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Higher-Level Mathematics Courses for Spring 2012
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Math 2142Q (244Q) - Spring 2012
Description
Description: A rigorous treatment of the mathematics underlying the main results of one-variable calculus. Intended for students with strong interest and ability in mathematics who are already familiar with the computational aspects of basic calculus. (May be taken for honors credit but open to any qualified student.)
Prerequisites: A year of calculus (that may include high school) and instructor consent. MATH 2141Q(243Q) may be used in place of MATH 1131(115) or 1151(135) to fulfill any requirement satisfied by MATH 1131(115) or 1151(135). MATH 2142Q(244Q) may be used in place of MATH 1132(116) or 1152(136) to fulfill any requirement satisfied by MATH 1132(116) or 1152(136).
Offered: Spring
Credits: 4
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Sections: Spring 2012 in Storrs Campus
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Math 2144Q (246Q) - Spring 2012
Description
Description: A rigorous treatment of more advanced topics, including vector spaces and their application to multivariable calculus and first-order, second-order and systems of differential equations. (May be taken for honors credit but open to any qualified student.)
Prerequisites: MATH 2143(245) or consent of the instructor. MATH 2144(246) may be used in place of MATH 2410(211) to fulfill any requirement satisfied by MATH 2410(211).
Offered: Spring
Credits: 4
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Sections: Spring 2012 in Storrs Campus
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Math 2144Q (246Q) - Spring 2012
Description
Description: A rigorous treatment of more advanced topics, including vector spaces and their application to multivariable calculus and first-order, second-order and systems of differential equations. (May be taken for honors credit but open to any qualified student.)
Prerequisites: MATH 2143(245) or consent of the instructor. MATH 2144(246) may be used in place of MATH 2410(211) to fulfill any requirement satisfied by MATH 2410(211).
Offered: Spring
Credits: 4
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Sections: Spring 2012 in Storrs Campus
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Math 2210Q (227Q) - Spring 2012
Description
Description: Systems of equations, matrices, determinants, linear transformations on vector spaces, characteristic values and vectors, from a computational point of view. The course is an introduction to the techniques of linear algebra with elementary applications.
Prerequisites: MATH 1132(116), 1152(121 or 136), or 2142(244). Recommended Preparation: a grade of C- or better in MATH 1132(116). Not open for credit to students who have passed MATH 3210(215).
Offered: Either semester
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 2360Q (223Q) - Spring 2012
Description
Description: A fresh look at geometry, old and new. Euclidean and non-Euclidean geometries are examined from from different perspectives. Topics may include symmetries, the role of the parallel postulate and some topics from 19th and 20th century geometry, e.g. fractals and knots.
Prerequisites: MATH 1121(113), 1126, or 1131(115).
Offered: Either semester
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 2410Q (211Q) - Spring 2012
Description
Description: Introduction to ordinary differential equations and their applications, linear differential equations, systems of first order linear equations, numerical methods.
Prerequisites: MATH 1132(116), or 121. Recommended preparation: a grade of C- or better in MATH 1132(116); and MATH 2110(210) or 220. Not open for credit to students who have passed MATH 2420(221). Open to sophomores or higher.
Offered: Either semester
Credits: 3
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Sections: Spring 2012 in Storrs Campus
| 2410Q |
001 |
Lecture |
TuTh 12:30:00 PM-1:45:00 PM |
MSB215 |
Huber, Greg |
| 2410Q |
002 |
Lecture |
MWF 9:00:00 AM-9:50:00 AM |
MSB319 |
Martin, Richard |
| 2410Q |
003 |
Lecture |
TuTh 2:00:00 PM-3:15:00 PM |
MSB215 |
Canakci, Ilke |
| 2410Q |
004 |
Lecture |
MWF 2:00:00 PM-2:50:00 PM |
MSB311 |
Martin, Richard |
| 2410Q |
005 |
Lecture |
TuTh 8:00:00 AM-9:15:00 AM |
MSB415 |
Lee, Kyu-Hwan |
| 2410Q |
010 |
Lecture |
MW 3:00:00 PM-3:50:00 PM |
TLS154 |
McKenna, Patrick |
| 2410Q |
011D |
