Courses in Mathematics (Division 428)
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This page was created at 2:52 PM on Mon, Aug 14, 2000.
Spring HalfTerm Courses
Take me to the Spring HalfTerm '00 Time Schedule for Mathematics.
To see what has been added or changed in Mathematics this week go to What's New This Week.
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 upperlevel 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 halfterm version of the same material offered as a selfstudy 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 halfterm 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.
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 115116215 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 156255256, 175176285286, 185186285286, and 295296395396 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 185285 covers much of the material of Math 115215 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 175176 assumes a knowledge of calculus roughly equivalent to Math 115 and covers a substantial amount of socalled combinatorial mathematics (see course description) as well as calculusrelated 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 295396 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 217316 (Linear AlgebraDifferential 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.
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.
Attention Potential Elementary School Teachers: Math 385 is Offered this Spring Term
All elementary teaching certificate candidates are required to take two math courses, Math 385 and Math 489, either before or after admission to the School of Education. Math 385 is offered in the Fall Term, Math 489 in the Winter Term. Due to heavy enrollment pressure, Math 385 will be offered this Spring Term (IIIA 2000) as well. Last Fall Term a number of students were closed out of Math 385. Next Fall Term, classsize limits will be STRICTLY enforced. Anyone who can elect Math 385 in the Spring Term is urged to do so. It is the surest way to guarantee yourself a place in the course. The next Spring Term offering of Math 385 will be in 2002. For further information, contact Prof. Krause at his email address, krause@math.lsa.umich.edu.
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: No Homepage Submitted.
Background and Goals. The sequence Math 115116215 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 two uniform exams during the term and a uniform final exam. Content. 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 reallife problems in various fields, and definite integrals. Text: Calculus by HughesHallett and Gleason. Students will need graphing calculators and should check with the Mathematics Department office to find out what is currently required.
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: No Homepage Submitted.
Background and Goals. See Math 115. Content. 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 the indefinite integral, techniques of integration, introduction to differential equations, infinite series. Text: Calculus by HughesHallett and Gleason. Students will need graphing calculators and should check with the Mathematics Department office to find out what is currently required.
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: No Homepage Submitted.
Background and Goals. See Math 115. Content. 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 lab using MAPLE.
Math. 216. Introduction to Differential Equations.
Instructor(s):
Prerequisites & Distribution: Math. 116, 119, 156, 176, 186, or 296. Credit can be earned for only one of Math. 216, 256, 286, or 316. No credit granted to those who have completed or are enrolled in Math 214. (4). (MSA). (BS).
Credits: (4).
Course Homepage: No Homepage Submitted.
Background and Goals. For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, 216417 (or 419) and 217316. The sequence 216417 emphasizes problemsolving 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 217316.
Content. 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. This course is not intended for mathematics concentrators, who should elect the sequence 217316.
Math. 333. Directed Tutoring.
Instructor(s):
Prerequisites & Distribution: Math. 385 and enrollment in the Elementary Program in the School of Education. (13). (Excl). (EXPERIENTIAL). May be repeated for a total of three credits.
Credits: (13).
Course Homepage: No Homepage Submitted.
An experiential mathematics course for elementary teachers. Students would tutor elementary (Math. 102) or intermediate (Math. 104) algebra in the Math. Lab. They would also participate in a weekly seminar to discuss mathematical and methodological questions.
Math. 385. Mathematics for Elementary School Teachers.
Section 101.
Instructor(s):
Prerequisites & Distribution: One year each of high school algebra and geometry. No credit granted to those who have completed or are enrolled in 485. (3). (Excl).
Credits: (3).
Course Homepage: No Homepage Submitted.
This course, together with its sequel Math 489, provides a coherent overview of the mathematics underlying the elementary and middle school curriculum. It is required of all students intending to earn an elementary teaching certificate and is taken almost exclusively by such students. Concepts are heavily emphasized with some attention given to calculation and proof. The course is conducted using a discussion format. Class participation is expected and constitutes a significant part of the course grade. Although only two years of high school mathematics are required, a more complete background including precalculus or calculus is desirable. Topics covered include problem solving, sets and functions, numeration systems, whole numbers (including some number theory) and integers. Each number system is examined in terms of its algorithms, its applications, and its mathematical structure.
