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Instructions

We call it a Quiz, but it's really a challenge: a chance for you to show us how you approach new problems and new concepts in mathematics. What matters to us are not just your final results, but your reasoning. Correct answers on their own will count for very little: you have to justify all your assertions and prove to us that your solution is correct. (For some general tips on writing proofs, see proof tips, or take a look at examples of solutions to past QQ problems.) Sometimes it may take a while to find the right way of approaching a problem. Be patient: there is no time limit on this quiz.

The problems are roughly in increasing order of difficulty, but even the later problems often have some easier parts. We don't expect every applicant to solve every problem: in the past, we have sometimes admitted people who could do only half of them, occasionally even fewer. However, don't just solve three or four problems and declare yourself done! The more problems you attempt, the better your chances. We strongly recommend that you try all the problems and send us the results of your efforts: partial solutions, conjectures, methods – everything counts. Also, if you come up with a solution that is messy and ugly, see if you can find a better way of thinking about the problem: elegance and clarity count too! None of the problems require a computer; you are welcome to use one if you'd like, but first read a word of warning about computers.

Getting Help [Please read this!]

If you need clarification on any problem, please contact us. We almost always reply within 24 hours, usually much sooner.

You may not consult or get help from anyone else on any aspect of the Qualifying Quiz. To be safe, we ask that you don't even discuss the problems with other people in a general way ("Wow, #7 was really tricky!") until the official discussion of solutions begins. (Note that this is considerably after the application deadline! We appreciate your patience.) If someone else uses ideas from your solution to cheat, we will hold both of you responsible.

While other people are completely off limits, you are welcome (in fact, encouraged) to use books or the Web to look up definitions, formulas, standard techniques, etc. (One underappreciated source of mathematical awesomeness that we love pointing students to: oeis.org.) Any information obtained from such sources must be clearly referenced in your solution, in a way that would make it easy for us to look up the exact source if we wanted to. But please do not try to look for the problems themselves: we want to see how well you can do math, not how well you can use Google.

For further clarification, read more about our policy on getting help. If in doubt about what is allowed, please ask!

Any deviation from these rules will be considered plagiarism and may permanently disqualify you from attending Mathcamp.

Writing Up Your Solutions

You may handwrite or type your Quiz. For those interested in typing mathematics beautifully, we also offer you the LaTeX source file for the Qualifying Quiz. Please don't let it distract you from solving the problems, though! For more information on LaTeX, take a look at our LaTeX tutorial for the QQ. No matter how you write up your solutions, we require that you upload them with your application as PDF files; visit our PDF tutorial if you need help.

Finally: don't write your name on your Quiz. (Really!) Instead, write your applicant ID number on your Quiz. (You will receive an applicant ID number when you start your online application, on the welcome page.) Why not your name? When we grade Quizzes, we want to be thinking just about the math. So we're doing an experiment in which we evaluate all applicants just by ID number and then uncover the names later. We appreciate your help with the experiment.

Proceed forward to the Quiz problems. Good luck and have fun!