Honors Math

The Math Honors Program

The philosophy of the Honors Math Program is that mathematics is a logical discourse and it is important that students adopt this viewpoint from the start. This requires developing rigorous reasoning and precise communication habits. These are acquired skills that have benefits beyond mathematics. Their importance will only continue to increase in this data and AI infused era.

The program provides outstanding preparation both for employment in a wide variety of fields that value strong analytic and quantitative skills, and for further study in all mathematical intensive areas of the sciences (pure and applied mathematics, statistics and biostatistics, physics, economics, computer science, engineering, ...).

The program includes carefully planned and thorough sequences in analysis and algebra, the two most important building blocks of modern mathematics, as well as the opportunity to work closely with a faculty member by completing a senior thesis.

During the summer between the Freshman and Sophomore year students are offered the opportunity to attend a six week research program on our campus. The participants receive a small stipend that covers most of their living expenses. Two or three teams of up to four students, supervised by a postdoc or graduate student, take up a concrete project. At the end of these six weeks they produce a research report, they get a taste of research and they are prepared to successfully apply for REUs organized by other campuses.

During the Junior year most honors students enroll in a graduate course and many also express interest in Directed Reading projects with a faculty. These directed reading efforts end with a senior thesis. By the end of the program, each Honors student would have taken 3-4 graduate courses.

The core courses of the Honors Program are:

• Freshman year: Honmath 1 2,
• Sophomore year: Honmath 3 4, Honors Algebra 1-2
• Junior year: Honanalysis 1 2, Honors Algebra 3-4.

The History of the Honors Program

In 1987, when it was noted that few Notre Dame students had been pursuing graduate work in any of the mathematical sciences, emeritus Professor Frank Connolly created the Seminar of Undergraduate Mathematical Research, or SUMR. Its original goal was to give encouragement and direction to the ablest mathematics students at Notre Dame. There were two students during each of the first three years. The program sought to create a cadre of undergraduates with an unusually high level of mathematical accomplishment and a strong capacity to pursue graduate work in one of the mathematical sciences.

SUMR graduates have established a remarkable tradition of accomplishment in postgraduate work. Recent alumni of this program have pursued Ph.D.s in such fields as Mathematics, Applied Mathematics, Computer Science, Physics, Statistics, Biostatistics, Economics and Ecology, the vast majority at highly-ranked schools such as Cornell, Brown, Stanford, IU, UCLA and Harvard. 

It has, by any measure, been highly successful in its original goal of placing Notre Dame students into the top graduate programs in the country, and it has repeatedly been singled out for praise in external reviews of the department.

Starting în the 2010s the philosophy of SUMR has been extended to all the Honors Program. This was due mostly to new opportunities available to our students and to their increased interest in pursuing research. Consequently SUMR is no longer a distinguished subentity of the program.

All of our students are encouraged to apply for national scholarships and we continue to live up to the reputation of the program slowly built by Professor Frank Connolly.

National Fellowship Winners

No other Notre Dame program has had such a high percentage of its graduates winning national fellowships. Here are the details of the national awards and scholarships won by the Honors Program Alumni.

Honors Math/SUMR Alumni

Here is a link to the complete list of Honors Math alumni, including details of the awards they have garnered.

The Honors Math/SUMR alumni have had remarkable success, from the program's inception in 1990 right through to today. 72 of the 75 SUMR graduates in the period 1990–2011 have pursued graduate degrees, 5 in medical or MBA programs and 67 in the mathematical sciences. Each of these 67 was admitted with financial support into some of the nation's top graduate programs. Indeed, 56 received offers from at least one of the top 25 graduate programs in their chosen field.

The students of this relatively small program have won more than 50 national fellowships—more than any single department at Notre Dame—including:

• 13 National Science Foundation Graduate Research Fellowships
• 12 Barry M. Goldwater Scholarships
• 7 National Science Foundation Postdoctoral Fellowships
• 4 National Defense Science and Engineering Graduate Fellowships
• a George C. Marshall Scholarship
• a Winston Churchill Scholarship
• a Fulbright Fellowship
• a Lucent Technology Fellowship
• a Sloan Fellowship
• an Alice Shaefer prize

Three SUMR students have been finalists in the Rhodes Scholarship competition, and five have finished as either first runner-up or with honorable mention for the Alice Shaefer prize.

More detailed information

• Fellowships and Scholarships: Information about applying for the many fellowships and scholarships in the mathematical sciences
• REUs: Information about REUs and other summer research opportunities
• Senior Thesis: Information about the option of graduating with a Senior Thesis, including a list of recent senior theses