<p>How hard is it? I know it's among the hardest in the nation. Does everyone who major in math in Caltech are USAMOer and IMOers? I really like math and wanna double major (or minor). My background is decent (I have no math comp. background or anything but I'll have taken at least courses in stats, prob, single variable cal, and series and diff equations by the end of senior year) Does anyone here have knowledge about Caltech math and its student body?</p>
<p>Yes, the Caltech math seems to be extremely demanding as said by everyone. I don’t attend Caltech myself, by I know very closely someone who does. Just make sure that you are quite proficient with the epsilon-delta proofs in calculus. They do this in your very first semester in Caltech, so rather than trying to catch up, if you know it already, that would be a great advantage to you.</p>
<p>Example: Give an epsilon-delta proof to show that limit of the function f(x)=2x^2+3 as x approaches 4 is equal to 35.</p>
<pre><code>Hope this helps slightly, and good luck!
</code></pre>
<p>TAD</p>
<p>Almost every student who comes to Caltech has a very good grounding in math by High School standards (some AP or even college level classes). However, CalTech is a different league and almost every student has to work at it. Very few high school students have exposure to proof based calculus and that is in the first term. If you are going to major in math, you are going to be among the some of the brightest and motivated young mathematicians. Are you willing to play at that level.</p>
<p>TAD,
What do you use for your Introductory Calculus textbook at Caltech? It seems that the epsilon-delta proof for finding limits is taught in the first semester of Calculus in every college in the country and nobody every seems to understand it. That was the case for me and my classmates when I took it at the University of Maryland College Park a number of years ago. My sons who go to Public Universities in California also confronted it and I was no help in explaining it to them. I think I used the Protter and Murray Text from UC Berkeley when I took Calculus and my sons are using the " Intermediate Trancedentals, 6th edition" Calculus text by James Stewart which strikes me as a very long and fairly challenging text, although maybe not so much for CalTech students. It is no more enlightening on the epsilon-delta proof than any other text I have ever seen.</p>
<p>They use Apostol. And I have never used that, but peruse an intro real analysis book, and epsilon delta stuff is well motivated (since they give you many ways of looking at the idea of it).</p>
<p>Or tell them this: Infinity does not really exist, and neither does infinitely small. Getting infinitely close means getting arbitrarily close. The epsilon delta proof is a formal way of showing the distance of the function f from the limit L can be made arbitrarily small (size epsilon) for the domain x, or more generally a point in k-dim space (x<em>1,…,x</em>k) close enough to some value b.</p>
<p>Then there are tricks for dealing with specific limits to specific functions explained in Apostol, Rudin, etc. Part of that is messing with enough for familiarity.</p>
<p>Caltech math is by design difficult and that is a function (no pun intended) of their educational mission; train the best academicians and authors of research work possible. I think the expectation is that Caltech grads are going to advance their respective fields of science. This is distinctly different from schools like Stanford and Cal, who while also producing researchers and educators are also trying to create business and political leaders. Stanford and Cal don’t feel the need to create theoretical thinkers as much as Caltech.</p>
<p>This is true. The other schools often have strong options for theoretical thinkers, but Caltech is probably more universally oriented that way.</p>
<p>First, realize that contest math is not the entirety of math. You honestly do not have to qualify for the AIME to major in math at Caltech. However, that doesn’t mean that it isn’t hard. Math in college is proof based, so make sure that you like what math really is before deciding to major in it. The math taught in high school is more used in the sciences. </p>
<p>I’m a current frosh at tech, and know a lot of people majoring in math (I’m going to major in theoretical CS, which we all joke is essentially math anyways). Like everyone at tech, they are very smart.</p>