<p>I have already taken Abstract Algebra, Number Theory. I working on Linear Algebra and Differential Equations (yes, I realize I am taking these items backwards in a sense.) What are some other course or subjects I can study not only to prepare for the Math Subject GRE but to meet some of the expectations at Harvard? </p>
<p>Also how many women have ever gotten into and completed the PHD in math program? </p>
<p>I am already studying German and Italian. (I am fluent in Spanish so Italian is easier to learn that I expected.)</p>
<p>math 55= hardest course in mathematics at harvard... Its essentially just doing proofs and lots of it... and from what ive heard its usually for math/physics concentrators... pure math usually... and class is usually small cuz not many people take it... it makes u reflect all your math understanding advanced topics to is key... and very strong base/fundamentals of advanced mathematics is required... id advise to brush up on elementary proofs and set theory... keys on writing proofs... but thats just me... im not even at harvard yet... its similar to the University of Toronto math specialist programs... except math 55 is x2 harder..</p>
<p>I already have a taken a number of math courses. If you read the requirements to apply for the PHD program, a BA is required and I already have one. (Suma Cum Laude) I need to know what courses I need to supplement my knowledge to get the required 800 or more on the Math Subject GRE and to understand the courses that will be covered the first two years of the program.</p>
<p>I envy you. There is no way that I could ever take on any advanced math class beyond Calculus II. My head would explode with boredom. Good luck with getting into Harvard's Math dept. for its Ph.d program. I am glad that the only graduate program that I must worry about is the MBA.</p>
<p>Math is not as boring as one may expect. Mathimaticans did not lead dull lives either. Math is boring to many in the US due to the fact that the teaching is procedure based. I know because I am trying to instill Number Sense into secondary level students. Ask any American certain questions and you will find that the answer they give is procedural answer and they do not know why. For example when my students are doing basic addition they believe that when they carry over from the ones they are carrying one unit. That is because when teachers explain addition they say "Well if you have more than ten in the ones place carry over one." WRONG! When you have a total of ten or more in the ones place you are carrying over ten.
When you have more than a hundred in the tens place you carry over a hundred. This misconception makes it hard to learn subtraction, mulitplication and division with integars well enough for students to feel comfortable learning operations with fractions. If you do not learn fractions well enough Algebra becomes much harder to grasp. Fractions are seen as numbers not as pieces of a whole which is what they are. When any American sees the fraction 7/16 do they see a fractions or 7 pieces of a whole that has been cut into 16 parts? I can assure you that it is the former in many cases. </p>
<p>We need to stop reducing the beauty of math to processes and start exploring the infinite possibilities that lie within the art of Math. After all the fore fathers of math in Greece and Egypt did not think of Algebra as a series of processes but rather as an extention of Geometric inquries which is why Algebraic Geometry is redundant in some ways but yet a perfect explantion of the subject.</p>
<p>For mathmom:
Math Subject GRE has only one book by Princeton press.</p>
<p>if you google math GRE the books listed are the general GRE exam where one only needs to have general knowledge. These books do not cover the extensive math that is needed by the GRE Subject exams. The Math Subject Exam deals with only Math. As described by the website
[Mathematics[/url</a>]</p>
<p>The subjects covered are Algebra, Linear Algebra, Abstract Alegra but it also says "The above descriptions of topics covered in the test should not be considered exhaustive; it is necessary to understand many other related concepts. Prospective test takers should be aware that questions requiring no more than a good precalculus background may be quite challenging; some of these questions turn out to be among the most difficult questions on the test. In general, the questions are intended not only to test recall of information but also to assess test takers' understanding of fundamental concepts and the ability to apply those concepts in various situations."</p>
<p>This is an error that has been made before. </p>
<p>As for the Math website it lists the classes that will be taught first and second year. The test that is given on the site shows what one will be tested on after the first year.</p>
<p>There is no pre requist math courses listed for the program. I have contacted Harvard directly. Acceptance hinges on interviews and passing the GRE Math Subject exam with 800 or more. I am limited to that one book by Princeton press. In this area. There in lies the problem. The subjects are previewed in this book but the Math GRE Subject Exam can throw in additional areas that may not covered by the book. (I already own this book.)</p>
<p>There's also the REA book. Both are notoriously riddled with errors, but I think you can request a correction sheet from Princeton Review.</p>
<p>You might take a look at "All the Mathematics You Missed: But Need to Know for Graduate School." I haven't heard it specifically recommended for the GRE subject test, but I've heard that it's a very concise overview of the most important bits of the core subjects.</p>
<p>The largest single portion of the test is Calculus, and I remember reading a recommendation to just pick up Stewart or what have you and work on the "challenge" problems towards the end of each section problem set. The person recommending this said that these are close to the difficulty of the test's calculus questions.</p>
<p>You mention your languages, and though the story may be different at Harvard, the language requirement is a joke at most schools. Most often, your competency test is to take as much time as you need to translate a page of mathematics with the help of a dictionary. If you can do that, you're golden. They don't care if you're fluent. And, I think German, French, and Russian are usually the languages offered to chose from.</p>
<p>Honestly, I think you'd need about 15 (if not more) classes past what you've already taken/are currently taking to be anywhere near what the average incoming Harvard math grad student will have taken.</p>
<p>I don't want to burst your bubble, but I know some people currently in the Harvard Math PhD program and I applied to it last year with great grades, 2 strong letters and I was in the process of writing a paper that was going to be published and I still didn't get in. One of the students I know at Harvard took 6 grad courses at a top notch undergrad and got all A's. </p>
