Courses in Mathematics (Division 428)

All courses in Mathematics presuppose a minimum of two years of high school mathematics including one year each of algebra and plane geometry. All of the calculus courses require an additional year of algebra or precalculus, and all except Math 112 require a course in trigonometry.

The standard precalculus course is Math 105/106. The content of the two courses is the same; Math 105 is taught in standard lecture-recitation format, while Math 106 is offered as a self-study course through the Mathematics Laboratory. Students completing Math 105/106 are fully prepared for Math 115. Math 103/104 (the algebra part of 105/106) and Math 101 are offered in the Summer half term exclusively for students in the Summer Bridge Program. Math 109/110 is offered as a 7-week course in each half of the Fall term for students who despite apparent adequate preparation are unable to complete successfully one of the calculus courses.

Each of Math 112, 113, 115, 175, 185, and 195 is a first course in calculus and normally credit is allowed for only one of these courses. Math 112 is designed primarily for pre-business and social science students who expect to take only one term of calculus. It neither presupposes nor covers any trigonometry. The sequence Math 113-114 is designed for students of the life sciences who expect to take only one year of calculus. Neither Math 112 nor Math 113-114 prepares a student for any further courses in mathematics. Math 113 does not prepare a student for Math 116.

The standard calculus sequence taken by the great majority of students is Math 115-116-215. These courses provide a complete introduction to calculus and prepare a student for further study in mathematics. Students who intend to concentrate in mathematics or who have a greater interest in the theory should follow Math 215 with the sequence Math 217-316. Math 217 provides the background in linear algebra necessary for optimal treatment of some of the material on differential equations presented in Math 316. Math 316 covers the material of Math 216 and Math 404. Other students may follow Math 215 with Math 216 which covers some of the material of Math 316 without use of linear algebra. Math 217 also serves as a transition to the more theoretical material of upper-division mathematics courses.

Math 175, 185, and 195 are Honors courses, but are open to all students (not only those in the LS&A Honors Program) with permission of a mathematics Honors counselor in 1210 Angell Hall. 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 sequence. The sequence Math 175-176 covers, in addition to elementary calculus, a substantial amount of so-called combinatorial mathematics including graph theory, coding, and enumeration theory. It is taught by the discovery method; students are presented with a great variety of problems and encouraged to experiment in groups using computers. Math 176 may be followed by either Math 285 or Math 215. The sequence Math 185-186-285-286 is a comprehensive introduction to calculus and differential equations at a somewhat deeper and more theoretical level than Math 115-116-215-216. Under some circumstances it is possible (with permission of a mathematics counselor) to transfer between these two sequences.

The sequence Math 195-196-295-296 is a more rigorous and intensive introduction to advanced mathematics. It includes all of the content of the lower sequence and considerably more. Students are expected to understand and construct proofs as well as do calculations and solve problems. No previous calculus is required, although many students in this course have had some calculus. Students completing this sequence will be ready to take advanced undergraduate and beginning graduate level courses.

Students who have achieved good scores on the College Board Advanced Placement Exam may receive credit and advanced placement in the sequence beginning with Math 115. Other students who have studied calculus in high school may take a departmental placement examination during the first week of the Fall term to receive advanced placement WITHOUT CREDIT. No advanced placement credit is granted to students who elect Math 185, and students who elect Math 195 receive such credit only after satisfactory completion of Math 296.

NOTE: Additional information on most of the Math courses (background and goals, alternative courses, and subsequent courses) can be found in the Mathematics Department's booklet Undergraduate Courses available at the Undergrad Math Program office, 3011 Angell Hall.

