Math Courses Taken by First-year Students
This document includes the catalogue descriptions of the math
courses usually taken by first-year students, as well as annotations
added by the Math Department to help incoming students understand
the content and purpose of each course. If you want detailed guidance on
placement, then refer to
of first-year students.
If you are looking for information on higher level courses, you can link to
Registrar's Official Schedule of Courses
or to the
If you have questions that are not answered by the information below, you
can contact the Supervisor of First-Year Instruction.
MATH 105L: Laboratory Calculus and Functions I.
study of functions with applications, and an introduction to differential
calculus, with a laboratory component. Topics include a review of algebra
and functions, mathematical modeling with elementary functions, rates of
change, inverse functions, logarithms and exponential functions, the
derivative, differential equations, and Euler's method. Not open to
students who have credit for Mathematics 21 or 111L.
- Additional Math 105L Notes:
- This course, which begins the two-semester sequence Math 105L and 106L,
will be offered only in fall semesters.
The sequence was created by taking the content of Math 19 (which no longer exists) and the
content of Math 111L,
and interweaving the topics in such a way that the precalculus topics are
reviewed when they are needed in the development of calculus.
Refer to the
home page for a link to a syllabus with a detailed list of topics and a day-by-day
schedule. Students in this course are required to have a
calculator with the capabilities that are listed
students who do not place into second-semester calculus or beyond should
normally begin with Math 105L or Math 111L (see
MATH 106L: Laboratory Calculus and Functions II.
continuation of Mathematics 105L. Topics include graphical interpretations
of the derivative, zeroes of functions, optimization, related rates,
antidifferentiation, initial value problems, review of trigonometry,
modeling with trigonometric functions, geometric sums and series, and the
Fundamental Theorem of Calculus. Students who complete this course
can enroll in Mathematics 112L. Not open to students who have credit for
Mathematics 21 or 111L. Prerequisites: Mathematics 105L.
- Additional Math 106L Notes:
- This course completes the two-semester sequence, Math 105L and Math 106L;
thus, it will be offered only in spring semesters. Upon completion of this
course a student will have covered the content of Math 19 and Math 111L,
and in addition will have studied much of the material on the Fundamental
Theorem of Calculus, which is part of Math 112L.
You can refer to the
home page for a link to the syllabus which gives a day-by-day schedule
of topics and labs. A student who completes this
course and wishes to continue in calculus should enroll in
MATH 121: Introductory Calculus I.
limits, continuity, trigonometric functions, techniques and applications
of differentiation, indefinite and definite integrals, the fundamental
theorem. Prerequisites: -none-
- Additional Math 121 Notes:
- This is the traditional course, such as that defined by the first several
chapters of a book like Calculus by Thomas and Finney. All calculus I
courses at Duke have been converted to a laboratory format with a very
different emphasis from this course (see below). Math 121 is no longer
offered, and is now used only in granting transfer credit in certain cases.
MATH 111L: Laboratory Calculus I.
Description: Functions, limits, continuity, trigonometric
functions, techniques and
applications of differentiation, indefinite and definite integrals,
the fundamental theorem.
- Additional Math 111L Notes:
- This course brings a new approach to the study of calculus, and it is
now the primary entry-level course for calculus at Duke.
Effective in the fall of 1997 the laboratory work in this course will be
done with a scientific, graphing calculator of the student's choice, as
long as it has
For a detailed list of
lecture topics, lab topics, and project topics refer to the syllabus which
is linked from the Math 111L
home page. To enroll in this course students should meet SAT
score and Achievement score requirements as described under
complete this course and who wish to take more calculus should enroll in
MATH 122: Introductory Calculus II.
Transcendental functions, techniques and applications of integration,
indeterminate forms, improper integrals, infinite series. Not open to
students who have had Mathematics 112L or 122L. Prerequisites: Mathematics 121.
- Additional Math 122 Notes:
- Effective in the fall of 2011 this listing will be used only
for the purpose of granting AP and transfer credit for calculus II.
Entering students who have AP credit for Math 21 and who want to take a
calculus II course in their first semester should sign up for Math 122L.
MATH 112L: Laboratory Calculus II.
Description: Second semester of introductory calculus with a
laboratory component. Emphasis on laboratory projects, group work, and
written reports. Methods of integration, applications of integrals,
functions defined by integration, improper integrals, introduction to
probability and distributions, infinite series, Taylor polynomials,
series solutions of differential equations, systems of differential
equations, Fourier series. Not open to students who have had Mathematics 122L. Prerequisites: Mathematics 111L or consent of instructor.
- Additional Math 112L Notes:
- This course is offered in both the fall and spring semesters.
In the fall semesters it is restricted to students continuing from Math
111L or Math 106L at Duke. Students entering in the fall who
want to take
a calculus II course should enroll in Math 122L. In the spring
Math 122L will not be offered, but Math 112L in the spring
will be open
to all students who are qualified to take a calculus II course. You can
read more about these courses in the document Second-semester Calculus.
