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MATH 105. Data, Functions, and Graphs.
UNIFORM EVENING EXAMS FOR MATH 105: WED, FEB 6 & MAR 20 68 PM. ALSO A UNIFORM FINAL EXAM.
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. A maximum of four credits may be earned in MATH 103, 105, and 110. (4). (MSA). (QR/1). May not be repeated for credit.
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 realworld applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing.
TEXT: Functions Modeling Change, Connally, Wiley Publishing.
MATH 107. Mathematics for the Information Age.
Section 001.
Instructor(s):
Prerequisites & Distribution: Three to four years high school mathematics. (3). (MSA). (QR/1). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
The course investigates topics relevant to the information age in which we live. Topics covered include cryptography, errorcorrecting codes, data compression, fairness in politics, voting systems, population growth, biological modeling.
MATH 110. PreCalculus (SelfStudy).
STUDENTS IN MATH 110 RECEIVE INDIVIDUALIZED SELFPACED INSTRUCTION IN THE MATHEMATICS LABORATORY.
Instructor(s):
Prerequisites & Distribution: See Elementary Courses above. Enrollment in MATH 110 is by recommendation of MATH 115 instructor and override only. No credit granted to those who already have 4 credits for precalculus mathematics courses. A maximum of four credits may be earned in MATH 103, 105, and 110. (2). (Excl). May not be repeated for credit.
Credits: (2).
Course Homepage: http://www.math.lsa.umich.edu/~meggin/math110.html
The course covers data analysis by means of functions and graphs. Math 110 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. The course is a condensed, halfterm version of Math 105 (Math 105 covers the same material in a traditional classroom setting) designed for students who appear to be prepared to handle calculus but are not able to successfully complete Math 115. Students who complete 110 are fully prepared for Math 115. Students may enroll in Math 110 only on the recommendation of a mathematics instructor after the third week of classes.
ENROLLMENT IN MATH 110 IS BY PERMISSION OF MATH 115 INSTRUCTOR ONLY. COURSE MEETS SECOND HALF OF THE TERM. STUDENTS WORK INDEPENDENTLY WITH GUIDANCE FROM MATH LAB STAFF.
MATH 115. Calculus I.
UNIFORM EVENING EXAMS FOR MATH 115: WED, FEB 6 & MAR 20 68 PM. ALSO A UNIFORM FINAL.
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). May not be repeated for credit.
Credits: (4).
Course Homepage: http://www.math.lsa.umich.edu/courses/115/
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 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 reallife 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 Math 115 and 116) and a graphing calculator (the Texas Instruments TI83 is recommended).
TEXT: Calculus, 3rd edition, HughesHallet, Wiley Publishing.
TI83 Graphing Calculator, Texas Instruments.
MATH 116. Calculus II.
UNIFORM EVENING EXAMS FOR MATH 116: THURS, FEB 7 & TUES, MAR 19 68 PM. ALSO A UNIFORM FINAL.
Instructor(s):
Prerequisites & Distribution: MATH 115. Credit is granted for only one course from among MATH 116, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1). May not be repeated for credit.
Credits: (4).
Course Homepage: http://www.math.lsa.umich.edu/courses/116/
See Math 115 for a general description of the sequence Math 115116215.
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, HughesHallet/Gleason, Wiley Publishing.
TI83 Graphing Calculator, Texas Instruments.
MATH 127. Geometry and the Imagination.
Section 001.
Instructor(s):
Prerequisites & Distribution: Three years of high school mathematics including a geometry course. Only firstyear students, including those with sophomore standing, may preregister for FirstYear Seminars. All others need permission of instructor. No credit granted to those who have completed a 200 (or higher) level mathematics course. (4). (MSA). (BS). (QR/1). May not be repeated for credit.
FirstYear Seminar
Credits: (4).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 147. Introduction to Interest Theory.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 115. No credit granted to those who have completed a 200 (or higher) level mathematics course. (3). (MSA). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 186. Honors Calculus II.
Instructor(s):
Prerequisites & Distribution: Permission of the Honors advisor. Credit is granted for only one course from among MATH 116, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1). May not be repeated for credit.
Credits: (4).
Course Homepage: No homepage submitted.
The sequence Math 185186285286 is the honors introduction to the calculus. It is taken by students intending to major in mathematics, science, or engineering as well as students heading for many other fields who want a somewhat more theoretical approach. Although much attention is paid to concepts and solving problems, the underlying theory and proofs of important results are also included. This sequence is not restricted to students enrolled in the LS&A Honors Program.
