The SPS Guide to

PHYSICS & Related Fields

2020-2021 Edition

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2020-2021Edition

TableofContentsIntroduction 2

TheSocietyofPhysicsStudents 3

WhyShouldIStudyPhysics? 4

WaystoStudyPhysicsatHarvard 6

PhysicsCourseStrategies 10

CourseDescriptionsandRecommendations 13FreshmanSeminars 14PhysicsDepartmentCourses 15MathematicsDepartmentCourses 27AstronomyDepartmentCourses 33OtherCoolStuff 34

ResearchatHarvard 40

Contacts 46

TheBackPage 48

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IntroductionThe Harvard-Radcliffe Society of Physics Students – SPS for short – hasproduced this booklet for students who are considering concentrating inphysics or a related field. Even if you’re not planning to become a physicsconcentrator,wehopeyou’llfindthisbooklethelpful. It canbehard todecideona field toconcentrate in. It’salsohard tochoosewhichcoursestotake,whetherthey’reinthephysicsdepartmentoroutsideofit.Wecan’thelpyouwithchoosinganExpositoryWritingclass,butwehopeourexperienceasphysicsconcentratorsatHarvardwillbeusefultoyou.Youcanusethisguideduringshoppingperiod,butyoumightwanttokeepitinadeskdrawerforfuturereference—itmightcomeinhandyoverthenextfewshopping periods. Take the guide out for a walk once in a while, it likesexercisetoo. Of course,when you’re choosing your concentration and classes, it’s a goodidea togetasmuch informationaspossible.Youcanobtainadvice from theinformationalmeetingsheld in the ScienceCenter a fewdaysbefore classesbegin, fromindividualmembersof thePhysicsDepartmentFaculty, fromtheHeadTutors,andfromupper-classstudentsbyemailingtheSPSlist.Youcanfind online resources atwww.physics.harvard.edu. In fact,we very stronglyencourageyoutogetadvicefromasmanysourcesasyoucan.(Ofcourse,sincenoonereadstheIntroduction,we’llstressthislaterontoo.) Every efforthasbeenmade to ensure the accuracy and completenessof theinformation in this booklet. Nevertheless, it may contain inadvertent errorsandomissions,soyoushouldbesuretoconsultthecourseinformationinthemy.harvard portal and the student handbook subsection Fields ofConcentrationbeforemakinganyfinaldecisions.

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TheSocietyofPhysicsStudentsOurnamesaysitall.TheHarvard-RadcliffeSocietyofPhysicsStudents(SPS)workstopromotetheinterestsofphysicsstudentsatHarvardandRadcliffe. SPS organizes many different kinds of activities throughout the year:academic, career-related, and just-for-fun events. To learn about researchgoing on in the various sub-fields of physics and related areas, be sure toattendtheMondaylunchesatnoonwiththevisitingcolloquiumspeakers(eatnice food, learn a lot) aswell as theWednesdayevening talkswithHarvardprofessorsaspartofPhysics95(allarewelcome;icecreamserved).Wealsohostanumberoftalksaboutgradschoolsandcareersforthosetrainedinthephysical sciences. Keep your eyes out for events such as movie nights, andliquidnitrogen fun.Don’tmissourannualnitrogen-frozenpumpkindroponHalloween. Fanciful ideas such as races across non-Newtonian cornstarchhavebeenproposed. TheSPSfunctionsasaliaisonbetweenthecommunityofphysicsstudentsandthePhysicsDepartment.Periodically, theofficersofSPSmeetwith the chairandundergradtutorsofthedepartmenttodiscussissuesofconcerntophysicsstudents.Wehopeallphysicsstudentswillbringideastothisprocess. Thephysicsundergraduatestudyservesasagreatplacetorelax,meetupwithother physics students, and get to know Undergraduate Coordinator (a.k.a.“undergradmom”)CarolDavis,whoseoffice is across thehall. Lookout forsweetsnacksandfreefood! AnotherimportantfunctionoftheSPSisinformingphysicsstudentsofeventsthatmaybeofinteresttothem.SPShasproducedthisbookletinanefforttoensure that new students are fully informed about the options available tothem.Thereisalsoanemaillist,sps-list@hcs(formajorSPSanddepartmentannouncements) as well as a more informal sps-open@hcs (for interestingevents,opportunities,classadvice,questionsfromstudents,andlinks).Ifyouwant to subscribe to the email list, you can visit our website,www.hcs.harvard.edu/~physics. Also, check out our Facebook group(www.facebook.com/groups/168759966574319)!

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WhyShouldIStudyPhysics?Goodquestion.Well,ifyouaskanyphysicistthisquestion,theywillprobablytellyouwithouthesitation: “It’s fun!”Of course,notallofusaredestined tobecomephysicsfaculty.Butevenifyou’renotsureifyouwanttobeaphysicspro–infact,evenifyou’renotsureyouwanttobeaphysicsconcentrator–wethinkyoushouldatleasttakeafewphysicsclasses.Giveusthechancetoconvinceyou. Ifyouwanttogointoanyscience,knowledgeofphysicsisavaluabletooltohave. Not to toot our own horn too much, but physics is the basis for allphenomena in the understandable universe. Having knowledge of theprinciplesbehindalltheothersciencesleadstoadeeperunderstandingandisawaytoavoidsillyerrors.Doyouwanttobethebiologistorinventorwhoseideas violate the conservation of energy? Probably not. A firm grounding inphysicscanonlyhelpyourworkinotherfields. Also,physicsisreallyfun. Even if you’re not sure if youwant to go into research at all, knowledge ofphysicscanhelpyouout.Ashasbecomemoreandmoreclear,thejobmarketof thenewmillenniumisunlikeanythingwe’veeverseenbefore.SociologistManuelCastells calls it an InformationAge,where the thriving centerof theeconomy isbasednotonlyontechnologybutontechnologyforcreatingevenmoretechnology.Desirablejobs–thekindthatpayoffHarvardtuitionbills–more and more demand rock-solid analytical skills and the ability tounderstandcomplex,difficultproblems.Aphysicseducationisallaboutthat. Aphysicseducationisalsofun. To put it a little bit more concretely, more and more physics students aretaking their undergraduate science degrees into the Big Three areas ofprofessional school: medicine, law, and business. Doctors now routinelyperformprocedures such as “positron emission tomography” and “magneticresonanceimaging.”Thestudyanddevelopmentofartificialjointsandorgansdemand cutting edge materials and biophysics knowledge. As debates overcloning and movie pirating have shown us, new sciences and technologieshavealsoledtoallsortsoflegalandsocialquandaries.Scientificallyeducatedlawyerswho can intelligentlywade through thesemorasses are becoming avaluable commodity. And as business and industry becomemore evermoretechnical,theexecutivewhocanactuallyunderstandtheircompany’sfunctionor product is becoming increasingly valuable. If you’re theWall Street type,hedge funds and investment banks are always looking for people with theanalyticalandmathematicalskillstodowhateveritistheydodownthere.Andtheyarewillingtopaythemlotsandlotsandlotsofmoney. The increasingly important roleof technology inoureveryday liveshasalsomade clear the need for quality science education in our schools, from

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elementary to high school. A teacher with a solid science background is alamentablyrarecreature,buttheyarealsoanimmenselyvaluableresourcetoa school and to society at large. If you have somephysics knowledge underyourbelt,schoolswillloveyou. Also,physicsisreallyfun. Basically, we’ve been saying the same thing in a bunch of ways: physicsdemands clear logical thinking and strongmath skills.Maybeyou’renot thekindofpersonwhoeatsGaussianintegralsforbreakfast,buttakingevenafewphysics classes will help you hone your analytical thinking and problemsolving.Asabonus,you’lllearnallabouttheuniversethatwelivein,whichitturns out is a lotwackier than it seems at first glance. If youwant to learnmoreaboutthecleverwaysphysicsappliestoeverydaylife,youmightthinkabout taking Physics 125. And if youwant to know all about the neat stuffgoing on in the forefront of physics, check out the Physics DepartmentColloquia (Mondayafternoons), or theWednesdayevening lecture series (inconjunctionwithPhysics95).Andpesteryourprofessors! Inconclusion,youshouldstudyphysics.It’sfun!

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WaystoStudyPhysicsatHarvardHarvardisaveryexcitingplace,butit’sabitconfusingforthefirstfewweeks.So much happens before you’ve really figured out where you are! You’veprobablycomewithalotofinterests,butyoumaynotbesurehowtopursuethemhere.TheSocietyofPhysicsStudents thoughtwecouldhelpyououtalittlebitasyougetacclimated,bygivingyousomeadviceonwhatyoucandowithyourinterestinthephysicalsciences. Thefirstthingtorealizeisthatyouhavemanyoptions.SomechoicesmustbemadebyNovemberofyoursophomoreyear,whenyouselectaconcentration.Youcouldconcentrateinphysics.Youmaywishtojointconcentrate.Youmayhave theoptionofadvancedstanding(inwhichcase thesedecisionsmaybeuponyouevenearlier).Oryoumighttakephysicsclassesforasecondaryfieldor as electives, with no thought of concentrating in physics at all. New anddifferentplansofstudyareconstantlybeinginvented,soyoushouldalsofeelfree to dream up just about anything and present it to Howard Georgi (theHeadTutor)orDavidMorin(theCo-HeadTutor).Chancesare they’veheardworse! (And after all this, you may very likely change your mind about thesedecisions.Noproblem—nothingiswritteninstone!) If you are considering concentrating in physics (or some variation on thattheme), this section describes the myriad options for concentration. Moredetails can be found in the Fields of Concentration section of the StudentHandbook. Or,youmaywishtojumpdirectlytothecoursedescriptions.

ThePhysicsConcentration Let’s start with the most straightforward case. You want to concentrate inphysics. (Yay!) For non-honors, you must take twelve semester courses inphysics or related fields. These twelve courses normally include theintroductorysequence(throughasemesterofquantummechanics)andmaththrough multivariable calculus and linear algebra. After that, almosteverythingyoucanthinkofcountseitherasaphysicscourseorasarelatedcourse.Soyoucanconcentrate inphysicswithoutactually takingthatmanyphysicscourses.However,ifyou’resittingherefiguringouthowfewyoucangetawaywith,youmightbehappierinanotherdepartment. We’re serious when we say twelve semester courses in physics or relatedfields. Theserelated fields’coursesmight includeofferingsof theChemistry,Mathematics, Applied Mathematics, Computer Science, Astronomy,Engineering,Statistics,andotherdepartments.Checkthemout!

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If you’re looking for a well-rounded physics education, the honors courserequirements serve as a good guideline. (Most people do honors, especiallysince there’s no thesis, tutorial, or general exam requirement; mostdepartments require at least a thesis.) For an honors degree, thirteen tofifteen courses are required, including the introductory sequence, twomathcoursesbeyondmultivariableandlinearalgebra,andtheadvancedlaboratoryclass (Physics 191r). Quantum beyond the first semester andthermodynamics/statistical mechanics courses are highly recommended,especially for those considering graduatework. If you already know single-variable calculus, you may be able to place into a higher math course andreducethenumberofcoursesrequiredforhonorstoasfewasthirteen.

JointConcentrations Sonowthatyou’retaking50millionclasses,whataboutcombiningaphysicsconcentration with something else? If you have a very strong interest inanotherarea,youmaywanttoconsiderajointconcentration(Harvardspeakfor a double major). Joint concentrations often require the completion ofhonors requirements in both departments. While this sounds like agargantuantask,it’susuallyfeasible. Some fieldscombinequitenaturallywithphysics.Forexample, “physicsandmath” works out to a mere three semesters of math beyond multivariablecalculusand linearalgebra(includingoneanalysis,oneabstractalgebra,andone geometry course) among your thirteen courses for the Honors Physicsdegree. “Physics and Astrophysics” is also easy; just substitute theastrophysics laboratory course for the lab course offered by the PhysicsDepartment,andtakefivesemestersofastronomy(16,17,98,andtwoothersthatcountasrelatedcoursesinPhysics). If that’s all you do, you may ask why you should bother to declare a jointconcentration. Perhaps most simply, it lets potential employers/graduateschools/significant others know what your real interests are. A jointconcentrationwillalsogiveyougreateraccesstobothdepartments. Somefields,ontheotherhand,donotcombinewithphysicsquitesonaturally.For a joint concentration like Physics and Classics, you’ll really have to talkwith the Head Tutor of each department. “Negotiate” might be the moreappropriateterm,butdonotdespair—withabitofpersistenceallthingsarepossible.And,suchjointconcentrationshaveprobablybeendonebefore!(Youwill probably soon learn the story of one dedicated concentrator in PhysicsandMusic and the physics-relatedmusical he wrote. Another student whograduatedin2009didaspecialconcentrationcombiningphysicsandtheater;herthesiswasaplayonquantummechanics!) Also,ajointconcentrationinphysicsiseasierthanoneinmanyotherareas.Ifboth departments require a thesis for an honors degree, then a jointconcentratormustwrite a thesis combining the two fields. Because physics

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doesnotrequireathesisforhonors,onlythethesisrequirementsoftheotherdepartmentapply. There are a few subtleties to joint concentrations. While the “physics andmath” joint concentration does not require a thesis, the “math and physics”concentration does. “Chemistry and Physics” is also a bit different— it is asingle concentration blending the two fields, technically not a jointconcentration.No,itdoesn’tmakemuchsense,soreadthefineprintcarefully!

