Flexible Tracks for Math Majors?

#1

We’ll be rolling out a series of questions to help inform our discussions at an upcoming meeting on Upper-Division Math Pathways and our subsequent implementation plan. To get us started:

Does your department offer tracks in your mathematics major(s) (or minor) that allow students flexibility to tailor their studies to align with their other interests? Please tell us about them!

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#2

At Pacific University, we have a fairly minimal mathematics major with optional specializations. This has worked very well for us in attracting majors, particularly those that double major.

Core Major (Semester Courses)

  • Calculus I, II, III
  • Discrete Mathematics (Transition course and intro to proof in context of discrete topics
  • Linear Algebra
  • Intro Analysis
  • Intro Programming (CS Course in C++)
  • Required additional course to see mathematics in context (Physics, economics, chemistry, CS)
  • 3 upper division courses (at least one senior level)

Optional Specializations (courses in the specializations can count toward core major)

Actuarial Science

  • Math. Prob/Stat
  • Macroecon and Microecon
  • Accounting
  • Finance
  • One additional related course

Advanced Mathematics

  • Differential Equations
    
  • Abstract Algebra
    
  • Real Analysis (typically Riemann and Lebesgue Integration)
    
  • Two more upper division mathematics courses (complex, number theory, graph theory, geometry, etc)
    

Biomathematics

  • Mathematical Modeling
  • Intro Biol
  • two more upper level biol
  • 2 matched mathematics courses (2 stats OR ode/pde OR stat and discrete topics)

Secondary Mathematics Education

  • algebra-based stats (similar to AP stats)
  • Math Prob and Stats.
  • ODE
  • Higher geometry
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#3

We have 4 different tracks for math majors: regular track, applied math track, statistics track, and math ed track. You probably know about them. If not, then I can write a brief statement about each, or send you an item from the Mathematics Department for students wishing to major in mathematics.

Denny Gulick

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#4

At the University of Georgia we have two mathematics tracks: the “regular” track and the applied track. Statistics and Math Ed are separate departments. Our total number of requirements are fairly minimal (similar to those listed for Pacific Univ.) — this allows for double majors (with statistics, math ed, econ, cs, etc.). Graduate school bound students are encouraged to take more math than the minimal requirements.

Malcolm Adams

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#5

A little more detail would be helpful. Thank you!

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#6

A list of courses required of math majors for each of the math major tracks
is located at the following University of Maryland Mathematics Department
website on math majors:

https://www-math.umd.edu/course-requirements.html

Looking at it would be much better than my trying to describe details.

Best wishes,
Denny Gulick
Professor of Mathematics
University of Maryland
College Park, MD 20742

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#7

At Cornell, we are proud of our very flexible major. We have 8 different math major “tracks” or “concentrations”, as well as a (relatively new) minor. In 2017, we will graduate over 80 Math Majors of the roughly 1,000 Cornell Arts&Sciences students who are eligible to major in Mathematics. Many of our majors are double majors, most commonly with Physics or Economics.

To be admitted to the major, a student must have performed well in Multivariable Calculus, Linear Algebra and a basic computer programming course. A major consists of 9 additional courses. For the minor, the pre-requisites are Multivariable Calculus and Linear algebra, and the minor consists of 4 additional courses including one algebra and one analysis.

There is no one course that is required for any major, but all math majors must take 2 algebra courses (from a list of 10 possible courses) and 2 analysis courses (from a list of 12 possible courses). The remaining 5 courses can vary widely. For some of the flavors of major, we count courses in other disciplines that have a significant mathematical component. The tracks are:

  • Mathematics
  • Applied Mathematics
  • Computer Science
  • Economics
  • Mathematical Biology
  • Mathematical Physics
  • Operations Research
  • Statistics

In particular, our Applied Mathematics concentration is new. The process to create that was complicated, involving approval by the State (though that may have been unnecessary, but it was how our Department was advised by the College).