Due to heavy enrollment pressure, Math 385 will be
offered this Spring Term (IIIA 2000) as well. Last Fall Term a number of
students were closed out of Math 385. Fall Term classsize limits
will be STRICTLY enforced.
Anyone who can elect Math 385 in the Spring
Term is urged to do so. It is the surest way to guarantee yourself a
place in the course. The next Spring Term offering of Math 385 will be in
2002. For further information, contact Prof. Krause at his email
address, krause@math.lsa.umich.edu.
Math. 399. Independent Reading.
Instructor(s):
Prerequisites & Distribution: (16). (Excl). (INDEPENDENT). May be repeated for credit.
Credits: (16).
Course Homepage: No Homepage Submitted.
Designed especially for Honors students.
Math. 417. Matrix Algebra I.
Instructor(s):
Prerequisites & Distribution: Three courses beyond Math. 110. No credit granted to those who have completed or are enrolled in 217, 419, or 513. (3). (Excl). (BS).
Credits: (3).
Course Homepage: No Homepage Submitted.
Background and Goals. 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 problemsolving, 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). Content. 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. 425/Stat. 425. Introduction to Probability.
Instructor(s):
Prerequisites & Distribution: Math. 215, 255, or 285. (3). (MSA). (BS).
Credits: (3).
Course Homepage: No Homepage Submitted.
Background and Goals. This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of Math 116 and 215. Content. Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances, central limit theorem. Different instructors will vary the emphasis. The material corresponds to most of Chapters 17 and part of 8 of Ross with the omission of some sections of 1.6, 2.6, 7.77.9, and 8.48.5 and many of the long examples. Recent Text(s): A First Course in Probability (Ross, 3rd ed.).
Math. 451. Advanced Calculus I.
Section 101.
Instructor(s):
Prerequisites & Distribution: Math. 215 and one course beyond Math. 215; or Math. 255 or 285. Intended for concentrators; other students should elect Math. 450. (3). (Excl). (BS).
Credits: (3).
Course Homepage: No Homepage Submitted.
Background and Goals. This course has two complementary goals: (1) a rigorous development of the fundamental ideas of calculus, and (2) a further development of the student's ability to deal with abstract mathematics and mathematical proofs. The key words here are "rigor" and "proof". almost all of the material of the course consists in understanding and constructing definitions, theorems (propositions, lemmas, etc.), and proofs. This is considered one of the more difficult among the undergraduate mathematics courses, and students should be prepared to make a strong commitment to the course. In particular, it is strongly recommended that some course which requires proofs (such as Math 412) be taken before Math 451.
Content. The material usually covered is essentially that of Ross' book. Chapter I deals with the properties of the real number system including (optionally) its construction from the natural and rational numbers. Chapter II concentrates on sequences and their limits, Chapters III and IV on the application of these ideas to continuity of functions, and sequences and series of functions. Chapter V covers the basic properties of differentiation and Chapter VI does the same for (Riemann) integration culminating in the proof of the Fundamental Theorem of Calculus. Along the way there are presented generalizations of many of these ideas from the real line to abstract metric spaces.
Math. 454. Boundary Value Problems for Partial Differential Equations.
Section 101.
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: http://www.math.lsa.umich.edu/~zenkov/SP2000/syllabus.454.html
Goals: 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.
Content: Classical representation and convergence theorems for Fourier series; method of separation of variables for the solution of the onedimensional heat and wave equation; the heat and wave equations in higher dimensions; spherical and cylindrical Bessel functions; Legendre polynomials; Fourier and Laplace transforms.
Text: Advanced Engineering Mathematics by E. Kreyszig, 8th edition.
Class Policy: Regular class attendance is expected. Homework will be assigned at the end of each class. Solving homework problems is an important part of preparation for tests in the class. Travel plans cannot be considered as a reason for making up the Midterm and Final Exams.
Grading:
 Homework (assigned every week, 30%)
 Midterm Exam (Friday, June 2, 30%)
 Final exam (Friday, June 23, 8:0010:00, 40%)
Math. 555. Introduction to Functions of a Complex Variable with Applications.
Section 101.
Instructor(s):
Prerequisites & Distribution: Math. 450 or 451. (3). (Excl). (BS).
Credits: (3).
Course Homepage: No Homepage Submitted.