SecondaryField TheFacultyofArtsandSciencesoffers“SecondaryFields”atHarvardCollege,whichmaybethoughtofastheequivalenttowhatarecalled“minors”atotherinstitutions.AmongstthedepartmentsofferingsecondaryfieldsisthePhysicsDepartment. Students who decide not to study Physics as their primaryconcentration and have difficulty “negotiating” a joint concentration withanotherdepartmentshouldcertainlyconsiderthisasanoption! The secondary field in Physics requires 4 courses. Students must take onecourseinelectricityandmagnetism(usuallyPhysics15bor153),onecourseinwave phenomena and/optics (normally 15c), and one course in quantummechanics (normally 143a). The final course should simply be a physicscourse at the 100 level or higher. Of course, students are welcome to takecourses of higher level that cover the specifiedmaterial. Note that althoughmechanics (normally15aor16) isnot required for a secondary field, it is aprerequisite for almost all other physics courses and is stronglyrecommended. Moreinformationonthedetailsandproceduresofthisoptioncanbefoundinthe Handbook for Students online. Interested students should, as always,consultDr.MorinorProf.Georgi!

OtherOptionsforPhysicsConcentrations TheUndergraduateTeachingandEducationProgram(UTEP)optionisgreatifyouhaveaninterestineducation;youwillreceiveteachingcertificationalongwithyourbachelor’sdegree.Theeducationrequirementsarequitesignificant,though,soforthisconcentrationyou’llwanttoplanahead.You’llneedsometimeforthestudentteachingsenioryear!(Thatmayseemfarawaynow,butit’llarrivebeforeyouknowit.) Biophysicsisgreatifyouhaveinterestsinbiologicalquestionsfromaphysicalstandpoint.Asaveryresearch-orientedoption,courseworkisflexibleenoughfor concentrators to continuewith classes in the physical sciences,many ofwhichhavedepartmentalcoursesatthe intersectionwithbiology.Workinaprofessor’s labisrequiredinsteadofthestandardphysics laboratorycourse.Formoreinformationonworkingwithprofessors,pleaseseethe“ResearchAtHarvard”section.

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For theexperimentally-orientedamongyou, there isalsoanAppliedPhysicsoption. It combines hands-on physics, the advanced laboratory 191r, andEngineeringSciencesclasses.

NotConcentratingatAll Maybeyou’reinterestedinphysicsbutyou’dratherspendmostofyourtimedoingsomethingelse.Great!Youcanstilltakealotofphysicsclasses.Asafirstyear,thereareafewdifferentoptionsofintroductorysequencesthatyoucanlook into: 12a and 12b; and 15a (or 16 or 19), 15b, and 15c. For the lifesciences, or if you are interested inmedical school, be sure to look into thePhysical Sciences 1, 2 and 3. You will typically need to have these classesunder your belt to take a higher-level course, but all the requirements arenegotiable– justtalktoProf.GeorgiorDr.Morin. Inparticular,weoftenseemath, chemistry, or even computer science concentrators taking quantummechanics(143a).Certainotherclassesarenotasmathematicalasmostandarealsoworththinkingabout.Moreadvancedundergraduatesinthesciencesshouldbewell-qualifiedtotakemany100-levelphysicsclasses.

Master’sDegree Beyond the different concentration tracks, youmay also have the option ofgettingamaster'sdegreeconcurrentlywithyourA.B.infouryears.ChecktheHarvardCollegewebsiteforeligibilityrequirements,astheruleshaverecentlychanged. An extremely challenging courseload is necessary to satisfy therequirements,soveryfewstudentspursuethisoption.

When pursuing the A.M., you continue to live as an undergraduate for fouryearsandcan fulfill therequirementswithclasses takenatanypointduringyour college career. TheA.M. requirements typically consist of eight classes,withatleastsixbeinggradclassesandatleastfourbeingphysics.Chem/PhysconcentratorsmayalsowanttoconsidertheA.M.inChemistry.Talktoupper-classstudentsandDr.MorinorProf.Georgiformoreinformation.

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PhysicsCourseStrategiesWecan'tbesurethatthisadvicewillbeusefultoeveryone,butifyoulearnthesamewaymostofusdo, thesehintsmayhelpyourphysicscareerrunmoresmoothly. Here are some general strategies that many of us wish we hadlearnedsooner. •Talktootherstudents! Upper-class students are the most valuable source of information aboutanything at Harvard. They can tell you about courses, professors, researchopportunities,summerprograms,waysaroundbureaucraticobstacles,wherethe party’s at — in short, how to get the most out of your Harvardexperience.Ifthepeopleyoutalktodon'tknowtheanswertoyourquestion,chancesaretheyknowsomeoneelsewhodoes. Self-promotiontime:comingtoSPSeventsisagreatwaytomeetolderphysicsconcentrators (andpeoplewho like physics, or peoplewho like peoplewholikephysics). The first fewSPS events focusheavily on course advising andgetting to know older physics concentrators. You should also feel free tocontacttheSPSofficersatanytime;seethebackcoverforcontactinformation.Thereisofcourseplentyoffreeadvice(andaddictivefood)tobehadatSPSevents,butyoushouldalsotakeadvantageoftheotheropportunities/peopleavailabletoyou. •LookintoclasseswithyouromnipotentfriendQ IfyougototheCOOPafewdaysbeforeclasses,youshouldhaveachancetolookatthetextforeachclass.Lookatthefirstchapter.Howdoyoufeel?Nowopenthebooktothemiddle.Excited?Great!Also,forbothphysicsandnon-physicscourses,consulttheQ-Guidetoseehowstudentshaveratedthecoursein the past. Note, however, that the professor for the course may havechanged; the Q-Guide will point you to another course they have taught ifpossible. Take this information into account! The professor makes thecourse!!! Check the online Q-Guide for ratings from previous years:www.fas.harvard.edu/~evals. •Takeadvantageofshoppingperiod Thesurestway toassessa courseand itsprofessor is toattend the lecturesduring shopping period. Be sure to grab a syllabus. This is your chance tocheckoutall thecoursesyou'reconsidering—andyoushould lookatmorecoursesthanyouplantotake.Evenifyouthinkyoualreadyknowwhatyou'retaking, shop around. You may discover a wonderful class you never evenknewabout,oryoucangetaglimpseofcoursesyoumay take in the future.Scienceclassesgenerallydiverightintomaterial,sobepreparedtotakenotesandhaveawaytocopythemonceyoufinalizeyourcourseselections. Don’ttakeaclassyoudon’tenjoyinthefirstfewlectures.Studieshaveshownthat

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initialimpressionsofHarvardclassesarealmostalwayscorrect. •Getthebestsectionleader Inmostphysicscoursesyouwon'tberequiredtoattendsection,butwefeelthat a good section can greatly enhance your experience. If you aredissatisfiedwithyourassignedsection,don't juststayhome;findthesectionmostworthwhileforyou.Ifyou'rerequiredtoattendaparticularsectionwithwhichyouareunhappy,keepinmindthata“scheduleconflict”couldmakeasectionchangenecessary. Justbecauseasectionisoptionaldoesn'tmeanit'suseless—attendingsectionhelps reinforce the material you're learning, demonstrates how to workcollege-levelproblems, andgivesyouanopportunity to askquestionsaboutpointsthatconfuseyou. Plus,aTFwhoseesyouregularlyinsectionmaybefriendlierwhen you come to ask her for help on your problem set. It’s alsogoodtogettoknowgradstudents:theycanbeverycoolpeople,andtheywillalsoexposeyoutothekindoflifethatyoumightliveforthenext5-10years,should you continue in physics. They can also introduce you to their ownresearchandtheirprofessorsandtellyouwheretofindfreefood. •Gotoyourprofessors'officehours! Remember when you were thinking about going to Harvard and everyonewarnedyouthatyouwouldneverhaveanycontactwithprofessors? This isyourbigchancetoprovethemwrong!Youcanuseprofessors'officehourstoget help with difficult course material, find out about their research, ordiscoverthattheyhavelivesoutsidephysics.Youwillhavetogooutofyourwaytoseriously interactwithmostprofessors,butmostwillbedelightedtoseeyouattheirofficehours—don'tbeintimidated!Severallonelyprofessorshavebeenoverheardbeggingstudentstovisittheirofficehours. •UsetheUndergraduatePhysicsStudyandthePhysicsReadingRoom The Undergraduate Physics Study (Jefferson 251) is an area specificallyreservedforundergraduatestowork,relax,andchatwithfriends. ThestudyisrightnexttotheofficesofDr.Morin,theCo-HeadTutor,andCarolDavis,theUndergraduate Coordinator. Look for SPS events, TF office hours, and freefoodhere! LocatedonthefourthfloorofJeffersonLaboratory,thePhysicsReadingRoom(formerlyPhysicsResearchLibrary)isoneofthemostpleasantplacestoworkorrelaxoncampus. The library isopentoallMonday-Friday9AM-5PM,butanyonewithkeycardaccesstoJefferson(includingallphysicsconcentrators)has 24-hour access. This space is open to the entire physics community,whether you want to do research, work on a problem set, or read thenewspaper.Anddon’t forget thecookieseveryMondayafternoonbefore thedepartmentalcolloquia–theycanbefoundhere.

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•Workwithotherpeopleonproblemsets! Wecannotemphasizeenoughtheimportanceofthis.Onapracticallevel,astudy group will make your life easier on problem set night and help youunderstandthematerialmorefully.Moreimportantly,you’llmeetandgettoknow your fellow concentrators. If you’re taking a class aimed at physicsconcentrators,checkouttheEliotdininghallonWednesdaynights–itiswhere many students, especially those in the intro classes, do theirproblem sets, in a celebratedweekly tradition known as PhysicsNight(the same goes for Math Night on Monday nights). There are alwayssubstantial supplies of baked goods available to fuel this endeavor. Eliot isusually chock-full of physics concentrators until the wee hours of themorning.NightsatEliotusuallyendupbeingoneofthebestpartsofbeingaphysicsconcentratoratHarvard. If you’re going to work outside Eliot, assembling a study groupmight takesomepersistence.Butdon'tbeshyaboutaskingpeople toworkwithyou. Ifyoucan’tfindastudygroup,justemailsps-open.AlsotryFacebookingpeopleinyourclasses(no it’snotsketchy,andyes, it reallyworks),orcometoSPSmeetingstomeetotherpeopleinyourclasses. Wefeelobligatedtowarnyou:don'trelyonyourstudygroupasacrutch—copyinganswersforproblemsetswon'thelpontheexam.Anditistechnicallyacademicdishonestyandcouldgetyouintrouble.Wehopethatyou’llfindthatyourfellowstudentsaremorevaluableasteachersthanassourcesofanswers. •Checkoutpreviousfinalexams. Final exams for many courses are available at Gordon McKay Library ofEngineeringandAppliedSciencesandtheHarvardUniversityArchives.Recentexams are often posted on course webpages. Studying problems from oldexams isagreatwaytoprepare foryourownfinal. Beware,however, if theprofessorfortheclasshaschanged,becausethefinalmaybeentirelydifferent.

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CourseDescriptionsandRecommendationsWe are only providing brief course descriptions here since you can look upmore detailed descriptions in the my.harvard portal. However, we’ve alsooffered some opinions that you won’t find in the official descriptions. Justremember that these are our opinions; yours may differ. Also, theprerequisiteslistedinthecourseguidearenotalwaysup-to-date.Checkwiththe professor if you are considering not following them, however. Theprerequisiteslistedbelowarealsoouropinions. Duetoeditorialconstraints(i.e. thePhysicsDepartmentgivesusmoney)weare unable to rate professors as well as courses. You should be aware,however, that in many cases the satisfaction one gains from a class hasmoretodowiththeprofessorwhoisteachingitthanthecoursematerialitself.TheQ-Guideisanexcellentresourceforprofessorratings.Ifyouwishtofindprofessorratingsfrompreviousyears,backissuesoftheQ-Guidecanbefoundatwww.fas.harvard.edu/~evals. Students who have taken the course provide an even better source ofinformation. (Always feel free to badger your SPS buddy or the SPS officersaboutsuchthings;we’vecertainlydoneourshareofaskingforinfo!)Wecan’temphasizethisstronglyenough:

Askaroundaboutprofessorsandcourses!! Also, the professors themselves are good source of information. You mightwanttotalktothem,towatchtheminactionduringshoppingperiod,orboth.Wesuggestthatifyouareunsureofwhichcourseisrightforyou,talkwiththeprofessorgivingthecourse. Ifyouthinkyoumaybefamiliarwiththematerial inacourse,checkoutthepastcoursewebpagesandfinalexams. Takealookatthesetogetanideaofthe level of the course. Even better, find outwhen this year’s professor lastgavethecourse,andcheckthefinalexamsfromthatyear,availableatGordonMcKayLibraryofEngineeringandAppliedSciences.

Below we have included all undergraduate courses offered by the PhysicsDepartment,andmanycourses in therelated fields. Courses inbracketsarenotofferedthisyear.