Topics covered include transcendental functions; techniques of integration; applications of calculus such as elementary differential equations, simple harmonic motion, and center of mass; conic sections; polar coordinates; infinite sequences and series including power series and Taylor series. Other topics, often an introduction to matrices and vector spaces, will be included at the discretion of the instructor. Math 116 is a somewhat less theoretical course which covers much of the same material. Math 285 is the natural sequel.
Text: Calculus, 4th edition, James Stewart,
Brooks/Cole.
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). May not be repeated for credit.
Credits: (4).
Course Homepage: No homepage submitted.
This course is intended for secondyear 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 34 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 following is a tentative outline of the course:
 Systems of linear equations, matrices, row operations, reduced row echelon form, free variables, basic variables, basic solution, parametric description of the solution space. Rank of a matrix.
 Vectors, vector equations, vector algebra, linear combinations of vectors, the linear span of vectors.
 The matrix equation Ax = b. Algebraic rules for multiplication of matrices and vectors.
 Homogeneous systems, principle of superposition.
 Linear independence.
 Applications, Linear models.
 Matrix algebra, dot product, matrix multiplication.
 Inverse of a matrix.
 Invertible matrix theorem.
 Partitioned matrices.
 2dimensional discrete dynamical systems.
 Markov process, steady state.
 Transition matrix, eigenvector, steady state lines (affine hulls).
 Geometry of two and three dimensions: affine hulls, linear hulls, convex hulls, half planes, distance from point to a plane, optimization.
 Introduction to linear programming.
 The geometry of transition matrices in 2 dimensions (rotations, shears, ellipses, eigenvectors).
 Transition matrices for 3D (rotations, orthogonal matrices, symmetric matrices)
 Determinants.
 2 and 3dimensional determinant as area and volume.
 Eigenvectors and Eigenvalues.
 Eigenvectors.
 Complex numbers including Euler's formula.
 Complex eigenvalues and their geometric meaning.
 Review of ordinary differential equations.
 Systems of ordinary differential equations in 2 dimensions.
Regular problem sets and exams.
MATH 215. Calculus III.
UNIFORM EVENING EXAMS FOR MATH 215: MON, FEB 11 & THURS, MAR 21 68 PM. ALSO A UNIFORM FINAL.
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). May not be repeated for credit.
Credits: (4).
Course Homepage: http://www.math.lsa.umich.edu/courses/215/
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MATH 216. Introduction to Differential Equations.
UNIFORM EVENING EXAMS FOR MATH 216: TUES, FEB 12 & THURS, MAR 21, 810 PM. ALSO A UNIFORM FINAL.
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). May not be repeated for credit.
Credits: (4).
Course Homepage: http://www.math.lsa.umich.edu/courses/216/
No Description Provided. Contact the Department.
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MATH 217. Linear Algebra.
Instructor(s):
Prerequisites & Distribution: MATH 215, 255, or 285. 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). (QR/1). May not be repeated for credit.
Credits: (4).
Course Homepage: No homepage submitted.
For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, Math 216417 (or 419) and Math 217316. The sequence Math 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 Math 217316. These courses are explicitly designed to introduce the student to both the concepts and applications of their subjects and to the methods by which the results are proved. Therefore the student entering Math 217 should come with a sincere interest in learning about proofs. The topics covered include: systems of linear equations; matrix algebra; vectors, vector spaces, and subspaces; geometry of R^{n}; linear dependence, bases, and dimension; linear transformations; eigenvalues and eigenvectors; diagonalization; and inner products. Throughout there will be emphasis on the concepts, logic, and methods of theoretical mathematics. Math 417 and 419 cover similar material with more emphasis on computation and applications and less emphasis on proofs. Math 513 covers more in a much more sophisticated way. The intended course to follow Math 217 is 316. Math 217 is also prerequisite for Math 412 and all more advanced courses in mathematics.
MATH 255. Applied Honors Calculus III.
EVENING EXAMS THURS FEB 7 & WED MAR 20, 68 PM.
Instructor(s):
Prerequisites & Distribution: MATH 156. Credit can be earned for only one of MATH 215, 255, or 285. (4). (MSA). (BS). May not be repeated for credit.
Credits: (4).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 286. Honors Differential Equations.
Instructor(s):
Prerequisites & Distribution: MATH 285. Credit can be earned for only one of MATH 216, 256, 286, or 316. (3). (MSA). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 289. Problem Seminar.
