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100-Level Math Courses

Math 105 - Data, Functions, and Graphs

Prerequisites:	3-4 years HS math including trigonometry
Credit:	4 Credits. No credit granted to those who have completed and mathematics course numbered 110 or higher. A maximum of four credits may be earned in Math 105 and 110
Background and Goals:	Math 105 serves both as a preparatory class to the calculus sequences and as a class for students who are interested in strengthening their math skills. Students who successfully complete 105 are fully prepared for Math 115.
Content:	This course presents concepts 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 class- room setting.

Math 110 - Pre Calculus (Self-Paced)

Prerequisites:	3-4 years HS math
Credit:	2 Credits. 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.
Background and Goals:	Math 110 is a condensed, half-term version of Math 105 designed specifically to prepare students for Math 115. It is open only to students who have enrolled in Math 115 and whose performance on the first uniform examination indicates that they will have difficulty completing that course successfully. This self-study course begins shortly after the first uniform examination in Math 115 and is completed under the guidance of an instructor without regular classroom meetings. Students must receive permission from the Math 115 Course Director or other designated representative to enroll in the course, and they must visit the Mathematics Learning Center (MLC) as soon as possible after enrolling to receive printed course information. Enrollment opens the day after the first Math 115 uniform examination, and enrollment must be completed by the Friday of the following week.
Content:	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 Mathematics Learning Center to complete paperwork and receive course materials. The course covers data analysis by means of functions and graphs.

Math 115 - Calculus I

Prerequisites:	3-4 years HS Math including trigonometry
Credit:	4 Credits: No credit for students who have completed any Math course numbered 111 or higher.
Background and Goals:	The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given two uniform midterms and a final exam.
Content:	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. The classroom atmosphere is interactive and cooperative. Both individual and team homework is assigned.

Math 116 - Calculus II

Prerequisites	Math 115 or AP Credit
Credit:	4 Credits. No credit for students who have completed or are enrolled in Math 156, 186, 215, 216, 276, 285, or 286
Background and Goals:	The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given two uniform midterms and a final exam.
Content:	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 techniques of integration, applications of integration, Taylor series, an introduction to differential equations, and infinite series. The classroom atmosphere is interactive and cooperative. Both individual and team homework is assigned.

Math 117 - Calculus II (Self-Paced)

Prerequisites:	Math 116 or BC Exam score of 5 in 2020
Credit:	2 Credits.
Background and Goals:	Math 117 is intended for students who have received a 5 on the BC Calculus AP exam in 2020. This course was created to bridge the knowledge gap that many of these student will have due to the pandemic, before attending more advanced U(M) Mathematics courses. It is a self-paced, online course and does not formally meet. The course is 2 credits, and students have the choice to officially enroll in the class for credit/ no credit (if their program requires proof of completion; please note that Engineering students will receive a mandatory P/F grade - an F in this course will not effect term GPA), OR students may elect to take the course unofficially and be given access to the course materials ahead of time. It is completely self-paced. For students who do not wish to take this course for credit, please complete the Series, Taylor Series, and Paramtric Equations (Math 117) Interest Form to be given access to the course materials.
Content:	This is a calculus course. Topics covered include calculus in polar coordinates; calculus in paramatric coordinates; sequences and series; convergence tests for series; power series; Taylor polynomials; Taylor series; applications of Taylor polynomials and Taylor Seriess.

Math 128 - Explorations in Number Theory

Prerequisites:	3 years HS math
Credit:	4 Credits. No credit after completeing any 200+ level amth course, except 385, 485, 489, and 497.
Background and Goals:	This course is intended for students who want to engage in mathematical reasoning without having to take calculus first. It is particularly well-suited for non-science majors or those who are thoroughly undecided. Students will make use of software to conduct numerical experiments and to make empirical discoveries. Students will formulate precise conjectures and in many cases prove them. Thus the students will, as a group, generate a logical development of the subject.
Content:	After studying factorizations and greatest common divisors, emphasis will shift to the patterns that emerge when the integers are classified according to the remainder produced upon division by some fixed number (congruences). Once some basic tools have been established, applications will be made in several directions. For example, students may derive a precise parameterization of Pythagorean triples.