NOTE:Coursesdemarcatedwith[brackets]willnotbeofferedthisyear.Those marked by an asterisk (*) are courses you should especiallyconsiderduringyourfirstyear.

Therestyoumightjustwanttomulloverforawhile.(Or,asNobelLaureateLeonLedermansaid:“Putyournosetotheglassandlookatallthecandy!”)

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FreshmanSeminarsFreshmanseminarsareverydifferentfrommostothercoursesyouwilltakeinyourfirstyear.Inthesecourses,asmallgroupofstudentsworkscloselywithaprofessor in the investigation of a field—there is a great deal of informalinteractioninadditiontostandardclassroomfare. Afreshmanseminarcansupplementtheintroductorysequence(seebelow)ifyou think you may concentrate in physics; it can also be a great way ofdabbling inphysics ifyou’resureyouwon’tconcentrate in it.Theonlygoodreason not to take a seminar is time. These courses are electives. If it’simportant to you to get started on the introductory sequences in physics,math,andchemistryallatonce,thenyoumightnothavetimeforafreshmanseminar. Still, don’t discount the option without some thought; a freshmanseminar (inside or outside your field) can be one of your best academicexperiencesatHarvard. We heartily recommend considering a freshman seminar in any area thatpiquesyourinterest;herewelistthoserelatedtophysics.Alsoconsidertakinga freshman seminar not in physics – it’s a great way to expand yourinterests. Note that there aremany seminars not listed here related to theothersciencesaswell. *FreshmanSeminar21G(Loeb):FirstStarsandLifeintheCosmos(Spring) *FreshmanSeminar21V(Strominger):BlackHoles,StringTheory,andtheFundamentalLawsofNature(Fall)

*FreshmanSeminar22I(Bloxham):TheScienceofSailing(Fall)

*FreshmanSeminar23C(Woodin):ExploringtheInfinite(Fall)

*FreshmanSeminar23P(Vafa):Physics,MathandPuzzles(Fall)

This seminar is intensely rewarding for students interested in physics,mathematics,andtheinterfacebetweenthetwo.Simpleyetprofoundresultsin physics are explored through the unique medium of puzzle-solving.Considerthispuzzle:Therearefourcitiesatthecornersofasquare.Youhavetobuildroadssothatyoucandrivefromanycitytoanyanotherinsomeway.Howdoyoudo it using theminimum lengthof road?Theanswerhas todowith why particles have mass. The ideas explored in this class, includingsymmetriesanddualityrelations,willcomeupoverandoverinfuturephysicsclasses.Thelightworkloadofaninterestingpuzzletothinkabouteachweekmakestheclassanidealadditionforabusyschedule.

*FreshmanSeminar23R(Alcock):AsteroidsandComets(Spring)

*FreshmanSeminar23Y(Doyle):AllPhysicsin13Days(Fall)

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*FreshmanSeminar26J(Randall):TheUniverse’sHiddenDimensions(Fall)

*FreshmanSeminar51C(Meade):ScienceintheAgeofArtificialIntelligence(Fall)

*FreshmanSeminar51H(Zipser):ModelsoftheWorld:ExplainingthePastandPredictingtheFuture(Fall)

*FreshmanSeminar51T(Dvorkin):TheUniverse:ItsOrigin,Evolution,andMajorPuzzles(Spring)

*FreshmanSeminar51U(Georgi):InsurrectioninaLittleKingdom—TheRealStoryoftheStandardModelofParticlePhysics(Spring)

*FreshmanSeminar51V(Kim):PhysicsofMeasurements:ExperimentalScience(Fall)

*FreshmanSeminar51X(Samuel):ChangingPerspectives:theScienceofOpticsintheVisualArts(Spring)

*FreshmanSeminar51Z(Finkbeiner):ThePathtoaLow-CarbonFuture(Fall)

*FreshmanSeminar52D(Vishwanath):QuantumEntanglementandtheSecondQuantumRevolution(Fall)

*FreshmanSeminar52E(Park):ScienceandTechnologyPrimerforFutureLeaders(Spring)

*FreshmanSeminar52H(Franklin):TheInteractionofLightwiththeWorld(Spring)

Seminarsrequireanapplicationand,occasionally,an interview,butarewellworth the effort. More information and a complete listing of seminars areavailablehere:https://freshmanseminars.college.harvard.edu/seminars.

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PhysicsDepartmentCoursesIntroductoryCourses

PhysicalScienceCourses: * Physical Sciences 1, 2, 3: an introduction to the physical sciences forbiologicalapplications(1,3Spring;2Fall) These are the introductory courses to physics aswell as physical chemistrywithanemphasisonbiologicalapplications.Theyareintendedespeciallyforpre-medstudents,butarerecommendedforanystudentswhoareinterestedinthephysicalsciencesbutdonothavemuchbackground(thoughAPChemishelpful). Among other things, Physical Sciences 1 (PS1) covers introductorygeneral and physical chemistry, while PS2 and PS3 cover mechanics andelectromagnetism, respectively. Note that PS2 and PS3 are not accepted forcredit towards a physics concentration, though they are accepted for otherconcentrations,suchaschemistry.Studentsshouldconsultthedepartmentformoreinformation. *PhysicalSciences10:Chemistry:AMicroscopicPerspectiveonMolecules,Materials,andLife(Fall) *PhysicalSciences11: Foundations and Frontiers ofModernChemistry: AMolecularandGlobalPerspective(Spring) Thesecourses,besidesyour typical introductorygeneral chemistrymaterial,intendtointroducefieldsandapplicationsthatyoumightnotgettooutsideofmoreadvancedphysicsandchemistryclasses.PS10, for instance,goesoverthe fundamentals of quantummechanics and statisticalmechanics,while PS11 looks at topics such as thermodynamics and quantum chemistry(overlapping topics with PS 1 as well). Both emphasize real-worldapplications,suchasmedicalimaging,globalwarming,andelectriccars.Thesecourses can also be taken independently of each other. Pre-med generalchemistry requirements can be fulfilledwith any two courses fromLife andPhysicalSciencesA,LifeSciences1a,PS1,PS10,andPS11.Studentsshouldconsultthedepartmentformoreinformation. * Physical Sciences 12a,b: Mechanics (Spring) and Electromagnetism andStatistical Physics (Fall) from an Analytic, Numerical, and ExperimentalPerspective These courses comprise a standard college-level one-year introduction tophysics, with emphasis on engineering applications and experimental dataanalysis. They satisfy medical school requirements and are highlyrecommendedforapre-medconcentratinginanareaotherthanphysicsbutlookingforamorerigoroustreatmentthanPS2andPS3.PS12a,bisacceptedforcreditinmanyconcentrations,includingchemistryandengineering.Math

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21a is listed as a corequisite; however, if you are comfortable with yourcalculusskills itmaynotbenecessary. IfyouwishtocountPS12a,btowardthePhysicsorChem/Physconcentrations,besuretoconsultthedepartmenttodevelopacoherentplanofstudy. *AppliedPhysics50a,b:PhysicsasaFoundationforScienceandEngineering Thesecoursesformauniqueyear-longproject-basedintroductiontophysics.Theyarerelativelynew,andpromisetoprovidetheequivalentofastandardintroductory physics course, but with a heavy emphasis on engineering-inspiredgroupprojects.MathatthelevelofMath1bconcurrentlyisrequired,though it’s recommended to take Math or Applied Math 21a concurrently;math contentwill be coordinatedwith AM 21a. Consult the department formoreinformation. Note:Where Math 21a is listed as a pre/corequisite, Applied Math 21a orMath 23b, 25a, or 55a will also satisfy the requirement. Similarly, AppliedMath21borMath23a,25b,or55bcansubstitutefor21b. PhysicsCourses: *Physics15a:IntroductoryMechanicsandRelativity(FallandSpring) *Physics16:MechanicsandSpecialRelativity(Fall)

[*Physics19(formerlyPhys101):IntroductiontoTheoreticalPhysics]

Ah,thegreatfirst-yeardilemma.Physics15a,16,and19areyourchoicesforyourfirstphysicsclassasaphysicsconcentrator–youcantakeanyoneofthethree; they all feed into the same sequence (15a/16/19, 15b, 15c,143a). Basically, 15a and 19 are hard, while 16 is very hard. They all gobeyondthehighschoolAPPhysicslevelandintroduceallsortsofinterestingtopics.Many freshmen are not surewhether theywill be able to handle 16.Fortunately, theDepartmentmakes iteasy toswitchbetweencoursesat thebeginningofthesemesteronceyougetafeelforthem.Youprobablywanttotakealookat16,butdon’tfeelobligatedtotakeit.Dependingonwhatyoutook inhighschool, itmightbeabetter idea tohoneyourmathbackgroundfirst – 16 is very demanding mathematically. And if you’re planning ontaking other difficult classes, there’s no point in killing yourself withwork.Ontheotherhand,Physics16isatrial-by-firebondingexperienceforthosewhotakeit.ManywhotakeitcallitoneofthestandoutexperiencesoftheirHarvardcareer.

Phys 19 covers a wider set of foundational topics in slightly less depth fortheoreticalphysicsthan15aand16,andisintendedtogiveabroaderpreviewof later courses in the physics concentration. Phys 19 is a designed toaccommodate awide range of backgrounds and interests: it assumes only afamiliarity with single-variable calculus, and teaches the necessarymathematicalbackgroundalongtheway.Sincethecoursestructureconsistsof

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problem sets and a final project, there are plenty of opportunities for thosethat wish to engage deeply with the material to further enrich theirunderstanding; for those that are just interested in a taste of a bit ofeverything,Phys19hasaplaceforyoutoo.

Themain point of 15a and 16 is to learnmechanics and solve challengingproblems simply because physics is cool. The main point of Phys 19 is toprovide a comprehensive grounding and experience in the concepts andmathematical tools of theoretical physics that show up in the rest of thephysicsconcentration.Butalsobecausephysicsiscool.

For 15a, concurrent enrollment in Math 1b is required (with 21a highlyrecommended), while for 16 concurrent enrollment in Math 21a or anequivalent is required: most students in 16 last year took one of Math23/25/55. And by theway,we also recommend 15a for non-concentratorswhowish to takephysics and comeoutwith a fairly deepunderstandingofmechanics (many chemistry and engineering concentrators choose thisoption). *Physics15b:IntroductoryElectromagnetism(FallandSpring) Physics15bcoverselectricityandmagnetismatalevelsignificantlybeyondAP,and follows15a/16/19 in the introductorysequence.Non-concentratorswill often take the class, leading to a wide range in students’ experience.However,thecourseisflexibleandprovidesplentyofsupportorchallengenomatter what your physics background. Math 21a is a formal corequisite;however,werecommendamultivariablebackgroundcomingintothecourse. A few students each year consider skipping 15b to take 153(Electrodynamics).ConsultwithProf.Georgiandthinklonganddeeplybeforedeciding. Remember that the PSI lab for 15b is still required of allconcentrators. Physics15c:WavePhenomena(FallandSpring) This is a course inwavesandoptics. It covers importantmaterial for futurecourses, including the wave equation, Fourier analysis, and a formalintroduction tooscillations.Oscillationsare thebasisofquantummechanics,and15cwillprovidepowerfultoolsforfuturephysicscourses(evenifballsonspringsandpendulaseemboringtoyounow).Math21bisacorequisite. Most of those taking this course are physics (or astronomy) concentrators,thoughsomechemists interested inphysicalchemistry take itaswell.Therearealsostillplentyofpeoplethereforinterest’ssake,andweencouragenon-concentratorswhohavethetimetogetatleastthisfar. Notethatthiscourse,moresothan15aand15b,canbeanoticeablydifferentexperienceunderdifferentprofessorswhomaytakedifferentapproachesorcoverdifferenttopics.AskaroundandchecktheQGuideforopinions. Ifyou

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are considering taking Physics 175 or another course to fulfill the 15crequirement,consultwithProf.Georgiandthinkcarefullybeforemakingthisdecision.Remember,thePSIlabfor15cisstillrequiredforallconcentrators. Physics143a:QuantumMechanicsI(FallandSpring) Ah, quantum mechanics. As Prof. John Doyle puts it, “this class is whatseparates physicists from everyone else.” This course is required of allconcentrators and is a prerequisite formost of the cool upper-level physicscourses. Physics 15c is a prerequisite (although every year a few studentswithastrongbackgroundskip15c). Math21bisalsoadefiniteprerequisite;wefeelthatthemorelinearalgebrayouknow,thebetteryouwillunderstandthe material. (Math 23a, 25a, or 121 will make this course even moreworthwhile!)If,bythetimeyouarereadytotake15c,youarealreadystrongin linear algebra, Fourier Analysis, and understand the wave equation, youmayconsidertaking143aconcurrentlywith15c,buthavingpreviouslytaken15cmakes143amuch,muchmorecomprehensible.Taking151(Mechanics)before thisclassalsohelps,especiallywithHamiltonians,althoughnotmanyconcentratorsgothatroute,andHamiltoniansaren’tdifficulttopickupduring143a. Concentrators inothersciencesoftentakethiscourse,especiallychemistsasanalternativetothequantumcourseinthechemistrydepartment.Thecoursewill have a very different flavor from Chem 160, so consider this decisioncarefully. The above introductory physics courses are offered every semester (exceptPhysics 16and19,whichare only offered in the fall), so if you think that youdon’t want to start right in (thoughwe can’t imaginewhy youwouldn’t) butlaterhaveachangeofheart,youdon’tneedtospendawholesemestertwiddlingyour thumbsandwaiting for the introcourseyouwant to take. If youdo takeyourphysicsclasses“outofphase,”theywillbesmallerandmayhaveadifferentsetofprofessors.Butonceyoufinish143a,you’llbebackinsyncwiththerestoftheconcentrators.

