Richard J. Brown
Director of Undergraduate Studies
Department of Mathematics
The Department
The Mathematics Department comprises the second, third and fourth floors of Krieger Hall on Homewood campus. The undergraduate program is part of the mathematics community which includes research faculty, postdoctoral students, a vibrant PhD program with 32 students, and about 80 undergraduate majors another 50 minors.
We offer a Bachelor of Arts degree in Mathematics, an honors track, a combined Bachelor of Arts/ Master of Arts degree, and various programs to augment our training. Our undergraduate majors usually are of three types: Those preparing for graduate study in mathematics and using Hopkins as a stepping stone to a solid PhD program, those combining the math major with another major and want to use mathematics and mathematical training in their other field, and those who simply love math and want to excel.
Below are my descriptions of the programs and the value of our community.
The Major
There are three core elements to the mathematics major here at Hopkins. The first is a full year of analysis. One can define analysis, effectively real analysis, as the formal properties of the real numbers and the structures we define on them, like sets, functions, topologies and such. A full year comprises two courses at a sufficiently high level, usually 400-level (read senior-level). We have a full year of real analysis at either the regular or the honors level. We also offer a host of analysis-based courses that we offer as options for those who want to fulfill the requirements and also focus on a narrower topic, perhaps more relevant to their other interests.
The second is a full year of abstract algebra, the study of the formal properties of operations on numbers and the mathematical structures we define on number systems utilizing these operations, like groups, rings and field. Again, we offer courses in algebra at both the honors and non-honors levels as well as options for a more focused study.
The last is a full year of upper-level, quantitative-based courses in another discipline. We often refer to these courses as the outside course requirement. There are many options here, but the general idea is two-fold: (1) to well-understand how high-level mathematics is used and viewed from outside the mathematics framework, and (2) to provide useful experience for those who will take their mathematics degree and use it in a math-centric profession or discipline.
The Minor
The mathematics minor is really just a number-of-courses-based set of requirements geared toward establishing a sufficient mathematical maturity. The basic idea is that one must take five courses in mathematics above the level of single variable calculus. One of these must be one of the 2 forms of vector calculus (multivariable calculus, or Calculus III) we offer, either AS.110.202 Calculus III, or AS.110.211 Honors Multivariable Calculus. In addition, one of the remaining four courses may be taken at the 200-level (AS.110.201 Linear Algebra is a fine choice here), while the others must be at the 300-level or above. A last option is that one of the final four courses may be taken in the Applied Mathematics and Statistics Department, our sister applied math department here at Homewood. There are no other substitutions allowed.
Honors Courses
Department Honors
Many of our courses have honors variants, with course curricula that are much more theory oriented, offering a deeper dive into some topics and extending the content into areas not offered in the regular versions. It should be stated that all of our courses are theory-based. Some are just more theoretical than others.
The Bachelors/Masters Option
The Bachelors/Masters option for the undergraduate degree in mathematics here at Hopkins is a path for students with advanced standing to explore mathematics at the graduate level while still an undergraduate student. Should the undergraduate complete 4 graduate courses while an honors student with us, the student will receive a Master of Arts Degree in Mathematics.