S P R I N G 2 0 1 3 - USS at Tufts - Tufts University

Course ListingsFall 2012MathematicsMATH0039HONORS CALCULUS I-II(Formerly MATH 17). The first course of the two-semester sequence ofhonors calculus. Intended for students who have had at least the ABsyllabus of advanced placement mathematics in secondary school.Stresses the theoretical aspects of the subject, including proofs ofbasic results. Topics include: convergence of sequences and series;continuous functions, Intermediate Value and Extreme ValueTheorems; definition of the derivative, formal differentiation, findingextrema, curve-sketching, Mean Value Theorems; basic theory of theRiemann integral, Fundamental Theorem of Calculus and formalintegration, improper integrals; Taylor series, power series and analyticfunctions.Prerequisites: AB syllabus of advanced placement mathematics.Students who receive credit for MATH 39 (formerly MATH 17) cannotreceive credit for MATH 30, 32, or 34 (formerly MATH 5, 11, or 12).Upon successful completion of MATH 39, all students receive twocredits: one course credit (with grade) and one mathematicsacceleration credit (without grade). At that time any AP or foreigndiploma credit equivalent to MATH 32 (formerly MATH 11) will bereplaced by this mathematics acceleration credit. A student who hastaken MATH 30 or 32 (formerly MATH 5 or 11), or has a transfer creditequivalent to one of these, will receive only one course credit uponcompletion of MATH 39. A student who has taken MATH 34 (formerlyMATH 12), or has a transfer credit equivalent to MATH 34 (formerlyMATH 12), will not be allowed to take MATH 39 for credit.Sections03472 MATH003901 E+ Nitecki, Zbigni 1.0 10 Cap SpacesForAdvisees;highSchool ApCourseMATH0042CALCULUS III(Formerly MATH 13). Vectors in two and three dimensions,applications of the derivative of vector-valued functions of a singlevariable. Functions of several variables, continuity, partial derivatives,the gradient, directional derivatives. Multiple integrals and theirapplications. Line integrals, Green's theorem and related results.Prerequisites: MATH 34 OR 39 (Formerly MATH 12 or 17).Sections034660346703468034690347003471MATH004201 C Gutierrez, Maur 1.0 Math 34 Or 39(formerly 12 Or17) All SectionsMATH004202 C Nitecki, Zbigni 1.0MATH004203 D Hao, Ning 1.0MATH004204 E Christensen, Je 1.0MATH004205 F Teixidor I Biga 1.0MATH004206 H Tu, Loring W 1.0MATH0051DIFFERENTIAL EQUATIONS(Formerly MATH 38). An introduction to linear differential equationswith constant coefficients, linear algebra, and Laplace transforms.Prerequisites: MATH 42 or 44 (formerly MATH 13 or 18).Sections034750347603477MATH005101 B Hasselblatt, Bo 1.0 Math 42 Or 44(formerly 13 Or18) All SectionsMATH005102 C Adler, James 1.0MATH005103 D Barthelme, Thom 1.0MATH0061DISCRETE MATHEMATICS(Formerly MATH 22). (Cross-listed as COMP 61.) Sets, relations andfunctions, logic and methods of proof, combinatorics, graphs anddigraphs.Prerequisites: MATH 32 (formely MATH 11) or COMP 11 or permissionof instructor.Sections03473 MATH006101 H Mcninch, George 1.0 Math 32 (old11) Or Comp 11Or Consent;C-lst Comp 61Tufts University Course Listings, Fall 201203474MATH006102 E+MW Cowen, Lenore J 1.0 C-list Comp61-02MATH0063NUMBER THEORY(Formerly math 41). An introduction to number theory, including theEuclidean algorithm, congruences, primitive roots, and the law ofquadratic reciprocity.Prerequisites: MATH 32 (formerly MATH 11) or permission ofinstructor.Sections03741 MATH006301 K+ Martin, Alberto 1.0 Math32(formerlyMath 11) OrConsentMATH0070LINEAR ALGEBRA(Formerly MATH 46). An introduction to the theory of vector spacesand linear transformations over the real or complex numbers, includinglinear independence, dimension, matrix multiplication, similarity andchange of basis, and some applications. Topics such as eigenvaluesand eigenvectors, the Cayley-Hamilton theorem, and inner productspaces may be included.Prerequisites: MATH 34 or 39 (formerly MATH 12 or 17) or permissionof instructor. Students may count only one of MATH 70 (formerlyMATH 46) and MATH 72 (formerly MATH 54) for credit.Sections03478 MATH007001 D+ Glaser, Mary E 1.0 Math 34 Or39(former 12 Or17)/consent;allSections03479 MATH007002 G+ Martin, Alberto 1.003742 MATH007003 G+ Mcgrath, Joseph 1.0MATH0072ABSTRACT LINEAR ALGEBRA(Formerly MATH 54). An introduction to the theory of linear algebrastarting with vector spaces. Subspaces, bases, dimension. Lineartransformations, invariant subspaces, eigenvalues, eigenspaces, anddiagonalizing linear operators. Inner product spaces and orthogonalprojections. The emphasis will, in general, be on proofs rather thancomputation. Additional topics may include normal forms, minimalpolynomials, determinant of an operator, normal operators overcomplex vector spaces as well as applications of linear algebra.Prerequisites: MATH 34 or 39 (formerly MATH 12 or 17) or permissionof instructor. Students may count only one of MATH 70 (formerlyMATH 46) and MATH 72 (formerly MATH 54) for credit.Sections03481 MATH007201 G+ Walsh, Geneviev 1.0 Math 34 Or 39(formerly Math12 Or 17) OrConsentMATH0087MATHEMATICAL MODELINGA survey of major techniques in the use of mathematics to modelphysical, biological, economic, and other systems; topics may includederivative-based optimization and sensitivity analysis, linearprogramming, graph algorithms, probabilistic modeling, Monte-Carlomethods, difference equations, and statistical data fitting. This courseincludes an introduction to computing using a high-level programminglanguage, and studies the transformation of mathematical objects intocomputational algorithms.Prerequisites: MATH 34 (formerly MATH 12), MATH 36 or MATH 39(formerly MATH 17), or consent.Sections03743 MATH008701 H+ Maclachlan, Sco 1.0 Math34(old12),math36(old50-01)orMath39(old17);or PermPage 118