**A.**
There are many excellent high school math camps. Probably the 4 most distinguished – they are very selective and draw students from all over – are Hampshire, Mathcamp, PROMYS and Ross. All the programs listed on the American Mathematical Society summer programs webpage are good.
There are also camps that take a wide age range – both middle school and
high school age.

It is important to realize that not all summer math programs are organized the same way. Some are quite structured; some allow a lot of choice. All the high school camps require more hours of math per day than MathPath, as befits a camp for older students who have longer attention spans.

We have started collecting statements from some MathPath grads who have gone on to high school math camps, or have attended broad age range camps either before or after MathPath. We asked these grads to highlight the similarities and differences from MathPath, so that MathPathers who go there will know what to expect. So far we have 5 statements, one about __AwesomeMath__, one about __Hampshire__, one about __Mathcamp__, one about __Math Zoom__,
and one about __PROMYS__.
They are below. There are also shorter comparisons between MathPath and
various camps on one of the __student comments pages__.

**AwesomeMath**

From Anonymous
As one of the few who have attended both the camps, I think I can compare both the programs. MathPath and AwesomeMath are both excellent summer math programs for bright students with excellent aptitude as well as strong interest in Math. However, they have slightly different objectives, mode of operation, and student population. MathPath is aimed at primarily middle school students within age range 11–14, while AwesomeMath is aimed at primarily early high school students. MathPath also has plenary sessions, where several distinguished Mathematicians lecture about some special topics in Math.

If someone is a middle school student in the age range 11–14, I strongly recommend going to MathPath, where (s)he can get an introduction to various areas of Mathematics, which they never get either in their school curriculum or other math programs I know. **MathPath is undoubtedly the best math summer program for middle school students.** It has the best blend of Math, other intellectually stimulating activities and lots of fun. I'll rate MathPath a 10 in a 10 point scale. Also, in MathPath, as the kids are middle schoolers, they make sure that kids are always under supervision and well taken care of.

If someone is a high school student, (s)he can go to either MathCamp, where they can get in-depth exposure to subjects that are typically not covered even until graduate school in a normal math curriculum or AwesomeMath, where they can get in-depth exposure to two specific areas of Math, such as Number Theory, Combinatorics, Algebra and Geometry.

Once again, I thank you for giving me an opportunity to go through MathPath. I'll cherish the experience forever (and I'll never forget Dr. Convey's antics such as eating the bag).

** Hampshire College Summer Studies in Mathematica (HCSSiM)**

From Daniel Kang, MathPath 2009, HCSSiM 2010
Talking about my Hampshire experience, it's 6 weeks, adequate for students to go deep enough on at least one topic. The schedule for HCSSiM is tough.

- 8 hours of math a day, Monday to Saturday
- 4 hours class, an hour lecture by a staff or guest speaker (usually), and 3 hour problem session.

- First three weeks: Workshops (A senior staff; 2~3 junior staff in a class; 3 separate classes)
- Remaining three week: Maxi (17-day course), two Minis (8~9 days each)

The points I want to make:
- High school camps are demanding

- A course per week, as at MathPath,is not enough for a student to understand the course material fully. One of the things about HCSSiM was that they taught us upto graduate, Ph.D level because we could take time understanding it over three weeks.

I saw Katherine and Jenn in Canada/USA Mathcamp [the two camps were located nearby in 2010], and they told me that although the classes weren't mandatory (ours was), they said a day was stacked with math classes. I remember that a large portion of students in MathPath were 7th&8th grade, who are preparing to apply to high school camps. I strongly recommend them to HCSSiM, but they might be too stressed for the first and second week like I did.
At MathPath I tried to avoid much of the Mathcount/ARML courses. It turned out to be a very good choice for me, since such courses as graph theory, and Dr.V/Dr.Su courses are also taught/recommended in high school programs. More camps in high school wants students to pursue their career in math major or related fields instead of contests. Hence, I recommend students to take something new, and topics which can be used for future research subjects, other than focusing on competition classes.

Note: What I felt this year, the level of maturity at Hampshire was a great deal for rising sophomores, because the camp is mostly juniors and seniors. I was second youngest this year. My opinion regarding the camps might be different from others because of this.