Discussion |
F 3:00:00 PM-3:50:00 PM |
MSB303 |
Huan, Tingting |
| 2410Q |
012D |
Discussion |
F 3:00:00 PM-3:50:00 PM |
MSB211 |
Xhumari, Sandi |
| 2410Q |
013D |
Discussion |
F 2:00:00 PM-2:50:00 PM |
MSB211 |
Xhumari, Sandi |
| 2410Q |
014D |
Discussion |
Tu 4:00:00 PM-4:50:00 PM |
MSB411 |
Huan, Tingting |
| 2410Q |
015D |
Discussion |
Th 4:00:00 PM-4:50:00 PM |
ARJ409 |
Lu, Lu |
| 2410Q |
017D |
Discussion |
F 9:00:00 AM-9:50:00 AM |
TLS79 |
Xhumari, Sandi |
| 2410Q |
018D |
Discussion |
Tu 5:00:00 PM-5:50:00 PM |
ITE127 |
Lu, Lu |
| 2410Q |
019D |
Discussion |
Tu 8:00:00 AM-8:50:00 AM |
MSB403 |
Huan, Tingting |
| 2410Q |
030 |
Lecture |
MW 12:00:00 PM-12:50:00 PM |
TLS154 |
McKenna, Patrick |
| 2410Q |
031D |
Discussion |
F 12:00:00 PM-12:50:00 PM |
MSB315 |
Xhumari, Sandi |
| 2410Q |
032D |
Discussion |
F 12:00:00 PM-12:50:00 PM |
CHMT113 |
Huan, Tingting |
| 2410Q |
033D |
Discussion |
F 8:00:00 AM-8:50:00 AM |
MSB219 |
Lu, Lu |
| 2410Q |
034D |
Discussion |
F 1:00:00 PM-1:50:00 PM |
MSB219 |
Lu, Lu |
| 2410Q |
035D |
Discussion |
Tu 4:00:00 PM-4:50:00 PM |
ITE127 |
Lu, Lu |
| 2410Q |
036D |
Discussion |
Th 4:00:00 PM-4:50:00 PM |
CHMT114 |
Xhumari, Sandi |
| 2410Q |
037D |
Discussion |
Tu 8:00:00 AM-8:50:00 AM |
ARJ241 |
Xhumari, Sandi |
| 2410Q |
039D |
Discussion |
Tu 9:00:00 AM-9:50:00 AM |
CHMT212 |
Huan, Tingting |
| 2410Q |
040D |
Discussion |
Th 9:00:00 AM-9:50:00 AM |
CB301 |
Huan, Tingting |
| 2410Q |
041D |
Discussion |
F 12:00:00 PM-12:50:00 PM |
CHMT212 |
Lu, Lu |
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Math 2710 (213) - Spring 2012
Description
Description: A course designed to prepare the serious student for the more theoretical upper division mathematics courses. It includes basic concepts, principles and techniques of mathematical proof. It will also cover concepts commonly assumed in some of the higher mathematics courses; these concepts include sets, set operations, indexed family of sets, equivalence relations and partitions, functions, one-to-one functions, onto functions, induced set functions,... This is a required course for most mathematics majors.
Prerequisites: MATH 2110(210) or 220 or consent of instructor.
Offered: Either semester
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 2720W (242W) - Spring 2012
Description
Description: A historical study of the growth of the various fields of mathematics.
Prerequisites: (i) MATH 2110Q(210Q) or 2130Q(230Q), and 2210 (227Q) or 2410Q(211Q), or (ii) MATH 2144Q(246Q) or 2420(221Q); and ENGL 1010 or 1011 or 3800. This course may not be counted in any of the major groups described in the Mathematics Department listing.
Offered: Either semester
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 2784 (200) - Spring 2012
Description
Description: The student will attend talks during the semester, and choose a mathematical topic from one of them to investigate in detail. The student will write a well-revised, comprehensive paper on this topic, including a literature review, description of technical details, and a summary and discussion.
Prerequisites: Either MATH 2110, 2130, or 2143; MATH 2410, 2420 or 2144; ENGL 1010 or 1011 or 3800.
Offered: Either semester
Credits: 2
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Sections: Spring 2012 in Storrs Campus
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Math 2794W (201W) - Spring 2012
Description
Description: The student will attend talks during the semester, and choose a mathematical topic from one of them to investigate in detail. The student will write a well-revised, comprehensive paper on this topic, including a literature review, description of technical details, and a summary and discussion, building upong the writing experience in MATH 2784.
Prerequisites: MATH 2784(200); ENGL 1010 or 1011 or 3800.
Offered: Either semester
Credits: 2
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Sections: Spring 2012 in Storrs Campus
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Math 3146 (252) - Spring 2012
Description
Description: Functions of a complex variable, integration in the complex plane, conformal mappings.
Prerequisites: MATH 2110(210) and 2410(211), or 2144 or 2420(221). Not open for credit to students who have passed MATH 5046(352).
Offered: Either semester
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3150 (273) - Spring 2012
Description
Description: Introduction to the theory of functions of one and several real variables.
