions, if you don’t mind. Thanks in advance!</p>
<p>1). I’m considering focusing on theoretical CS (but not in crypto). What math classes are the most beneficial for it? Off the top it seems like Analysis and Linear Algebra are pretty much foundational, with Abstract Algebra, Number Theory, Set Theory/Undecidability and Numerical Analysis being also possibly beneficial.
Now, even if I were willing to pick up a second major such as Engineering Math/Stats, it seems like there are simply too many courses to take, given that I also have to deal with CS17x classes.
Furthermore there are probably Stats classes that are also useful.
So I guess my question is, which classes are essential/extremely useful, which ones are useful for a specific sub-field, and which ones aren’t useful at all? Is my listing accurate?</p>
<p>2) Is there much opportunity to use pure math in EE? I’m assuming not really.</p>
<p>mathboy98 getting some love 
This is a pretty informative thread.</p>
<p>Yes, thank you for the love 
I’ll try to answer as best as I can…</p>
<p>So my answer to the EE and CS concerns is it depends which area you want to pursue. Do you use pure math? Well, all of applied math somehow has its basis in some standard mathematics, but the application process is its own beast as well. </p>
<p>In EE, the signals and systems material tends to consider functions on the complex plane, so some complex analysis can be useful. So can linear algebra, simply because you like to deal with large collections of functions and consider transformation on the vector space spanned by them – the “systems” are the transformations, and the functions are the signals. You can see the terminology itself lends itself to using some sort of abstract transformation. You put convolution products on things – it turns out you can put those products on more general objects.</p>
<p>The usual rule is that you do not NEED higher math to do EE classes, because they usually make it so the prerequisites aren’t so bad, but to do EE research, I am sure you’ll see Jordan normal forms and various analytic objects. The “more general objects” may not come up in class, but may be better models when you’re doing research. After all, that’s what the signals stuff is about – modeling. </p>
<p>In theoretical CS, I can see linear and abstract algebra being good foundational things to know. I think your list is quite complete. The probability/statistics type thing is used for certain EE specializations, and there’s even a class on it (EE 126), at that a pretty intense one I heard. </p>
<p>The other major math topic that tends to come up in applied settings is ODE’s and PDE’s. </p>
<p>If you like theoretical CS, you may also enjoy some logic and set theory actually.</p>