**Canada/USA Mathcamp**

From Lillian Chin, MathPath 08-09, Mathcamp 2010
Going to Mathpath (2008 and 2009) over the summer was certainly an eye-opening experience. After exploring intriguing, fascinating branches of mathematics as well as creating a network of friends among like-minded math nerds, I found that my school environment at home was notably lacking in appreciation and support for people like me. Once I turned 15, I was eager to continue being a part of a loving, intellectual community and went to Mathcamp in 2010. I had heard several great reviews of the camp from my friends and was interested to see Dr. T's first camp for mathematically-inclined students. I was not disappointed when I arrived; even from just the first week, I felt like I was home again: from taking classes on theoretical computer science and ring theory to making jokes about Stephen Wolfram and the triviality of problems, it was obvious that the same quirky spirit that made me love Mathpath lived in Mathcamp as well.

Strictly by the numbers, Mathcamp is a bigger and more internationally-accepting camp than Mathpath. There are around 120 campers here ranging from the US to Europe to India and Southern Asia. This does not impact the friendships or culture at camp in any negative way; I still felt that I got to know the entire camp as well, and international students gave a more global perspective to the universality of mathematics. Financially, the cost of Mathcamp is considerably less than that of Mathpath, and Mathcamp also offers greater financial aid than Mathpath. Again, this did not create an obvious difference between the environment of the two camps; social status never came up as an issue and no one felt very conscious about these things.

The classes at Mathcamp, similarly to Mathpath's, worked on a scoring system: this time with chili peppers (to show the spiciness of the course) rather than stars. The work week ran from Tuesdays to Saturdays, while Monday and Sunday were left for excursions. In an average day, there were 4 breakout-style sessions which were simply called classes and only 1 plenary session called Colloquium. We were encouraged to not attend all class sessions but instead to take a break to not burn out or stress. There was planned-in time in the schedule to do homework or independently study math called TAU, Time: Academic Unscheduled, where all teachers were free to discuss the course material. Some students used this time to work on their Project. About midway through the camp, Project Fair was given instead of Colloquium, where campers could check out the various types of Projects suggested by the teachers, ranging from programming a game on the Hyperbolic Plane to studying Markov chains. Projects can also be independently formulated, such as the student-run inquiry into quantum mechanics.

Mathcamp is clearly geared more towards high schoolers, not just in subject difficulty but in overall freedoms given to campers. The structure is considerably laxer than Mathpath's: students are not required to go to class, there is not set bedtime (though there is a quiet hour), and campers are allowed to go off campus. Likewise, there are no limits to class size; students simply show up to the classes that they want to go to. Rather than have all of the classes have about the same number of attendees, classes range from 4 students to 50 students. Essentially, Mathcamp gives college-esque permissions to its campers, whereas Mathpath gives a more high school permissions. Both are still relatively free compared to the home environment and are appropriate given the maturity and responsibility of the campers. Similarly, at Mathcamp, organized activities are scheduled by both counselors and students, rather than just by the counselors. A wall is dedicated off from the main lounge as a scheduling board, and campers are encouraged to put up whatever zany events they wish, ranging from chess tournaments to Human Turing Machines to a campaign to get New York bagels to camp.

One of the greatest things that I appreciated at Mathcamp was this sense of freedom and equality; campers, teachers, and counselors were all equal, only settling into a hierarchy to reflect the respect of knowledge that the campers had for the elders. Though looking back, Mathpath seems more regimentalized, it was appropriate for me at the time, so that now I can appreciate the responsibilities given to me. I felt that I had greater freedom to pursue any branch of mathematics rather than just the ones offered as a class. The quirkiness, however, still lives equally brightly in both camps. Whatever crazy ideas that materialize at camp come directly from the students, and no infrastructure differences can change them.

All in all, I loved my time at both camps and strongly recommend both programs to any gifted student interested in mathematics.

*
Actually, this is Lilly's second statement comparing the two camps.
It is aimed at students who have already been to MathPath.
Earlier she wrote a statement aimed more at parents and students who had not yet been to either camp. If you want to read Lilly's earlier statement,
*__look here__.

