Course ListingsFall 2012M<strong>at</strong>hem<strong>at</strong>icsMATH0112HISTORY OF MATHEMATICSThe evolution of m<strong>at</strong>hem<strong>at</strong>ical concepts and techniques from antiquityto modern times.Prerequisites: MATH 34 or 39 (formerly MATH 12 or 17) or permissionof instructor.Sections03744 MATH011201 I+ Duchin, Moon 1.0 M<strong>at</strong>h 34 Or 39(formerly M<strong>at</strong>h12 Or 17) OrConsentMATH0126NUMERICAL ANALYSIS(Cross-listed as COMP 126.) Analysis of algorithms involvingcomput<strong>at</strong>ion with real numbers. Interpol<strong>at</strong>ion, methods for solving linearand nonlinear systems of equ<strong>at</strong>ions, numerical integr<strong>at</strong>ion, numericalmethods for solving ordinary differential equ<strong>at</strong>ions.Prerequisites: MATH 51 (formerly MATH 38) and programming abilityin a language such as C, C++, Fortran, or M<strong>at</strong>lab.Sections02374 MATH012601 E+WF Adler, James 1.0 M<strong>at</strong>h 51(formerly 38) &Programming;C-lst Comp 126MATH0135REAL ANALYSIS IAn introduction to analysis. Metric spaces (with Euclidean spaces asthe primary example), compactness, connectedness, continuity anduniform continuity, uniform convergence, the space of continuousfunctions on a compact set, contraction mapping lemma withapplic<strong>at</strong>ions.Prerequisites: MATH 42 or 44 (formerly MATH 13 or 18), and MATH 70or 72 (formerly MATH 46 or 54); MATH 72 (formerly MATH 54)recommended, or permission of instructor.Sections02375 MATH013501 F Tu, Loring W 1.0 M<strong>at</strong>h 42 Or44(old 13 Or18)& 70 Or72(old 46 Or54)02376 MATH013502 G+ Gonzalez, Fulto 1.0 M<strong>at</strong>h 42 Or 44(old 13 Or 18)&70 Or 72(old 46Or 54)MATH0145ABSTRACT ALGEBRA IAn introduction to the basic concepts of abstract algebra, includinggroups and rings.Prerequisites: MATH 70 or 72 (formerly MATH 46 or 54); MATH 72(formerly MATH 54) recommended.Sections02377 MATH014501 D+ Teixidor I Biga 1.0 M<strong>at</strong>h 70 Or 72(old 46 Or 54);72 (old 54)RecommendedMATH0150ADVANCED SPECIAL TOPICSContent and prerequisites vary from semester to semester. Topicscovered in recent years have included m<strong>at</strong>hem<strong>at</strong>ical neuroscience, Liealgebras, and nonlinear dynamics and chaos.Please see departmental website for specific details:http://m<strong>at</strong>h.tufts.eduSectionsMATH BHND MATH YOU TEACH04157 MATH015001 ARR Quinto, Eric To 1.0 Ed Dept GradStudents,Teachers, M<strong>at</strong>StudentsTOMOGRAPHY04379 MATH015002 ARR Quinto, Eric To 1.0MATH0151APPL OF ADVANCED CALCThe solutions of certain boundary-value problems in m<strong>at</strong>hem<strong>at</strong>icalphysics, including the following topics: inner-product spaces, functionspaces, orthogonaliz<strong>at</strong>ion, Fourier series, orthogonal families ofpolynomials, Sturm-Liouville problems, separ<strong>at</strong>ion of variables in partialdifferential equ<strong>at</strong>ions, applic<strong>at</strong>ions.Prerequisites: MATH 51 (formerly MATH 38). ME 150 may besubstituted for MATH 151 and in no case may both courses be takenfor credit.Sections02381 MATH015101 J+ Borgers, Christ 1.0 M<strong>at</strong>h 51(formerly 38);Also Offered AsMe 150MATH0161PROBABILITYProbability, conditional probability, random variables and distributions,expect<strong>at</strong>ion, special distributions, joint distributions, laws of largenumbers, and the central limit theorem.Prerequisites: MATH 42 or 44 (formerly MATH 13 or 18), or permissionof instructor.Sections02382 MATH016101 F+ Kobayashi, Kei 1.0 M<strong>at</strong>h 42 Or 44(formerly M<strong>at</strong>h13 Or 18), OrConsentMATH0193SPECIAL TOPICSGuided individual study of an approved topic. Credit as arranged.Prerequisites: Permission of instructor.SectionsMULTIGRID ON SPHERES04376 MATH019301 ARR Borgers, Christ 1.0GAMMA RHYTHMS04377 MATH019302 ARR Borgers, Christ 1.0NMRCL MTHDS FISHERS EQ04378 MATH019303 ARR Borgers, Christ 1.0RUNAWAY NEURONAL FIRING04395 MATH019304 Borgers, Christ 1.0MATH0195SENIOR HONORS THESISThesis course for thesis honors