I was a math major in university, and have worked in high tech for my entire career. I have worked with a lot of U.Mass graduates (literally tons of them). The best of them are superb, and are every bit as smart and every bit as successful as the strongest graduates from MIT, Stanford, or anywhere else.
A while ago on a different thread I mentioned a very tough problem I was asked to work on that totally stumped two MIT graduates. The second of them took one look at the problem and said “You have to go talk to [name]”. I went to talk to [name] who quickly, clearly, and very concisely explained the solution to me. At this point it was about noon, so I said “would you like to get lunch”. We went to lunch. Since my older daughter had just started university and he and I both had other children in high school, we started talking about universities. He mentioned that he was a U.Mass graduate. He is also one of the top experts in the world in one very specific high tech area, and a very nice guy, and very successful.
He is however not even remotely close to being the only really, really technically excellent U.Mass graduate that I could mention. I could give you a pretty long list, all of whom are very successful, and all of whom have earned some significant money. I would not want to name any names however given the name of this web site (particularly the “confidential” part).
And U.Mass is very good for mathematics.
And if you look at graduate students, such as master’s degree students, at any highly ranked university, then you will find that they got their bachelor’s degrees at a very wide range of universities, many of which (probably most of which) will be ranked no higher and in many cases lower than U.Mass.
For a math major it is generally a good idea IMHO to get some background in computer science (eg, some knowledge of algorithms and data structures would be a good idea). U.Mass is very good for CS also.
In terms of what you are actually asking about on this thread: I think that ship has sailed. However, in general I recommend that high school students when deciding on summer activities should not even think about university admissions. Instead, do what is right for you. Be genuine. Be yourself. Treat people well, be fair. Whatever you do, do it well. This approach has worked for our family at a range of universities, including some that are ranked a bit lower than U.Mass (but were very good and a very good fit for the student) and some that were ranked rather highly.
And none of us are likely to ever know why we either did or did not get accepted to a highly ranked summer program or a highly ranked university. We can guess, but it is only a guess.
What we can do, it to do the best we can where we are, treat people well, and be responsible. We can keep ahead in our class work. We can attend every class and pay attention. We can look for good internship opportunities (particularly after we get some time into university). It sounds like you are good at math. This is an ability that is going to help you, and that will bring in opportunities. Some of these opportunities will be interesting and fun and eventually lucrative as well.
And U.Mass Amherst is a very good place to get your bachelor’s degree in mathematics (or CS, or any one of multiple other fields).