NOTE: For most Mathematics courses the Cost of books and materials is $25-50 WL:3 for all courses

105. Algebra and Analytic Trigonometry. See table in Bulletin. Students with credit for Math. 103 or 104 can elect Math. 105 for only 2 credits. No credit granted to those who have completed or are enrolled in Math 106 or 107. (4). (Excl).
This is a course in college algebra and trigonometry with an emphasis on functions and graphs. Functions covered are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Students completing Math 105/106 are fully prepared for Math 115. Text: Algebra and Trigonometry by Larson and Hostetler, second edition. Math 106 is a self-study version of this course.

106. Algebra and Analytic Trigonometry (Self-Paced). See table in Bulletin. Students with credit for Math. 103 or 104 can elect Math. 106 for only 2 credits. No credit granted to those who have completed or are enrolled in Math 105 or 107. (4). (Excl).
Self-study version of Math 105. There are no lectures or sections. Students enrolling in Math 106 must visit the Math Lab during the first full week of the term to complete paperwork and to receive course materials. Students study on their own and consult with tutors in the Math Lab whenever needed. Progress is measured by tests following each chapter and by scheduled midterm and final exams. Math 106 students take the same midterm and final exams as Math 105 students. More detailed information is available from the Math Lab.

110. Pre-Calculus (Self-Paced). Two years of high school algebra. No credit granted to those who already have 4 credits for pre-calculus mathematics courses. (2). (Excl).
Self-study version of Math 109. There are no lectures or sections. Students enrolling in Math 110 must visit the Math Lab during the first full week of the term to complete paperwork and to receive course materials. Students study on their own and consult with tutors in the Math Lab whenever needed. Progress is measured by tests following each chapter and by scheduled midterm and final exams. More detailed information is available from the Math Lab.

112. Brief Calculus. Three years of high school mathematics or Math. 105 or 106. Credit is granted for only one course from among Math. 112, 113, 115, 185 and 195. (4). (N.Excl).
This is a one-term survey course that provides the basics of elementary calculus. Emphasis is placed on intuitive understanding of concepts and not on rigor. Topics include differentiation with application to curve sketching and maximum-minimum problems, antiderivatives and definite integrals. Trigonometry is not used. The text has been Hoffman, Calculus for the Business, Economics, Social, and Life Sciences, fourth edition. This course does not mesh with any of the courses in the other calculus sequences.

113. Mathematics for Life Sciences I. Three years of high school mathematics or Math. 105 or 106. Credit is granted for only one course from among Math. 112, 113, 115, and 185. (4). (N.Excl).
The material covered includes functions and graphs, derivatives; differentiation of algebraic and trigonometric functions and applications; definite and indefinite integrals and applications.

114. Mathematics for Life Sciences II. Math. 113. Credit is granted for only one course from among Math. 114, 116, and 186. (4). (N.Excl).
The material covered includes probability, the calculus of three-dimensions, differential equations and vectors and matrices.

115. Analytic Geometry and Calculus I. See table in Bulletin. (Math. 107 may be elected concurrently.) Credit is granted for only one course from among Math. 112, 113, 115, and 185. (4). (N.Excl).
Topics covered include functions and graphs, derivatives, differentiation of algebraic and trigonometric functions and applications, definite and indefinite integrals and applications. This corresponds to Chapters 1-5 of Thomas and Finney. Text: Calculus and Analytic Geometry, 7th ed. (G. Thomas and R. Finney)

116. Analytic Geometry and Calculus II. Math. 115. Credit is granted for only one course from among Math. 114, 116, and 186. (4). (N.Excl).
Topics covered include transcendental functions, techniques of integration, introduction to differential equations, conic sections, and infinite sequences and series. This corresponds to Chapters 6-8 and 11 of Thomas and Finney. Text: Calculus and Analytic Geometry, 7th ed. (G. Thomas and R. Finney)

118. Analytic Geometry and Calculus II for Social Sciences. Math. 115. (4). (N.Excl).
Math 118, a sequel to Math 115, is a combination of the techniques and concepts from Math 116, 215, and 216 that are most useful in the social and decision sciences (especially economics and business). Topics covered include: logarithms, exponentials, elementary integration techniques (substitution, by parts and partial fractions), infinite sequences and series, systems of linear equations, matrices, determinants, vectors, level sets, partial derivatives, Lagrange multipliers for constrained optimization, and elementary differential equations. (Students planning to take Math 215 and 216 should still take 116, although one can pass from 118 to 215 with a bit of work and redundancy.) No credit for 118 after having taken 116 or 186. Like Math 116, this course will require two one-hour examinations, a midterm, and a final exam. Text: Calculus and Analytic Geometry by Thomas and Finney (7th ed.).