Prerequisites: MATH 2142(244), a grade of C or better in 2710(213), or 214; MATH 2410(211) or 2420(221).
Offered: Either semester
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3151 (274) - Spring 2012
Description
Description: This is the second semester of a year long transitional course in analysis. The subject is the theory of functions of several variables. As in Math 3150(273), the emphasis is on understanding, constructing and writing mathematical proofs. Topics include: rigorous treatment of fundamental concepts in calculus, including limits and convergence of sequences and series, continuity and differentiability of functions in a Euclidean space.
Prerequisites: MATH 3150.
Offered: Spring
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3160 (231) - Spring 2012
Description
Description: Introduction to the theory of probability. Discussion of some of the probability problems encountered in scientific and business fields.
Prerequisites: MATH 2110(210) or 220, which may be taken concurrently with the consent of the instructor. Not open if passed MATH 3610(283) or 3660(284).
Offered: Either semester
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3170 (232) - Spring 2012
Description
Description: A sequel to Math 3160(231). The course covers conditional probability and conditional expectation, Markov Chains in discrete time and continuous time, renewal theory, the Poisson process, and the Brownian Motion process.
Prerequisites: STAT 3025 or 3345 or 3375 or MATH 3160(231).
Offered: Spring
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3210 (215) - Spring 2012
Description
Description: Linear algebra is one of the most productive branches of mathematics. Almost no science can survive without a serious use of linear algebra. Moreover, ideas throughout higher mathematics are often at some point related to "simple" linear algebra manipulations. The key idea is "linearization," which deals with the attempt at describing the information one wants to study in terms of linear algebra objects (vector spaces, operators, etc). We will try to understand such notions and make use of them in studying problems which at first glance may not seem to be "linear". Examples we will look at include explicit formulas for the famous Fibonacci and Lucas numbers, polynomial interpolation, factoring integers, solving difference and differential equations, and Hurwitz's celebrated 1,2,4,8 theorem.
Prerequisites: MATH 2210(227) and either MATH 2142(244), a grade of C or better in 2710(213), or 214.
Offered: Spring
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3231 (217) - Spring 2012
Description
Description: The main goal of this course is to discuss Galois theory, which is the study of relationships among roots of polynomials. For example, we will use Galois theory to prove that there is no formula analogous to the quadratic formula for the roots of xn - x - 1 when n is at least 5, or in fact for the roots of most polynomials of degree at least 5. More generally, Galois theory provides a correspondence between two different topics in algebra: fields and groups. Our study of fields will use linear algbera in interesting ways. For example, we will see how to show certain polynomials are irreducible using the concept of dimension. Only towards the end of the course will group theory be needed in a serious way, at which point what we need from group theory will be reviewed.
Prerequisites: Math 3230(216).
Offered: Spring (odd years)
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3240 (258) - Spring 2012
Description
Description: Number theory is the study of the integers, but this description hardly conveys the beauty of this part of mathematics. One of the main goals of this course is pedagogical: to see that mathematics is a vibrant intellectual activity and not a set of fixed rules developed by some higher authority. This viewpoint is especially useful for future teachers. Students will carry out many numerical experiments, generate conjectures based on patterns observed, and then prove or disprove these conjectures.
The content focuses on those parts of classical number theory which still have modern relevance in the subject: the Euclidean algorithm, modular arithmetic, distribution of primes, diophantine equations, applications to cryptography, arithmetic in quadratic rings and polynomial rings, and quadratic reciprocity. The examples in this course will provide a lot of food for thought for anyone who later takes abstract algebra.
Prerequisites: MATH 2142(244), a grade of C or better in 2710(213), or 214.
Offered: Fall
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3250 (251) - Spring 2012
Description
Description: Combinatorics concerns itself with problems involving discrete structures, generally on finite or countably infinite sets. Often we want to count the number of ways something can be done: arranging 5 books on a shelf, partitioning a sports club into 5 disjoint teams, or dividing a polygon into triangles using diagonals which only intersect at a vertex. Sometimes we consider the relationships among such objects, and the discrete structures involved, yielding graphs (imagine an airline route map that connects some pairs of cities, but not all) or partially ordered sets. In all of these we look for elegant ways of understanding and proving our answers are correct, avoiding simpleminded brute-force computations. This course will give an overview of combinatorial techniques and applications. We will count things using basic principles of arithmetic, using infinite series, and using bijections that help us translate objects we want to count into a different form that is easier to count. We will see surprisingly deep applications of the obvious Pigeonhole Principle. This course is an excellent way for students to strengthen their proof writing in contexts which are more easily accessible and concrete than many other areas of mathematics. These ideas come up frequently in other areas of mathematics in computer science, and in parts of chemistry and biology.
