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, 128, and 174 are courses containing selected topics from geometry, and number theory. 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 MATH 115 or 185. The sequence MATH 115-116-215 is appropriate for most students who want a complete introduction to calculus. One of MATH 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 LSA 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 396 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 terms of AP credit – MATH 156. MATH 156 is an Honors course intended primarily for science and engineering concentrators and emphasizes 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 296, 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.
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: www.lsa.umich.edu/undergrad/reu.shtml
Special Departmental Policies. All prerequisite courses must be satisfied with a grade of C– or above. Students with lower grades in prerequisite courses must receive special permission of the instructor to enroll in subsequent courses.