147(247). Mathematics of Finance. Math. 112 or 115. (3). (Excl).
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 424 which covers the same topics but on a more rigorous basis requiring considerable use of the calculus. Topics covered include: various rates of simple and compound interest, present and accumulated values based on these; annuity functions and their application to amortization, sinking funds and bond values; depreciation methods; introduction to life tables, life annuity, and life insurance values. The course is not part of a sequence. Students should possess financial calculators.

176. Combinatorics and Calculus II. Math. 175. (4). (N.Excl).
The general theme of the course will be dynamical systems, the dynamic behavior of functions. Specific topics will include: iterates of functions, orbits, attracting and repelling orbits, limits and continuity, space-filling curves, Taylor series, exponentials and logarithms, self-similarity, and fractals. The course material will review and supplement a first course in calculus.

186. Honors Analytic Geometry and Calculus II. Permission of the Honors Counselor. Credit is granted for only one course from among Math. 114, 116, and 186. (4). (N.Excl).
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.

196. Honors Mathematics II. Permission of the Honors Counselor. (4). (N.Excl).
Sups and infs, sequences and series, Bolzano-Weierstrass Theorem, uniform continuity and convergence, power series, C raised to infinity and analytic functions, Weierstrass Approximation Theorem, metric spaces: R to the nth and C raised to 0[a,b], completeness and compactness.

215. Analytic Geometry and Calculus III. Math. 116 or 186. (4). (Excl).
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. This corresponds to Chapters 13-19 of Thomas and Finney. Text: Calculus and Analytic Geometry (G. Thomas and R. Finney)

216. Introduction to Differential Equations. Math. 215. (4). (Excl).
Topics include first-order differential equations, higher-order linear differential equations with constant coefficients, linear systems. Recent Text(s): Differential Equations, 2nd ed. (Sanchez, Allen, and Kyner)

217. Linear Algebra. Math. 215. (4). (Excl).
The topics covered are systems of linear equations, matrices, vector spaces (subspaces of R to n power), linear transformations, determinants, Eigenvectors and diagonalization, and inner products. This corresponds to chapters 1, 2, 5, 6, (7), 8.1-8.6, 3, and (4) of Schneider in that order (parenthesized chapters are optional). Texts: Linear Algebra 2nd. ed. (D. Schneider); Linear Algebra (B. Jacob)

286. Honors Differential Equations. Math. 285. (3). (Excl).
Topics include first-order differential equations, high-order linear differential equations with constant coefficients, linear systems.

288. Math Modeling Workshop. Math. 216 or 316, and Math. 217 or 417. (1). (Excl). Offered mandatory credit/no credit. May be elected for a total of 3 credits.
During the weekly workshop students will be presented with real-world problems on which techniques of undergraduate mathematics offer insights. They will see examples of (1) how to approach and set up a given modelling problem systematically, (2) how to use mathematical techniques to begin a solution of the problem, (3) what to do about the loose ends that can't be solved, and (4) how to present the solution to others. Students will have a chance to use the skills developed by participating in the UM Undergraduate Math Modelling Competition. This course may be repeated for credit.

289. Problem Seminar. (1). (Excl). May be repeated for credit with permission.
Students and one or more faculty and graduate student assistants will meet in small groups to explore problems in many different areas of mathematics. Problems will be selected according to the interests and background of the students. This course may be repeated for credit.

