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Symbol manipulation doesn’t receive near the
emphasis it did 20 years ago in the high school curriculum. Proofs too are
becoming increasingly rare in the high schools. |
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A professional mathematician may think of
himself as an inspired artist (and he might be), but proofs and tedious
symbol manipulation are still 90% of the game. |
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Career-oriented, scientifically-inclined
students can major in any number of different fields and don’t have to
“explain” their abilities to a recruiter. |
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A math major must be able to answer the
question, “What can you do for me?”
A math major must bear a relatively huge burden of self-marketing. |
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Pre-calculus (admission price) |
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Calculus I, II, III |
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Foundations (Proofs) |
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Linear Algebra |
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Two of DE, Number Theory, Geometry, Complex
Variables, Modeling |
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One year of Modern Algebra, Analysis, or
Statistics plus one semester of one
of the others |
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Nine additional hours of upper division |
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Total = 41 hours |
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Phil 110-120 (admission price) |
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Phil 160 |
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Phil 210 |
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Phil 314, 315 |
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18 additional hours in upper division |
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Total = 30 hours |
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History 121-122, History 201-202 (admission
price) |
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History 301 |
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History 499 |
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21 additional hours in upper division |
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Minimum score on exit exam |
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Total = 24 hours |
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Ole Miss (30 hrs math) |
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Calc Sequence + Proofs + Linear Algebra + 12 hrs
+ Programming |
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University of Arkansas (34 hrs math) |
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Calc Sequence + Discrete Math + Linear Algebra +
15 hrs + Paper |
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Miami University (34 hrs math) |
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Calc Sequence + Linear Algebra + 19 hrs + Programming + 12 “related hours” |
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Miami U has 306 “math” majors, 15000 undergrads |
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153 BSEd, 28 BSM, 2 BSS, 58 BSM/S, 65 BA. |
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At least 1/3 of BA students are double majors |
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U Arkansas
has 141 math majors, 12800 undergrads. |
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95 BS, 46 BA |
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Traditional (33 hrs math) |
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Calc Sequence
(11 hrs) + Math 241 + Math 310 + 16 hrs |
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There is a clear difference between an artist
and an art historian, between a musician and a music historian. |
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Colleges have long recognized the intellectual
value of both fields by credentialing majors in both areas of study. |
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Algebra + Trig? [Math 140, 141?] (admission price) |
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Statistics [Math 210] |
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One year of Calculus for Humanities [Math
220-221?] |
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Proofs [Math 241] |
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Linear Algebra [Math 310] |
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18 additional hours of upper division courses |
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require double major? |
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minimum score on exit exam? |
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Total = 33 hours |
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Math 350, 410, 420 |
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None of these courses requires the traditional
calculus ramp |
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Math 340, 365, 455, 461, 462, 465 |
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These courses claim to need Math 252 |
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Math 451, 491, 492 |
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These courses claim to need Math 320 |
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We could aim for breadth: Maple + Mathematica + Derive + Excel |
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We could specialize in just one package, and use
the course as a lens through which to view a single mathematical topic,
say, differential equations. |
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Mathematical Literature (Gardner, Stewart,
Hofstadter, etc) |
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Philosophy of Mathematics |
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Symbolic Logic (Phil 360) |
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Math History II |
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Mathematics of Art |
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Math “Recital” or Paper |
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Exit exam prep |
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Math 141 Trig? |
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Math 221 Calculus for Humanities II |
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Math 380 Mathematical Software |
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Two Math Humanities Upper Division |
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The mathematical sciences bachelor's
degree program should be consistent with the current recommendations of the
MAA Committee on the Undergraduate Program in Mathematics (CUPM)
Guidelines. … Programs with no curricular track that conforms to the CUPM
guidelines should be justified by a detailed and persuasive rationale for
departing from those guidelines. A summary of the CUPM Report comprises
Appendix B of this document. |
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Guidelines for Programs and
Departments in Undergraduate Mathematical Sciences |
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Calculus (with Differential Equations) |
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Linear Algebra |
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Probability and Statistics |
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Proof-based courses |
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An in-depth experience in mathematics |
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Applications and connections |
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Track courses, departmental requirements and
electives |
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B.A. Option 1 – Traditional (33 hrs) |
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This is an excellent option for students who
enjoy mathematics for the “purity” of the discipline and are not terribly
interested in applications. Also an excellent choice for students wishing
to pursue a double major in a discipline of the humanities. Students hoping
to pursue grad study or employment in mathematics will be better served by
a B.S. degree. |
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B.A. Option 2 – Nontraditional (33 hrs) |
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This is an excellent option for students who are
primarily interested in the study of mathematics as a cultural artifact.
Though students will pick up some mathematical skills as a matter of
course, students taking this degree should do so primarily to become
conversant in the philosophical/historical issues of the discipline. This is an excellent choice for students
hoping to double major in a discipline of the humanities. Students hoping to pursue grad study or
employment in mathematics will be better served by a B.S. degree. |
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Where in the world are these new courses going
to come from? |
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If we are serious about the answer to this
question being “release time”, we must also be serious about going after
external grants to fund the development of any new courses. |
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Could B.S. majors use any of these new courses
to satisfy their nine additional hours of upper division courses? |
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This would be one sure way of guaranteeing that
our exit exam scores fall closer to the 50th percentile. |
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Would B.A. folks leave with any career
competencies? |
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Who knows.
An exit exam minimum might be some insurance. So would requiring a double major. In any case, UTM offering a B.A. in
Mathematics would be no more irresponsible than UTM offering a B.A. in
Philosophy. |
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Wouldn’t it be misleading to graduate people
with a B.A. in Mathematics when they would in fact have little in the way
of true competency in the field? |
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As regards option 1, we have seen three schools
not overcome by such moral qualms. More of a worry for option 2 grads, I
would argue this concern is not realistic: the kind of students attracted
to this option are unlikely to be seeking future employment in mathematics. |
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What makes you think THEC is going to let us add
a new B.A., when we haven’t been able to award the old B.A.? |
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I’m not proposing a new degree. I’m proposing we
renovate the old one “down to the girders”. If we are troubled by the
prospect that we are falsely credentialing our graduates in mathematics, we
could apply to rename the degree in the years following the renovation
(e.g. B.A. in Mathematical Arts). |
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Who would major? |
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The Miami data suggests that quite a few might
take B.A. Option 1. Praxis refugees
certainly. At least four of these
refugees took BUS degrees with 32 hours of math to their credit. They would
be just a capstone paper away from a B.A. in math. |
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But who would take that silly B.A. Option 2? |
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If the humanities calc ramp is sufficient to do
upper level statistics, a few “statistics majors” might come from there.
But who knows? Maybe no one. If we’re serious though about finding new
majors we need to fish in fresh ponds.
The sciences pond appears to have all but dried up nationwide. The
humanities pond is one the mathematical community has not yet seriously
tried to farm. |
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Wouldn’t this destroy our B.S. in Mathematics? |
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The Miami data suggests that offering a more
easily obtained B.A. is not a zero sum game. Far from stealing from the
pool of B.S. majors, a more easily obtained B.A. appears to add to the
total pool of majors. There may even be some unexpected synergies between
the nontraditional B.A. and the traditional B.S.; this could add a fresh
dynamic to the department. |
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Notes