We have careful descriptions of what is allowed/required in each track here:
http://www.math.cornell.edu/m/Undergraduate/Major/major.html

The Math Minor is described here:
http://www.math.cornell.edu/m/Undergraduate/minor.html

I’m happy to answer any questions!

Tara Holm

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#8

Rutgers University (main campus)
traditional math major track
honors track
biomath track
actuarial track
math/stat track advised through the Stat Dept
a 5-course math-content option for future K-8 teachers
(state law prohibits a “math for HS teachers” major but we have various works in progress to make the traditional major more accessible and better motivated for future HS teachers)

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#9

Data science/analytics and cybersecurity are two areas of apparently high demand in the workforce. Should math departments respond to these needs? If so, are there examples of successful responses through flexible tracks?

Brit Kirwan

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#10

Hello! At the United States Naval Academy we have three tracks for the math major, plus honors tracks within each of these.

Mathematics major focuses on proof and argument,
Applied mathematics major focuses on differential equations and numerical analysis
Operations research major focuses on mathematical modeling and making better decisions with OR techniques

Our operations reearch major is the most popular of the three, with about 50 majors per year, while the math and applied math tracks have about 10-20 majors each, per year.

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#11

At Harvard the Applied Math program graduates 75-100 majors per year out of about 1650 students. We currently require 14-15 courses (no double majors):

  1. multivariable calculus + linear algebra + up to three prior math courses.
  2. probability, intro to computation, diff eqs or analysis, algebra or optimization or discrete, 1 additional elective from an approved list + two more electives if needed to bring the total to 14.
  3. five courses (>= three of which are quantitative) in a field of application of mathematics

Data science can fit in that set of five courses, as does econ, biology, other social sciences (with a heavy dose of statistics), physics, engineering, earth science, etc. There is little flexibility in part 1, some flexibility in part 2, and substantial flexibility in part 3.

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#12

We have essentially 4 tracks for mathematics majors. We are a regional comprehensive 4-year university enrolling about 7000 students per year. Our tracks include a comprehensive (more or less standard) major with no minor required, a non-comprehensive major (requires a minor), a data science track and a math education track (secondary). We can also taylor a comprehensive major into one that prepares students for a career as an actuary.

I think our most innovative “track” is at the minor level. We have just created a non-calculus based minor where the computational requirement is only precalculus or calulus 1.

Information on all of these can be found at: http://www.nwmissouri.edu/math/programs/index.htm

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#13

At Augsburg College, we offer both the Bachelor of Arts and the Bachelor of Science in Mathematics. For the B.S. students must select a “focus area”. The requirements include 12 courses:

  • 5 core courses: Calculus 1, 2, 3, Linear Algebra, Discrete Mathematical Structures;
  • 4 additional Math/Stats courses: three at the junior level or higher, one may be sophomore level or higher; and
  • 3 additional supporting courses: usually from other departments, although additional mathematics courses may count here too, including introductory statistics.

Participation in our department’s colloquium series and a senior-level “Augsburg Experience” are also required.

Within those choices students must select

  • At least one “theoretical structures” course emphasizing proofs and writing chosen from : Abstract Algebra, Real Analysis, Graph Theory, or Dynamical Systems;
  • At least one “applied projects” course emphasizing projects, technology, writing, and speaking chosen from: Numerical and Computational Mathematics, Modeling and Differential Equations, Operations Research, Statistical Theory and Practice; and
  • At least one “statistics” course emphasizing data analysis.

Also within those choices students must also complete a “focus area” chosen from our list (Biology, Business, Chemistry, Computer Science, Data Analytics, Economics, Finance, Physics, Psychology, Teaching Mathematics, or Theoretical Mathematics (pre-PhD)) or propose a new area of their own. Each focus area includes at least 5 courses on a theme, usually a mix of supporting courses and mathematics/statistics courses. Students must also complete either an undergraduate research experience or internship related to the focus area, which usually simultaneously meets the Augsburg Experience requirement.

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