CoursesBeyondtheIntroductorySequence

Physics125:WidelyAppliedPhysics(Spring) This course uses physics to analyze important technologies and real worldsystems; it emphasizes physical intuition and order-of-magnitudecalculations. It aims to develop a toolbox that all physicists should have attheirfingertips.The15a/b/cseriesisaprerequisite,with143arecommendedat least as a concurrent course. Thematerial covered in this course variesgreatlydependingontheinstructor. Physics129:EnergyScience(Spring) Consultthedepartmentformoreinformation.

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Physics141:ThePhysicsofSensorySystemsinBiology(Fall) Consultthedepartmentformoreinformation. Physics143b:QuantumMechanicsII(Fall) Thiscourse takeswhatyou learned in143aanduses it to studyallkindsofphysicalsystems.Theexactdetailsofwhatiscoveredvaryfromyeartoyear,but they generally involve atomic systems and approximations. You won’tlearn much more about fundamental quantum theory in 143b; the maindevelopments are differentways to approximate various situations tomakethemamenabletosolutionbyquantummechanicalmeans. However, keep inmind that 143b covers somebasicmaterial physicists areexpected toknowand thatyoumightnotget inanyother class; atomicandmolecular physics are fundamental applications of quantum mechanics.Physics143bwillnotonlyfirmupwhatyoulearnedin143a,butitalsoopensthedoors tomanymodern fieldsofresearch, likecondensedmatterphysics,quantuminformation,andAMOtheory.Itmaybealittletediousforsome,butyou’llbeabetterphysicist for it–andit’scritical forgradschool.Forall theChem/Phys students out there, keep inmind that this is the class inwhichyou’ll learnwhyelements, atoms,andmoleculeswork theway theydo.Andoften the last week is an introduction to quantum computing. Interested?Awesome! Physics145:ElementaryParticlePhysics(Fall) Elementaryparticlephysics isa largeanddifficultarea thatrequiresagreatdeal of mathematical and physical preparation to understand fully. Moststudents never see much of the theory until graduate school. This coursesuccessfullyremediesthatsituationbyfocusingonintuitiveunderstandingoftheconceptsinvolvedratherthanthecalculationalaspects. Thisisusuallyasmallclass,withagreateropportunityforinteractionwiththeprofessorbothinandoutoftheclassroom.Afunandrewardingcoursethatishighlyrecommended! Physics151:Mechanics(Fall) Thiscoursestudiesmechanicsfromamoreadvancedpointofviewthan15aor16, startingwith theLagrangian formulation.However,onceyougetpastLagrange’sandHamilton’sequations, there isa lotof time leftover, and thecourseseemstovarygreatlywiththeidiosyncrasiesofitsinstructors.Becauseofthis,wesuggestthatyoudosomeresearchbeforetakingthiscourse,tofindoutwhattheinstructorplanstocover.Manyconcentratorschoosetoskipthisclass because themath can get dense, but classicalmechanics can be prettyinteresting.Takingthiscourseconcurrentlywith15cisagreatwaytopreparefor 143a, which will involve lots and lots of Hamiltonians. Oftentimes, thiscoursecoverstopics likeclassical fieldtheoryandforaysintotheconnection

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between classical and quantum mechanics via discussions of the Feynmanpathintegral.Thesetopicsareespeciallyimportantforbuddingtheorists! Physics153:Electrodynamics(Spring) Physics153 is an intermediate course inelectrodynamics. It reconsiders thenon-electronicsmaterialof15bwithgreatermathematicalsophisticationandoveralldepth.Priorunderstandingofconceptsfromelectricityandmagnetismare assumed, however, so we do not normally recommend skipping 15b totake 153 (certain topics, such as circuits, are not covered in 153; hence theasterisk on the asterisk). Some professors also spend part of the coursecovering important mathematical techniques (e.g. Bessel functions). Somestudents are particularly happy with David Griffiths' IntroductoryElectrodynamics,whichistypicallythetextforthiscourse.

[Physics160:IntroductiontoQuantumInformation]

Physics160isawonderfulandwide-rangingintroductiontothenascentbutbooming field of quantum information, guided by one of its foremosttorchbearers, Prof. Misha Lukin. The course starts with a basic review ofquantummechanics,theconceptoftwo-levelsystems,andanintroductiontoopen-quantumsystemsandentanglement,andendsbydescribingthestateofthe art in quantum algorithms and the research frontier in quantumsimulation(includingmanyexperimentsintheHarvard-MITregion).Allalong,the class strives to buildup strong intuition in quantum information, and attheendofthesemesterleavesstudentswithenoughbackgroundtogenuinelybeginresearchinthefield(thisisnotanexaggeration).Ifyou’reinterestedinquantumcomputationandquantuminformation,thisistheclassforyou.Evenifyouthinkthatquantumcomputingismalarkey,takethisclasstogetmoreindepthpracticewithtopicsfromquantummechanicssuchasdensitymatrices,two levelsystems,entanglement,anddynamics.Such topics,usuallycoveredrapidly in 143a and 143b, are integral to many research areas (condensedmatter,atomicphysics,andofcourse,quantuminformation),anddevelopingintuitionforthemisoftenessential.

Physics175:LaserPhysicsandModernOpticalPhysics(Spring) Introduction to quantum electronics (laser physics) and modern opticalphysicsaimedatadvancedundergraduates,withanemphasisonapplications.This course is often taught by Marcus Greiner who brings a superlativeexperimentalperspective(andsweetdemostoo)tothecourse.

Physics181:StatisticalMechanicsandThermodynamics(Spring) For perhaps the first time in physics, you’ll be looking at not one-body, nottwo-body,but1023-bodysystems!Thiscourse,orEngineeringSciences181orChemistry161,isstronglyrecommendedforconcentratorsatsomepoint.Youreallycan’tgetbyasaphysicistwithoutknowingsomethingaboutthisstuff.

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ThePhysicsDepartmentcourseismoregearedtowardsstatisticalmechanics,whiletheEScourseemphasizesthermodynamics.Chemistry161coversmuchof the samematerial, butwith a focus on applications to chemistry. Physics143aisaprerequisite. Physics195:IntroductiontoSolidStatePhysics(Fall) Getreadytoapplyyournewlygainedquantumandstatisticalmechanicsskillstoaveryimportantsystem:Solids!StartingwiththeclassicalDrudetheoryofmetals, the course aims to derive the electronic and thermal properties ofmetals, insulators and semiconductors by applying quantum mechanics toperiodic systems. It is an essential course for research in condensedmatterphysics!ThiscourseistypicallyjointlyofferedasAppliedPhysics195. AppliedPhysics195:IntroductiontoSolidStatePhysics(Fall) ThesameclassasPhysics195,butjointlylistedthroughSEAS.

LaboratoryCourses *Physics123:LaboratoryElectronics(FallandSpring) This course in laboratory electronicspresents the skills needed to constructscientific instruments, a valuable ability for those wanting to go intoexperimental physics or just those wanting to leave Harvard actually beingable to do something useful. The broad introduction to analog and digitalelectronicsisalsovaluableforengineeringconcentratorsandsomeComputerScience concentrators; both undergrads and grad students take the class.Therearenoformalprerequisites,butat leasthighschoolphysicsandsomefamiliaritywithcalculus isuseful.Previousexperiencewithbasicelectronicsor low-level programming can be immensely useful. Engineering Sciences151,154and156coversimilartopics,butthephysicscourseismorefocusedon “seat-of-the-pants” electronic design emphasizing broad understandingover calculational proficiency. As might be expected, the class requires asubstantial time commitment, but you get out of it everything you put in.Estimatesofworkloadrangefrom1.5to2.5normalclasses. [Physics191:AdvancedLaboratory] In this laboratory course, required of all honors concentrators (and highlyrecommended for all concentrators), students carry out three experimentschosen from a list. These are not your basic high school measure-g-with-a-pendulum-and-stopwatch experiments: topics include superfluid helium, thelifetimeof them-meson, andNuclearMagneticResonance. Physics15abc isrequired,and143aishighlyrecommended.Theactualknowledgeneededforthese courses is highly dependent on the experiments performed; someexperiments make more sense if you’ve also taken 181. If you are leaningtowards Astrophysics (and have taken enough courses in that department),talktotheheadtutorsaboutthepossibilityoftakingAstronomy191instead.

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The90's:Research,Reading,andIceCream Physics90r/91r:SupervisedResearch/Reading(FallandSpring) These two courses allow students to pursue research or reading in areas ofphysicsnotcoveredinthecurriculumorinwhichmorein-depthknowledgeiswanted.Theyareveryvaluableforthosewhothinktheymaywishtopursuephysics after their undergraduate years. Since the subject matter can beanything, so can the prerequisites. See the section on research for hints onfiguring out what to study. These courses sometimes culminate in a seniorthesis.Donothesitatetoreachouttoprofessorstodiscussthepossibilityofpursuingsupervisedreadingorresearch!Manystudentsfindthisexperienceincrediblyhelpful. Physics95:TopicsinCurrentResearch(Fall) Physics95 is first and foremost a course in science communication,with anemphasisonupperclass-levelphysics.Thecenterpieceoftheclassisthethree20-minuteoralpresentationsthateachstudentisrequiredtogivethroughoutthe semester; individual attention is given by the professor in this seminar-stylecoursetoeverystudent'spresentingskills,ensuringthatyouwalkawaywith a clear understanding of how to get in front of people and give anengaging,comprehensibletalkaboutanysubject. Directed toward juniors and seniors, this course offers a wider variety oftopics to titillate the imagination.The course is complemented byweeklyWednesdayeveninglecturesbydifferentHarvardprofessors;eachprofessordiscussestheir ongoing research, and free post-lecture ice cream is servedeveryweek.(Theseeveninglecturesareopentoallphysicsstudents,notjustthe enrollees in Phys 95!) This course is an excellent opportunity tolearnabouttheongoingresearch interestsof the faculty, todevelopeffectivecommunication skills as a scientist, and to follow up on oneresearch topicfromlectureintherequiredtermpaper.

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GraduateCourses

Someundergraduatesinthepast,usuallyaftercompletingthecorresponding100-levelcourse,haveventuredonintotherealmofgraduatecourses.Theseareoftenverydifferentfromundergraduatecoursesduetothedifferingneedsof their students, and typically they represent quite a significant workload.That disclaimer aside, here are a few graduate courses highly advancedundergraduateshavetakenwithsuccess.

Physics210:GeneralTheoryofRelativity(Spring)

Generalrelativityisthefinalcourseastudenttakesinclassicaltheory.Curvedspacetime,blackholes,anexpandinguniverse, thewholenineyards.Physics210isnotaprerequisiteformanyothercoursesasidefromPhysics211r;itisan end in itself. The mathematical tools required, such as familiarity withtensors and differential geometry, are developed naturally as the courseprogresses.However, itmay take awhile to get to the actual physics of theclass. Long, tedious calculations of quantities involving rank-4 tensors are astapleofthecoursework-sobeprepared.Alltheeffortisworthitintheend,asthecourseprovidesagreatintroductiontogeneralrelativity.

[Physics216:MathematicsofModernPhysics]

This course requires significant prior background in mathematical physics,and it assumes knowledge of a lot ofmathematics from real and functionalanalysis toquantum field theory.As anadvanced survey coveringparticulartopicsingreatdepth,however,itisanexcellentcourse.

Physics232:AdvancedClassicalElectromagnetism(Spring)

This course definitely requires some sort of previous background inelectromagnetism,ideallyattheadvancedundergraduatelevelofPhysics153.Thesyllabusbeginswithrelativityandquantummechanicsandexplains thefundamental underpinnings of Maxwell’s Equations before going through amoretraditionalEMcurriculum,oftenfromJ.D. Jackson’sclassic textbook, toendupanywherefrommagneticmonopolestonon-abeliangaugetheoriestosuperconductivity.Thisisagreatcourseforlearningaboutelectromagnetismindepth.Beaware,though,thatthematerialcoveredinthelatterpartsofthecoursemayvarygreatlydependingontheprofessor.

Physics251a/b:AdvancedQuantumMechanicsI/II(aFall,bSpring)

Astheintroductoryquantumsequenceforgraduatestudents,Physics251a/boffer an advanced, fresh beginning for quantum mechanics. Starting fromscratch, the class clarifies the mathematical and physical foundations ofquantumtheory.Instructorsvaryinpaceandmaterial,buttypicallytheclassmoves quickly and the lectures are at a high level. Students who havecompleted the 143a/b sequence and are interested in strengthening theirquantummechanicsfoundationsshouldkeeptheseclassesontheirradar.

