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Transfer Student Courses in MathematicsThis page was created at 7:20 PM on Mon, Jan 21, 2002. Winter Academic Term, 2002 (January 7 - April 26)Open courses in Mathematics Wolverine Access Subject listing for MATH Winter Academic Term '02 Time Schedule for Mathematics. 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 admissions 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 Math 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 through the Math Lab and directed towards students who are unable to complete a first calculus course successfully. A maximum total of 4 credits may be earned in courses numbered 110 and below. Math 103 is offered exclusively in the Summer half-term for students in the Summer Bridge Program. 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 received credit for a 200- (or higher) level mathematics course (except 385, 489 or 497). Each of Math 115, 185, and 295 is a first course in calculus and generally credit can be received for only one course from this list. The sequence 115-116-215 is appropriate for most students who want a complete introduction to calculus. One of Math 215, 285, or 395 is prerequisite to most more advanced courses in Mathematics. The sequences 156-255-256, 175-176-285-286, 185-186-285-286, and 295-296-395-396 are honors sequences. All students must have the permission of an Honors advisor to enroll in any of these courses, but they need not be enrolled in the LS&A Honors Program. All students with strong preparation and interest in mathematics are encouraged to consider these courses; they are both more interesting and more challenging than the standard sequences. 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 175-176 assumes a knowledge of calculus roughly equivalent to Math 115 and covers a substantial amount of so-called combinatorial mathematics (see course description) as well as calculus-related topics not usually part of the calculus sequence. Math 175 and 176 are 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. The student who completes Math 396 is prepared to explore the world of mathematics at the advanced undergraduate and 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 are two courses expressly designed and recommended for students with one or two semesters of AP credit, Math 119 and Math 156. Both will review the basic concepts of calculus, cover integration and an introduction to differential equations, and introduce the student to the computer algebra system MAPLE. Math 119 will stress experimentation and computation, while 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 or 295 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, students 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 Math 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 for optimal treatment of differential equations in Math 316. Math 216 is not intended for mathematics concentrators. All elementary teaching certificate candidates are required to take two mathematics courses, Math 385 and Math 489, either before or after admission to the School of Education. Math 385 is offered in the Fall, Math 489 in the Winter. The next Spring Term offering of Math 489 will be in 2003. For further information, contact Prof. Krause at 763-1186 or at his office, 3086 East Hall. A maximum total of 4 credits may be earned in Mathematics courses numbered 110 and below. 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 105. Data, Functions, and Graphs.
Instructor(s):Prerequisites & Distribution: Students with credit for Math. 103 can elect Math. 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. (4). (MSA). (QR/1).
Credits: (4). Course Homepage: http://www.math.lsa.umich.edu/courses/105/ Math 105 serves both as a preparatory course to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who complete 105 are fully prepared for Math 115. 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. Math 110 is a condensed half-term version of the same material offered as a self-study course through the Math Lab. TEXT: Functions Modeling Change, Connally, Wiley Publishing.
MATH 107. Mathematics for the Information Age.
Section 001.Instructor(s): Karen Rhea (krhea@umich.edu)Prerequisites & Distribution: Three to four years high school mathematics. (3). (MSA). (QR/1).
Credits: (3). Course Homepage: No homepage submitted. From computers and the Internet to playing a CD or running an election, great progress in modern technology and science has come from understanding how information is exchanged, processed, and perceived. Typical topics: cryptography, error-correcting codes, data compression, fairness in politics, voting systems, population growth, and biological modeling. Grading will be based on homework, at least one written report, a midterm, and a final.
MATH 115. Calculus I.
Instructor(s):Prerequisites & Distribution: Four years of high school mathematics. See Elementary Courses above. Credit usually is granted for only one course from among Math. 112, 115, 185, and 295. No credit granted to those who have completed Math. 175. (4). (MSA). (BS). (QR/1).
Credits: (4). Course Homepage: http://www.math.lsa.umich.edu/courses/115/ 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 concentrate 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: geometric (graphs); numerical (tables); and algebraic (formulas). 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. Math 185 is a somewhat more theoretical course which covers some of the same material. Math 175 includes some of the material of Math 115 together with some combinatorial mathematics. A student whose preparation is insufficient for Math 115 should take Math 105 (Data, Functions, and Graphs). Math 116 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 186. The cost for this course is over $100 since the student will need a text (to be used for 115 and 116) and a graphing calculator (the Texas Instruments TI-83 is recommended). TEXT: Calculus, 3rd edition, Hughes-Hallet, Wiley Publishing.