<p>If you want to really go to math grad school, be realistic. Even if you get a 99% on the GRE Math that is not going to get you into Harvard. Kids at Harvard have multiple publication and sometimes have taken double digit grad courses and aced all of them.</p>
<p>If you are serious about math, look at other schools.</p>
<p>While we've got the eyes of math grad students here, I have a question about "elite" admissions.</p>
<p>How thoroughly expected are research and publications, particularly in pure math? The maxim for the laboratory sciences is research, research, research, but that's a far more difficult prospect for pure math. Any thoughts?</p>
<p>Edit: To answer OP's question:</p>
<p>Real analysis, complex analysis, and topology are also "bread and butter" courses in mathematics.</p>
<p>I am currently working on my Masters in Math so list all the classes that I need. Realism works only to "fuel" my desire to continue on. </p>
<p>I was told from young that I would not be able to accomplish ANYTHING. Here I am graduated Summa Cum Laude and working on a Masters in Math. All when my HS teachers questioned weather I would be able to attend college at all. </p>
<p>I just do not feel the need to list all my accomplishments as so many have done because the only thing I wanted was a list of courses for Math that I can select from my grad school from people who have already tried to get in. That is all. I will compare it to the list that my counselors give. Considering that all my HS Counselors did was suggest that a person of my impoverished background would be better off in a vocation, I approach all counselors with eye brows raised. </p>
<p>Now that you have told me that entering Harvard was long shot. Tell me what is needed to make that long shot. Better yet tell me why YOU didn't get in so that way I do not make the same errors. You have pointed out only publication. Was that the only reason? As for the grades in the Math courses that is nothing I need to worry about. I work at the problems and get the answers. Sometimes it requires a lot of work and sometimes I can sense the answer. The only time I will believe I can not get in is when Harvard says so. But if I work at getting into Harvard the qualifications to enter into a PHD Math elsewhere would be covered already. I aim high because anything else is not considered trying in my book. I have time on my side. </p>
<p>So no I am not the "traditional" applicant to a PHD in math program but why should I stop trying? WEB De Bois was not the typical college student when he applied in the 1800's. So again way should I be "realistic" as you aptly put it. If MLK Jr had be "realistic" I would still be sitting on the back of the bus. It takes a dreamer to make a dream come true.</p>
<p>Grades and coursework are much more important in math grad school admissions than in lab science, since math homework is a lot closer to math research than, say chemistry coursework is to chemistry research.
If you're an undegrad in a school with a math department that sends lot of people to grad school, take lots of graduate classes, get top grades in them, and get great letters of recommendation from well known professors, it is possible to get into "elite" programs without any research experience. Since recommendation letters are the most important factor in grad school admissions, and succesfully working on a research project with a prof is a great way to convince them that you are really smart, research experience is useful. Whether or not you have publications in itself doesn't really matter much, since it depends on so many factors other than the quality of your research.
Also, to the OP, why are you so set on Harvard specifically?</p>
<p>@OP: Maybe someone here can give you a better list than me, but a very good book to check out would be Krantz's Mathematician's Survival Guide. I know he does list 7 or so subject areas. Additionally, it's a very readable and has a pretty comprehensive guide to admissions.</p>
<p>That said, if you're doing a taught masters try to pick up at least a year of grad algebra and real analysis. Looking at Harvard's qual syllabus--I guess they've just got one monolithic test--I see four other areas that you should focus on. You should probably soak up as much of these as possible at the grad level.</p>
<p>I'm going to double-tap happyentropy's question. Also, for the classes you're taking, are these at the graduate level? Is your undergrad degree in math? Are you presently at a decent uni?</p>
[quote]
...Abstract algebra and number theory: elementary
topics from group theory, theory of rings and
modules, field theory, and number theory</p>
<p>Introductory real analysis: sequences and
series of numbers and functions, continuity,
differentiability and integrability, and elementary
topology of R and Rn</p>
<p>Discrete mathematics: logic, set theory,
combinatorics, graph theory, and algorithms</p>
<p>Other topics: general topology, geometry,
complex variables, probability and statistics, and
numerical analysis
<p>All classes are at the Grad level. Thank y'all. You have given other ideas not focused on just classes. I had not thought of approaching a prof to assist them in anyway. I have on prof that has been working on a theory for years. I have a good relationship with him and I will see what I can do to help him. At the very least I can learn from being under his wing.</p>
<p>As for why Harvard. When I was three going on four I was pulled out of Pre-K and placed in Kindergarden. The teacher asked us "What do you want to be when you grow up." I had heard my older sister talk about Harvard at home. I though Harvard was a job. So in class I responded to my teacher" I want to a Harbard!". "What?" She replied. "A Harbard where all smart people go." The name stuck.</p>
<p>Here is the thing, I am a very ambitious person. I was really hung up on going to Columbia. That was my goal, I wanted it so badly. I remember when I got rejected, I kept Peter Osvath on the phone for almost an hour, asking what I need to do to get in.</p>
<p>And then one of my professors asked me, do you care about going to Columbia or becoming a mathematician? It's good to have high goals, but it's also good to have a backup plan. I care about becoming a mathematician rather than being a Columbia PhD.</p>
<p>To me sure it's great to work at Harvard, but the odds are just against you. I'm not saying don't apply, but focus on MATH. Odds of getting into Harvard, if the applications were randomly picked is roughly less than 5%. That's if the applications are random. </p>
<p>Look at other schools as well as Harvard. What field do you want to pursue? Harvard is quite good in most subjects, but there are a lot of schools that are also good in a lot of those subjects.</p>