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Physics253a:QuantumFieldTheoryI(Fall)

Physics253aisthefirstcourseinthegraduatequantumfieldtheorysequence.Youwill want to take a quantum field theory course at some point in yourcareer if you are interested in high-energy physics, nuclear physics, orcondensedmatter physics, and it is nice to have someunderstanding of thesubjectifyouintendtocontinueyourstudiesinphysicsatthegraduatelevel.While it is a very advanced course, you can probably handle it if you havetakenatleastPhysics143aand143b.Physics151mightalsobehelpfultogaina grounding in classical field theory, but it is not strictly necessary as thecourse typically starts with a fast-paced introduction. The course is oftentaughtbyProf.MatthewSchwartz,whosecelebratedtextbookQuantumFieldTheoryandtheStandardModelprovidesagoodintroductiontothesubjectandisusuallythetextofchoicefortheclass.Theproblemsetswillrequireaverysignificant time commitment, however, and you should bear in mind thatPhysics253aisnotagreatadditiontoanalreadycrowdedschedule.QuantumFieldTheory is an incredibly vast subject, sowhile this course offers a verysolid introduction to the field (Chapters 1-19 of Prof. Schwartz’s textbook),keepinmindthatthereismuchmoretocome.AlsonotethatwhileMIThasa3-semesterQFTseriesjustlikeHarvard,Harvard’sversioncoverssignificantlymorematerialinashorteramountoftime.

Physics253b:QuantumFieldTheoryII(Spring)

ThesecondofHarvard’s3-semesterQFTseries,thiscoursestartswherePhysics253aleavesoffandturnsthedifficultyuptenfold.ItcoverstheremainingchaptersofProf.Schwartz’stextbookaswellasalargechunkofWeinberg’ssecondvolume.Takingthiscourseonitsownwillhaveyouworkingharderthanmostofyourpeers,soonlyconsideritifyouaresureyouwanttodohighenergyorcondensedmattertheory.YoumayalsowanttoconsiderPhysics254whenit’sofferedasagood,lessextremealternative.

Physics253c:QuantumFieldTheoryIII(Fall)

ThethirdofHarvard’s3-semesterQFTseries,thisisatopicscoursewhichcoversdifferentmaterialbasedonwhenitisbeingtaught.Thiscourseisaveryexcitinggemonceyou’vetakenPhysics253a,andmaycovertopicssuchassupersymmetryorconformalfieldtheory.

Physics254:TheStandardModel(Spring)

AnamazingsequeltoPhysics253a,thiscourseputsthematerialyoulearnedinPhysics253atogoodusebyintroducingthebuildingblocksoftheStandardModel.IfyoueverwantedtogobeyondtheQuantumElectrodynamicsfromPhysics253a,andlearnabouttheweakandstrongforces,aswellastheHiggsMechanism,thisisthecourseyou’relookingfor.WhileyoucantakeitalongwithPhysics253b,studentsusuallytakeoneortheother.

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Physics262/AppliedPhysics284:GraduateStatisticalMechanics

This class is an ambitious survey of the vast and integral field of statisticalmechanics.WhentaughtbyProf.Manoharan, theclass touchesuponvariousaspects of Physics 181 (except for thermodynamics) in a slightly moresophisticatedmanner,beforetacklingessentialconceptsinstatisticalphysicssuchastheIsingmodel,universality&scaling,andrenormalizationgroup,allinaphysicallyintuitivelyalbeitnotintimidatinglytechnicalmanner.Whiletheclass has some shortcomings in terms of rigor, a result of the necessarilyambitiousscopeoftheclass, it isanextremelycogentadvancedintroductionto statistical physics and develops intuition that is useful in variousquantitative fields outside of physics as well. A very reasonable option,perhapsbest takenafterPhysics181, that is challengingbutultimatelyveryapproachableformotivatedundergraduates.

[Physics264:LieAlgebrasinParticlePhysics]

This course explores useful applications of group theory to particle physics.Liegroupsareessentialtoparticlephysicssincetheyarethegaugegroupsfortheories of interacting spin 1 bosons, like the strong and electroweakinteractions which are building blocks of the Standard Model. A handful ofadvancedundergraduateswithastrongmathbackgroundtake iteveryyear,andthosewhofinditmostusefuloftenhavetakenPhysics253a.ConsultProf.Georgiifyouarethinkingoftakingit.

Physics271:TopicsinthePhysicsofQuantumInformation(Fall)

ThiscourseisespeciallyhelpfulforstudentswhohavealreadytakenPhysics175andareconsideringresearchorgraduateschoolinquantuminformation.Physics285a:ModernAtomicandOpticalPhysicsI(Spring)

ThiscourseisespeciallyhelpfulforstudentswhohavealreadytakenPhysics175andareconsideringresearchorgraduateschoolinatomic,molecular,andopticalphysics.

Physics/AppliedPhysics295a:IntrotoQuantumTheoryofSolids(Fall)

ThiscourseisespeciallyhelpfulforstudentswhohavealreadytakenPhysics195 and are considering research or graduate school in condensed matterphysics.

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MathematicsDepartmentCoursesPartofbeingaphysicistislearningalotofmath,whetheryouwanttoornot.Sohere’sabriefoutlineof themathclassesyou’llprobablybeencounteringsoon.Moredetailed information on these andother courses inmathematicsmay be found in Mathematical Sciences at Harvard, available from theMathematicsDepartment.YoucanalsocheckouttheAppliedMathematicsandStatistics Departments for more math and related courses. Another usefulsourceisAStudentPerspectiveontheMathDepartment,anunofficialguideputtogetherbyGenderInclusivityinMathematicsandavailableontheirwebsiteatharvardgiim.org/advising. All freshmen take a math placement exam during their first week atHarvard. This exammay place students in any of the pre-calculus and firstyearcalculuscourses,oritmayindicateMath21a.(IfyouareplacedinMath21a, any of the multivariable calculus courses may be appropriate foryou.)However,studentsshouldrememberthatthisplacementexam,whileaguideline,isonlythat:aguideline.Ifyoufeelyouhavebeenmisplaced,youareultimatelyfreetodecideforyourself.

Pre-calculusandFirstYearCalculusCourses *MathMa,b:IntroductiontoFunctionsandCalculus This isapre-calculusand introductorycalculussequence for thosenotquitereadytojumpintoMath1a.Applicationsareemphasized.Unfortunately,itisverydifficulttoconcentrateinphysicsifonebeginsmathwiththesecourses. *Math1a,b:IntroductiontoCalculus Thesecoursesarea firstyearstudyof calculus.A fewphysicsconcentratorsbegin math in one of these two courses; however, the large number ofprerequisitesformanyphysicscoursesgivesthesestudentsfewerchoices intheirlaterschedules.

MultivariableCalculusandLinearAlgebra * Math 21a,b: Multivariable Calculus; Linear Algebra and DifferentialEquations(FallandSpring) Math21apresentsmultivariable calculus. It is appropriate for studentswhohave completed Math 1b or received a 4 or 5 on the AP Calculus BCexam. Math 21b is a course in linear algebra and beginning differentialequations.Thoughmostpeopletake21aand21binthatorder,thecoursescanactuallybetakentheotherwayaroundtoo.Mostphysicsconcentratorsbeginmathin21a.Veryfewskipthesecourses;ifamoretheoreticalperspectiveisdesired,Math23,25,or55maybemoreappropriate,but21willgiveyouthemostknowledgeyouneed for earlyphysics classes.Amultivariable calculussequence (21, 23, 25, or 55) is a prerequisite for most 100-level math or

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physicscourses. Note that although you are assigned a particular section for the 21a,bsequence, it is important to have a good section leader. Therefore, there issome“flexibility”in“picking”thesectionyouattend. * Applied Math 22a,b: Solving and Optimizing; Integrating andApproximating(aFall,bSpring) TheredesignedreplacementsforAM21ab,thispairofclassescovermuchofthesamematerialasMath21ab.Historically,theseclassescansometimesbemuchmorecalculation-basedandlesstheory-basedthanMath21aandb,butinthelastcoupleofyearsthetwosetsofcourseshavebeenmoresimilar.The22aportionsometimesspendsacouplefewerweeksonlinearalgebraandacouple more weeks on differential equations, which has benefits anddisadvantages since both are very important in physics. Logistically, thecourses are often taught in onemedium professor-led lecture rather than amultitudeofsmallgraduatestudent-ledsections,asMath21a,btypicallyare.Intheend,theMath21andAM22sequencesareprettysimilar,andinterestedstudentsshouldshopthembothtomakeadecisionaligningwiththeirtastesandpreferences. *Math22a,b:LinearAlgebraandVectorCalculus(aFall,bSpring) Thiscourseisprimarilyforstudentswhoareinterestedinamoretheoreticalunderstandingoflinearalgebraandvectorcalculus.Itcoversthesametopicsas Math 21, but with more rigor and in the opposite order. Math 22 alsocontains an introduction to mathematical reasoning through proofs. Linearalgebra andmultivariable calculus aremore interconnected throughout thisclass,as linearalgebra techniques fromMath22aareused toprove ideas inMath22b’svectorcalculus.

* Math 23a,b,c: Linear Algebra and Real Analysis; Mathematics forComputation,Statistics,andDataScience(aFall,bSpring,cSpring) Thiscourseisaimedatpeoplewhowanttoseewhattheoreticalmathislikebutdon’twanttokillthemselvesbytakingMath25or55.ThecoursecoverslinearalgebraandmultivariablecalculusinamoresophisticatedmannerthanMath21.Itisdifficultbutwellworththeeffortifyou’rewillingtospendsomeserioustimethinkingaboutmath.Itcanbehelpful,thoughunnecessary,ifyouhave already taken a non-theoretical version linear algebra ormultivariablecalculussothatyouhavethemathtodoyourphysicssets. The23sequencehasrathermixedreviewsinthepastandvariesquiteabitbyprofessor;askaroundandconsulttheQGuideforopinions. *Math25a,b:HonorsLinearAlgebraandRealAnalysis(aFall,bSpring) Math 25 presents a rigorous treatment of linear algebra and real analysis

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(read:abstractmultivariableanddifferentialcalculus).Itisintendedformathconcentrators, but not even a majority of the enrollment ends upconcentrating in math. We suggest it for those who would like a deepunderstanding of elementary calculus from a rigorous, proof-based point ofviewandwhoarewillingtomakeasubstantialtimecommitment.Whilemuchofthematerialhasnodirectbearingonphysics,studentswhoqualifyforthiscoursecangenerallylearnwhatisnecessaryforthephysicscoursesontheirown. Realize that this requires a lot of work, and dedication. Thus, for aphysics concentrator, this is a “pleasure course” (in the intellectual sense—nottheworkloadsense).Theofficialprerequisiteisa5ontheAPCalculusBCexamorpermissionoftheinstructor,butthereareusuallyalsostudentswhohave donemath competitions and/or taken the equivalent ofMath 21a,b inhighschool.Makesureyouaresolidonyourmathandknowenoughforyourproblemsetsbeforetakingthisclass.Thepacecanvaryquiteabitdependingon the instructor, so make sure to read past Q-Guide evaluations and askformerstudents. *Math55a,b:HonorsAbstractAlgebraandAnalysis(aFall,bSpring) Thiscoursecoversthesametopicsas25and122butatanevenmoreintenselevel (and often goes much further in depth). If you are interested in pureabstractmathematicsinitsownright,therigorsof55maybeforyou,butbewarnedoftheworkload.Thosewhotakethecourse,however,rarelyregretit.LikeinMath25,thepacecanvaryquiteabitdependingontheinstructor,somakesuretoreadpastQ-Guideevaluationsandaskformerstudents. Notethatthetopicscoveredinthe“a”and“b”semestersdonotlineupinallthe various introductory math sequences. 21 covers multivariable calculusbeforelinearalgebra,whereastheotherclassesroughlycoverthesametopicsin the reverse order. It is easiest to switch between AM22a and 21b, andamong 22/23/25/55, though you can switch easily between any of theseclasses--consult the math department for more information: https://www.math.harvard.edu/undergraduate/first-year/.

Post-CalculusCourses AppliedMath104:ComplexandFourierAnalysis(Fall) AM 104 and AM 105 present extremely valuable subjects for physicsconcentrators, presenting the basis formuch of themath used in advancednatural science courses. (Note that the two classes, while often referred totogether,aretotallyindependentandmaybetakenseparately.)Thematerialand problem sets in AM 104 are somewhat shorter on theory, which suitssomephysicsmajorsbetterthanothers.SomesimpleMatlab is incorporatedintosomeof theassignments (an introduction is taught, foranynot familiarwith it). Some topics covered are contour integration, uniform convergence,andconditionalprobability.

