<p>hi guys. im currently a soon to be 3rd year student econ/biz major. i want to apply to LSE for econ masters and i've heard that math analysis is a key class that the adcoms look at. having said this, i really only intended on taking 1a-54 (which i have done). but i thot about it and realized i mite need more rigorous mathematical training than just lower div. math classes so i was wondering is it feasible for me to take math 104 next summer even tho i havent had any formal training in proofs as i intend to devote all my time towards it. by next summer i will have completed stats 134 and econometrics 142 (dunno if thatll help or not). and i have gotten A's in all the lower div. maths. thanks for the help.</p>
<p>Yes, you can do it. I admittedly had written several linear algebra proofs before I ever read analysis, but you can learn to write proofs in analysis too. I believe you should work through the first chapter of an analysis book of your choice if you want to be very comfortable going in, though. The first chapter typically introduces very simple ideas, but really gets you in the mode of proving things. Standard things include proofs like: “Prove the sum of a rational and irrational is irrational”, “Prove the square root of 2 is irrational”, and other work more closely related to the special properties of real numbers. It’s not hard, but the stuff later can be challenging if you’ve not dealt with it before, but frankly a friend of mine and I felt analysis at the intro level was not challenging for someone who’d not seen it before, <em>except</em> for a few topics which’re relatively abstract to someone with little mathematical training. </p>
<p>If you’re doing economics, and are into statistics/mathematical stuff, learn 104 and then take 105 also if you can manage it – maybe your senior year (it’s offered only in Spring). That teaches you a second course in analysis, and actually <em>that</em>, not 104, will probably teach you the kind of analysis you may use in more mathematical economics – measure theory, etc. Best of luck, and let me know if you have other questions.</p>
<p>mmm ok so ud think even if i havent done math 55 or (now discontinued 74) it wouldnt put me at a disadvantage? cuz all ive done mainly is computation math up till this point. and on another note do u recommend any good books that would explain the intro material well and cheap? ive heard goodthings about rudins book. thanks a bunch again</p>
<p>Rudin’s book is good for 104 material, but not so much for 105. For that, you’ll want to try a book such as Royden’s one. Overall Rudin is a classic, and I recommend having a copy, and I think you should look for the version that’s inexpensive (I think one of the versions is very expensive, over 100 dollars, and as nice as the writing is, it’s far from worth that much to me). </p>
<p>You would be at a disadvantage, and a severe one, if you never wrote a proof in your life. That is why I suggested trying to work through Ch. 1, for instance of Rudin, and solidify your communication of ideas by solid practice. Rudin was one of the first more rigorous math books I read, and it’s a little challenging in Ch. 2 for those who’ve not had much abstract math before perhaps. Another good book is by Pugh, called Real Mathematical Analysis. This one takes a slightly less abstract approach at the start, more friendly, and yet proves that its approach is equivalent to the Rudin approach roughly speaking. My preference is Rudin, since I used that, and frankly to someone who actually has some familiarity with abstract math, it’s not that tough to work through and in my opinion has the nicest order of presentation. </p>
<p>The standard easier book for this subject is Ross’s. I think for those who just want to learn the theory of calculus well, that’s fine, but if you want to go on to 105 and stuff, you need to really get Rudin down cold.</p>