MATH 116. Calculus II.
Instructor(s):Prerequisites & Distribution: Math. 115. Credit is granted for only one course from among Math. 116, 119, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1).
Credits: (4). Course Homepage: http://www.math.lsa.umich.edu/courses/116/ See Math 115 for a general description of the sequence Math 115-116-215. Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. Math 186 is a somewhat more theoretical course which covers much of the same material. Math 215 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 285. Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing.
MATH 214. Linear Algebra and Differential Equations.
Instructor(s):Prerequisites & Distribution: Math. 115 and 116. 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. (4). (MSA). (BS). Credits: (4). Course Homepage: No homepage submitted. This course is intended for second-year students who might otherwise take Math 216 (Introduction to Differential Equations) but who have a greater need or desire to study Linear Algebra. This may include some Engineering students, particularly from Industrial and Operations engineering (IOE), as well as students of Economics and other quantitative social sciences. Students intending to concentrate in Mathematics must continue to elect Math 217. While Math 216 includes 3-4 weeks of Linear Algebra as a tool in the study of Differential Equations, Math 214 will include roughly 3 weeks of Differential Equations as an application of Linear Algebra. The textbook is Linear Algebra and its Applications, second edition, David Lay, Addison Wesley. The following is a tentative outline of the course:
Regular problem sets and exams.
MATH 215. Calculus III.
Instructor(s):Prerequisites & Distribution: Math. 116, 119, 156, 176, 186, or 296. Credit can be earned for only one of Math. 215, 255, or 285. (4). (MSA). (BS). (QR/1).
Credits: (4). Course Homepage: http://www.math.lsa.umich.edu/courses/215/ 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 concentrate 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 midterm and final exam. 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. There is a weekly computer lab using Maple software. Math 285 is a somewhat more theoretical course which covers the same material. For students intending to concentrate in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217. Students who intend to take only one further mathematics course and need differential equations should take Math 216. TEXT: STUDENTS HAVE CHOICE OF EITHER: Calculus, 4th edition, James Stewart, Brooks/Cole Publishing, or Multivariable Calculus, 4th edition, James Stewart, Brooks/Cole Publishing.
MATH 216. Introduction to Differential Equations.
Instructor(s):Prerequisites & Distribution: Math. 116, 119, 156, 176, 186, or 296. Not intended for Mathematics concentrators. Credit can be earned for only one of Math. 216, 256, 286, or 316. (4). (MSA). (BS). Credits: (4). Course Homepage: http://www.math.lsa.umich.edu/courses/216/ For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, Math 216-417 (or 419) and Math 217-316. The sequence Math 216-417 emphasizes problem-solving and applications and is intended for students of engineering and the sciences. Math concentrators and other students who have some interest in the theory of mathematics should elect the sequence Math 217-316. After an introduction to ordinary differential equations, the first half of the course is devoted to topics in linear algebra, including systems of linear algebraic equations, vector spaces, linear dependence, bases, dimension, matrix algebra, determinants, eigenvalues, and eigenvectors. In the second half these tools are applied to the solution of linear systems of ordinary differential equations. Topics include: oscillating systems, the Laplace transform, initial value problems, resonance, phase portraits, and an introduction to numerical methods. There is a weekly computer lab using MATLAB software. This course is not intended for mathematics concentrators, who should elect the sequence 217-316. Math 286 covers much of the same material in the honors sequence. The sequence Math 217-316 covers all of this material and substantially more at greater depth and with greater emphasis on the theory. Math 404 covers further material on differential equations. Math 217 and 417 cover further material on linear algebra. Math 371 and 471 cover additional material on numerical methods. Text: Differential Equations, Computing and Modeling, 2nd edition, Edwards and Penney, Prentice Hall Publishing.
MATH 289. Problem Seminar.Instructor(s):Prerequisites & Distribution: (1). (Excl). (BS). May be repeated for credit with permission. Mini/Short course Credits: (1). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 312. Applied Modern Algebra.