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AppliedMath105:OrdinaryandPartialDifferentialEquations(Spring) This course is a straightforward look into themethods of solvingODEs andPDEs, tools essential to the field of physics. Again, the course is short ontheory. The pedagogical progression typically goes as: proof of method,specificexampleofmethod,andthengeneralexampleofmethod.(Sometimestheproofcomesafterward.) Ifyouareabletokeepupwiththemultitudeofmethods being thrown at you, this course is manageable and mostimportantly,useful.Youwillfindthatamultitudeofstudentstakethiscourse,from engineers to economists to geologists. Some Matlab applications willcropupinthiscoursetoo. AppliedMath108:NonlinearDynamicalSystems(Fall) TheclosestyouwillgetatHarvardtoanundergradclassinchaostheory(butalsocheckoutMath118r).OK,sothisclassspendsjustafewweeksingivingaqualitative explanation of chaos. The other topics it covers are also veryrelevant to modern physics: oscillations and bifurcations in ordinarydifferentialequations,approximationbymaps,andrescalingsofsystems.Theapplications to physics are not thoroughlymotivated; instead, it focuses onevaluatingphysicalproblemsthroughcertaintechniques.Biology,economics,engineering, and applied math students also take this class, though thesystemsstudiedmoreoftencomefromphysicsthanfromanyothersubject. Math101:Sets,GroupsandTopology(FallandSpring) This course is an introduction to the methods of rigorousmathematics.Throughavarietyoftopicsfromgeometry,analysis,andalgebra(thethreemajorsubfieldsofmath),studentsaretaughthowtowriteproofs.Ifyouwould like to learn how realmath is donewithout the drink-from-the-firehose approach of Math 25+, this course may be exactly what you arelookingfor. Manyupper-levelmathcoursesrequire theability towriteproofs. Math22,23,25,and121aretheonlyothercoursesthatexplicitlyteachthisimportantskill,andthiscoursecannotbetakenforcreditifyouwillalsobetakingeitherMath22,23,25,or55.Sincethiscourseteachesbrand-newmaterialinsteadofbuildingonwhatyou’velearnedalready,therearenoformalprerequisites.APCalculusisrecommended. [Math110:VectorSpaceMethodsforDifferentialEquations] Thiscourselooksatfinite-andinfinite-dimensionalinnerproductspaces,withapplicationstodifferentialequations,andgoesovervariousformsofthewaveequationandFouriertransforms.Thisstuffisespeciallyrelevantforquantummechanics,andhelpsyouwrapyourheadaroundthemathinPhysics143a,b.

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Math112:IntroductoryRealAnalysis(Spring) This course introduces concepts of real analysis (metric-space topology,differential and integral calculus) in a rigorous manner. It treats similarmaterial toMath23,25and55, thoughata less intensepace,andcannotbetaken for credit in addition to these courses. Every theoretician (andmostphysicists ingeneral)shouldhaveaworkingknowledgeofrealanalysis.Theclasscanbevariableinhowitistaught,however,socheckwhichprofessoristeachingitandtalktomathstudents. Math113:AnalysisI:ComplexFunctionTheory(Spring) Complex analysismakes its appearance in all sortsof areasofphysics. Thiscoursedealswiththematerial inarigorousmannerforitsownsake.Ifyourinterest inthismaterial isonly itsuseasacalculationaltool forphysics,youmaywishtoconsiderMath115orAppliedMath104inlieuofthiscourse. Math114:AnalysisII:Measure,IntegrationandBanachSpace(Fall) AnenhancedversionofrealanalysisforpeoplewhohavecompletedMath23,25,or55.Topicscoveredinclude:Lebesguemeasureandintegration;generaltopology; introduction toLp spaces,BanachandHilbertspaces,andduality.Much of the math, especially Hilbert spaces and Fourier analysis, is quiterelevanttophysicaltheory,butonthemath-ysideofthings. [Math115:MethodsofAnalysis] The course is billed as being designed for those with a strong interest inphysics, and indeedmostof the subjectmatter ishighly relevant tophysics.The course covers the basics of complex analysis and then moves on toapplications such as Fourier analysis, Laplace’s equations, and Besselfunctions,allofwhichappearfrequentlyinphysics.However,mostwhohavetakenthecoursesaythatfewexamplesrelatingtophysicswerepresentedandthus the relevance was not apparent until the topics appeared in physicscourses.Wesuggestthiscourseforthosewhosefocusliesinphysicsbutwhowish to learn the rootsof themathmoredeeply than theymight inAppliedMath104. Math116:ConvexityandOptimizationwithApplications(Fall) Justasthetitlestates:anin-depthlookatoptimization,especiallyrelevanttoengineering, applied sciences, and economics. Consult the department formoreinformation. Math118r:DynamicalSystems(Fall) Dynamical systemsappear inall sortsofphysicalprocesses, and this courseprovides themathematical tools necessary to analyze such systems,with anemphasis on applications. It is targeted at both physics and math

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concentrators. Math121:LinearAlgebraandApplications(Fall) ThiscoursepresentsamorecompleteandrigorousviewoflinearalgebrathanMath 21b, which is the prerequisite. It is quite valuable for quantummechanics.Thiscourseisalsosupposedtobedesignedtoteachproofsshouldyounotalreadyhaveexperiencewiththem.However,itisnottobetakeninadditiontoMath23,25,or55. Math122,123:AbstractAlgebra(122Fall,123Spring) The former is an introduction to groups fromwhichmost physicists wouldbenefit. (It is quite valuable for particle physics in particular.) The latterfocuses on Galois theory and hence is far less relevant for physics. Thoughthesecoursesdofunctionasasequence,itisquitereasonable(andcommon)totaketheformerwithoutthelatter. Math131:TopologyI:TopologicalSpacesandFundamentalGroup(Fall) An introductory course in topology. Very interesting, but only relevant forgung-hotheorists.Ifthat’syou,though,thisstuffisessential.Familiaritywithgroups(viaMath101or122)wouldbehelpful,thoughsomepeoplepickitupastheygoalong. Math132:TopologyII:DifferentialTopology(Spring) AnindependentcoursefromMath131,aimedatstudentswithMath23,Math25orMath55background.Topicscoveredare:differentialmanifolds,smoothmaps and transversality, winding numbers, vector fields, index and degree,differential forms, Stokes’ theorem, and an introduction to cohomology. Themathisrelevanttowhat’sbehindgeneralrelativityandotherdeepertheories,thoughinafairlyabstract,indirectsense.

Applied Math 203: Introduction to Disordered Systems and StochasticProcesses

While this is a class that is purportedly about applied mathematics andstatistics,whentaughtbyProf.ArielAmir,itlargelyservesasathrillingsurveyofvarioustopicsinequilibriumandnon-equilibriumstatisticalmechanicsanddisordered systems. Even topics that are not exactly physics (e.g. randommatrix theory) are either strongly related to it or rely on intuition fromstatistical physics. At the end of the day come for Black-Scholes (and fatstacks),leavewithpercolation,barriercrossings,andtheLangevinequation.

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AstronomyDepartmentCourses*Astronomy16:StellarandPlanetaryAstronomy(Spring) Astronomy 16 is a class aimed at incoming freshmen with an interest inastronomy. The only corequisite is 15a, although Astro 16 is offered in thespring.Thisclassisafunintroductiontothefieldofastrophysics,andishighlyrecommended for those considering furtherpursuit of astronomyaswell asthosewhoareinterestedinthesubject. Ahighlightof the class is theoptional exoplanet labwhere studentsuse theClay Telescope to observe the transit of a known exoplanet. If you aresuccessful,youwillgetanautomaticAfortheclass. *Astronomy17:GalacticandExtragalacticAstronomy(Fall) This course, offered in the fall, dealswith thephysical principles of galaxiesand,moregenerally,theuniverse.ItformsasetwithAstronomy16,although17isarelativelynewercoursewhichhasbeenfindingitsbearings.Althoughithasbecomebetter integratedwithAstronomy16, it seems thatorganizationandqualityoflecturesisstillanissue.Notethatyoucantake16and17inanyorder if you want, but 16 before 17 makes the most sense. Just like withmicroeconomicsandmacroeconomics,itseemsasthoughgettingthesmallerscale picture before the bigger scale picture is most effective. Similar toAstronomy16,thiscourseonlyrequiresconcurrentenrollmentinmechanics. Astronomy91r:SupervisedReadingandResearch(FallandSpring) ThisisjustlikePhysics90rand91rcombined,butwithanastronomyfocus. Astronomy98:ResearchTutorialinAstrophysics(Fall) This introductory tutorial is normally open to juniors considering aconcentrationinastronomyorajointconcentration.Thisisanexcellentwaytogetabroadoverviewofatopicandseewhatisactuallybeingdoneattheforefront of research. We highly recommend this course for anyone evenvaguelyconsideringanastronomyconcentrationorfocus.Astronomy16or17istheofficialprerequisite. Astronomy100:MethodsofObservationalAstronomy(Spring) This course teaches you how to use the basic tools of astronomy research:telescopes,spectrometers,detectors,etc.Thecourseisdesignedtogiveyouarealistic, hands-on approach to examining astronomical data, and studentsreport that it is successful in that regard aswell as an enjoyable class. Theclassalsotakesatripoverspringbreak(makesureyouhavethattimefree!)to the F. L. Whipple Observatory on Mount Hopkins in Arizona, which is

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always fun. Note that although work during the semester is not overlyrigorous,thefinalprojecttypicallyrequiresasubstantialtimeinvestment. [Astronomy110:Exoplanets] Consultthedepartmentformoreinformation. [Astronomy120:StellarPhysics] Consultthedepartmentformoreinformation. Astronomy130:Cosmology(Fall) Consultthedepartmentformoreinformation. Astronomy191:AstrophysicsLaboratory(Spring) The astrophysics lab course is intended for concentrators in astronomy ordual concentrators; however, physics concentrators with a demonstratedinterest in astronomy may take it. As always, if you’re not sure if you’reeligible,checkwithProf.GeorgiorDr.Morin.UnlikePhysics191r,Astronomy191presentsmoreopportunities forparticipation in real research, andpastprojects have actually produced publishable results. This course is highlyrecommendedforstudentswithaninterestinastronomywhowantatasteofrealresearch. Astronomy200:RadiativeProcessesinAstrophysics(Fall) This class, primarily for graduate students, investigates light in all of itsastrophysical detail, covering various emission mechanisms and radiativetransfer. Whilestudentswithnoastronomyexperiencebutastrongphysicsbackgroundcouldsurvivethiscourse,backgroundisrecommended.

Astronomy201:AstrophysicalFluidsandPlasmas(Spring,every2years)

Agreatfluiddynamicsclassofferedintheastronomydepartment.Knowledgeof mechanics, thermodynamics, and E+M along with comfort with vectorcalculusisstronglyrecommended.Fluiddynamicsisnotofferedinthephysicsdepartment,butit’sanimportantsubjecttoknownevertheless!Afairamountofworkisneeded,butwhentaughtbyProf.LarsHernquist,itisanespeciallygreat,low-stressclass.

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OtherCoolStuff* Computer Science 50,51: Introduction to Computer Science; AbstractionandDesigninComputation(50Fall,51Spring) Thesecoursespresentanintroductiontocomputerscienceandprogramming,includinglanguagessuchasC,PHP,SQL,ML,andJava.CS50isoneofthemostpopularclassesatHarvard,withanenrollmentofmorethan700studentslastyear.TheprogrammingskillsandcomputerknowledgepresentedinCS50willbe valuableboth in general and to someone considering a career in science.Thematerial covered in CS50 is highly recommended, though theremay belesspainfulwaystopickupthatknowledge.CS51tendstobelessimmediatelyrelevanttophysicists. Statistics110:IntroductiontoProbability(Fall) This course gives a thorough overview of probability theory, includingcommonprobabilitydistributionsandconditionalprobability(unlikethesub-110 Stat classes, which brush over probability theory and focus onapplications in data analysis). Comfortwith basic probability theory is veryhelpfulinquantummechanicsandstatisticalmechanics,andwhileStat110iscertainlynotrequired,itprovidesasolidfoundationinprobabilityforphysicsandthensome.Itcanalsobeaveryenjoyableclass:itinvolvesadifferentkindof intuition from typical math, and it’s been wonderfully taught by Prof.Blitzsteininthelastfewyearswithenrollmentcontinuingtogrow. EngineeringSciences181:Thermodynamics(Fall) This isathermodynamicsandstatisticalmechanicscoursesimilartoPhysics181,butwithafocusonmorepracticalapplications,andemphasizingthermoover statmech.Mostpeople find itmorecomprehensibleaswell.Wehighlyrecommend eitherPhysics 181orES181,withphysics being the choice forthosewhowillstudythermoandstatmechmoredeeply later(mostphysicsconcentrators),andprobablyESforthosewhojustneedtohavesomethermointheirlives(allphysicsconcentrators,inouropinion). ManyotherEngineeringSciencescoursesarealsorelevant tophysics.Checkout Courses of Instruction, and talk to engineering concentrators for moreinformation (especially about instructors). Below we have listed someparticularlyrelatedtophysics(whosetopicsarenotaswellcoveredinphysicscourses): EngineeringSciences120:IntroductiontotheMechanicsofSolids(Spring) Engineering Sciences 123: Introduction to Fluid Mechanics and Transport

Processes(Spring)

[Engineering Sciences 135: Physics and Chemistry: In the Context of EnergyandClimateattheGlobalandMolecularLevel]

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[EngineeringSciences154:ElectronicDevicesandCircuits] EngineeringSciences170:EngineeringQuantumMechanics(Spring)

EngineeringSciences173: Introduction toElectronic andPhotonicDevices(Fall)

EngineeringSciences190:IntroductiontoMaterialsScienceandEngineering(Fall)

[DramaticArts163x:PuppetryinPerformance] Puppet theater has almost nothing to do with science, with the possibleexceptionoftheannualpuppetshowputonbysecond-yeargradstudents,andwementionithereonlytoseeifyouarestillreading:)

*LifeandPhysicalSciencesA/LifeSciences1a;PhysicalSciences1(Fall) These courses represent a standard year-long introductory course inchemistry. We recommend a basic knowledge of chemistry for all physicsconcentratorssimplybecausewethinkbroadbackgroundsareimportantforavoiding falling into thought ruts later in life.Also,youmay learn importantskillsformakingexcitingdemonstrationsinvolvingfire. Unfortunately,theseclassesarevery largeandtendtobedominatedbypre-medandbiologystudents,whichcanbefrustrating. *PhysicalSciences10:Chemistry:AMicroscopicPerspectiveonMolecules,

Materials,andLife(Fall) *PhysicalSciences11: Foundations and Frontiers ofModernChemistry: A

MolecularandGlobalPerspective(Spring) Thesecourses,besidesyour typical introductorygeneral chemistrymaterial,intendtointroducefieldsandapplicationsthatyoumightnotgettooutsideofmoreadvancedphysicsandchemistryclasses.PS10, for instance,goesoverthe fundamentals of quantummechanics and statisticalmechanics,while PS11looksattopicssuchasthermodynamicsandquantumchemistry,bothwithmany real-world applications. Consult with the department for moreinformation. *Chemistry20,30:OrganicChemistry(20Spring,30Fall) ThissequenceisHarvard’sorganicchemistrysequenceforchemistsandotherscience concentrators that want a taste of real chemistry (although a fewhumanities and social science concentrators make an appearance). MostChem/Phys concentrators take this route over the alternative (Chemistry17/27). Thesecourseshaveareputationofbeingbothdifficultandtimeconsuming,so

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keep that in mind when planning your schedule. They are, however, well-taughtandorganizedandareveryfulfillingforthosewhoareinterested.