Section 001.
Instructor(s):
Prerequisites & Distribution: (1). (Excl). (BS). May be repeated for credit. Repetition requires permission of the department.
Credits: (1).
Course Homepage: No homepage submitted.
One of the best ways to develop mathematical abilities is by solving problems using a variety of methods. Familiarity with numerous methods is a great asset to the developing student of mathematics. Methods learned in attacking a specific problem frequently find application in many other areas of mathematics. In many instances an interest in and appreciation of mathematics is better developed by solving problems than by hearing formal lectures on specific topics. The student has an opportunity to participate more actively in his/her education and development. This course is intended for superior students who have exhibited both ability and interest in doing mathematics, but it is not restricted to honors students. This course is excellent preparation for the Putnam exam. 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.
MATH 296. Honors Mathematics II.
Section 001.
Instructor(s):
Prerequisites & Distribution: Prior knowledge of first year calculus and permission of the Honors advisor. Credit is granted for only one course from among MATH 116, 156, 176, 186, and 296. (4). (Excl). (BS). (QR/1). May not be repeated for credit.
Credits: (4).
Course Homepage: No homepage submitted.
The sequence Math 295296395396 is a more intensive honors sequence than 185186285286. The material includes all of that of the lower sequence and substantially more. The approach is theoretical, abstract, and rigorous. Students are expected to learn to understand and construct proofs as well as do calculations and solve problems. The expected background is a thorough understanding of high school algebra and trigonometry. 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 courses. This sequence is not restricted to students enrolled in the LS&A Honors Program. The precise content depends on material covered in 295 but will generally include topics such as infinite series, power series, Taylor expansion, metric spaces. Other topics may include applications of analysis, Weierstrass Approximation theorem, elements of topology, introduction to linear algebra, complex numbers.
MATH 310. Elementary Topics in Mathematics.
Section 001 – Math Games & Theory of Games.
Instructor(s):
Prerequisites & Distribution: Two years of high school mathematics. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
The current offering of the course focuses on game theory. Students study the strategy of several games where mathematical ideas and concepts can play a role. Most of the course will be occupied with the strructure of a variety of two person games of strategy: tictactoe, tictactoe misere, the French military game, hex, nim, the penny dime game, and many others. If there is sufficient interest students can study: dots and boxes, go moku, and some aspects of checkers and chess. There will also be a brief introduction to the classical Von Neuman/Morgenstern theory of mixed strategy games.
MATH 312. Applied Modern Algebra.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 217. Only one credit granted to those who have completed MATH 412. (3). (Excl). (BS). May not be repeated for credit.
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, prooforiented 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 realworld 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 publickey 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 prooforiented 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 followup 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). May not be repeated for credit.
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. Firstorder equations: solutions, existence and uniqueness, and numerical techniques; linear systems: eigenvectoreigenvalue solutions of constant coefficient systems, fundamental matrix solutions, nonhomogeneous systems; higherorder 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 333. Directed Tutoring.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 385 and enrollment in the Elementary Program in the School of Education. Permission of instructor required. (13). (Excl). (EXPERIENTIAL). May be repeated for a maximum of 3 credits.
Credits: (13).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 351. Principles of Analysis.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 215 and 217. (3). (Excl). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
The content of this course is similar to that of Math 451 but Math 351 assumes less background. This course covers topics that might be of greater use to students considering a Mathematical Sciences concentration or a minor in Math. Course content includes: analysis of the real line, rational and irrational numbers, infinity – large and small, limits, convergence, infinite sequences and series, continuous functions, power series and differentiation.
MATH 354. Fourier Analysis and its Applications.
Section 001.
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). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
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MATH 371 / ENGR 371. Numerical Methods for Engineers and Scientists.
Instructor(s):
Prerequisites & Distribution: ENGR 101; one of MATH 216, 256, 286, or 316. No credit granted to those who have completed or are enrolled in Math 471. (3). (Excl). (BS). CAEN lab access fee required for nonEngineering students. May not be repeated for credit.
Credits: (3).
Lab Fee: CAEN lab access fee required for nonEngineering students.
Course Homepage: No homepage submitted.
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MATH 396. Honors Analysis II.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 395. (4). (Excl). (BS). May not be repeated for credit.
Credits: (4).
Course Homepage: No homepage submitted.
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MATH 399. Independent Reading.