Instructor(s):Prerequisites & Distribution: Math. 217. Only one credit granted to those who have completed Math. 412. (3). (Excl). (BS). Credits: (3). Course Homepage: http://www.math.lsa.umich.edu/courses/312/ One of the main goals of the course (along with every course in the algebra sequence) is to expose students to rigorous, proof-oriented mathematics. Students are required to have taken Math 217, which should provide a first exposure to this style of mathematics. A distinguishing feature of this course is that the abstract concepts are not studied in isolation. Instead, each topic is studied with the ultimate goal being a real-world application. As currently organized, the course is broken into four parts: the integers "mod n" and linear algebra over the integers mod p, with applications to error correcting codes; some number theory, with applications to public-key cryptography; polynomial algebra, with an emphasis on factoring algorithms over various fields, and permutation groups, with applications to enumeration of discrete structures "up to automorphisms" (a.k.a. Pólya Theory). Math 412 is a more abstract and proof-oriented course with less emphasis on applications. EECS 303 (Algebraic Foundations of Computer Engineering) covers many of the same topics with a more applied approach. Another good follow-up course is Math 475 (Number Theory). Math 312 is one of the alternative prerequisites for Math 416, and several advanced EECS courses make substantial use of the material of Math 312. Math 412 is better preparation for most subsequent mathematics courses.
MATH 316. Differential Equations.
Instructor(s):Prerequisites & Distribution: Math. 215 and 217. Credit can be earned for only one of Math. 216, 256, 286, or 316. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. This is an introduction to differential equations for students who have studied linear algebra (Math 217). It treats techniques of solution (exact and approximate), existence and uniqueness theorems, some qualitative theory, and many applications. Proofs are given in class; homework problems include both computational and more conceptually oriented problems. First-order equations: solutions, existence and uniqueness, and numerical techniques; linear systems: eigenvector-eigenvalue solutions of constant coefficient systems, fundamental matrix solutions, nonhomogeneous systems; higher-order equations, reduction of order, variation of parameters, series solutions; qualitative behavior of systems, equilibrium points, stability. Applications to physical problems are considered throughout. Math 216 covers somewhat less material without the use of linear algebra and with less emphasis on theory. Math 286 is the honors version of Math 316. Math 471 and/or 572 are natural sequels in the area of differential equations, but Math 316 is also preparation for more theoretical courses such as Math 451.
MATH 354. Fourier Analysis and its Applications.
Instructor(s):Prerequisites & Distribution: Math. 216, 256, 286, or 316. No credit granted to those who have completed or are enrolled in Math. 454. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. This course is an introduction to Fourier analysis at an elementary level, emphasizing applications. The main topics are Fourier series, discrete Fourier transforms, and continuous Fourier transforms. A substantial portion of the time is spent on both scientific/technological applications (e.g., signal processing, Fourier optics), and applications in other branches of mathematics (e.g., partial differential equations, probability theory, number theory). Students will do some computer work, using MATLAB, an interactive programming tool that is easy to use, but no previous experience with computers is necessary.
MATH 417. Matrix Algebra I.
Instructor(s):Prerequisites & Distribution: Three courses beyond Math. 110. 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 Math. 513. (3). (Excl). (BS). Credits: (3). Course Homepage: http://www.math.lsa.umich.edu/courses/417/ Many problems in science, engineering, and mathematics are best formulated in terms of matrices – rectangular arrays of numbers. This course is an introduction to the properties of and operations on matrices with a wide variety of applications. The main emphasis is on concepts and problem-solving, but students are responsible for some of the underlying theory. Diversity rather than depth of applications is stressed. This course is not intended for mathematics concentrators, who should elect Math 217 or 513 (honors). Topics include matrix operations, echelon form, general solutions of systems of linear equations, vector spaces and subspaces, linear independence and bases, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalues and eigenvectors, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations. Math 419 is an enriched version of Math 417 with a somewhat more theoretical emphasis. Math 217 (despite its lower number) is also a more theoretical course which covers much of the material of 417 at a deeper level. Math 513 is an honors version of this course, which is also taken by some mathematics graduate students. Math 420 is the natural sequel, but this course serves as prerequisite to several courses: Math 452, 462, 561, and 571.
MATH 419. Linear Spaces and Matrix Theory.Instructor(s):Prerequisites & Distribution: Four terms of college mathematics beyond Math. 110. 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. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 452. Advanced Calculus II.
Instructor(s):Prerequisites & Distribution: Math. 217, 417, or 419; and Math. 451. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. This course does a rigorous development of multivariable calculus and elementary function theory with some view towards generalizations. Concepts and proofs are stressed. This is a relatively difficult course, but the stated prerequisites provide adequate preparation. Topics include:
Math 551 is a higher-level course covering much of the same material with greater emphasis on differential geometry. Math 450 covers the same material and a bit more with more emphasis on applications, and no emphasis on proofs. Math 452 is prerequisite to Math 572 and is good general background for any of the more advanced courses in analysis (Math 596, 597) or differential geometry or topology (Math 537, 635).