296. Honors Analysis II. Math. 295. (4). (Excl).
Differential and integral calculus of functions on Euclidean spaces.

300/EECS 300/CS 300. Mathematical Methods in System Analysis. Math. 216 or 316 or the equivalent. No credit granted to those who have completed or are enrolled in 448. (3). (Excl).
See Computer Science 300.

312. Applied Modern Algebra. Math. 116, or permission of mathematics counselor. (3). (Excl).
There are many possible topics which are natural here including counting techniques, finite state machines, logic and set theory, graphs and networks, Boolean algebra, group theory, and coding theory. Each instructor will choose some from this list and consequently the course content will vary from section to section. One recent course covered chapters 1, 3, 4, 5, 7, and 16 of Grimaldi. Recent Text(s): Discrete and Combinatorial Mathematics (R.P.Grimaldi)

316. Differential Equations. Math. 215 and 217, or equivalent. Credit can be received for only one of Math. 216 or Math. 316, and credit can be received for only one of Math. 316 or Math. 404. (3). (Excl).
First-order equations, exposure to graphics-based software implementing numerical techniques, solutions to constant-coefficient systems by eigenvectors and eigenvalues, higher-order equations, qualitative behavior of systems (using software). Applications to various physical problems are considered throughout. This corresponds to much of Chapter 1 and sections 2.1-2.7, 2.15, 3.1-3.12, 4.1-4.4, 4.7 and other selected sections of Braun. Texts: Differential Equations and their Applications (M. Braun); Elementary Differential Equations with Linear Algebra, 2nd ed. (Finney and Ostberg)

371/Engin. 371. Numerical Methods for Engineers and Scientists. Engineering 103 or 104, or equivalent; and Math. 216. (3). (Excl).
Floating point arithmetic, Gaussian elimination, polynomial interpolation, numerical integration, solutions to non-linear equations, ordinary differential equations. Other topics may include spline approximation, two-point boundary-value problems, and Monte-Carlo methods. Recent Text(s): An Introduction to Numerical Computation (Yakowitz and Szidarovsky)

404. Intermediate Differential Equations. Math. 216. No credit granted to those who have completed Math. 286 or 316. (3). (Excl).
Linear systems, solutions by matrices, qualitative theory, power series solutions, numerical methods, phase-plane analysis of non-linear differential equations. This corresponds to chapters 4 and 7-9 of Boyce and DiPrima. Recent Text(s): Differential Equations (Boyce and DiPrima)

412. Introduction to Modern Algebra. Math. 215 or 285; and prior or concurrent election of 217, 417, or 419 recommended. No credit granted to those who have completed or are enrolled in 512. Students with credit for 312 should take 512 rather than 412. One credit granted to those who have completed 312. (3). (Excl).
The initial topics include ones common to every branch of mathematics: sets, functions (mappings), relations, and the common number systems (integers, rational numbers, real numbers, complex numbers). These are then applied to the study of two particular types of mathematical structures: groups and rings. These structures are presented as abstractions from many examples such as the common number systems together with the operations of addition or multiplication, permutations of finite and infinite sets with function composition, sets of motions of geometric figures, and polynomials. Notions such as generator, subgroup, direct product, isomorphism, and homomorphism are defined and studied. A possible syllabus would include the material from Chapters 1, 2.1-2.10, 3, and 4.1-4.5 of Herstein or Chapters I-VII, X, and XI of Durbin. Recent Text(s): Abstract Algebra (I.N.Herstein); Modern Algebra, 2nd ed. (J.R.Durbin)

416. Theory of Algorithms. Math. 312 or 412 or CS 303, and CS 380. (3). (Excl).
Typical problems considered are: sorting, searching, matrix multiplication, graph problems (flows, travelling salesman), and primality and pseudo-primality testing (in connection with coding questions). Algorithm types such as divide-and-conquer, backtracking, greedy, and dynamic programming are analyzed using mathematical tools such as generating functions, recurrence relations, induction and recursion, graphs and trees, and permutations. The course often includes a short final section on abstract complexity theory including NP completeness. A possible syllabus includes chapters 1-4 and part of 5 of Wilf. Recent Text(s): Algorithms and Complexity (H. Wilf)