This course is an introduction to the theory of complex valued functions of a complex variable with substantial attention to applications in science and engineering. Concepts, calculations, and the ability to apply principles to physical problems are emphasized over proofs, but arguments are rigorous. The prerequisite of a course in advanced calculus is essential. Differentiation and integration of complex valued functions of a complex variable, series, mappings, residues, applications. Evaluation of improper real integrals, fluid dynamics. Math 596 covers all of the theoretical material of Math 555 and usually more at a higher level and with emphasis on proofs rather than applications. Math 555 is prerequisite to many advanced courses in science and engineering fields.
Math. 561/SMS 518 (Business Administration)/IOE 510. Linear Programming I.
Section 001.
Instructor(s): Goldberg
Prerequisites & Distribution: Math. 217, 417, or 419. (3). (Excl). (BS). CAEN lab access fee required for nonEngineering students.
Credits: (3).
Lab Fee: CAEN lab access fee required for nonEngineering students.
Course Homepage: No Homepage Submitted.
Formulation of problems from the private and public sectors using the mathematical model of linear programming. Development of the simplex algorithm; duality theory and economic interpretations. Postoptimality (sensitivity) analysis; applications and interpretations. Introduction to transportation and assignment problems; special purpose algorithms and advanced computational techniques. Students have opportunities to formulate and solve models developed from more complex case studies and use various computer programs.
Spring/Summer Term Courses
Take me to the Spring/Summer Term '00 Time Schedule for Mathematics.
To see what has been added or changed in Mathematics this week go to What's New This Week.
Math. 399. Independent Reading.
Instructor(s):
Prerequisites & Distribution: (16). (Excl). (INDEPENDENT). May be repeated for credit.
Credits: (16).
Course Homepage: No Homepage Submitted.
Designed especially for Honors students.
Summer HalfTerm Courses
Take me to the Summer HalfTerm '00 Time Schedule for Mathematics.
To see what has been added or changed in Mathematics this week go to What's New This Week.
Math. 103. Intermediate Algebra.
Math 103 – Bridge Program Students Only.
Instructor(s):
Prerequisites & Distribution: Only open to designated summer halfterm Bridge students. (2). (Excl).
Credits: (2 in the halfterm).
Course Homepage: No Homepage Submitted.
This course is an indepth review of high school algebra. It covers linear, quadratic, and polynomial functions and their graphs. This course is restricted to students enrolled in the Bridge Program.
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: No Homepage Submitted.
This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of realworld applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. Students completing Math. 105 are fully prepared for Math. 115. Text: Contemporary Precalculus. Students will need graphing calculators and should check with the Math Department office to find out what is currently required.
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: No Homepage Submitted.
Background and Goals. The sequence Math 115116215 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 two uniform exams during the term and a uniform final exam. Content. 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 reallife problems in various fields, and definite integrals. Text: Calculus by HughesHallett and Gleason. Students will need graphing calculators and should check with the Mathematics Department office to find out what is currently required.
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: No Homepage Submitted.
Background and Goals. See Math 115. Content. 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 the indefinite integral, techniques of integration, introduction to differential equations, infinite series. Text: Calculus by HughesHallett and Gleason. Students will need graphing calculators and should check with the Mathematics Department office to find out what is currently required.
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: No Homepage Submitted.
Background and Goals. See Math 115. Content. 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 lab using MAPLE.
Math. 216. Introduction to Differential Equations.
Instructor(s):
Prerequisites & Distribution: Math. 116, 119, 156, 176, 186, or 296. Credit can be earned for only one of Math. 216, 256, 286, or 316. No credit granted to those who have completed or are enrolled in Math 214. (4). (MSA). (BS).
Credits: (4).
Course Homepage: No Homepage Submitted.
Background and Goals. For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, 216417 (or 419) and 217316. The sequence 216417 emphasizes problemsolving 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 217316.
Content. 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. This course is not intended for mathematics concentrators, who should elect the sequence 217316.
Math. 399. Independent Reading.
Instructor(s):
Prerequisites & Distribution: (16). (Excl). (INDEPENDENT). May be repeated for credit.
Credits: (16).
Course Homepage: No Homepage Submitted.
Designed especially for Honors students.
Math. 417. Matrix Algebra I.