MATH 454. Boundary Value Problems for Partial Differential Equations.
Instructor(s):Prerequisites & Distribution: Math. 216, 256, 286, or 316. Students with credit for Math. 354 can elect Math. 454 for one credit. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. This course is devoted to the use of Fourier series and other orthogonal expansions in the solution of boundary-value problems for second-order linear partial differential equations. Emphasis is on concepts and calculation. The official prerequisite is ample preparation. Classical representation and convergence theorems for Fourier series; method of separation of variables for the solution of the one-dimensional heat and wave equation; the heat and wave equations in higher dimensions; spherical and cylindrical Bessel functions; Legendre polynomials; methods for evaluating asymptotic integrals (Laplace's method, steepest descent); Fourier and Laplace transforms; and applications to linear input-output systems, analysis of data smoothing and filtering, signal processing, time-series analysis, and spectral analysis. Both Math 455 and 554 cover many of the same topics but are very seldom offered. Math 454 is prerequisite to Math 571 and 572, although it is not a formal prerequisite, it is good background for Math 556. There is no textbook listed for this course.
MATH 462. Mathematical Models.
Instructor(s):Prerequisites & Distribution: Math. 216, 256, 286, or 316; and 217, 417, or 419. Students with credit for Math. 362 must have department permission to elect Math. 462. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. This course will cover biological models constructed from difference equations and ordinary differential equations. Applications will be drawn from population biology, population genetics, the theory of epidemics, biochemical kinetics, and physiology. Both exact solutions and simple qualitative methods for understanding dynamical systems will be stressed (anticipated text is Mathematical Models in Biology by Leah Edelstein-Keshet).
MATH 471. Introduction to Numerical Methods.
Instructor(s):Prerequisites & Distribution: Math. 216, 256, 286, or 316; and 217, 417, or 419; and a working knowledge of one high-level computer language. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. This is a survey of the basic numerical methods which are used to solve scientific problems. The emphasis is evenly divided between the analysis of the methods and their practical applications. Some convergence theorems and error bounds are proven. The course also provides an introduction to MATLAB, an interactive program for numerical linear algebra, as well as practice in computer programming. One goal of the course is to show how calculus and linear algebra are used in numerical analysis. Topics may include computer arithmetic, Newton's method for non-linear equations, polynomial interpolation, numerical integration, systems of linear equations, initial value problems for ordinary differential equations, quadrature, partial pivoting, spline approximations, partial differential equations, Monte Carlo methods, 2-point boundary value problems, and the Dirichlet problem for the Laplace equation. Math 371 is a less sophisticated version intended principally for sophomore and junior engineering students; the sequence Math 571-572 is mainly taken by graduate students, but should be considered by strong undergraduates. Math 471 is good preparation for Math 571 and 572, although it is not prerequisite to these courses. Text: An Introduction to Numerical Analysis, Kendall Atkinson Wiley.
MATH 476. Computational Laboratory in Number Theory.
Instructor(s):Prerequisites & Distribution: Prior or concurrent enrollment in Math. 475 or 575. (1). (Excl). (BS). Credits: (1). Course Homepage: No homepage submitted. Students will be provided software with which to conduct numerical explorations. Students will submit reports of their findings weekly. No programming necessary, but students interested in programming will have the opportunity to embark on their own projects. Participation in the laboratory should boost the student's performance in Math 475 or Math 575. Students in the lab will see mathematics as an exploratory science (as mathematicians do). Students will gain a knowledge of algorithms which have been developed (some quite recently) for number-theoretic purposes, e.g., for factoring. No exams.
MATH 490. Introduction to Topology.
Instructor(s):Prerequisites & Distribution: Math. 412 or 451 or equivalent experience with abstract mathematics. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. This course in an introduction to both point-set and algebraic topology. Although much of the presentation is theoretical and proof-oriented, the material is well-suited for developing intuition and giving convincing proofs which are pictorial or geometric rather than completely rigorous. There are many interesting examples of topologies and manifolds, some from common experience (combing a hairy ball, the utilities problem). In addition to the stated prerequisites, courses containing some group theory (Math 412 or 512) and advanced calculus (Math 451) are desirable although not absolutely necessary. The topics covered are fairly constant but the presentation and emphasis will vary significantly with the instructor. These include point-set topology, examples of topological spaces, orientable and non-orientable surfaces, fundamental groups, homotopy, and covering spaces. Metric and Euclidean spaces are emphasized. Math 590 is a deeper and more difficult presentation of much of the same material which is taken mainly by mathematics graduate students. Math 433 is a related course at about the same level. Math 490 is not prerequisite for any later course but provides good background for Math 590 or any of the other courses in geometry or topology.