Students in Math 112L will need a calculator as described
For details of the content of Math 112L you can refer to the
Math 112L home page for a link to the fall and spring versions of the syllabus.
Upon completion of Math 112L a student may take
MATH 122L: One Variable Calculus.
Description: Topics include sequences and series, the
definition of the integral and its uses, Taylor and Fourier Series,
differential equations and mathematical models. The weekly labs will
involve explorations of applications, techniques, and Theory.
Prerequisite: Advanced placement credit for Mathematics 21. Not open to
students who have taken Mathematics 106L, 111L, 112L, or 122 or who have
taken this course as Mathematics 41. Prerequisites:AP credit for Math 21.
- Additional Math 122L Notes:
- Math 122L is designed for first year students who have AP credit for
Math 21. Students continuing from Math 111L or Math 106L are not allowed
to take Math 122L; those students should enroll in Math 112L. In addition
to Calculus II material, Math 122L covers topics that are typically
omitted or poorly explored in high school Calculus I courses. The
course emphasizes series, and covers the definition of the integral,
integration techniques, and basic differential equations. Math 122L is
meant to develop both an understanding of the formal structure of
calculus and an understanding of how calculus is used in applications.
If another department lists Math 122 or
Math 112L as a requirement, Math 122L will satisfy that
requirement. For more
information on Math 122L, 112L, and 122 please refer to
the document Second-semester Calculus.
Upon successful completion of Math 122L, a
student may enroll in
Math 202 or
MATH 89S(49S): First-Year Seminar.
Topics vary each semester offered. Prerequisites: -none-
- Additonal Math 89S(49S) Notes:
- The following is a list of topics which have been offered over the
last several years. These seminars are given only in spring
semsesters, and in general the Math Department has offered one or two
seminars each spring since the inception of first-year seminars. For more
information on each seminar, click on its name. Note that in any particular
spring semester the Math Department will offer only one or two seminars.
MATH 202: Multivariable Calculus.
Gaussian elimination, matrix algebra, determinants, linear
independence. Calculus of several variables, chain rule, implicit
differentiation. Optimization, first order conditions, Lagrange
multipliers. Integration of functions of several variables. Prerequisite: Mathematics 122, 112L or 122L. Not open to students who have taken Mathematics 212.
- Additional Math 202 Notes:
- This course is designed for economics majors. Students who are
planning on getting a double major in economics and another major which
requires Math 212 (such as math or certain science majors) should
enroll in Math 212 instead of this course. For more information please
refer to the Math 202 information page.
MATH 212: Intermediate Calculus.
Description: Partial differentiation, multiple integrals, topics in
differential and integral vector calculus.
Prerequisites: Mathematics 122, 112L, or 122L.
- Additional Math 212 Notes:
- Many first-year students who receive AP credit for Math 21 and Math 22
are hesitant about enrolling in a "sophomore-level" course. In fact
usually about half of the students in Math 212 in the fall
are first-year students. Their success rate is quite high, and those who
do forego their Math 22 AP credit to repeat that material often find Math 22
to be just as time-consuming as their fellow students who proceed
with Math 212. The content of this course is essentialy the last third
of a calculus textbook such as Calculus by Thomas and Finney.
Refer to the
Math 212 home page
where there is a link to a detailed syllabus for the course.
Students who continue in math
beyond calculus III usually take either Math 221
or Math 216 next. (See
for the official description of Math 216.) For most engineering
students Math 216 is
the next course, although those engineering students who want to get a
double major with math should ask the engineering dean of first-year
students for permission to
substitute Math 221 AND Math 356 AND Math 453 for the
Engineering School's Math 216 AND Math 353
requirement. Trinity College students often take Math 221 after
Math 212, because Math 221 is a prerequisite for several
upper-level courses and because linear algebra is needed in a number of
other disciplines. Note however, that there are some upper-level
courses for which Math 212 is the only prerequisite.
MATH 221: Linear Algebra and Applications.
Systems of linear equations and elementary row operations, Euclidean
n-space and subspaces, linear transformations and matrix representations,
Gram-Schmidt orthogonalization process, determinants, eigenvectors and
eigenvalues; applications. Prerequisites: Mathematics 122 or 122L.
- Additional Math 221 Notes:
- We strongly encourage prospective mathematics majors, who have
advance credit for Math 21 and Math 22, to take Mathematics 221 in
their first semester, to be followed by Mathematics 222 in the spring.
Note that with this plan for math majors, the sequence Math 221/Math222
relaces the sequence Math 212/Math 221.
Description: Partial differentiation,
multiple integrals, and topics in differential and integral vector
calculus, including Green's theorem, Stokes's theorem, and Gauss's
theorem for students with a background in linear algebra. Not open to
students who have taken Mathematics 202 or 212. Prerequisite: Mathematics 221.
- Additional Math 222 Notes:
- This course is offered only in the spring. The students in this course
are almost always first-year students who are prospective math majors and who started with
in the fall. You can read more information about Math 222
This information is provided by Clark Bray