Chemistry40:InorganicChemistry(Spring) ThiscourseisbothusefulforChem/Physconcentratorsaswellasanyonewithan interest inmaterials science. Consult thedepartment andother studentsformoreinformation. Chemistry160:QuantumChemistry(Fall) This course is an introduction to quantum for chemistry people. If you areinterestedinachemist’sperspectiveonquantummechanics,thismaybethecourse for you. However, Physics 143a is required of all pure physicsconcentrators, and thus this course has relevance primarily to Chem/Physconcentrators.Chemistry160focusesmoreonmeasurableresultsofquantumtheory, while Physics 143a focuses on the mathematical underpinnings ofquantummechanics.Thiscourseisalsoknownforemphasizingcomputationaltoolsoveranalyticalcalculations. Chemistry161:StatisticalThermodynamics(Spring) ThiscourseisunlikePhysics181andES181initsstrongfocusonchemistry.Though not recommended for those interested in the physical aspects ofthermo, it is certainly a good choice for Chemistry concentrators with aninterest in physics or for Chem/Phys concentrators. It also serves a goodintroductiontosometopicsinbiophysicsresearch. Once again, there are lots of other good chemistry courses of interest tophysicsconcentrators.

Neuroscience131:ComputationalNeuroscience(Spring)

Neuro131isafascinatingcourseonmodernbraintheorytaughtbyaformertheoreticalphysicist(HaimSompolinsky)turnedtheoreticalneuroscientist.Itbuildsupmathematicalmodelsofneuralcomputationusinginspirationfromstatistical mechanics, information theory, and statistical inference, amongmanyothersubjects.Donotbefooledbythecoursenumber;Neuro131isagraduate-level class and is mathematically very rigorous, but ultimately isworth it if youare interested inexploringhowquantitative techniques fromphysics and other related domains can be used to try and explain how thebrainworks.

Other departments that have more specialized courses of interest to physicsconcentratorsincludeEarthandPlanetarySciences,andMolecularandCellularBiology,socheckwiththeirconcentratorsortheCoursesofInstructionformoredetails.TheHistoryofScienceandPhilosophydepartmentsalsoofferinteresting

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courses relating tophysics thataregood funeven though theydon’t count forconcentration.They’realsoreallywonderfulforpeoplewhohavenoinclinationtoconcentrateinphysics.Forthosewhojustwishtodabbleinphysics,manyoftheScienceofthePhysicalUniverse(GenEd)coursesareexcellent(andpeopletend to forget... there’s nomaximum to the number of GenEds you can take).There are about 1800 other courses in the catalog thatmight interest you aswell,sotakealook!

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MITCoursesMIToffers somephysicscourses (Course8) thatmaynotbeofferedhere.Mostnotableisanundergradclassinstringtheory(8.251)!Formoreinformation,gotohttp://catalog.mit.edu.Hereareafewthatsomephysicsconcentratorshaveenjoyedovertheyears.

8.333-4: Statistical Mechanics of Particles/Statistical Physics of Fields (8.334Fall,8.333notofferedthisyear)

Statistical physics is an extremely deep and beautiful subject with variousmotifs that are undercurrents in modern research, especially in condensedmatter.AnalternativetoPhysics262iscrossregisteringfor8.333&8.334atMIT.While262inprinciplecoversmuchofthematerialin8.333&8.334andisbrilliantlytaught,Prof.Kardar's8.333/4courseisaninvaluableexperiencewhichcoverssimilarmaterialinaclear,highlyrigorous,anddeeplytechnicalmanner.

8.613/22.611:IntroductiontoPlasmaPhysicsI(Fall)

A hidden gem of theMIT physics department, this is the first of a series ofgraduate courses in plasma physics. Although plasma physics is a relativelysmallsubfield,itisessentialtoastrophysics,controlledfusion,andmanyotherfields. This course is amust-take for anyone interested in the subject and agreatadditiontoyourscheduleafterPhysics153.

SomeNotesonFeedback SPSdoesalotofworktomakesuretheadvisingsystemandclassesofferedatHarvard for physics students are truly worthwhile. It’s why we meet withmembersofthedepartmentsofrequentlyandalsowhywemakethisbooklet–sostudentscanmakeinformeddecisions. In order to help us along, we need you to participate in this process ofcontinual reform. Come to SPSmeetings and let us knowwhat needs to befixed!FilloutQ-Guideevaluations!Anddon’tjustwaituntilsomeonetellsyouaboutgivingfeedback–theDerekBokCenterforTeachingandLearninghasan anonymous feedback form (bokcenter.harvard.edu) that provides anyone(a professor, TF, advisor, anyone with an email address) with immediatecomments. Your feedback is key to informing future students about classesandalsodirectlyimprovingthedepartment’scurriculum.

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ResearchatHarvardDo it. Do it! Do it! Undergraduate research is one of the most valuableexperiencesHarvardhastooffer. Don’t think that research is only for those who already knowwhat area ofstudy theywould like to pursue. One of the best ways of seeing if you likesomethingisdoingit!Therefore,researchmayactuallybemoreimportantforthosewhoareundecided. Fortunately,Harvard’s science departments have plenty of opportunities forundergraduates. There are quite a few reasons why you would want to doresearch. For one thing, research can often be a very exhilarating andrewardingexperience.Itwillgiveyouaglimpseintothelifeofascientistandthenatureof real sciencebeyond the sterile classroomenvironment. It alsolooksreallygoodongraduateschoolapplications—evenifyoudon’tapplytothefieldinwhichtheresearchwasperformed–andispracticallyrequiredforgraduateschoolinexperimentalphysics. Unfortunatelyfortheundergraduate,mostprofessorswouldlikeyoutohavesomeclueaboutsomethingbeforeyoubegin.Solet’sbeginwiththat.

Goodthingstoknow Computers are indispensable tools in pretty much every branch of sciencethesedays.Theoreticalphysicistsusethemtosimulatemathematicalmodels,experimentalists perform complex data analysis and reduction, chemists domolecularmodeling, and computer scientistsmake themdoall sortsofneatthings. A background in programming is highly sought after (though by nomeans necessary!) in research positions. Many scientists these days areamateur programmers by necessity; you can become one too with a littleeffort. Ifyouhappen tobearealprogrammer, though, somuch thebetter --youcanbeveryvaluabletoafacultymember.What(usually)mattersisnotsomuchwhichlanguagesyouknowasageneralabilitytomakethecomputerdowhatisneededofit.Ifyou’dliketogetyourfeetwet,checkoutCS50and51,aswellascoursesinotherdepartments(suchasAM111)--orpickupabookandlearnsomeyourself. Mathematica and Matlab are becoming increasingly important in boththeoretical and experimental physics. Many of the introductory math andphysicscoursesusethem,sotheyoftenprovideashorttutorial.ThereisalsoacourseofferedbyEarth andPlanetary Sciences calledEPS100:TheMissingMatlabCourse,whichprovidesamoreformalintroductiontoMatlab,althoughitseemsthatthelabsaregearedtowardtheearthsciencesratherthanmathor physics. The ability to use programs like Mathematica and Matlabeffectivelywillwinyoufriendsvery,veryquickly.Onceyou’vegotthehangofoneofthem,though,putitonyourresume!Professorswillloveyouifyoucanteachthemhowtogetmoreoutofthetoolsthey’realreadyusing.

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On theother endof the spectrum, experiencewith electronics can alsobe aplus.Evenabasicunderstandingofhowtoputtogethersimplecircuitscanbeusefulingettinginthedoortoamorehands-onresearchexperience.(Physics123mightnotbeabadwaytogetstarted.)Somelabsmayhaveyoubuildingthingsinthemachineshop,locatedinthebasementofLyman.Itisalsoopenfor general use for physics and SEAS students. Be sure to check out thetraining classesoffered there if you’d like to startmachiningand say “hi” toStan,the(sarcastic,amazing)personwhorunsit. Butingeneral,mostprofessorsdon’treallyexpectmuchpreviouslaboratoryexperience from their undergraduate students, since most labs are verydifferent and experience in one often does not completely prepare you foranother.Basicconceptssuchaslabsafetyandcareofexpensiveequipmentaregenerally all they ask. The professors and graduate students will help youlearneverythingyoudon’tknowaheadoftime(whichwillbeaheftymajorityofwhatyou’llbedoingnomatterwhatexperienceyoubringtothejob). Many professors would like some course experience, though this is highlydependenton the typeofwork. Ingeneral, the introductorycourses ineachdepartment are a good launching point. But far more important is yourattitudeandtheinterestyoudisplayintheirparticularareaofresearch.Evenifyoudon’treallyknowanythingabouttheirfield,they’llbeinterestedifyouseemtobegenuinelycuriousaboutit.

Howyoucangetinvolved “SohowdoIgethookedupwithajob?”youask.Well,it’salluptoyou.Truthbetold,thephysicsdepartmentwon’tgooutofitswaytojusthandyouajob.You have to take the initiative yourself. But you, being a resourceful andintelligentHarvardundergraduate, shouldbeundaunted.Professorswant tohireyou;youjustneedtomakesuretheyknowyouexist.Hereareafewtips:

*Talktoprofessors Thisisallthereistoit.Ifyoumightliketoworkforsomeonethatteachesoneof your classes, go to office hours and ask them about theirwork and theircolleagues’ work. The physics department website also lists professors byresearcharea.Iftheresearchsoundsinteresting,asktheprofessoriftheyneedsomehelp!Professorsmaynotevenknowtheyneedanassistantuntilyoutellthemso.Anddon’tbeafraid toknockonthedoorofrandomprofessors. (Inthismodernage,werecommendanemailtointroduceyourselfandschedulean appointment ahead of time.) To give guidance to this random knocking,mostdepartmentspublishlistsoftheresearchtakingplacefortheirgraduatestudents.Thereis,however,noreasonanundergraduateshouldn’tgetacopyof that list and look it over. Once again, the initiative is yours. If somethingsoundsinteresting,getintouchwiththeprofessor.

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*Talktostudentswhoalreadyhavejobs Youmightalsohangaround in thedepartmentyou’d like towork in: talk tothe students who are already working there! Most of the happy studentsdidn’t find their position through official channels. They might know whoneeds help, or who else to talk to. Again, you are welcome to contact SPSofficers,oranyothermembersofSPS,toaskforadvice.

*CheckdepartmentofficesandtheSEO Ifaparticularprofessorisinneedofstudents,theymaymakethatknowntothe department office. Department offices are a good first contact point.Another source is the Student Employment Office. Some professors indesperateneedofstudentswillpostontheSEO’sbulletinboards.Checkthoseout.TheSEOisonlineatwww.seo.harvard.edu.

*Attenddepartmentalseminars Another way of finding out about interesting research is to attend theseminars held by most departments. The Physics Department, for example,holds aWednesday night lecture series (in conjunctionwith Physics 95) inwhichprofessorsspeakabouttheirresearchatanundergradlevel.AlsolookoutfortheMondayPhysicscolloquia.Itisimportantnottobeintimidatedbyresearch you cannot completely understand. In fact, “Iwas really interestedbut I didn’t quite follow this part . . .” can be a good way of openingconversationwiththeprofessorlater.Ifyougetinvolved,you’lllearnquicklyenough.