Instructor(s):
Prerequisites & Distribution: Permission of instructor required. (16). (Excl). (INDEPENDENT). May be repeated for credit.
Credits: (16).
Course Homepage: No homepage submitted.
Designed especially for Honors students.
MATH 412. Introduction to Modern Algebra.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 215, 255, or 285; and 217. No credit granted to those who have completed or are enrolled in MATH 512. Students with credit for MATH 312 should take MATH 512 rather than 412. One credit granted to those who have completed MATH 312. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
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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). May not be repeated for credit.
Credits: (3).
Course Homepage: http://www.math.lsa.umich.edu/courses/417/
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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). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
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MATH 422 / BE 440. Risk Management and Insurance.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 115, junior standing, and permission of instructor. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
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MATH 423. Mathematics of Finance.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 217 and 425; EECS 183. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
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MATH 424. Compound Interest and Life Insurance.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 215, 255, or 285. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
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MATH 425 / STATS 425. Introduction to Probability.
Instructor(s):
Prerequisites & Distribution: MATH 215, 255, or 285. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 450. Advanced Mathematics for Engineers I.
Instructor(s):
Prerequisites & Distribution: MATH 215, 255, or 285. No credit granted to those who have completed or are enrolled in MATH 454. (4). (Excl). (BS). May not be repeated for credit.
Credits: (4).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 451. Advanced Calculus I.
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). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
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. Topics include: logic and techniques of proof; sets, functions, and relations; cardinality; the real number system and its topology; infinite sequences, limits, and continuity; differentiation; integration, and the Fundamental Theorem of Calculus; infinite series; and sequences and series of functions.
There is really no other course which covers the material of Math 451. Although Math 450 is an alternative prerequisite for some later courses, the emphasis of the two courses is quite distinct. The natural sequel to Math 451 is 452, which extends the ideas considered here to functions of several variables. In a sense, Math 451 treats the theory behind Math 115116, while Math 452 does the same for Math 215 and a part of Math 216. Math 551 is a more advanced version of Math 452. Math 451 is also a prerequisite for several other courses: Math 575, 590, 596, and 597.
MATH 452. Advanced Calculus II.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 217, 417, or 419; and MATH 451. (3). (Excl). (BS). May not be repeated for credit.
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:
 partial derivatives and differentiability;
 gradients, directional derivatives, and the chain rule;
 implicit function theorem;
 surfaces, tangent plane;
 maxmin theory;
 multiple integration, change of variable, etc.; and
 Green's and Stokes' theorems, differential forms, exterior derivatives.
Math 551 is a higherlevel 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. No credit granted to those who have completed or are enrolled in MATH 450. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 462. Mathematical Models.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 216, 256, 286, or 316; and MATH 217, 417, or 419. Students with credit for MATH 362 must have department permission to elect MATH 462. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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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. No credit granted to those who have completed or are enrolled in MATH 371 or 472. (3). (Excl). (BS). May not be repeated for credit.
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 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, 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 571572 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.
MATH 475. Elementary Number Theory.
Section 001.
Instructor(s):
Prerequisites & Distribution: At least three terms of college mathematics are recommended. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
This is an elementary introduction to number theory, especially congruence arithmetic. Number theory is one of the few areas of mathematics in which problems easily describable to a layman (is every even number the sum of two primes?) have remained unsolved for centuries. Recently some of these fascinating but seemingly useless questions have come to be of central importance in the design of codes and cyphers. The methods of number theory are often elementary in requiring little formal background. In addition to strictly numbertheoretic questions, concrete examples of structures such as rings and fields from abstract algebra are discussed. Concepts and proofs are emphasized, but there is some discussion of algorithms which permit efficient calculation. Students are expected to do simple proofs and may be asked to perform computer experiments. Although there are no special prerequisites and the course is essentially selfcontained, most students have some experience in abstract mathematics and problem solving and are interested in learning proofs. A Computational Laboratory (Math 476, 1 credit) will usually be offered as an optional supplement to this course. Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity, and quadratic fields. Math 575 moves much faster, covers more material, and requires more difficult exercises. There is some overlap with Math 412 which stresses the algebraic content. Math 475 may be followed by Math 575 and is good preparation for Math 412. All of the advanced number theory courses, Math 675, 676, 677, 678, and 679, presuppose the material of Math 575, although a good student may get by with Math 475. Each of these is devoted to a special subarea of number theory.
MATH 476. Computational Laboratory in Number Theory.