candid<strong>at</strong>es; see Thesis HonorsProgram for details. Open to seniors. Normally two credits.Prerequisites: Permission of instructor.Sections02385MATH019501 ARR Staff 1.0 Permission OfInstructorMATH0211ANALYSISAn introduction to modern analysis in abstract spaces, includingpoint-set topology and measure and integr<strong>at</strong>ion. Topological spaces,compactness, completeness, Baire c<strong>at</strong>egory, function spaces,measures, integr<strong>at</strong>ion, convergence theorems, Fubini theorem,Radon-Nikodym theorem, Riesz represent<strong>at</strong>ion theorem, Banach andHilbert spaces.Prerequisites: MATH 135 and 136 or equivalent, or permission ofinstructor.Sections02388 MATH021101 M+ Gonzalez, Fulto 1.0 M<strong>at</strong>h 135 & 136Or Equiv OrConsent<strong>Tufts</strong> <strong>University</strong> Course Listings, Fall 2012Page 119
Course ListingsFall 2012M<strong>at</strong>hem<strong>at</strong>icsMATH0215ALGEBRAGeneral properties of groups, rings, especially polynomial rings,modules over a principal ideal ring, field extensions and Galois theory.This m<strong>at</strong>erial may require more than one semester.Prerequisites: MATH 145 or equivalent, or permission of instructor.Sections02389MATH021501 D+ Mcninch, George 1.0 M<strong>at</strong>h 145 OrEquiv OrConsentMATH0218TOPICS:GEOMETRY&TOPOLOGYTopics in geometry and topology selected by the instructor. Topicschange from year to year, and the course may be taken more thanonce for credit. In recent years, these have altern<strong>at</strong>ed among algebraictopology, differential geometry, and Lie groups.Prerequisites: Normally MATH 217; for algebraic topology: MATH 135and 145; or permission of instructor.SectionsALGEBRAIC TOPOLOGY02391 MATH021801 H+ Ruane, Kim 1.0 M<strong>at</strong>h 135 &145, OrConsentMATH0250GRADUATE SPECIAL TOPICS:Please see departmental website for specific details:http://m<strong>at</strong>h.tufts.eduSectionsHYPERBOLIC GEOMETRY02392 MATH025001 E+MW Walsh, Geneviev 1.0 Grad StandingOr Consent;Grad Alg TopolPreferredMEASURE THEO PROBABILITY02393 MATH025002 F+TR Hahn, Marjorie 1.0 M<strong>at</strong>h 211LINEAR PARTIAL DIFF EQNS03745 MATH025003 J+ Maclachlan, Sco 1.0 M<strong>at</strong>h 135 OrPermission OfInstructorSEM:COMPUTNL&APPLD MATHM04234 MATH025004 ARR Adler, James 1.0MORSE THEORY04375 MATH025005 ARR Walsh, Geneviev 1.0MATH0293SPECIAL TOPICSGuided individual study of an approved topic. Credit as arranged.Prerequisites: Permission of instructor.SectionsSPACE-TIME MULTIGRID04086 MATH029301 ARR Maclachlan, Sco 1.0NON LINEAR FINITE ELEMEN04235 MATH029302 ARR 1.0ADV. APPLIED MATH04300 MATH029303 ARR Adler, James 1.0CUBED STRTURS&COMMNSRBTY04387 MATH029304 ARR Walsh, Geneviev 1.0RECENT DYNAMICS04397 MATH029305 ARR Hasselbl<strong>at</strong>t, Bo 1.0MATH0295THESISGuided research on a topic th<strong>at</strong> has been approved as suitable for amaster's thesis. Credit as arranged.Prerequisites: Permission of instructor.Sections02404MATH029501 ARR Staff 1.0 Permission OfInstructorMATH0296THESISGuided research on a topic th<strong>at</strong> has been approved as suitable for amaster's thesis. Credit as arranged.Prerequisites: Permission of instructor.Sections02405MATH029601 ARR Staff 1.0 Permission OfInstructorMATH0297GRADUATE RESEARCHGuided research on a topic suitable for a doctoral dissert<strong>at</strong>ion. Credit asarranged.Prerequisites: Permission of instructor.Sections02406MATH029701 ARR Staff 1.0 Permission OfInstructorMATH0298GRADUATE RESEARCHGuided research on a topic suitable for a doctoral dissert<strong>at</strong>ion. Credit asarranged.Prerequisites: Permission of instructor.Sections02407MATH029801 ARR Staff 1.0 Permission OfInstructorMATH0401MASTERS DEGREE CONT P/TSections02409MATH0401PT ARR Staff 0.0MATH0402MASTERS DEGREE CONT F/TSections02410MATH0402FT ARR Staff 0.0MATH0501DOCTORAL CONTIN P/TSections02413MATH0501PT ARR Staff 0.0MATH0502DOCTORAL CONTIN F/TSections02414MATH0502FT ARR Staff 0.0<strong>Tufts</strong> <strong>University</strong> Course Listings, Fall 2012Page 120