First-Year Courses in MathematicsConsult the new Course Guide at: http://www.lsa.umich.edu/lsa/cg_subjectlist/0,2030,8,00.html?show=20&termArray=f_04_1510&cgtype=ug This page was created at 1:00 PM on Wed, May 5, 2004. Fall Academic Term, 2004 (September 7 - December 23)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 and 128 are courses containing selected topics from geometry and number theory, respectively. 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 or 128 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 115 or 185. The sequence MATH 115-116-215 is appropriate for must students who want a complete introduction to calculus. One of 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 LS&A 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 185-285 covers much of the material of MATH 115-215 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 175-186 assumes a 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 the discovery method: students are presented with a great variety of problems and encouraged to experiment in groups using computers. The sequence MATH 295-396 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 295-396 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 expressly designed and recommended for students with one or two semesters of AP credit, MATH 156. MATH 156 is an Honors course intended primarily for science and engineering concentrators and will emphasize 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 396, 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 to optimal treatment of differential equations in MATH 316. MATH 216 is not intended for concentrators in pure mathematics. A maximum total of 4 credits may be earned in MATH 103, 105, and 110. A maximum total of 16 credits may be earned for calculus courses MATH 112 through MATH 396, and no credit can be earned for a prerequisite to a course taken after the course itself. MATH 110. Pre-Calculus (Self-Study).Instructor(s):Prerequisites & Distribution: See Elementary Courses above. Enrollment in MATH 110 is by recommendation of MATH 115 instructor and override only. (2). (Excl). 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 101, 103, 105, and 110. Credits: (2). Course Homepage: No homepage submitted. The course covers data analysis by means of functions and graphs. MATH 110 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. The course is a condensed, half-term version of MATH 105 (MATH 105 covers the same material in a traditional classroom setting) designed for students who appear to be prepared to handle calculus but are not able to successfully complete MATH 115. Students who complete MATH 110 are fully prepared for MATH 115. Students may enroll in MATH 110 only on the recommendation of a mathematics instructor after the third week of classes. ENROLLMENT IN MATH 110 IS BY PERMISSION OF MATH 115 INSTRUCTOR ONLY. COURSE MEETS SECOND HALF OF THE TERM. STUDENTS WORK INDEPENDENTLY WITH GUIDANCE FROM MATH LAB STAFF.
MATH 128. Explorations in Number Theory.Instructor(s):Prerequisites & Distribution: High school mathematics through at least Analytic Geometry. Only first-year students, including those with sophomore standing, may pre-register for First-Year Seminars. All others need permission of instructor. (4). (MSA). (BS). (QR/1). May not be repeated for credit. No credit granted to those who have completed a 200- (or higher) level mathematics course (except for MATH 385 and 485).
Credits: (4). Course Homepage: No homepage submitted. This course is intended for non-science concentrators and students in the pre-concentration years with no intended concentration, who want to engage in mathematical reasoning without having to take calculus first. Students will be introduced to elementary ideas of number theory, an area of mathematics that deals with properties of the integers. Students will make use of software provided for IBM PCs 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. 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 a2 + b2 = c2. Students who like math but don't especially like calculus will want to enroll in this first-year MSA seminar. Students will do hands-on experimentation with numerical patterns and will tackle numerical riddles and brainteasers as they focus on empirical discovery and proof of theorems. Students will write their own text in number theory and enjoy their growing ability to think like mathematicians.
MATH 147. Introduction to Interest Theory.Section 001.Instructor(s):Prerequisites & Distribution: Three to four years high school mathematics. (3). (MSA). (BS). May not be repeated for credit. No credit granted to those who have completed a 200- (or higher) level mathematics course. Course Homepage: No homepage submitted. No Description Provided. Contact the Department.
MATH 156. Applied Honors Calculus II.Instructor(s):Prerequisites & Distribution: Score of 4 or 5 on the AB or BC Advanced Placement calculus exam. (4). (MSA). (BS). (QR/1). May not be repeated for credit. Credit is granted for only one course among MATH 116, 119, 156, 176, and 186. Course Homepage: No homepage submitted. No Description Provided. Contact the Department.
MATH 214. Linear Algebra and Differential Equations.Instructor(s):Prerequisites & Distribution: MATH 115 and 116. (4). (MSA). (BS). (QR/1). May not be repeated for credit. Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513. Most students take only one course from among MATH 214, 217, 417, 419, and 513. Course Homepage: No homepage submitted. No Description Provided. Contact the Department.
MATH 215. Calculus III.Instructor(s):Prerequisites & Distribution: MATH 116. (4). (MSA). (BS). (QR/1). May not be repeated for credit. Credit can be earned for only one of MATH 215, 255, or 285. Course Homepage: No homepage submitted. No Description Provided. Contact the Department.
MATH 216. Introduction to Differential Equations.Instructor(s):Prerequisites & Distribution: MATH 116, 119, 156, 176, 186, or 296. (4). (MSA). (BS). (QR/1). May not be repeated for credit. Credit can be earned for only one of MATH 216, 256, 286, or 316. Course Homepage: No homepage submitted. No Description Provided. Contact the Department.
Consult the new Course Guide at: http://www.lsa.umich.edu/lsa/cg_subjectlist/0,2030,8,00.html?show=20&termArray=f_04_1510&cgtype=ug This page was created at 1:00 PM on Wed, May 5, 2004.
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