<p>wat do u think of a major in math and minor in either psych, philosophy, or history (which one would u suggest)</p>
<p>wat do u think of a major in math and minor in either psych, philosophy, or history (which one would u suggest)</p>
<p>S is a double major, math and philosophy.</p>
<p>Take whichever interests you most. There is more overlap with philosophy (primarily in logic but also in philosophy of math).</p>
<p>
[quote]
Here's a good sample requiring little background to solve. Say a set S has |S| elements. Show that the set of all subsets of S has 2^|S| elements. Include, in the set of all subsets, the null set and the set itself.
[/quote]
I don't know formal proof syntax but here goes...</p>
<p>s-elements means that the total of all subsets consist of integral elements from 0 to s itself
(0,1,2,3...s)</p>
<p>for each group of subsets with n elements, the number of sets which may be formed from that distinct number of elements is s choose n.
(sC0, sC1, sC2...sCS)</p>
<p>Note that this sequence of numbers corresponds to row s in pascals triangle.</p>
<p>For any given row q in pascal's triangle, the sum of each of the numbers in that row equals 2^q.</p>
<p>Therefore we have 2^s subsets!</p>
<p>Is that the right sort of thing?</p>
<p>I hope this is somewhat related, but what about a major in statistics, either regular or applied? I'm not as much of a math/science person as I am an artsy type, but it looks like an intriguing field that is very open to interdisciplinary work.</p>
<p>Pawn -</p>
<p>That's good, and you're on the right track. Certainly, if you have proved, as a previous result, that sC0+sC1+sC2...+sCs=2^s, you're done. (Or if you can prove it now, as a "lemma" to your proof; want to have a go at that?) There is another, simpler proof, that doesn't depend on that lemma, but this one is perfectly fine, subject to having proved that lemma. (By the way, suppose you had found that other direct proof; what would that tell you about the lemma?)</p>
<p>hmmm, I can't think of a way to prove the lemma right now, maybe I'll look for the other proof when I have more time. (Fermat's last theorem)</p>
<p>Abstract math is where you write proofs that take a few hours and don't seem to have many numbers in them. That was when it fell apart for me. What I remember about those classes was that the professor said "proof by induction" or "proof by contradiction", then he turned around, started writing on the board, and started speaking Greek.</p>
<p>"Abstract math is where you write proofs that take a few hours and don't seem to have many numbers in them. That was when it fell apart for me. What I remember about those classes was that the professor said "proof by induction" or "proof by contradiction", then he turned around, started writing on the board, and started speaking Greek."</p>
<p>My goodness! Scaring off our poor OP! Anyway, the best way to deal with this is in my humble opinion is to pay less attention to the overly formal way professors and textbooks do these things, and realize that you can be pretty informal and casual in your language, if you're crisp. Explain all your proofs to yourself in a mushy, friendly way, and just write it out prettily. That's how I like to look at it.</p>
<p>For instance, to my own problem, I like to just think of it and say "Where does the 2 come from!!" And once you guess the answer to that, it's easier. Vaguely speaking, when you find a subset of S, an element of S is either there or not there. There you have two choices.</p>
<p>Statistics is a great major for someone who likes math and thinks logically and can communicate well. Also consider a master's degree in statistics or biostatistics. Even in this economy, there are many jobs available for biostatisticians.</p>