Math Courses Taken by First-year Students

This document includes the catalogue descriptions of the math coures 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 placement of first-year students. If you are looking for information on higher level courses, you can link to the Registrar's Official Schedule of Courses or to the University Bulletin. If you have questions that are not answered by the information below, you can send an email message to the Supervisor of First-Year Instruction, Lewis Blake, at sfi@math.duke.edu

Course Descriptions

MTH 025L: Laboratory Calculus and Functions I. Description: A 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 19 or 31 or 31L. Prerequisites: -none-
Additional Math 25L Notes:
This course, which begins the two-semester sequence Math 25L and 26L, will be offered only in fall semesters. The sequence was created by taking the content of Math 19 and the content of Math 31L, 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 Math 25L 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 here . First-year students who do not place into second-semester calculus or beyond should normally begin with Math 25L or Math 31L (see placement.).

MTH 026L: Laboratory Calculus and Functions II. Description: A continuation of Mathematics 25L. 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 32L. Not open to students who have credit for Mathematics 31 or 31L. Prerequisites: Mathematics 25L.

Additional Math 26L Notes:
This course completes the two-semester sequence, Math 25L and Math 26L; 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 31L, and in addition will have studied much of the material on the Fundamental Theorem of Calculus, which is part of Math 32L. You can refer to the Math 26L 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 32L.

MTH 031: Introductory Calculus I. Description: Functions, limits, continuity, trigonometric functions, techniques and applications of differentiation, indefinite and definite integrals, the fundamental theorem. Prerequisites: -none-

Additional Math 31 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 31 is no longer offered, and is now used only in granting transfer credit in certain cases.

MTH 031L: Laboratory Calculus I. Description: Functions, limits, continuity, trigonometric functions, techniques and applications of differentiation, indefinite and definite integrals, the fundamental theorem. Prerequisites: -none-

Additional Math 31L 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 sufficient capabilities . For a detailed list of lecture topics, lab topics, and project topics refer to the syllabus which is linked from the Math 31L home page. To enroll in this course students should meet SAT score and Achievement score requirements as described under placement. Students who complete this course and who wish to take more calculus should enroll in Math 32L.

MTH 032: Introductory Calculus II. Description: Transcendental functions, techniques and applications of integration, indeterminate forms, improper integrals, infinite series. Not open to students who have had Mathematics 41. Prerequisites: Mathematics 31.

Additional Math 32 Notes:
Almost all students who enroll in this course are first-year students who received AP or transfer credit for Math 31. The course was redesigned in the fall of 1995. The goal of the changes was to raise the level of mathematical rigor from the level of Math 32 in previous years and to adopt a more advanced textbook than we had been using. Math 32 is a traditional calculus course, the format of which will probably closely resemble the format of high school calculus courses. On the other hand, the content will probably be more difficult than high school AP calculus, and the exercises and exams will be more challenging. You will be expected to solve problems that are not identical to ones done in class or on the homework and that will involve more conceptual understanding than memorization of techniques. Refer to the Math 32 home page for a link to the syllabus which shows the topics covered in the course. Students who continue in calculus beyond this course should take Math 103.

MTH 032L: 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 41. Prerequisites: Mathematics 31L or consent of instructor.

Additional Math 32L Notes:
This course is offered in both the fall and spring semesters as a continuation of Math 31L or Math 26L. As compared to Math 32 (no L), this course focuses more on concepts and applications, rather than on mathematical rigor or on developing integration techniques. The graded work in Math 32 consists of 4 or 5 major tests, whereas the graded work in Math 32L consists of, not only major tests, but also lab reports, lab quizzes, and homework quizzes. Students in this course will need a calculator as described here . For details of the content of Math 32L you can refer to the Math 32L home page for a link to the fall and spring versions of the syllabus. Upon completion of Math 32L a student may take Math 103.

