Serious mathematics for serious high-school students: There is more to mathematics than competitions.
FAQ
How do Euler Circle classes differ from other math activities in the Bay Area?
There are many other wonderful math activities in the Bay Area, but we believe that there is always a need for more, and students agree with us. Other classes are primarily focused on mathematics for competitions. At math circles, instructors can give a brief overview of a topic, but there is not enough time to develop it, so that students can learn it really well, and there also isn’t time to go through a topic that requires many weeks of preparation to reach a satisfying conclusion to a long story. Classes at Euler Circle are as intensive as college classes and ought to be treated as such. We emphasize deeper understanding and access to open problems, something that is not typically done in these other settings.
What are you hoping to accomplish in these classes?
So many things! One of our main goals for our students is that we want them to learn how to see mathematics and think about mathematics as a professional mathematician does. We want our students to see what mathematics is like at a deeper level than they would in any other way, to work on challenging problems, both those that are already solved and those that aren’t, to learn to grapple with difficult topics and develop intuition for them.
What is the sense of community at Euler Circle?
We strongly encourage collaboration. Students work on problems together and make strong and meaningful friendships over their shared love of mathematics, and even the quietest students who naturally gravitate toward working alone eventually find the joy in working collaboratively. Working on challenging problems and achieving that “aha” moment together is a great bonding experience for students. We love facilitating math debates, where groups of students toss out various conjectures and try to challenge each other with probing examples and counterexamples. Many of our students choose to work in groups on their final presentations, and that gives them even more time to get to know one another. Since most of our students come back quarter after quarter, their friendships do not have to end or become less convenient after one class is over.
Will these classes help me to win math competitions?
Any mathematics you do will help you to do other mathematics, so yes, sort of. However, Euler Circle classes are not competition-focused, and there are far more efficient ways of learning how to win competitions. Our goal is not to help students win competitions, although we encourage them to do so if they enjoy the competition environment.
So, what’s the point in taking these classes if they don’t help me get better at competitions?
There is more to mathematics than competitions! Most of the best things in mathematics are far outside the scope of the competition curriculum, and we believe that students will enjoy seeing a flavor of real mathematics, at the college level and beyond. We believe that competitions are valuable for many students, and that it can be very empowering and inspiring to students to improve at competitions and even win them. However, students ought to have the opportunity to be exposed to other flavors of mathematics as well, especially those that look more like modern mathematics.
What background should students have before taking these classes?
Prerequisites vary from class to class. Some of the classes require background in calculus, and some do not. Fortunately, calculus is easy to self-learn from a book.
Where can I find information on the classes? Click here for general information about the classes. Click here for information about the upcoming advanced class on cryptography, and here for information about the upcoming intermediate proof techniques class.
What is the format of the classes?
Advanced classes meet twice a week, on Tuesdays and Wednesdays, for two hours each session, for ten weeks. In the Tuesday sessions, the instructor gives lectures, and in Wednesday sessions, students work on problems in groups and go over problems with the teaching assistants. Intermediate classes meet once a week, on Mondays, for three hours each session, for ten weeks. Students in all classes are expected to work hard on the problems both in the problem sessions and at home. We encourage students to form working groups with their friends in the class so that they can work on problems together and go over the class material outside of the class sessions. In the last week of the quarter in the advanced classes, students give short presentations on topics of their choosing related to the class and write expository papers related to their presentations.
Is there homework? How much?
Yes. It is very difficult to learn mathematics without solving problems. Thus, we give many problems for students to solve, and students are expected to do them. There is time set aside in all the classes for students to work on problems in groups and discuss them with the instructors. However, there is not enough time in class to solve all the problems, so students need to work on problems outside of class, ideally with other students in the class. Instructors are happy to respond to emails regarding the problems throughout the week.
Where can I find information on doing a research project? Click here. But do keep in mind that doing research is extremely demanding and is not for everyone. In particular, doing research is much more difficult than taking Euler Circle classes. We provide research opportunities to students taking our classes if they have demonstrated a willingness to work hard, solve lots of problems at a moderate level of difficulty, and commit to the subject seriously.
Who can take the classes?
In general, students should not have graduated high school before the class starts, although it may be possible to make arrangements in exceptional circumstances. There is no set lower age limit for students, but the younger you are, the more you will need to do to convince us that you will benefit from the classes. If you are a middle-school student who is ready to take college-level classes, then we are definitely prepared to teach you!
Is admission competitive?
The traditional way that admissions are competitive is that there are applicants and spaces available. That is most likely not the case here: we can accommodate many students, and we dislike the idea of depriving worthy students of an education; we will certainly not take any pride in doing so, and we will never release statistics on admissions rates. However, you have to convince us that you are prepared for the classes, and that you are the sort of student we will enjoy teaching.
How much does the class cost?
The cost is $900 per 10-week class. However, financial aid may be available. If you are not able to pay, please let us know (after being admitted only).
Can I get credit for these classes? We do not have the ability to offer credit for these classes. However, if you would like to set up an independent study or something similar at your school so that you have more time to learn the material from Euler Circle classes, we are happy to arrange matters with a teacher at your school.
I live in the East Bay. Can you teach classes there too?
This is not possible at the moment, although we would eventually like to expand if there is sufficient interest. We are happy to help you set up carpools to and from Palo Alto if there are other students who live close to you.
I don’t live in the Bay Area. Can you teach classes in my area?
Feel free to tempt us! Convince us that there are many interested students in your area, and we may be willing to set up a camp, say over the winter or summer break, in your area.