<p>I’m a college sophomore who plans to pursue a PhD in economics. I will be taking a lot of abstract math courses in junior year, but I’m not sure if I’m prepared. Besides practicing my math, are there any supplementary steps that I can take to improve my abstract thinking abilities? I heard studying chess helps. And so does learning to play a musical instrument, which might be a little too late for me now, no? Would reading difficult texts like philosophy and poetry help, or is that a different kind of abstraction? What about learning a new language? Or solving puzzles like the Rubik’s cube? Some of these might sound bizarre, but I’m really running short of ideas.</p>
<p>When you say abstract math, are you referring to real analysis or abstract algebra? The problem most students face is not abstraction but the rigor: how to read math (upper-level math lectures are often given in a definition-theorem-proof style), how to write math (proofs) and how to “think” math (math is written up in nice clean proofs, but that’s not the way you come up with an answer.)</p>
<p>Most colleges have a course that helps student develop those skills. Some colleges use linear algebra to introduce rigorous and abstract math, some use discrete math, some have a separate bridge-course and some colleges introduce proofs in real analysis or abstract algebra. Find out which math course serves that purpose at your college and try to take it.</p>
<p>If such a math course is not an option, I would highly recommend a course in logic or computer science or philosophy. Computer science and philosophy may or may not help you with mathematical logic and how to write up proofs, but in philosophy you might learn how to follow and find flaws in logical arguments. Computer science might help you develop your problem solving skills and show you how to break up a large problem into smaller junks, which is a very useful skill in math as well.</p>
<p>^agreed. also normally colleges usually have a team that participate at Putnam Competition. Try to join it or at least go and listen when they are training… it will give you a better understanding about proof writing</p>
<p>I’m taking a logic deduction class in preparation for the proof based math classes. Many of the symbols are the same, especially the stuff from set theory.</p>
<p>Mathematical logic is a good way to go, if you have it. It’s in my school’s philosophy department.</p>
<p>You should really tell somebody in your math department about your situation and ask what courses they recommend.</p>
<p>a Discrete or is it discreet math course? I hear it helps with upper level math.</p>
<p>Hey, thanks for the replies. I’ve browsed through my school’s catalog and I’ve found the following courses which might help:</p>
<p>Discrete Mathematics for Computer Science
Linear Algebra
Real Analysis
Abstract Algebra
Mathematical Logic
Logic and Language
Intermediate Logic
Philosophy of Logic
Philosophy of Mathematics</p>
<p>and Putnam training once every week.</p>
<p>I think I should take all of the above if I want to prepare for the rigor of Econ/Math grad school.</p>
<p>Would Physics courses help? Or are they too applied? How about a class on computer algorithms?</p>
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<p>I think those would both be a waste of time.</p>
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<p>Poetry is not abstraction in the sense you are looking for. Taking an introductory logic course would certainly make sense, especially if it included proofs.</p>
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<p>That involves mostly rote memorization at the beginning level, it is not going to improve the skills you need.</p>
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<p>There are lots of logic puzzles out there, those might be of some help.</p>
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<p>Many colleges offer an intro to proofs math class, “preparation for upper division math” or something. There are lots of textbooks written for such classes, you can try to get one and work through the problems. “How to Prove it: A Structured Approach” by Velleman is an example. Type that into amazon see what else pops up.</p>
<p>Perhaps “How to Solve It” by Polya or Euclid’s Elements would also be helpful.</p>
<p>You need abstract algebra for a PhD in economics?</p>
<p>Wellesley about the amount of math an economics major should take:</p>
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<p>[Economics</a> Department -Related Courses](<a href=“http://www.wellesley.edu/Economics/Courses/related.html]Economics”>http://www.wellesley.edu/Economics/Courses/related.html)</p>
<p>As I understand it, abstract algebra is not necessary for admission into top PhD programs. Adcoms look more kindly on real analysis and topology.</p>
<p>^ That’s surprising because topology seems even less relevant to economics than abstract algebra. Can you elaborate?</p>
<p>I have just seen it recommended on several department pages. [Admissions</a> Information to the Ph.D. Program in Economics](<a href=“http://www.econ.upenn.edu/Graduate/Admissions.htm]Admissions”>http://www.econ.upenn.edu/Graduate/Admissions.htm). is one example. All top programs like to see real analysis though.</p>