Mathematics
is the language and tool of the sciences, a cultural phenomenon
with a rich historical tradition, and a model of abstract reasoning.
Historically, mathematical methods and thinking have been extraordinarily
successful in physics, and engineering. Today, they are used successfully
in many new areas, from computer science to biology and finance.
A Mathematics concentration provides a broad education in various
areas of mathematics in a program flexible enough to accommodate
a wide range of interests.
The
study of mathematics is an excellent preparation for many careers;
the patterns of careful logical reasoning and analytical problem
solving essential to mathematics are also applicable in contexts
where quantity and measurement play only minor roles. Thus students
of mathematics may go on to excel in medicine, law, politics,
or business as well as any of a vast range of scientific careers.
Special programs are offered for those interested in teaching
mathematics at the elementary or high school level or in actuarial
mathematics, the mathematics of insurance. The other programs
split between those which emphasize mathematics as an independent
discipline and those which favor the application of mathematical
tools to problems in other fields. There is considerable overlap
here, and any of these programs may serve as preparation for either
further study in a variety of academic disciplines, including
mathematics itself, or intellectually challenging careers in a
wide variety of corporate and governmental settings.
Elementary
Mathematics Courses. In
order to accommodate diverse backgrounds and interests, several
course options are available to beginning mathematics students.
All courses require three years of high school mathematics; four
years are strongly recommended and more information is given for
some individual courses below. Students with College Board Advanced
Placement credit and anyone planning to enroll in an upper-level
class should consider one of the Honors sequences and discuss
the options with a mathematics advisor.
Students
who need additional preparation for calculus are tentatively identified
by a combination of the math placement test (given during orientation),
college admission test scores (SAT or ACT), and high school grade
point average. Academic advisors will discuss this placement information
with each student and refer students to a special mathematics
advisor when necessary.
Two
courses preparatory to the calculus, MATH 105 and 110, are offered.
MATH 105 is a course on data analysis, functions and graphs with
an emphasis on problem solving. MATH 110 is a condensed half-term
version of the same material offered as a self-study course taught
through the Math Lab and is only open to students in MATH 115
who find that they need additional preparation to successfully
complete the course. A maximum total of 4 credits may be earned
in courses numbered 103, 105, and 110. MATH 103 is offered exclusively
in the Summer half-term for students in the Summer Bridge Program.
MATH 107, Mathematics for the Information Age, is a course for
students who may not want or need to take calculus. It encourages
mathematical exploration of a variety of topics both inside and
outside of mathematics.
MATH
127, MATH 128 and MATH 174 are courses containing selected
topics from geometry, number theory, and proofs respectively.
They are intended for students who want exposure to mathematical
culture and thinking through a single course. They are neither
prerequisite nor preparation for any further course. No credit
will be received for the election of MATH 127, 128, or 174 if
a student already has credit for a 200-(or higher) level MATH
course.
Each
of MATH 115, 185, and 295 is a first course in calculus. Generally
credit can be received for only one of 115 or 185. The sequence
MATH 115-116-215 is appropriate for most students
who want a complete introduction to calculus. One of 215, 255,
285, or 395 is prerequisite to most more advanced courses in Mathematics.
The
sequences MATH 156-255-256, 175-186-285-286, 185-186-285-286,
and 295-296-395-396 are Honors sequences. Students need not be
enrolled in the LS&A Honors Program to enroll in any of these
courses but must have the permission of an Honors advisor. Students
with strong preparation and interest in mathematics are encouraged
to consider these courses.
MATH
185 through 285 covers much of the material of MATH 115 through
215 with more attention to the theory in addition to applications.
Most students who take MATH 185 have taken a high school calculus
course, but it is not required. MATH 175 through 186 assumes knowledge
of calculus roughly equivalent to MATH 115 and covers a substantial
amount of so-called combinatorial mathematics as well as calculus-related
topics not usually part of the calculus sequence. MATH 175 is
taught by Inquiry-Based Learning (IBL): students are presented
with a great variety of problems and encouraged to experiment
in groups using computers. The sequence MATH 295 through 396 provides
a rigorous introduction to theoretical mathematics. Proofs are
stressed over applications and these courses require a high level
of interest and commitment. Most students electing MATH 295 have
completed a thorough high school calculus course. MATH 295 through
296 is excellent preparation for mathematics at the advanced undergraduate
and beginning graduate level.
Students
with strong scores on either the AB or BC version of the College
Board Advanced Placement exam may be granted credit and advanced
placement in one of the sequences described above; a table explaining
the possibilities is available from advisors and the department.
In addition, there is one course especially designed and recommended for students with one or two semesters of AP credit, MATH 156.
MATH 156 is an Honors course intended primarily for science and
engineering concentrators and will emphasize both applications
and theory. Interested students should consult a mathematics advisor for more details.