MATH 498. Topics in Modern Mathematics.
Markov Chains: Theory and Applications.Instructor(s): Divakar ViswanathPrerequisites & Distribution: Senior mathematics concentrators and Master Degree students in mathematical disciplines. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. Markov chains form an elegant topic with numerous applications. In the first half of the course, we will discuss basic questions: What is a Markov chain? What is its eventual behaviour? How fast does it converge? The second half will make the following relatively advanced topics accessible:
The final project has to make a connection to any area you like. Your options will be plenty: math, physics, compsci, econ, biology, and chemistry are all fair game.
MATH 513. Introduction to Linear Algebra.Instructor(s):Prerequisites & Distribution: Math. 412. Two credits granted to those who have completed Math. 214, 217, 417, or 419. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 521. Life Contingencies II.Instructor(s):Prerequisites & Distribution: Math. 520. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 525 / STATS 525. Probability Theory.Instructor(s):Prerequisites & Distribution: Math. 450 or 451. Students with credit for Math. 425/Stat. 425 can elect Math. 525/Stat. 525 for only one credit. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 526 / STATS 526. Discrete State Stochastic Processes.Instructor(s):Prerequisites & Distribution: Math. 525 or EECS 501. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 550 / CMPLXSYS 510. Introduction to Adaptive Systems.
Section 001 – Introduction to Dynamical Systems for Biocomplexity.Instructor(s): Carl P Simon (cpsimon@umich.edu)Prerequisites & Distribution: Math. 215, 255, or 285; Math. 217; and Math. 425, and Permission of instructor. Working knowledge of calculus, probability, and matrix algebra. (3). (Excl). (BS). Credits: (3). Course Homepage: http://precisione.physics.lsa.umich.edu/CSCS/education/CSCS-courses/cscs510-w01.html
MATH 555. Introduction to Functions of a Complex Variable with Applications.Instructor(s):Prerequisites & Distribution: Math. 450 or 451. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 557. Methods of Applied Mathematics II.Instructor(s):Prerequisites & Distribution: Math. 217, 419, or 513; 451 and 555. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 558. Ordinary Differential Equations.Instructor(s):Prerequisites & Distribution: Math. 450 or 451. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 559. Selected Topics in Applied Mathematics.
Section 001 – Advanced Mathematical Methods for the Biological Sciences – Partial Differential Equations in BiologyInstructor(s): Trachette Jackson (tjacks@umich.edu)Prerequisites & Distribution: Math. 451; and 217 or 419. (3). (Excl). (BS). May be repeated for a total of six credits. Credits: (3). Course Homepage: No homepage submitted. Natural systems behave in a way that reflects an underlying spatial pattern. For example, on the molecular level, rarely do reactions occur in a homogenous environment and the spatial organization does somehow influence the way in which particles interact. In this course, we will discover the way in which spatial variation influences the motion, dispersion, and persistence of species. We shall become aware of the fine balance that exists between interdependent species and demonstrate that spatial diversity can have subtle, but important effects or can lead to the emergence of remarkable spatial patterns from a previously uniform state. The concepts underlying spatially dependent processes and the partial differential equations which model them will be discussed in a general manner with examples taken from the molecular, cellular, and population levels. We will then apply these ideas to more specific cases with the aim of understanding interesting biological phenomena. Topics include: Population dispersal based on diffusion models; Cell movements ( e.g., chemotaxis and haptotaxis); Growth of branching organisms; Traveling waves in microorganisms; Transport of biological substances; Models for development and pattern formation; and Age-Structured models of HIV dynamics.
MATH 567. Introduction to Coding Theory.Instructor(s):Prerequisites & Distribution: One of Math. 217, 419, 513. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 571. Numerical Methods for Scientific Computing I.Instructor(s):Prerequisites & Distribution: Math. 217, 417, 419, or 513; and one of Math. 450, 451, or 454. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 592. Introduction to Algebraic Topology.Instructor(s):Prerequisites & Distribution: Math. 591. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 594. Algebra II.Instructor(s):Prerequisites & Distribution: Math. 593. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability MATH 597. Analysis II.Instructor(s):Prerequisites & Distribution: Math. 451 and 513. (3). (Excl). (BS). Credits: (3). Course Homepage: No homepage submitted. No Description Provided Check Times, Location, and Availability This page was created at 7:20 PM on Mon, Jan 21, 2002.
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