MTH 032X: Introductory Honors Calculus II. Description: Similar to Mathematics 32, but faster paced and more challenging. Open to students who score at least 750 on the SAT Mathematics Aptitude Test. Prerequisites: -none-

Additonal Math 32X Notes:
This course parallels Math 32, but presents the topics at a more challenging level, with an emphasis on creative problem solving using mathematical thinking. There are two conditions a student should meet before enrolling in this course:
  1. The student must have a 5 on the Advanced Placement Calculus AB exam or other approved credit for Math 31.
  2. The student's SAT math and SAT-II math scores must be 750 or higher.
Students who do not meet the requirements above must have permission of the instructor to enroll.
This course is offered only in fall semesters. Upon completion of Math 32X students are encouraged to take Math 103X.

MTH 041: One Variable Calculus. Description: Quickly reviews selested topics from first-semester calculus, covers integral calculus, including infinite series and various applications. Not open to students who have had Mathematics 32 or 32L or 31L. Prerequisites: -none-

Additional Math 41 Notes:
This course has been redesigned for fall 2007. The new version covers a combination of selected traditional topics from Math 32, some topics from Math 31L which do not appear in typical high school calculus courses, and some applications from Math 32L. There is now a weekly lab wherein students participate in group work. To enroll in this course a student should have AP credit for Math 31, an SAT score of at least 680, and a strong interest in mathematical rigor, mathematical concepts, and applications of mathematics. Students with a 4 on the AB test and over 700 SAT may also enroll in this course. For more information about Math 41L please refer to the Math 41 homepage. Upon successful completion of Math 41, a student may enroll in Math 103.

MTH 049S: First-Year Seminar. Description: Topics vary each semester offered. Prerequisites: -none-

Additonal Math 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.

MTH 102: Multivariable Calculus. Description: 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 32, 32L or 41. Not open to students who have taken Mathematics 103.

Additional Math 102 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 103 (such as math or certain science majors) should enroll in Math 103 instead of this course. For more information please refer to the Math 102 information page.

MTH 103: Intermediate Calculus. Description: Partial differentiation, multiple integrals, topics in differential and integral vector calculus. Prerequisites: Mathematics 32, 32L, or 41.

Additional Math 103 Notes:
Many first-year students who receive AP credit for Math 31 and Math 32 are hesitant about enrolling in a "sophomore-level" course. In fact usually about half of the students in Math 103 in the fall are first-year students. Their success rate is quite high, and those who do forego their Math 32 AP credit to repeat that material often find Math 32 to be just as time-consuming as their fellow students who proceed with Math 103. 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 103 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 104 or Math 107 next. (See ACES for the official description of Math 107.) For most engineering students Math 107 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 104 AND Math 131 for the Engineering School's Math 107 requirement. Trinity College students often take Math 104 after Math 103, because Math 104 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 103 is the only prerequisite.

MTH 103X: Honors Intermediate Calculus and Linear Algebra. Description: Similar to Mathematics 103, 104, but more theoretical. Students who have taken 32X are encouraged to enroll. Students continuing from 103X should take 104X rather than 104. This course is continued in MTH 104X.

Additonal Math 103X Notes:
This course is presented with a more theoretical approach than either Math 103 or Math 103L. There are three conditions a student should meet before enrolling in this course:
  1. The student should have credit for Math 31 and Math 32, and should, of course, know first-year calculus material well.
  2. The student should have a Math SAT score between 750 and 800.
  3. The student should be strongly motivated to study abstract mathematics.
If a student fall short on any of these requirements but is also qualified for Math 103, then it would be best for the student to enroll in the regular Math 103 course.

MTH 104: Linear Algebra and Applications. Description: 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 32 or 41.

Additional Math 104 Notes:
Although Math 32 or Math 41 is listed as a prerequisite for this course, it is not a good idea for an incoming student with AP credit for Math 32 (and no other math credit) to enroll in this course. Those first-year students who take this course usually enter with transfer credit for Math 103, or they take this course in the spring after taking Math 103 in the fall. Some students who enter with Math 31 credit and take Math 32 in the fall, go on to this course in the spring, but that is unusual. The question here is one of college experience and "mathematical maturity." Most students who take Math 104 have already had Math 103 at Duke.

MTH 104X. Description:This course is a continuation of MTH 103X. Prerequisites: -none-

Additional Math 104X Notes:
This course is offered only in the spring. The students in this course are almost always the same students who took Math 103X in the fall. Any student who did not take Math 103X and who wishes to take this course should get the permission of the teacher first.

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