*Attendotherphysicsevents Whilewe’reonthetopicofseminars,it’sgoodtoknowthatthereareenoughtalks in thearea toreplaceyourcourse load. AtHarvard, therearenotonlydepartmental talks (physics, chemistry, astronomy, etc.), but also subgroupseminars(MaterialsScience,SquishyPhysics,CondensedMatter,HighEnergyTheory,CNS,variousCfAdivisions).OutsideofHarvard,thereareevenmoreopportunities: sign up for theweekly Boston Area Physics Calendar (BAPC)emaillistatcosmos.phy.tufts.edu/bapc.html.

*Checkouttutorialcourses Yet another way to find out about research is through the tutorial coursesoffered by most departments. These provide a more in-depth discussion ofvarious professors’ research as well as personal interaction with theprofessors.WehighlyrecommendtheintroductorytutorialinthedepartmentofAstronomy.

*ChecktheRadcliffeInstitute TheRadcliffeInstituteforAdvancedStudyhasanumberoffellowseveryyear

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that are looking for enthusiastic undergraduates to help them with theirresearch.ContacttheInstituteorprofessorsindividually;alsotalktostudentsfortheirexperiences.

*TalktodepartmentofficesandHeadTutors Forallthesedepartments—Physics,aswellasChemistry,Astronomy,andtheSchoolofEngineeringandAppliedSciences(which includesAppliedPhysics,ComputerScience,EngineeringSciences,AppliedMathematics,andEarthandPlanetarySciences)—startby contacting thedepartmentofficeand theheadtutor. Tobehonest, as a first year, youprobablywon’t get involved inheavy-dutyresearch.Butyou’llprobablyhaveyourhandsfullwithclassesandsocializinganyway.Ifyouhavespecialskillsyoucanprobablymakeyourselfuseful,andyoucanatleaststartcultivatingcontactsthatwillhelpyoufindsummerandterm-timejobsinthefuture.

SummerJobsandResearch For summer jobs, in addition to local employment, there are manyopportunities outside of Harvard. For example, check out the RowlandInstituteforScience(www.rowland.org)andotheruniversitiesandcompaniesin the area. The department office compiles a notebook with summeropportunities for undergraduates. Additionally, the SPS will disseminateinformationoveremail.Therearealsomanysummerprogramswithsitesontheweb. “REU”s (Research Experiences for Undergraduates) are one of the mostpopularways to get paid to do research over the summer. The NSF runs anetwork of REU programs in all branches of science and engineering. Thecentralhomepageisatwww.nsf.gov/home/crssprgm/reu.Deadlinesfortheseprogramsareoftenprettyearly—JanuaryandFebruaryarecommon.

TherearealsomanyHarvardprogramsthatwillfundresearchatHarvard,intheUS,andabroad:forexample,PRISE,HCRP,HerchelSmith,andWeissmann.Check them out at the URAF (Undergraduate Research and Fellowships)website here: uraf.harvard.edu/undergraduate-research. The PhysicsDepartmentalsoprovidesfunding,supplementaltoHCRPfunding,tosupportstudentsdoingresearchon-campuswithaphysicsprofessor.

Beforewarnedthatthereisalotofcompetitionforthesepositions(especiallyREUs)andfreshmenareunlikelytosnagthem.Buttheyoftendotakenoteofthe brave people who apply against all odds, and first year applicants aresometimes solicited thenextyear.Alsonote thatmostof thesehaveamoreformalapplicationincludinglettersofrecommendationfromprofessors.Sogoto those office hours and buddy up to your professors! Knowing and beingliked by a few professors has benefits far beyond summer job applications.

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Justletsomeoftheirfameandgloryoozeontoyou. Forstudentslookingtogoabroad,RISE(ResearchInternshipsinScienceandEngineering) is a neat summer internship program at institutions all overGermanyforstudentsfromtheUS,Canada,andtheUK.AnumberofHarvardstudentshavedone it, so talk to them formore information. Thewebsite iswww.daad.de/rise/en.

The Physics Department website has a good list of places to do research:www.physics.harvard.edu/academics/undergrad/summer.

Whentostartscopingouttheprofs As early as possible! For summer positions, you should start talking withprofessorsbeforespringbreak,ideallyinFebruaryformanygrantdeadlines.Term-timeemploymentisoftenmoreflexibleandprofessorsmaybehiringatany time. Still, if possible,making contactduring the summer canbea goodidea.Also,keepatit!Ifyouwalkintoanyprofessor’sofficeyouarelikelytoseeadeskpiled sohighwithpapers you can’t even see the little sign saying “Adisorganizeddeskisasignofgenius.”Thatnotewithyourphonenumbercaneasilyget lost in thatvastness.Pesterprofessorsuntil theyhireyouor sendyou to another professor to get a job. They can be pestered in person, byphone, or via email (physics professors are generally available via email atlastname@physics.harvard.edu). And if you’ve submitted something to adepartment office, definitely pester them. Bureaucracy can move if it isproddedenough.

WhatIreallywanttoknowabout:$$$$$ The first thing todecide inundertakingresearch iswhetheryouwant togetpaid! Therearea lotofgrantsout therethatcanhelpyouout,even ifyourprofessorisfeelingalittlestrappedforcash.Forthegrantsdiscussedbelow,deadlinesareusuallyearlyandprettystringent.Semesterapplicationsaredueeitherbefore thesemesterbeginsorveryearlyon(1or2weeksafterward)andsummerapplicationscanbedueasearlyasFebruary. If the research experience is more important to you thanmoney, you havemoreoptions.The90rseriesofcoursesinPhysics,Astronomy,Chemistry,andEngineeringareaneasyway todoresearch.Youwon’tgetpaid,butat leastyou’llgetcredit!Anotheradvantageisthatyou’realmostguaranteednottobedoinggruntwork.Ifyouare,talktosomeone.Thereisbetterresearchtobedone. Ifyou’refeelingverygenerous,youmaywishtoworkforsomeprofessorsfora while without pay until you’ve learned the ropes. This is a good way tonegotiate a position somewhere you really want to work even though theprofessorwantsexperienceyoudon’thave.Italsogivestheprofessortimetofreeuporfindfundstopayyouwith.

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Okay,yousay,cutthealtruism.Iwantdough.Well,don’texpecttobecomerichovernight (or ever, for that matter). Most research positions will keep yousomewhatlean.Therearesomewaystoincreasethosepaychecks,however.Ifyouqualify for theWork-Studyprogram,professorswill loveyoubecause itpaysabigchunkofthebill(thoughbecarefulwiththelogisticsbehindit).Ifnot,makesureyourprofessorappliesforaFacultyAidegrant.Thisfundwillprovidehalfofyourpayuptoacertainamount. Another important thing to know about is the Harvard College ResearchProgram.Grantsfromthisprogramwillpayyoutoperformalmostanykindofresearchundertheguidanceofafacultyadviser.Thegrantslastonesemester,so there are three deadlines throughout the year (for fall, spring, andsummer). More information is available on the HCRP website aturaf.harvard.edu/research-funding.

There are plenty of other sources of funding – search around and you’reguaranteed to find something. If you work at the CfA, and your professorworksforNASAorNSF,theycanapplyforadditionalfundingfromthem,justforyou.ArelativelynewgrantistheAPS/IBMWomeninScienceInternship,which is especially for women in the “hard sciences.” Other grants areavailable;theStudentEmploymentOfficeanddepartmentofficescanhelpyoufind them. In addition, try out theOffice of Career Services. They publish abookcalled“TheHarvardCollegeGuidetoGrants”whichyoucanlookatforafewminutesbysacrificingyourHarvardIDbrieflyorbypurchasingfor$5.

For summer research here on campus, the Physics Department (in tandemwithHCRP)essentiallyguaranteesfunding.SeeDr.Morinfordetailsonhowtoapply.

Goodluck,andremembertoinviteustoStockholmwhenyougetyourNobelPrize!

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ContactsBelowwehave tried to list some importantpeopleandwebpages. Youcanalwaysfindphonenumbers fromHarvardInformation,5-1000.AndwehearthisWorldWideWebthingisprettyusefulforfindinginformation,too. DepartmentofPhysics,JeffersonLaboratory,3rdfloor

www.physics.harvard.edu Chair,EfthimiosKaxiras(kaxiras@physics)DirectorofAdministration,AnneTrubia(trubia@fas) DirectorofUndergraduateStudies,HowardGeorgi(hgeorgi@fas) Co-DirectorofUndergraduateStudies,DavidMorin(djmorin@fas) UndergraduateCoordinator,CarolDavis(davis@physics) TheemailaddressofProfessorLastnameofthePhysicsDepartmentisusually:lastname@physics.harvard.eduorlastname@fas.harvard.edu.

SocietyofPhysicsStudents IfyouhavequestionsaboutanythingrelatedtophysicsatHarvard,sendusanemailat:

harvardradcliffesps@gmail.com (ifyoudon’tgetaresponsewithinaweek,emailoneoftheofficers)

Forevents,SPSboardminutes,picturesandmore,goto www.hcs.harvard.edu/~physics

Signupforourmailinglist: sps-list@lists.hcs(majorSPSandDepartmentannouncements): https://lists.hcs.harvard.edu/mailman/listinfo/sps-list

YourSPSofficersthisyearare: Co-Presidents:ChrisFechisin(cfechisin@college.harvard.edu)

SambuddhaChattopadhyay(chattopadhyay@college.harvard.edu)

EventCoordinator:

BenjiKan(benji_kan@college.harvard.edu)

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Secretary: RajathSalegame(rajathsalegame@college.harvard.edu)

Webmaster: AndrewWinnicki(awinnicki@college.harvard.edu)

Postalmail,althoughwehaven’tthefoggiestideaofwhatyou’deverwanttomailus:

H/RSocietyofPhysicsStudentsJeffersonLaboratoryHarvardUniversityCambridge,MA02138

OtherDepartmentsandImportantPeople DepartmentofAstronomy,ObservatoryP-212 astronomy.fas.harvard.edu CenterforAstrophysics www.cfa.harvard.edu KarinÖberg,DirectorofUndergraduateStudiesinAstrophysics koberg@cfa.harvard.edu DepartmentofChemistry,Mallinckrodt118 chem.harvard.edu GreggTucci,HeadTutorinChemistry tucci@fas.harvard.edu DepartmentofEarthandPlanetarySciences,Hoffman4thfl. www.eps.harvard.edu SchoolofEngineeringandAppliedSciences,Pierce212a www.seas.harvard.edu DepartmentofMathematics,ScienceCenter325 math.harvard.edu STAHR(StudentAstronomersatHarvard-Radcliffe) www.hcs.harvard.edu/~stahr HarvardChemistryClub www.hcs.harvard.edu/chemclub

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TheBackPageThe precedingwonderful and useful bookletwas prepared by the Harvard-RadcliffeSocietyofPhysicsStudents,anon-profitorganization(areallynon-profit organization) dedicated to making physics students happy throughmentorshipandadvising,establishingexcitementaboutthewonderfulfieldofphysics, and by fostering a social and friendly physics community. And, ofcourse,obtainingfreefood.Allarewelcometojoinourmeetings. This booklet was originally written by Derrick Bass, Theresa Lynn, andCynthiaPhillips. Itwasupdatedin1996and1997byCharleneAhnandBenRahn;in1998and2000bythethenSPSOfficers;in2001and2002byCraigHetheringtonandGenevieveReynolds;in2003byWilliamZaientz;in2004byDougMcClure,BartHornandMarcParris;in2005byPeterWilliams;in2006byLimorSpectorandBailesBrown; in2007byBenedictHuangandOgnjenIlic;in2008byLinCong;in2009byKennyGotliebandAnjaliBhatt;in2010by Nikko Pomata; in 2011 by Phil Yao, Marlee Chong, Kristin Barclay, AmyChen, Tom Rice, and Annie Baldwin; in 2012 by Joanna Behrman and AmyChen;in2013byKateDonahue,AmyChen,andAbelCorver;in2014byMarkArildsenandEricMetodiev; in2015byMarkArildsen,PatrickKomiske,EricMetodiev,andEricAnschuetz;in2016byEricAnschuetz,KaanYay,SidharthChand, Alexander Nie, and Samuel Liu; in 2017 by Kaan Yay, Peter Chang,Adam Frim, Samuel Liu and Pradeep Niroula; in 2018 by Elba Alonso-Monsalve and Vaibhav Mohanty; in 2019 by Maya Burhanpurkar, AbijithKrishnan, Sambuddha Chattopadhyay, and Dan Stefan Eniceicu; in 2020 byBenji Kan, Sambuddha Chattopadhyay, and Rajath Salegame. We take soleresponsibilityfortheopinionsexpressedinthisbookandonceagaincautionyouthatmuchofthismaterialisopinion. Wewouldalso like to thankthe followingpeople for theirvaluablehelpandinsight: DerrickBass,CarolDavis,GaryFeldman,HowardGeorgi,MargaretLaw,DavidMorin,andChrisStubbs Wewouldgreatlyappreciatefeedbackonthisbooklet:didithelpyou?Whichsectionsweremostuseful? Wouldyouliketoseemoreofsomething, lessofsomething? Suggestionsforothersections,betterorganization,abettertitle,oramorefashionablewardrobeforSPSofficersarewelcome.DropcommentsintheSPSbox,giveusacall,orsendusemail! Haveawonderfulyear,andwehopetoseeyourpictureontheconcentrators’bulletinboardinthespring!