**Math Zoom**

From Jeannie Wang, MathPath 2015, Math Zoom 2014
MathPath and Math Zoom are both excellent summer camps for students who want to broaden their knowledge on math. MathPath is a camp for students aged 11-14 while Math Zoom has a wide age range for its students.

From my experience at MathPath, I will say that it is definitely one of the best summer camps that I have ever had the opportunity to participate in. MathPath offers a variety of classes ranging from competition math to real world college math. To be given the ability to choose which class I want to take is a very important part of MathPath. MathPath classes are challenging, interesting, and intriguing. The classes encouraged me to want to learn more and to do my very best in the class, no matter how hard it might be. The teachers at MathPath were simply amazing. You can hear the passion they have in teaching mathematics in every class and in every plenary. Because of that, I felt compelled to do my very best in the homework and to participate in math conferencing times and to ask questions just to make sure that I had understood every detail in the class before. I think that that is a very important highlight of MathPath. MathPath gave me valuable time in mathematics and inspired me to pursue more mathematics in the future.

The MathPath staff is very responsible and know what they're doing. They well plan every weekend and make sure that we have as much fun as possible. The staff is fantastic in ensuring that we have a great time at MathPath. However, I feel as if some of the counselors are too strict. Some counselors that I have encountered in MathPath aren't that fun to be around and are too uptight at times. There were times where I wished for some counselors to be more fun and to let loose more. There were also times that I had wished the rules at MathPath may have been a little looser and the campers would've been given more freedom. But I also do understand that since it is also a camp for younger students that they have to ensure the safety of all of us.

Math Zoom was the first math camp that I had ever went to, and I had an amazing time there with new friends and just having fun altogether. But the math experience there wasn't that exciting. The classes offered focused on four core subjects in math: Combinatorics, Geometry, Algebra, and Number Theory. The classes at Math Zoom were mostly based on competition math. Though there were some good teachers, the teachers at MathPath were more passionate. The classes in Math Zoom were also way to long for me. It was 3 hours in the morning and 3 hours in the afternoon. Somedays it became suffocating and my attention went elsewhere, especially if the teachers weren't that great at teaching the classes. Unlike MathPath, Math Zoom did not designate a math conferencing time for students to go to their teachers and ask for help or clarification on the previous class that day. Nor did Math Zoom designate mandatory homework for its students. The only way to get the most out of the classes is if you took your own time to study the handouts and materials. As a student, I did not feel as compelled to learn in Math Zoom as I did in MathPath.

The Math Zoom staff was not as big as MathPath but they were very fun to be around. We could talk to our counselors openly and treat them as a friend of ours. At Math Zoom we were given freedom to spend our time. I think that was important to have in Math Zoom. To be able to include your counselors in as one big family is a great way to make your experience at a Math Zoom. Though MathPath did have very fun counselors, Math Zoom as a whole had the best group of counselors, in my opinion. Math Zoom was not as organized as MathPath. We did not receive anything such as a monthbook or a diploma or a hat. It is not important that we receive those things, but having a monthbook and all is great to keep in touch with your fellow campers.

MathPath has a smaller age range which I think is important. Because the age range in Math Zoom was so large, with most of the campers focusing around 9th and 10th graders, it was hard for some of the younger campers to fit in. Though it is easy for some people to fit in easily at both camps, it is best to go to MathPath if you are in the 11-14 age range.

Both camps has their highlights and their downsides. But both camps are also both fantastic camps to attend!

**PROMYS**

From Nic Trieu, MathPath 2009–10, PROMYS 2011–12
I really enjoyed PROMYS, but the kind of fun you get at PROMYS is based on really hard work and interaction with others who like the same thing, as you will see below.

I first went to PROMYS after my freshman year of high school. I chose to go to PROMYS because I wanted do math that was out of the regular high school curriculum. I particularly wanted exposure to math research. PROMYS combined an intense study of number theory and as well as an introduction to math research. This camp is similar to ROSS which I also thought about, but ROSS was further away. I did not have any interest in the camps that emphasized math competition preparation.