Prerequisites: MATH 2142(244) or a grade of C or better in 2710(213).
Offered: TBA
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3330 (250) - Spring 2012
Description
Description: Topology is the study of properties of shape that persists under "nice" continuous perturbations---stretching, shrinking and twisting, the description given by the author of the textbook. A disk and a triangle, for instance, are regarded as the same shape in topology. This presents a stark contrast to another field in the study of shape, namely, geometry. Geometry, in general, studies the properties of shape that are more "visually" rigid and distinguishable, such as length, angle, area etc. These quantities are somewhat more familiar to most of us, whereas the criteria used in topology demand a certain degree of trained awareness and effort. This course begins with a brief introduction to the tools for the study. The first application is to see how many distinct closed surfaces exist in this world under the eyes of topologists. We will introduce a topological invariant called "Euler characteristic", which assigns an integer to an individual surface. Surprisingly, the Euler characteristic alone completely determines the topological shape of surfaces in spite of all those possible "geometric-shape-deforming" continuous perturbations. This process, which is called the "classification of closed compact surfaces", epitomizes one nature of topology, namely, simplicity. By the way, do you now see how many distinct compact closed surfaces exist from the topological point of view? When time allows, we will introduce more "topological invariants" such as fundamental groups, homology etc for the study of graphs, simplicial complex, knots etc. These concepts have major applications to computer science, biology and other fields. As the final remark, we will try to visit as many websites, some of which are suggested in the textbook, to enjoy the visual aspects of topology during the course.
Prerequisites: MATH 2142(244), a grade of C or better in 2710(213), or 214.
Offered: Spring (even years)
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3410 (272) - Spring 2012
Description
Description: Series solutions of differential equations, Bessel functions, Fourier series, partial differential equations and boundary value problems, nonlinear differential equations.
Prerequisites: MATH 2110(210) and 2410(211), or 2420(221). Not open for credit to students who have passed MATH 3412(279).
Offered: Either semester
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3511 (282) - Spring 2012
Description
Description: This is a second introductory course to modern numerical techniques, i.e., a sequel to Mathematics 3510(281). It starts with a survey of modern approximation techniques and explains how, why, and when the techniques can be expected to work. Using this background the course covers difference equations, numerical methods for the solution of ordinary and partial differential equations, eigenvalue computations. The course demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. The exercise sets include many applied problems from diverse areas of engineering, as well as from the physical, computer, biological, and social sciences.
Prerequisites: MATH 3510(281).
Offered: Spring
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3610 (283) - Spring 2012
Description
Description: Problems in calculus and probability designed to help students prepare for the first actuarial examination.
Prerequisites: MATH 2110(210) and 3160(231).
Offered: Either semester
Credits: 1
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Sections: Spring 2012 in Storrs Campus
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Math 3615 (280) - Spring 2012
Description
Description: Preparation for the financial mathematics actuarial examinaton, which tests a student's knowledge of the theory of interest and financial economies at an introductory level.
Prerequisites: MATH 2620(285).
Offered: Either semester
Credits: 1
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Sections: Spring 2012 in Storrs Campus
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Math 3631 (288) - Spring 2012
Description
Description: A continuation of Actuarial Mathematics I. This course, along with MATH 3630, helps students prepare for the actuarial examination on models for quantifying risk.
Prerequisites: MATH 3630. Not open to students who have passed MATH 5631.
Offered: Spring
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3634 (276) - Spring 2012
Description
Description: Introduction to the design of computerized simulations for analyzing and interpreting actuarial and financial problems. This course, together with MATH 5637, 5640, and 5641 helps the student prepare for the actuarial examination on the construction and evaluation of risk models.
Prerequisites: MATH 3160(231) or STAT 3025Q(220Q) or 3375Q(230Q); and MATH 2620(285).
Offered: Spring
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3650 (289) - Spring 2012
Description
Description: The continuation of MATH 2620. Measurement of financial risk, the mathematics of capital budgeting, mathematical analysis of financial decisions and capital structure, and option pricing theory.
Prerequisites: MATH 2620(285). Also ACCT 2001, which may be taken concurrently.
Offered: Every Semester
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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Math 3670W (291W) - Spring 2012
Description
Description: Students will write a technical report on an advanced topic in actuarial science.
Prerequisites: ENGL 1010 or 1011 or 3800. Consent of Director of Actuarial Science is required.
Offered: Every Semester
Credits: 3
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Sections: Spring 2012 in Storrs Campus
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