In
rare circumstances and with permission of a Mathematics advisor,
reduced credit may be granted for MATH 185 after MATH 115. A list
of these and other cases of reduced credit for courses with overlapping
material is available from the department. To avoid unexpected
reduction in credit, a student should always consult an advisor
before switching from one sequence to another. In all cases a
maximum total of 16 credits may be earned for calculus courses
MATH 115 through 396, and no credit can be earned for a prerequisite
to a course taken after the course itself.
Students
completing MATH 116 who are principally interested in the application
of mathematics to other fields may continue either to MATH 215
(Analytic Geometry and Calculus III) or to MATH 216 (Introduction
to Differential Equations); these two courses may be taken in
either order. Students who have greater interest in theory or
who intend to take more advanced courses in mathematics should
continue with MATH 215 followed by the sequence MATH 217-316 (Linear
Algebra-Differential Equations). MATH 217 (or the Honors version,
MATH 513) is required for a concentration in Mathematics; it both
serves as a transition to the more theoretical material of advanced
courses and provides the background required for optimal treatment
of differential equations in MATH 316. MATH 216 is not intended for concentrators in pure mathematics.
The
Undergraduate Math Club is mentoredby a faculty advisor for all students with
an interest in Mathematics. It is an informal organization,
which sponsors talks by faculty and students. A typical meeting
begins with free pizza and drinks, shortly followed by a 45-minute
talk on an interesting mathematical problem, application, or idea
(or all three!). The selected topic is something, which isn't
usually seen, in the standard curriculum. Some of these topics
lead into important concepts in theoretical or applied research,
while others explain a clever solution to an interesting problem.
Everything is formulated so as to avoid needing technical background
beyond calculus, some exposure to methods of proof, and a moderate
capacity for abstract thought. For more information, see the web
page:
Student
Actuaries at Michigan is
an organization for undergraduates and graduates interested in
the field of actuarial and financial mathematics. There are monthly
meetings on topics of interest, sometimes featuring speakers from
industry. The Club organizes study groups for the professional
examinations and coordinates visits to campus of industry recruiters.
It also sponsors a variety of athletic and social activities,
including an end-of-year picnic.
William
Lowell Putnam Competition. A
departmental team participates in the annual William Lowell Putnam
Competition sponsored by the Mathematical Association of America.
Interested students with exceptional mathematical aptitude are
asked to contact the department office for detailed information.
The department also sponsors other competitions and activities.
Scholarships
and Awards
M.S.
Keeler and Math Merit Scholarships are
available, generally to entering first year students, in varying
amounts up to the current level of in-state tuition. These scholarships
are renewable, up to three times, based upon satisfactory progress
by declared mathematics concentrators. Multiple scholarships are
awarded each year.
Margaret
S. Huntington Scholarships in
the amount of $1,000 each are available to first year students
who receive a grade of A” in their first semester mathematics
courses. Up to ten scholarships are awarded. The goal is to broaden
awareness of the actuarial profession.
Evelyn
O. Bychinsky Awards are
given to continuing students (that is students with less than
90 credits) who show exceptional promise in mathematics deserving
of recognition and encouragement. Up to five awards are given
annually in amounts of $1,000.
Irving
S. Wolfson Award is
given to an undergraduate actuarial student who has shown substantial
promise of professional actuarial achievement through academic
accomplishments and participation in employment and/or extracurricular
achievement. The award is $7,500.
Lois
Zook Levy Memorial Award is
given annually to an outstanding graduating senior majoring in
mathematics who will pursue a teaching career in K-12 mathematics.
The initial award is $1,500.
The
Wirt and Mary Cornwell Award is
given annually to a student who, during the four previous years,
has demonstrated the greatest intellectual curiosity and has given
the most promise of original study and creative work in mathematics.
The award is for $10,000 and is available to both undergraduates
and graduate students.
There
are a number of other scholarships and prizes which honor faculty
and alumni/ae that students are eligible for after they have declared
a mathematics concentration. These are funded by the CIGNA, Cortright,
Davis,
Fischer, Glover, Leveque, Myers, Newsome, Poorman, Richter, Shields,
Van Eanam, and Zukowski funds.
Summer
Research. The
department has opportunities for a number of undergraduate students
to pursue on-site summer research under the auspices of the Research
Experience for Undergraduates (REU) program. Students pursue a
7-8 week summer research project under the mentorship of regular
departmental faculty, and are paid a stipend for this work. For
more information, see the web
page: http://www.math.lsa.umich.edu/undergrad/reu.shtml.
Special
Departmental Policies. All
prerequisite courses must be satisfied with a grade of Cc or above.
Students with lower grades in prerequisite courses must receive
special permission of the instructor to enroll in subsequent courses.
Content Author(s): lsa saa advising technology: rickey