Math 145 - Houghton Scholars Calculus Worskhop I

Prerequisites:	Concurrent enrollment in Math 115 and permission of instructor
Credit:	2 Credits.
Background and Goals:	This course is an intensive supplemental workshop experience for students in the Douglas Houghton Scholars Program. In a small-class setting, students work in small groups on problems more challenging than those in the regular section of Math 115. The goal is to develop the student's problem-solving capabilities and promote their interest in challenging problems.
Content:	The workshop follows the structure of Math 115. Content includes 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.

Math 146 - Houghton Scholars Calculus Workshop II

Prerequisites:	Concurrent enrollment in Math 116 and permission of instructor
Credit:	2 Credits.
Background and Goals:	This course is an intensive supplemental workshop experience for students in the Douglas Houghton Scholars Program. In a small-class setting, students work in small groups on problems more challenging than those in the regular section of Math 116. The goal is to develop the students' problem-solving capabilities and promote their interest in challenging problems.
Content:	The workshop follows the structure of Math 116 (Calc II). Content includes 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 techniques of integration, applications of integration, Taylor series, an introduction to differential equations, and infinite series.

Math 147 - Introduction to Interest Theory

Prerequisites:	Math 115
Credit:	3 Credits. No credit after completing any 200+ level math course, except 385, 485, 489, or 497.
Background and Goals:	This course is designed for students who seek an introduction to the mathematical concepts and techniques employed by financial institutions such as banks, insurance companies, and pension funds. Actuarial students, and other mathematics majors, should elect Math 424 which covers the same topics but on a more rigorous basis requiring considerable use of calculus. The course is not part of a sequence. Students should possess financial calculators.
Content:	Topics covered include: various rates of simple and compound interest, present and accumulated values based on these; annuity functions and their application to amortization, sinking funds, and bond values; depreciation methods; introduction to life tables, life annuity, and life insurance values.

Math 156 - Applied Honors Calculus II

Prerequisites:	Score of 4 or 5 on Advanced Placement AB or BC Calculus exam
Credit:	4 Credits. Credit is granted for either 116 or 156, but not both.
Background and Goals:	Math 156 is part of the applied honors calculus sequence for engineering and science majors. The course is an alternative to Math 116 for students with appropriate prior calculus experience and an interest in both theory and application. Applications and concepts receive equal treatment. Theorems are stated precisely and are derived, but technical details are omitted. Examples are given to illustrate the theory. Critical thinking and class participation are encouraged. The goal is to provide students with the solid background needed for subsequent courses in mathematics, engineering, and science.
Content:	Riemann sums, definite integral, fundamental theorem of calculus, applications of integral calculus (e.g. arclength, surface area, work, center of mass, probability density functions), improper integrals, infinite sequences and series, geometric series, alternating series, power series, Taylor series, differential equations, complex numbers. Students are introduced to MAPLE.

Math 185 - Honors Calculus I (IBL)

Prerequisites:	Permission of honors advisor during orientation
Credit:	4 Credits.
Background and Goals:	Most students take calculus in high school, and it may seem that there isn't much new to learn. The goal of this course is to develop the familiar concepts of calculus using a more rigorous and theoretical approach. In particular, with its emphasis on how to use appropriate mathematical language, this course lays a solid foundation for future math courses, and is suitable for students intending to pursue a major in mathematics, science, or engineering who desire a more complete understanding of the underpinnings of calculus. This sequence is not restricted to students enrolled in the LSA Honors Program.
Content:	Topics covered include functions, graphs, continuity, limits, derivatives, and integrals. Tuesday meetings are usually devoted to introducing linear algebra.

Math 186 - Honors Calculus II

Prerequisites:	Permission of honors advisor or Math 185
Credit:	4 Credits
Background and Goals:	Most students take calculus in high school, and it may seem that there isn't much new to learn. The goal of this course is to develop the familiar concepts of calculus using a more rigorous and theoretical approach. In particular, with its emphasis on how to use appropriate mathematical language, this course lays a solid foundation for future math courses, and is suitable for students intending to pursue a major in mathematics, science, or engineering who desire a more complete understanding of the underpinnings of calculus. This sequence is not restricted to students enrolled in the LSA Honors Program. This course is a continuation of Math 185.
Content:	Topics include integral calculus, transcendental functions, infinite sequences and series (including Taylor’s series), and time permitting some simple applications to elementary differential equations. Tuesdays are mostly devoted to an introduction to linear algebra.