These are two really great schools. There is a little bit of misinformation on this thread that I’d like to clear up. But I also want to emphasize that both Penn and Dartmouth would be outstanding places to study mathematics.
In terms of undergraduate research opportunities, Penn is definitely an outstanding choice and second to none. There is so much more research being done at Penn by virtue of it’s larger size and substantially greater funding from both private and public funds, and it is incredibly easy to become involved as an undergraduate. Penn’s Center for Undergraduate Research and Fellowships (CURF) connects students to professors and graduate students conducting research in the fields in which they would like to study. Consequently, research is readily accessible and professors/grad students are grateful to have the assistance of undergrads to whom they often give substantive and exciting assignments, as well as small stipends. There is a culture of mentorship at Penn that is truly exciting to experience. Additionally, because of Penn’s One University Policy, you will also be able to take classes and do research across Penn’s undergraduate, graduate, and professional schools. With the most well regarded business school in the world (Wharton) right on campus, math majors often find it easy to use their quant skills in more applied scholarly work. Students in the college are able to take on University Minors in Wharton and Engineering and College students can even add a double major with the engineering school without having to officially enroll in the Engineering school. Additionally, Penn’s graduate math program is actually top notch (ranked #17 compared to Dartmouth’s #52). That may not seem like it matters at the undergraduate level but it’s often superior graduate programs that are able to pull in the best scholars to a university. And at Penn, as a result of the One University Policy, you have the opportunity to take those advanced, graduate level math classes and do research with those incredible professors who are always looking to incorporate undergrads into their studies. Finally, because you’re in Philadelphia, there are myriad opportunities to work with a non-profit or a think tank in research related to math or to work for the city of Philadelphia, applying your mathematics research to real-world policy problems. I worked at Penn’s school of government as a research assistant on a project related to modifying the philly tax code to encourage the development of small businesses that was eventually published and presented to the city itself.
Penn’s larger student body definitely does not make it challenging to get to know peers or professors. In fact, according to US News & World Report (and each school’s own website), Penn’s student to faculty ratio is 6:1 compared to Dartmouth’s 7:1 student to faculty ratio. Class sizes at both schools will be incredibly small, even at the intro level since Penn specifically creates smaller sections of intro level courses for students who thrive in more intimate environments and larger section options for those who don’t necessarily prefer the higher level of interaction in a smaller class. Additionally (according to USNWR), Penn has a higher percentage of classes with fewer than 20 students than Dartmouth (P’s 67.4% compared to D’s 64%). Do not let Penn’s seemingly larger size scare you; it only really has an effect on the number of students you have the opportunity to meet, not the quality of those interactions or your interactions with professors and administrators. The College at Penn is a quintessential liberal arts college in the heart of a major research university. You will definitely be able to find faculty mentors for recommendations to grad school and to better your learning experience while in college.
And in terms of grad school admissions, Penn students do incredibly well. Dartmouth unfortunately does not publish comparable materials, but be sure to check out Penn’s post graduate results survey to see where Penn Math majors choose to go after graduation: http://www.vpul.upenn.edu/careerservices/files/FINAL_REPORT_COMBINED.pdf
For the most recent graduating class, Penn math majors went onto Yale, Penn (Wharton), UC Davis, Princeton, Imperial, Duke (Fuqua), Drexel, and Columbia. Others accepted job offers at Bank of America, Citigroup, Google, Morgan Stanley, Delta Airlines, Credit Suisse, and more. And Dartmouth definitely does NOT edge out Penn CAS in terms of wall street recruitment. Penn is one of the two most highly recruited schools in the country. Because of Wharton’s presence on campus, it has the largest number of elite firms recruiting on campus of any of its peers and Penn CAS students take full advantage of the opportunities that this affords to them. Penn undergrads all share one career services office, no matter which undergrad school they’re in (college, Wharton, engineering, nursing) and they are each given an equal opportunity to do On Campus Recruiting. While many students interested in Wall Street will have self-selected into Wharton, others who chose liberal arts majors in the College are at no disadvantage when applying to these firms and they are recruited in huge numbers. It is easy to find in those career services surveys how many Penn College of Arts and Sciences students took jobs on Wall Street- I invite you to compare that data to any you can find on peer institutions.
Additionally, Penn’s social life is definitely not fraternity- and sorority-centric. At Dartmouth, about 50% of students are in Greek life (http://www.dartmouth.edu/stulife/greek-soc/cfs/faqs.html#students). At Penn, about 25% are involved in Greek life (http://www.vpul.upenn.edu/ofsl/greeklife). Student clubs are the most common form of social affiliation for students at Penn and each club (from the debate team to the rugby team) hosts its own parties and invites students from around campus. Club sponsored events greatly outnumber Greek parties and the student life revolves largely around those. That being said, Penn fraternities and sororities do host a TON of fun parties and charity events to which students are invited and at which students often have a good time. In addition to the regular clubs, restaurants and music venues in center city that students go to with great frequency, Penn fraternities will often also rent spaces for “downtowns,” or parties that happen in center city. There is a really solid mix of Greek life and other social activities but no one component could be said to be the prevailing culture at Penn. Finally, Penn isn’t known as the ‘party’ ivy as much as it’s reputation is actually that of being the “Social Ivy.” Though playboy did once rank Penn the number 1 party school in the country, so take that for what you will.
Also, Penn’s alumni giving rate is about 34% (https://www.alumnifactor.com/node/5854), not 8%-- not sure where the 8% figure in that article came from. And finally, I rarely meet people who confuse Penn with Penn State- especially professionally, I travel a TON for my job around the US and in Europe and Asia and almost everyone with whom I’ve discussed Penn has known I meant UPenn.
At the end of the day I think both schools are incredible and I often felt that if you could pick up Dartmouth and put it closer to Boston, NYC or Philly it would have been a really great fit for me. The D-Plan seems really interesting and the quaint, New England college vibe really jives with me. I think both will give you an outstanding education and incomparable professional opportunities. You cannot go wrong by choosing either one. If you have any questions about Penn, I’m happy to answer them. Going to Penn was the best decision of my life and I’m always excited to share that experience with an interested applicant.