Instructor(s):
Prerequisites & Distribution: Three courses beyond Math. 110. No credit granted to those who have completed or are enrolled in 217, 419, or 513. (3). (Excl). (BS).
Credits: (3).
Course Homepage: No Homepage Submitted.
Background and Goals. 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 problemsolving, 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). Content. 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/EECS 400/CS 400. Linear Spaces and Matrix Theory.
Instructor(s):
Prerequisites & Distribution: Four terms of college mathematics beyond Math 110. No credit granted to those who have completed or are enrolled in 217 or 513. One credit granted to those who have completed Math. 417. (3). (Excl). (BS). CAEN lab access fee required for nonEngineering students.
Credits: (3).
Lab Fee: CAEN lab access fee required for nonEngineering students.
Course Homepage: No Homepage Submitted.
Background and Goals. Math 419 covers much of the same ground as Math 417 but presents the material in a somewhat more abstract way in terms of vector spaces and linear transformations instead of matrices. There is a mix of proofs, calculations, and applications with the emphasis depending somewhat on the instructor. A previous prooforiented course is helpful but by no means necessary. Content. Basic notions of vector spaces and linear transformations: spanning, linear independence, bases, dimension, matrix representation of linear transformations; determinants; eigenvalues, eigenvectors, Jordan canonical form, innerproduct spaces; unitary, selfadjoint, and orthogonal operators and matrices, applications to differential and difference equations.
Math. 425/Stat. 425. Introduction to Probability.
Instructor(s):
Prerequisites & Distribution: Math. 215, 255, or 285. (3). (MSA). (BS).
Credits: (3).
Course Homepage: No Homepage Submitted.
Background and Goals. This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of Math 116 and 215. Content. Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances, central limit theorem. Different instructors will vary the emphasis. The material corresponds to most of Chapters 17 and part of 8 of Ross with the omission of some sections of 1.6, 2.6, 7.77.9, and 8.48.5 and many of the long examples. Recent Text(s): A First Course in Probability (Ross, 3rd ed.).
Math. 450. Advanced Mathematics for Engineers I.
Instructor(s):
Prerequisites & Distribution: Math. 216, 256, 286, or 316. (4). (Excl). (BS).
Credits: (4).
Course Homepage: No Homepage Submitted.
Background and Goals. Although this course is designed principally to develop mathematics for application to problems of science and engineering, it also serves as an important bridge for students between the calculus courses and the more demanding advanced courses. Students are expected to learn to read and write mathematics at a more sophisticated level and to combine several techniques to solve problems. Some proofs are given and students are responsible for a thorough understanding of definitions and theorems. Students should have a good command of the material from Math 215, and 216 or 316, which is used throughout the course. A background in linear algebra, e.g., Math 217, is highly desirable. Content. Topics include a review of curves and surfaces in implicit, parametric, and explicit forms; differentiability and affine approximations; implicit and inverse function theorems; chain rule for 3space; multiple integrals; scalar and vector fields; line and surface integrals; computations of planetary motion, work, circulation, and flux over surfaces; Gauss' and Stokes' Theorems, derivation of continuity and heat equation. Some instructors include more material on higher dimensional spaces and an introduction to Fourier series.
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 highlevel computer language. (3). (Excl). (BS).
Credits: (3).
Course Homepage: No Homepage Submitted.
Background and Goals. 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 proved. 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. Content. Topics include computer arithmetic, Newton's method for nonlinear 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, 2point boundary value problems, Dirichlet problem for the Laplace equation.
Math. 485. Mathematics for Elementary School Teachers and Supervisors.
Instructor(s):
Prerequisites & Distribution: One year of high school algebra. No credit granted to those who have completed or are enrolled in 385. (2). (Excl). (BS). May not be included in a concentration plan in mathematics.
Credits: (3; 2 in the halfterm).
Course Homepage: No Homepage Submitted.
The history, development, and logical foundations of the real number system and of numeration systems including scales of notation, cardinal numbers, and the cardinal concept; and the logical structure of arithmetic (field axioms) and relations to the algorithms of elementary school instruction. Simple algebra, functions, and graphs. Geometric relationships. For persons teaching in or preparing to teach in the elementary school.
This page was created at 2:52 PM on Mon, Aug 14, 2000.
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