Section 001.
Instructor(s):
Prerequisites & Distribution: Prior or concurrent enrollment in MATH 475 or 575. (1). (Excl). (BS). May not be repeated for credit.
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 numbertheoretic purposes, e.g., for factoring. No exams.
MATH 485. Mathematics for Elementary School Teachers and Supervisors.
Section 001.
Instructor(s):
Prerequisites & Distribution: One year of high school algebra. No credit granted to those who have completed or are enrolled in MATH 385. (3). (Excl). (BS). May not be included in a concentration plan in mathematics. May not be repeated for credit.
Credits: (3).
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.
MATH 486. Concepts Basic to Secondary Mathematics.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 215, 255, or 285. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 489. Mathematics for Elementary and Middle School Teachers.
Instructor(s):
Prerequisites & Distribution: MATH 385 or 485. May not be used in any graduate program in mathematics. (3). (Excl). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
This course, together with its predecessor Math 385, 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. Enrollment is limited to 30 students per section. Although only two years of high school mathematics are required, a more complete background including precalculus or calculus is desirable. Topics covered include fractions and rational numbers, decimals and real numbers, probability and statistics, geometric figures, and measurement. Algebraic techniques and problemsolving strategies are used throughout the course.
MATH 490. Introduction to Topology.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 412 or 451 or equivalent experience with abstract mathematics. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
This course in an introduction to both pointset and algebraic topology. Although much of the presentation is theoretical and prooforiented, the material is wellsuited 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 pointset topology, examples of topological spaces, orientable and nonorientable 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.
Section 001 – Polynomial Equations.
Instructor(s):
Prerequisites & Distribution: Senior mathematics concentrators and Master Degree students in mathematical disciplines. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
In this course we will discuss Grobner Bases. These bases can be used to solve systems of polynomial equations. Some applications are in algebraic geometry, robotics, and automated theorem proving in geometry. There will be a weekly lab where students can familiarize themselves with computer algebra systems such as MAPLE.
MATH 501. Applied & Interdisciplinary Mathematics Student Seminar.
Section 001.
Instructor(s):
Prerequisites & Distribution: At least two 300 or above level math courses, and graduate standing; Qualified undergraduates with permission of instructor only. (1). (Excl). (BS). Offered mandatory credit/no credit. May be repeated for a maximum of 6 credits.
Credits: (1).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 512. Algebraic Structures.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 451 or 513. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 513. Introduction to Linear Algebra.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 412. Two credits granted to those who have completed MATH 214, 217, 417, or 419. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 521. Life Contingencies II.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 520. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 523. Risk Theory.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 425. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 525 / STATS 525. Probability Theory.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 450 or 451. Students with credit for MATH 425/STATS 425 can elect MATH 525/STATS 525 for only one credit. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 526 / STATS 526. Discrete State Stochastic Processes.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 525 or EECS 501. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 555. Introduction to Functions of a Complex Variable with Applications.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 450 or 451. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 557. Methods of Applied Mathematics II.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 217, 419, or 513; 451 and 555. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 558. Ordinary Differential Equations.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 450 or 451. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 561 / IOE 510 / SMS 518. Linear Programming I.
Section 001.
Instructor(s): Amy Ellen Mainville Cohn
Prerequisites & Distribution: MATH 217, 417, or 419. (3). (Excl). (BS). CAEN lab access fee required for nonEngineering students. May not be repeated for credit.
Credits: (3).
Lab Fee: CAEN lab access fee required for nonEngineering students.
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 566. Combinatorial Theory.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 216, 256, 286, or 316. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 567. Introduction to Coding Theory.
Section 001.
Instructor(s):
Prerequisites & Distribution: One of MATH 217, 419, 513. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 571. Numerical Methods for Scientific Computing I.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 217, 417, 419, or 513; and one of MATH 450, 451, or 454. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 572. Numerical Methods for Scientific Computing II.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 217, 417, 419, or 513; and one of MATH 450, 451, or 454. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 582. Introduction to Set Theory.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 412 or 451 or equivalent experience with abstract mathematics. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 592. Introduction to Algebraic Topology.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 591. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 594. Algebra II.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 593. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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MATH 597. Analysis II.
Section 001.
Instructor(s):
Prerequisites & Distribution: MATH 451 and 513. (3). (Excl). (BS). May not be repeated for credit.
Credits: (3).
Course Homepage: No homepage submitted.
No Description Provided. Contact the Department.
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