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No credit granted to those who have completed any Mathematics course numbered or higher. A maximum of four credits may be earned in MATH , , , and MATH serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics.
This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing.
The classroom atmosphere is interactive and cooperative and homework is done in groups. The course investigates topics relevant to the information age in which we live. Topics covered include cryptography, error-correcting codes, data compression, fairness in politics, voting systems, population growth, biological modeling.
No credit granted to those who already have 4 credits for pre-calculus mathematics courses. Math is a condensed, half-term version of Math designed specifically to prepare students for Math It is open only to students who have enrolled in Math 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 , and is completed under the guidance of an instructor without regular classroom meetings.
Students must receive permission from the Math Course Director or other designated representative to enroll in the course, and must visit the Math Lab as soon as possible after enrolling to receive printed course information.
Enrollment opens the day after the first Math uniform examination, and must be completed by the Friday of the following week. The course is a condensed, half-term version of Math designed for students who appear to be prepared to handle calculus but are not able to successfully complete Math Students may enroll in Math 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 Data, Functions and Graphs covers the same material in a traditional classroom setting.
Credit is granted for only one course from among MATH , , and No credit granted to those who have completed MATH The sequence MATH 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 a uniform midterm and final exam. The course presents the concepts of calculus from three points of view: Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals.
I is a somewhat more theoretical course which covers some of the same material. Math Combinatorics and Calculus is a non-calculus alternative for students with a good command of first-semester calculus.
A student who has done very well in this course could enter the honors sequence at this point by taking MATH Honors Anal. MCSP has reserved ten spaces in Math The advantage of registering for this section is that you will be in the same class with other MCSP students so it will be convenient for you to study with others. In addition, this class is not held in Couzens Hall. Credit is granted for only one course among MATH , , , , and Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series.
MATH is a somewhat more theoretical course which covers much of the same material. MATH is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH No credit granted to those who have completed a or higher level mathematics course except for MATH and This course introduces students to the ideas and some of the basic results in Euclidean and non-Euclidean geometry.
Beginning with geometry in ancient Greece, the course includes the construction of new geometric objects from old ones by projecting and by taking slices.
The course is intended for students who want an introduction to mathematical ideas and culture. Emphasis is on conceptual thinking — — students will do hands-on experimentation with geometric shapes, patterns and ideas. The section begins with the independence of Euclid's Fifth Postulate and with the construction of spherical and hyperbolic geometries in which the Fifth Postulate fails; how spherical and hyperbolic geometry differs from Euclidean geometry.
The last topic is geometry of higher dimensions: This course does not provide preparation for any further study of mathematics. Three years of high school mathematics including a geometry course.
Only first-year students, including those with sophomore standing, may pre-register for First-Year Seminars. All others need permission of instructor. Each section of the two workshops for which course approval is requested will be limited to 18 students, who will be required to be concurrently enrolled in Math or , respectively, for DHSP Workshops I and II. The students will work together in groups of size three or four on very challenging problems that will develop their conceptual understanding of calculus and skill at solving difficult multistep problems.
The workshops will meet for four hours per week, in two class meetings of two hours each. As is common with the ESP model, little or no graded homework will be assigned, although the problems on which the students work will be challenging enough that they will not always finish them during class time. The experience of other ESP programs has been that in many, perhaps most, cases, they will continue to work on them outside of class rather than wait until the next class period to finish them.
As Treisman himself has pointed out, implementation of this program at UM will have some particular challenges, since the standard UM calculus sequence has already incorporated some of the elements of ESP programs, particularly the group work in class on problems.
However, the problems selected for the DHSP workshop sections will be particularly challenging, multistep exercises that will extend the students beyond what they will generally experience in their regular calculus sections. Participants in the Douglass Houghton Scholars Program.
Students will be evaluated on the basis of attendance and participation in activities during scheduled sessions. Course is credit-no credit. No credit granted to those who have completed a or higher level mathematics course. 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 concentrators, should elect Math 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. Math Compound Interest and Life Ins covers the same material in greater depth and with a higher level of mathematical content.
Credit is granted for only one course from among MATH , , , , and The sequence Math is the honors introduction to the calculus. It is taken by students intending to major in mathematics, science, or engineering as well as students heading for many other fields who want a somewhat more theoretical approach. Although much attention is paid to concepts and solving problems, the underlying theory and proofs of important results are also included.
Topics covered include transcendental functions; techniques of integration; applications of calculus such as elementary differential equations, simple harmonic motion, and center of mass; conic sections; polar coordinates; infinite sequences and series including power series and Taylor series. Other topics, often an introduction to matrices and vector spaces, will be included at the discretion of the instructor. Math Calculus II is a somewhat less theoretical course which covers much of the same material.
Credit can be earned for only one of MATH , , , or No credit granted to those who have completed or are enrolled in MATH An introduction to matrices and linear algebra.
This course covers the basics needed to understand a wide variety of applications that use the ideas of linear algebra, from linear programming to mathematical economics. The emphasis is on concepts and problem solving. The course is designed as an alternative to Math for students who need more linear algebra and less differential equations background than provided in An introduction to the main concepts of linear algebra… matrix operations, echelon form, solution of systems of linear equations, Euclidean vector spaces, linear combinations, independence and spans of sets of vectors in Euclidean space, eigenvectors and eigenvalues, similarity theory.
There are applications to discrete Markov processes, linear programming, and solutions of linear differential equations with constant coefficients. Math Linear Spaces and Matrix Theory has a somewhat more theoretical emphasis. Math is a more theoretical course which covers much of the material of Math at a deeper level. Mathematics majors are required to take Math or Math MATH and Most students take only one course from among MATH , , , , and The sequence Math is the standard complete introduction to the concepts and methods of calculus.
Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; line, surface, and volume integrals and applications; vector fields and integration; Green's Theorem and Stokes' Theorem.
For students intending to major in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math Linear Algebra. Students who intend to take only one further mathematics course and need differential equations should take Math Intro. The sequence MATH emphasizes problem-solving and applications and is intended for students of Engineering and the sciences.
Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH MATH is a basic course on differential equations, intended for engineers and other scientists who need to apply the techniques in their work. The lectures are accompanied by a computer lab and recitation section where students have the opportunity to discuss problems and work through computer experiments to further develop their understanding of the concepts of the class.
Topics covered include some material on complex numbers and matrix algebra, first and second order linear and non-linear systems with applications, introductory numerical methods, and elementary Laplace transform techniques. To Numerical Methods cover additional material on numerical methods.
For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH or and MATH These courses are explicitly designed to introduce the student to both the concepts and applications of their subjects and to the methods by which the results are proved.