417. Matrix Algebra I. Three courses beyond Math. 110. No credit granted to those who have completed or are enrolled in 513. No credit granted to those who have completed 217. (3). (Excl).
Topics include matrix operations, vector spaces, Gaussian and Gauss-Jordan algorithms for linear equations, subspaces of vector spaces, linear transformations, determinants, orthogonality, characteristic polynomials, Eigenvalue problems, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations. A possible syllabus includes most of Chapters 1-6 of Strang. Recent Text(s): Linear Algebra and its Applications 3rd ed. (G. Strang); Linear Algebra 2nd ed. (D. Schneider)

419/EECS 400/CS 400. Linear Spaces and Matrix Theory. Four terms of college mathematics beyond Math 110. No credit granted to those who have completed or are enrolled in 417 or 513. (3). (Excl).
Basic notions of vector spaces and linear transformations: spanning, linear independence, bases, dimension, matrix representation of linear transformations; determinants; eigenvalues, eigenvectors, Jordan canonical form, inner-product spaces; unitary, self-adjoint, and orthogonal operators and matrices, applications to differential and difference equations. This corresponds to Chapters 1, 2, 3, 5 and parts of 4, 6, and 7 of Friedberg et. al. Recent Text(s): Linear Algebra 2nd ed. (Friedberg, Insel, and Spence)

420. Matrix Algebra II. Math. 217, 417 or 419. (3). (Excl).
Similarity theory, Euclidean and unitary geometry, applications to linear and differential equations, interpolation theory, least squares and principal components, B-splines.

425/Stat. 425. Introduction to Probability. Math. 215. (3). (N.Excl).
Topics include the basic results and methods of both discrete and continuous probability theory. Different instructors will vary the emphasis between these two theories. The material corresponds to most of Chapters 1-8 of Ross with the omission of sections 1.6, 2.6, 7.7-7.9, and 8.4-8.5 and many of the long examples. Recent Text(s): A First Course in Probability, 3rd ed. (S. Ross)

431. Topics in Geometry for Teachers. Math. 215. (3). (Excl).
Topics selected depend heavily on the instructor but may include classification of isometries of the Euclidean plane; similarities; rosette, frieze, and wallpaper symmetry groups; tesselations; triangle groups; finite, hyperbolic, and taxicab non-Euclidean geometries. This corresponds to Chapters 1-11, 13, and 14 of Transformation Geometry: an Introduction to Symmetry by Martin together with Taxicab Geometry by E. Krause.

450. Advanced Mathematics for Engineers I. Math. 216, 286, or 316. (4). (Excl).
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 3-space; 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. This corresponds to Chapters 2, 3, 5, 7, and 8 and sometimes 4 of Marsden and Tromba. Recent Text(s): Vector Calculus, 3rd ed. (Marsden and Tromba); Boundary Value Problems, 3rd ed. (Powers)

451. Advanced Calculus I. Math. 215 and one course beyond Math. 215; or Math. 285. Intended for concentrators; other students should elect Math. 450. (3). (Excl).
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 aplication 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. Recent Text(s): Elementary Analysis: The Theory of Calculus (K. Ross)

452. Advanced Calculus II. Math. 217, 417, or 419; and Math. 451. (3). (Excl).
Topics include (1) partial derivatives and differentiability, (2) gradients, directional derivatives, and the chain rule, (3) implicit function theorem, (4) surfaces, tangent plane, (5) max-min theory, (6) multiple integration, change of variable, etc., (7) Green's and Stoke's theorems, differential forms, exterior derivatives, (8) introduction to the differential geometry of curves and surfaces. This corresponds to Chapters 3, 7, 8, and 9 of Advanced Calculus (3rd ed) by R. Buck.

