Click here and follow the instructions closely.
No. The problems will be made available on this website. If you are registered on this site for the USAMTS, you will receive an email when they are available.
Follow the instructions described here.
See the eligibility information here.
Yes! Simply follow the ordinary registration instructions.
You can frequently check the USAMTS web page, or you can register for the USAMTS. Those registered on this site will receive an email when the next set of problems are posted.
All people who are registered on this site will receive information via email regarding the USAMTS.
Use . is the typesetting system used by most mathematicians and scientists. Click here to learn how to install and use . However, the use of is not required; you may use any other typesetting system, or you may handwrite your solutions. Click here for more information.
Each student's solutions will be evaluated by a group of mathematicians and university students of mathematics. A copy of the evaluations, and the scores will be placed in a database each round. These scores will be accessible to the student on the My USAMTS page. Except in cases of obvious oversights on our part, the scoring of the problems will be final. After each round's scores are released, the My USAMTS page will have detail about filing appeals.
Full credit will be given only for complete, well presented solutions; answers alone will be rewarded more frugally. The amount of detail necessary to justify one's conclusions will naturally vary from problem to problem.
Grading is done by NSA mathematicians, other mathematicians, and students at prominent universities. The graders vary from round to round, depending on their schedules and commitments. We cannot thank these graders enough for volunteering their time. Without their effort this competition could not exist.
The term "mathematician" is used loosely here because many of the graders carry the official title of electrical engineer, computer scientist, physicist, or even manager. They know, however, that mathematics is an enabling skill that opens the doors to many diverse careers. By supporting this contest they support not only the U.S. mathematics community, but also all these career fields and many more.
Please note that the efforts of much of the USAMTS staff are voluntary; we are involved in this program because we strongly believe that mathematical problem solving should become a favorite national pastime for our talented young students, and we want to provide an opportunity for them to exercise their skills.
We believe that all students who use the USAMTS to practice problem solving and technical writing will see their improved skills as the major benefit of their participation.
See the prizes page for more information about prizes.
Using a computer to answer a question is okay. You can still receive full credit of 5 points for a computer solution to a problem.
However, can you think of a way to answer a problem without a computer? Non-computer answers usually give more insight into a problem than computer solutions. Sometimes using a computer to get an answer is helpful in devising non-computer solutions. (It helps to know the answer!)
Computer solutions must be accompanied by an outline of the program or process used. You must also prove that the process you use with the computer does in fact solve the problem. It is not reasonable to expect that the graders are computer programming experts: the burden of proof is on you to convince the graders that your computer-aided solution is correct and complete.
The USAMTS is not a programming contest. All USAMTS problems are intended to be solvable without writing a computer program.
You certainly are allowed to look things up on the Internet. What you may not do is ask another person for help on a problem. Asking the question on a message board or a math help site would be asking another person for help.
The USAMTS works on the honor system. USAMTS participants must deal with issues of professional ethics common in all scientific circles. Participants must sign a statement declaring that they are the sole author of the solutions they submit. They must refrain from discussing the problems with one another or with any other person until after the solution deadline.
The ethical thing to do if someone helps you is to at the very least acknowledge them - on homework, or in a paper you write, even listing them as a co-author as is commonly done on scientific papers. To fail to acknowledge the work of others, in essence to commit plagiarism, will harm your reputation in academic and professional circles, and is dishonest.
Whether or not to ask "general" questions when you are not supposed to get help is a difficult decision. Basically it is a "slippery slope" where it can be very easy to "cross the line" and ask an inappropriate question. We recommend that you do not do it, unless it is very clear in your mind that the question you are asking is very general.
A complete, well-written solution to a problem should convince a person knowledgeable about mathematics - but not that particular problem - that your solution is correct. It should not be just the equations or figures that you might write down, but also the words and sentences (without being verbose) that you would use if you were sitting down to explain your solution to someone. Finally, it should be legible and easy to read.
You might want to take a look at some of the solutions to old USAMTS problems in order to get a sense of what good solutions look like.
If you think you have finished all five problems, make sure that your solutions are clear and well written. Your write-ups should have sufficient detail without being verbose to convince another person that your solution is correct.
