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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 underpinnings of calculus, and they lay a solid foundation for future Mathematics courses. The sequence concludes with Honors versions of multivariable calculus (MATH 285) and differential equations (MATH 286). Most students who take MATH 185 have taken a high school calculus course, but it is not required.

Honors MATH Sequence (MATH 295-296-395-396): The Honors MATH Sequence provides a rigorous introduction to theoretical mathematics. These courses require an extremely high level of interest and commitment and provide excellent preparation for mathematics at the advanced undergraduate and beginning graduate level. Most students electing MATH 295 have completed a thorough high school calculus course.

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.

Mathematics (MATH)
MATH 100 / STATS 100. Introduction to Statistics, Probability and Mathematical Modeling
Consent of department required. 3-4 years of high school mathematics, including trigonometry. (4; 3 in the half-term). (MSA). (BS). May not be repeated for credit. No credit granted to those who have completed or are enrolled in SOC 210, STATS 280, 250, 400, 405 or 412, IOE 265, or ECON 404 or 405.

Statistical reasoning for learning from observations; continuous and discrete mathematical approaches for modeling a variety of scientific phenomena. Emphasis is on the interplay between data, statistical and mathematical principles and the human activity of modeling, as opposed to specific methods or theories.

MATH 103 / CSP 103. Intermediate Algebra
Only open to designated summer half-term Bridge students. (2 in the half-term). May not be repeated for credit. Su.

Review of elementary algebra; rational and quadratic equations; properties of relations, functions, and their graphs; linear and quadratic functions; inequalities, logarithmic and exponential functions and equations.

MATH 104 / CSP 104. Mathematical Thinking
Only open to designated Summer half-term Bridge and M Academy students. (2 in the half-term). (QR/2). May not be repeated for credit.

This course is an introduction to rigorous mathematical reasoning, for students planning on a career in the humanities. The focus is on significant ideas in mathematics but not on notation or computation.

MATH 105. Data, Functions, and Graphs
(4). (MSA). (QR/1). May not be repeated for credit. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 105 and 110.

This course presents the concepts of precalculus from four points of view: geometric (graphs), numeric (tables), symbolic (formulas), and written (verbal descriptions). The emphasis is on the mathematical modeling of real-life problems using linear, polynomial, exponential, logarithmic, and trigonometric functions. Students develop their reading, writing, and questioning skills in an interactive classroom setting.

MATH 110. Pre-Calculus (Self-Study)
MATH 110 is by recommendation or permission of MATH 115 instructor. (2). May not be repeated for credit. No credit granted to those who already have 4 credits for pre-calculus mathematics courses. A maximum of four credits may be earned in MATH 105 and 110.

The course is a condensed, half-term version of Math 105 designed for students who appear to be prepared to handle calculus but are not able to successfully complete Math 115. Students may enroll in Math 110 only on the recommendation of a mathematics instructor after the third week of classes in the Fall and must visit the Math Lab to complete paperwork and receive course materials. The course covers data analysis by means of functions and graphs.

MATH 115. Calculus I
Four years of high school mathematics. (4). (MSA). (BS). (QR/1). May not be repeated for credit. No credit for students having completed Math 116, 185, 215, or 216.

The course presents the concepts of calculus from four points of view: geometric (graphs), numeric (tables), symbolic (formulas), and verbal descriptions. Students will develop their reading, writing, and questioning skills, as well as their ability to work cooperatively. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and an introduction to integration.