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Courses in LSA Mathematics

Introductory Mathematics Courses

In order to accommodate students’ diverse backgrounds and interests, there are five introductory sequences in Mathematics: the Standard Calculus Sequence (MATH 115-116-215), the Applied Honors Calculus Sequence (MATH 156-255-256), the Honors Seminar MATH Sequence (MATH 175-176-285-286), the Honors Calculus Sequence (MATH 185-186-285-286), and the Honors MATH Sequence (MATH 295-296-395-396). Students with strong preparation and interest in mathematics, students with College Board Advanced Placement (AP) or International Baccalaureate (IB) credit, and students planning to enroll in a course other than Calculus I (MATH 115) should discuss their options with a Mathematics advisor during summer orientation. In particular, students need not be enrolled in the LSA Honors Program to enroll in the Honors Sequences, but, with the exception of MATH 156, they must have the permission of a Mathematics advisor to do so.

Students who need additional preparation before beginning one of these introductory sequences 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 Mathematics advisor when necessary. An excellent preparatory course is MATH 105, a course on data analysis, functions, and graphs with an emphasis on problem solving, concepts, and interpretations.

The Standard Calculus Sequence

The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. This sequence is taken by the majority of Michigan students intending to concentrate in the sciences or engineering, as well as students heading for many other fields.

Calculus I and II (MATH 115 and 116) emphasize conceptual understanding and the solving of real world problems. Both are taught in small, interactive classrooms that focus on cooperative learning, and both achieve extremely high scores in national measures of teaching effectiveness. The sequence concludes with multivariable calculus, Calculus III (MATH 215).

Students who have an interest in theory or who intend to take more advanced courses in Mathematics should follow MATH 215 by the sequence MATH 217-316 (Linear Algebra-Differential Equations). MATH 217 (or the Honors version, MATH 420) is required for a major in Mathematics; it both serves as a transition to the more theoretical material of advanced courses and provides the background required for MATH 316.

Students who are principally interested in the application of mathematics to other fields will typically need to complete coursework in linear algebra and/or differential equations. Such students usually take either MATH 214 (Linear Algebra) and/or MATH 216 (Introduction to Differential Equations); students should consult with an advisor in their intended field of study to determine which plan of study will best suit their needs. Note that the courses MATH 214, 215, and 216 can be taken in any order, but a student electing 216 will typically choose one of Matrix Algebra I (MATH 417) or Linear Spaces and Matrix Theory (MATH 419) for their linear algebra course.

The Honors Sequences

Students need not be enrolled in the LSA Honors Program to enroll in any of the courses that form the Honors Sequences, but, with the exception of MATH 156, they must have the permission of an Honors Mathematics advisor to do so.

Applied Honors Calculus Sequence (MATH 156-255-256): Applied Honors Calculus II (MATH 156) is designed for engineering and science majors who received a score of 4 or 5 on the AP exam (AB or BC). MATH 156 is an alternative to MATH 116 with more emphasis on science applications and theory. The sequence continues with courses in multivariable calculus and differential equations (MATH 255-256), which are alternatives to MATH 215-216.

Honors Seminar MATH Sequence (MATH 175-176-285-286): MATH 175 (Introduction to Cryptography) and MATH 176 (Explorations in Topology and Analysis) are taught in the Inquiry-Based Learning (IBL) style. The IBL method emphasizes discovery, analysis, and investigation to deepen understanding. These courses assume a knowledge of calculus roughly equivalent to MATH 115; they cover a substantial amount of basic number theory (MATH 175) and provide a good, high level understanding of calculus (MATH 176). The sequence concludes with Honors versions of multivariable calculus (MATH 285) and differential equations (MATH 286).

Honors Calculus Sequence (MATH 185-186-285-286): Honors Calculus I and II (MATH 185 and 186) rigorously develop the concepts of calculus. These courses are intended for students who desire a complete understanding of the theoretical underp