If you have answered all five problems, the next thing you should do is see if you can generalize the problems - and then see if you can answer the generalizations! This is how mathematical research is done. Of course, generalizing in a trivial way is not very interesting.
For example, if the problem is to sum the integers from 1 to 100, one generalization might be to sum the integers from 1 to n. How to generalize a problem is something that you have to figure out. There may be several ways, and there is no right or wrong answer. This is one of those areas where mathematical aesthetics comes into play. Generalizing a problem is an important skill that every mathematician uses and the first thing a mathematician thinks of after solving a problem.
The USAMTS User IDs are used to help us with all the paperwork involved with the USAMTS. Solutions are filed according to User ID and scores are saved in our database by User ID. We can sort the paperwork and search the database by name and address, but that is slower (especially when people have the same last name)
You can find your User ID on the My USAMTS Profile page if you are logged in.
We want to assure you that we are not reducing you to "just a number". But we want to streamline our administrative procedures to be as efficient as possible. The less time we spend shuffling paper, the more time we spend on mathematics education.
Your solutions are received at the office which handles our administrative affairs. Your solutions are then bundled with other solutions and sent to our graders.
Our graders look carefully at each solution, and make comments about each of your solutions on the cover sheet. If you did a great job, they say so; if you went off track somewhere, they try to indicate where. Note that a great many of our graders are volunteers who donate their spare time to do the grading.
After your score is recorded, the results are entered into our database and the graders' comments on your work will be available on this site. Because of all the solutions that have to be graded, it can take as much as two months from the time a round ends till you receive your results. Frequently the next round has already begun before you receive your results from the previous round.
The USAMTS is a sponsor of the AMC. The AMC sponsors the American Mathematics Competition 12 (AMC 12, formerly known as the AHSME), the AMC 10, the AMC 8, the American Invitational Mathematics Examination (AIME), the USA Mathematical Olympiad (USAMO), and U.S. participation in the International Mathematical Olympiad (IMO). Students who score well on the AMC 10 and AMC 12 are invited to take the AIME, with the top students of that exam participating in the USAMO. The top scoring students of the USAMO make up the USA Mathematical Olympiad Team which participates in the International Mathematical Olympiad.
We encourage all high school students to participate in these competitions. We hope you will find the USAMTS helpful as you prepare.
NSA is one of the largest employers of mathematicians in the United States and perhaps the world. Mathematics is important for NSA's mission. NSA wants to encourage bright high school students to continue studying mathematics.
The USAMTS comes with no strings attached. And you might find the benefits - working challenging problems and getting your name mentioned to colleges, universities, and potential employers - to be worth the effort.
Yes! See the NSA website for details.
Other companies where you might consider applying are any place that employs a large number of mathematicians.
Yes, there are! Perhaps the most famous is the Putnam Mathematical Competition. Started in 1938 and sponsored by the Mathematical Association of America (MAA), the Putnam is open only to regularly enrolled undergraduates, in colleges and universities in the United States and Canada who have not yet received a college degree. The Putnam exam takes place once a year, usually around the beginning of December. No individual may participate in the competition more than four times.
The Putnam competition is divided into two sessions, morning and afternoon. There are six problems in each section and they are graded on a 0-10 point scale, for a maximum possible score of 120 points. The problems are difficult! For example, the median score on the 1998 Putnam exam was 10 points, so participants who worked one problem correctly scored in the top half of the entries.
After the Putnam exam is given, the problems and solutions are published in the American Mathematical Monthly, a journal published by the MAA. For more information about the Putnam, see their web site.
Like many mathematics competitions, the Putnam has a short time limit. But short time limits are not how research mathematics is done. More realistic is the mathematician who struggles for days, months, or even years with a problem - trying different approaches, and coming back again and again in an attempt to solve the problem. (The USAMTS is one of the few competitions that has a more realistic time limit - at least a month, encouraging such perseverance.)
For students who want a taste of what research is like, many mathematics journals have problem sections, where challenging problems are posed and the answers revealed several issues later. Those who send in correct solutions to the problems are mentioned in the journal. A good place to start for a new college student who likes to solve mathematical problems is the problem section of the College Mathematics Journal, published by the MAA and most likely available in the college or university library.