<p>I am a prospective math major and I am taking advanced courses such as Abstract Algebra and Analysis while in my junior year of high school. This year, I was introduced to mathematics competitions such as the AMC, and was destroyed (I scored in the low 90s :( ). After overcoming my disappointment on doing poorly on a high school exam, I started looking into mathematics competitions to make up for my failures.</p>
<p>I am planning on preparing for the putnam exam this summer and attempting it for the first time next year. My question is this: with my currently limited knowledge of competition maths, is it possible for me to score as a putnam fellow within the next three years? If so how much work would this take? Referring to a list on wikipedia, I noticed that most putnam fellows were IMO medalists... I don't have that experience under my belt. How much of a disadvantage does this put me at?</p>
<p>In my experience, students who are not competition-trained can score in the top 200 but not much higher on the Putnam. Most Putnam fellows (and all I know personally) have a past record of high achievement on math competitions (e.g. IMO medals). That doesn’t mean that past achievement is necessary - but you will have to learn everything they already know and then some. </p>
<p>Many of the strongest math competitors in high school lose interest in competitions in college. As one student put it: “In high school, competitions were my creative outlet and my opportunity to learn interesting math. In college, there is so much advanced material that doing competitions would only hold me back.”</p>
<p>Many people who do putnam exams never even get 1 question right. Some of the hardest questions come from just your basic calculus courses. The putnam exam is probaby even harder than the AMC. Becoming a putnam fellow would put you on the field with the likes of Feynman, Einstein, and a whole host of other Fields medal winners.</p>
<p>What? There are many more Putnam fellows than Fields Medal winners. And the two reward completely different skill sets.</p>
<p>And I would say that if you really wanted to, you could become a Putnam fellow. People make similar improvements in high school, going from not being able to qualify for AIME to making the US IMO team in a few years, so if you put in the same amount of work they did, then you have a good chance. The reason that so many Putnam fellows were IMO gold medalists is because most people have better things to worry about in college than the Putnam.</p>
<p>But like b@r!um said, math contests are fun work on in high school, but you’re a big kid now; you should have better things to focus on. (I think you should definitely participate though, just don’t worry about being a Putnam fellow or anything).</p>
<p>I’ve read somewhere that Putnam questions are actually easier than IMO questions, but they require more knowledge of higher mathematics. Is this true? I have done a few Putnam problems but I have never even seen IMO questions before.</p>
<p>This year, I was less than one question away from qualifying for the AIME through the AMC 12A, so would qualifying for USAMO next year be a reasonable goal? Also, a lot of people seem to be recommending the Art of Problem Solving Books. Which specific books would help me the most?</p>
<p>Once again, thanks for the helpful input! :)</p>
<p>The Putnam is a different type of contest than IMO. You have to be faster on the Putnam, since you have on average 30 minutes per problem, rather and 1.5 hours on the IMO. Putnam doesn’t really emphasize higher math so much. There may be a problem or two where you have to be familiar with linear algebra, or multi-variable calculus, or know what a group is, but knowing more math by itself is probably not going to increase your score. Also, the Putnam is a lot stricter than IMO; it’s really easy to think you have a correct solution but come out with only zero points. My guess is that since the Putnam is open to everyone, there is more of an effort to make problems more doable, but there are definitely really hard problems on there too. For example, this year, there was one problem solved by no one, and another problem only solved by one person.</p>
<p>If you’re still in high school, there’s still tons of things you can do to prepare for math contests. AoPS is a really good resource, they have books (I recommend the original books), classes, and even a message board that’s has a bunch of problems. There’s still time to apply for math camps for the summer too if that’s something you’re interested in. And yes, it’s reasonable for you to make USAMO next year.</p>