PROMYS 2011 was an intense, but satisfying 6 weeks of math. There were students from all 4 years of high school, but most were rising Juniors or Seniors so I was one of the few coming after freshman year. In the morning at 9:00 AM, we would head down to Glenn Stevens' number theory lecture and receive our daily number theory problem sets, which we would work on for the rest of the day. It was hard core; the problem sets tested your ability to think rather than any factual knowledge. Instead of having stuff taught to you, you figured out the number theory on your own. The counselors helped us by strengthening the rigor of our proofs while withholding the actual proof itself, letting the problem sets guide us to prove from scratch what we "knew" (and theorems we didn't know) about the system of integers. We were tested in a midterm and final exam in sections of rigor, proofs, numericals, and "miscellaneous."

In addition to the number theory, we had the option (which most of us took) of conducting a research project, choosing from a list of topics of interest. With some general questions to develop on, we explored in groups of three to four and presented our findings at the end of PROMYS in a presentation and paper. The topics remain the same from year to year, but the experience of researching, making a paper, and presenting was invaluable.

Every week, we would have a taste of new and exciting math related topics in guest lectures from distinguished mathematicians from around the country. Every Friday, we would be forced to take a break and participate in Mandatory Fun, which ranged from poker night, to a dance, to an intriguing "movie" night. On the weekends, you can play sports and take trips around Boston. For the math-hungry, never fear: there is an extra long week-end problem set.

More about the activities outside of math: We played chess, ultimate frisbee, basketball, went swimming and took short trips throughout Boston (memorable excursions include Harry Potter opening at the movie theater summer 2011, fireworks July 4 at the Esplanade summer 2012). Usually a counselor or a group of kids decided they wanted to go to an event and organized it themselves. Still, most of the weekdays and weekends involved a lot of work on problem sets. This is where the time management comes inÑ you need to manage your schedule outside lectures yourself. It sounds like boot camp to say that we worked really intensely each day on problem sets. However, it was also a terrific feeling to be challenged to stretch your mind and the ultimate bonding experience with your peers to be struggling together.

I went for a second time to PROMYS after my sophomore year of high school. As a second year student, you have the opportunity to choose in-depth seminars. These seminar offerings vary each year. You can choose more than one topic, but they each have their own challenging problem sets. There are no midterm or final exams for these second year topics; instead, you take the number theory midterm and final for the second time. If you got a really high score the previous time you took the tests, you can take a shorter, but harder test. If you come back for a third year and you scored well on the short test, you can take an even shorter test with impossible questions that have never been solved before (or at least within the time limit).

Second years also have the option of conducting research projects, but the topics you choose from are new and unsolved problems posed yearly by professors with an interest in them. The process is much the same: in groups of three to four, you research, collect your findings, make a paper, and present at the end of PROMYS, but finding something new is incredibly exciting. This was my favorite part of last summer's camp.

I would highly recommend PROMYS to former alumni from MathPath. Both types of camps explore math outside of the school curriculum, require that you enjoy doing math around the clock, and are opportunities to meet other people with the same interests. However, MathPathers need to adjust to a different style of learning at PROMYS. MathPathers have elective classes with varying topics at MathPath. PROMYS is all about number theory the first year. There is a lot of unstructured time at PROMYS. PROMYS is a lot like college where you seek out your counselors and work on your problem sets. Lectures are review because a lot of the learning is self driven.

MathPath was the place where I first learned about writing rigorous proofs and number theory. The exposure to proofs was especially helpful for PROMYS. After MathPath, I had the confidence to go to PROMYS. I think if you have never gone to a camp like MathPath, the PROMYS description of what you will do can be intimidating.

I think attending different camps with different styles is a good idea in terms of overall exposure for students who are uncertain what they might like. There is a danger in attending one camp and judging all math camps by the one. I was just fortunate to attend a camp that was a good fit for me from the start. I really liked number theory and I enjoyed the independence of unstructured time to think. I also connected with a lot of brilliant kids who I hung out with from the start. Late nights working on problem sets and eating ramen noodles while chatting with people who really like math was my kind of fun. Several of my friends came back the second year as I did.