454. Fourier Series and Applications. Math. 216, 286 or 316. Students with credit for Math. 455 or 554 can elect Math. 454 for 1 credit. (3). (Excl).
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); discrete Fourier transform; applications to linear input-output systems, analysis of data smoothing and filtering, signal processing, time-series analysis, and spectral analysis. This corresponds to Chapters 2-6 of Pinsky) Recent Text(s): Introduction to Partial Differential Equations (M. Pinsky); Fourier Series and Boundary Value Problems (Churchill and Brown)

462. Mathematical Models. Math. 216, 286 or 316; and 217, 417, or 419. (3). (Excl).
Content will vary considerably with the instructor. One recent version covered use and theory of dynamical systems, difference and differential equations: one-dimensional, multi-dimensional, linear and nonlinear, deterministic and stochastic. The high points included chaotic dynamics, phase diagrams of two-dimensional systems, a variety of ecological and biological models, and classical mechanics. Other versions may focus on discrete and combinatoric approaches.

471. Introduction to Numerical Methods. Math. 216, 286, or 316; and 217, 417, or 419; and a working knowledge of one high-level computer language. (3). (Excl).
Topics 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. This corresponds to Chapters 1-6 and sections 7.3-4, 8.3, 10.2, and 12.2 of Numerical Analysis (4th ed.) by Burden and Faires.

475. Elementary Number Theory. (3). (Excl).
Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Diophantine equations, primitive roots, quadratic reciprocity and quadratic fields. This material corresponds to Chapters 1-3 and selected parts of Chapter 5 of An Introduction to the Theory of Numbers by Niven and Zuckerman) or essentially all of An Introduction to Number Theory by H.M. Stark.

476. Computational Laboratory in Number Theory. Prior or concurrent enrollment in Math. 475 or 575. (1). (Excl).
Students will be provided software with which to conduct numerical explorations. Student 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.

489. Mathematics for Elementary and Middle School Teachers. Math. 385 or 485, or permission of instructor. May not be used in any graduate program in mathematics. (3). (Excl).
Topics covered include decimals and real numbers, probability and statistics, geometric figures, measurement, and congruence and similarity. Algebraic techniques and problem-solving strategies are used throughout the course. The material is contained in Chapters 7-11 of Krause. Recent Text(s): Mathematics for Elementary Teachers (E. Krause)

490. Introduction to Topology. Math. 412 or 451 or equivalent experience with abstract mathematics. (3). (Excl).
The topics covered are fairly constant but the presentation and emphasis will vary significantly with the instructor. Point-set topology, examples of topological spaces, orientable and non-orientable surfaces, fundamental groups, homotopy, covering spaces. Metric and Euclidean spaces are emphasized. This corresponds to Chapters 0-9, 11-19, and 21-26 of A First Course in Algebraic Topology by Kosniowski.

497. Topics in Elementary Mathematics. Math. 489 or permission of instructor. (3). (Excl). May be repeated for a total of six credits.
Selected topics in geometry, algebra, computer programming, logic, and combinatorics for prospective and in-service elementary, middle, or junior high school teachers. Content will vary from term to term.

525/Stat. 525. Probability Theory. Math. 450 or 451; or permission of instructor. Students with credit for Math. 425/Stat. 425 can elect Math. 525/Stat. 525 for only 1 credit. (3). (Excl).
Topics include the basic results and methods of both discrete and continuous probability theory. Different instructors will vary the emphasis between these two theories. The material corresponds to all 9 chapters of Introduction to Probability Theory by Hoel, Post, and Stone, together with some additional more theoretical material

526/Stat. 526. Discrete State Stochastic Processes. Math 525 or EECS 501. (3). (Excl).

See Statistics 526. (Belisle)


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