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  • 8/8/2019 October 2010 Issue v3 1

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    overloadingviaacademicdarwinismbethefittestduringthemadscrambleofregistration

    awhiteandgoldenhomecomingvariousmembersofthecommunitysharetheirexperiences

    (P=NP)?The claim to an age-old questionthat could revolutionize computingsparks speculation in the CoC community.

    FIREWALL

    OCTOBER 2010 COLLEGE OF COMPUTINGAN

    NIVERSARYISS

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    12 grace hopper conference 2010Jamie and Jessica Crabb

    14upcomingeventsthe FIREWALL

    Checking the solution is relatively simple...but can nding the solution be just as easy?

    President chancello

    Karthik Narayan lvl

    editor-in-Chief minstrel

    Aurel Lazar lvl

    Chief CoPy editor countess

    Cristina Gonzalez lvl 314

    Chief Layout editor sorceress

    Jeanie Choi lv

    LeadWeb deveLoPer master ch

    Andrew Panfel lvl

    the firewall team

    4linux, from startto finishMatthew Amidon

    6academic darwinism: overloadsTom Pilsch

    8 programmingpuzzler()the Programming Team

    10(to p=np) or(to p=np)Michael Riley

    Writers

    Jamie CrabbJessica Crabb

    Michael RileyKlee Simmond

    Matthew Amidon

    CoPy-editingteam

    Cristina Gonzalez

    Aurel LazarAmanda ONeal

    Nicholas Smith

    Layoutteam

    Jeanie Choi

    Jamie CrabbJessica Crabb

    Taylor Kelly

    Courtney Smith

    Web deveLoPmentteam

    Andrew PanfelTaylor Kelly

    Courtney Smith

    Community Contributors

    Tom Pilsch

    2 october 2010the firewall

    contents OCTOBER 2010

    coverby jeaniechoi

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    Hey there, CoC!

    First of all, Id like to wish FIREWALL a very happy second birthday! Personalit has been really fun to watch FIREWALL evolve as an organization, wheAjai Karthikeyan and Mansi Sharma rst put things together. The rst issu

    a black and white newspaper, has evolved into a nice color magazine, thankto our dedicated staff members. Meanwhile, its been a really busy pamonth, hasnt it? Midterms, Grace Hopper, rst place at homecoming where do we begin? Meanwhile, behind stages, FIREWALL has worked realhard to produce this better-than-ever issue!

    Our feature piece for this issue is about the famous P versus NP problemHanging around Georgia Tech and especially the CoC, chances are thayouve been in a conversation or a class where P versus NP was brought u

    Were you twiddling your thumbs about, looking around, feeling nonplussedor should I say, NPed? Then read up on this introduction toP versus NP to get up to speed (no pun intended).

    Did you read an interesting article that youd like to hear more about?Let us know at [email protected]!

    If youd like to become more involved with FIREWALL, whether its wit

    writing a single article or its with joining the organization, please send us aemail at [email protected].

    From the FIREWALL team, hope you guys enjoy this issue!Karthik NarayanChancellor of FIREWALL

    3the president's letter

    WritingLayout Editing

    Web DevelopmentIllustratingArt/Graphic DesignPhotographySponsorship positionsMarketing/Publicity positionsPrinting and Distribution

    Experience is welcome but byno means necessary!

    COME HELP SPREAD THE FIREYou can contribute to the College of Computing Student Community!

    FIREWALL

    www.gtfirewall.com

    If you are interested, contact us [email protected]

    tWo

    the firewall

    turns

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    proceeding. First, the Linux le system is somewhatdifferent than Windows. There are no lettered drives,C,D. There is only the root folder, denoted by /.Take the path /home/users/you; the equivalentwindows path would be C:\home\users\you.

    Also, executable les are not indicated by their

    extensions alone (.bin, .sh, etc.), they all musthave the executable permission set. In Ubuntu, thispermission is found under a les properties. So, if youdownload an executable le and cant run it, be sure tomake sure it has been marked as executable.

    So, now that youve started running Ubuntu, youll

    probably have run into some of the more obviousdifferences between Windows and Ubuntu. For starters,the equivalent of the start menu, my documents, andthe control panel are now all on the left side of the

    upper panel. They are, respectively, applications, places,and system. On windows, if you wanted to install arandom program to do something, you would go toGoogle. In Ubuntu, all you have to do is go to System> Administration > Synaptic Package

    Manager. Programs are distributed in what are calledpackages, which are indexed by third party servers andexposed to your synaptic client. All you have to do issearch for a program, select it for installation, and thenhit apply. Synaptic will then download the package, anyof its dependents, and install it to your system. It isincredibly easy, and there are over 30,000 packageslisted as I write this.

    What if you run into a problem? For example, yourwireless doesnt work. Unlike Windows, Linux has atruly thriving community built up which is eager to helpnewcomers resolve their issues. You can either google

    a description of your problem, or search various forumssuch as www.ubuntuforums.org for a solution. In theunlikely event that there isnt a forum post detailinghow to solve your problem, you will most likely notneed to wait more than a day or two for a correct

    answer.

    Now that youve downloaded and resolved any issueswith Ubuntu, you may want to personalize it a bitLinux has a very open ended window managementsystem, which allows your bland default installationto get more eye candy than even the most expensiveversion of Windows. Simply install your video driver

    open a terminal, and type the following:

    sudo apt-get install compiz compizconfg-

    settings-manager emerald

    This is basically the command line equivalent ofsynaptic which will download and install CompizFusion, a window manager, and Emerald, a windowdecorator. Then go to System > Preferences

    > CompizConfg Settings Manager and checkthe following boxes: desktop cube, rotate cube, andwindow decorator. Then select the window decorator(not the check box) and alter the command propertyfrom whatever it is now to /usr/bin/emerald replace. Now you will have basic eye candy enabledYou can nd easy to install themes at various sites likecompiz-themes.org.

    By now, you should have a fully functioning and ratherpretty installation of Ubuntu. Hopefully, you will enjoyusing Linux as much as the rest of us.

    5linux, from startto finish

    CompizCong SettingsThe Synaptic Package Manager.

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    MEMO FOR:Georgia Tech Students

    FROM:The Student Services Team

    It is time to start thinking about

    the courses you want to takenext semester. If you are seriousabout graduating someday, you will

    come in to see one of us aboutyour options. You might even re-read and heed the advice we gaveyou last spring (see AcademicDarwinism, FIREWALL, Feb 2010)about registering as soon as your

    time ticket opens. These are thethings that will put you ahead of thecompetition in the great registrationlottery.

    Yet despite all your best efforts, you

    still might have difculty getting theclass you need at the time you wantand will have to go to Oscar and

    apply for an overload. As dauntingas this may seem to you, there aresome things you can do to improveyour chances of hitting the jackpotand getting that precious last seatin the class you must have. Here is

    our advice to you from the ghostsof registrations past.

    If you are a graduating senior and

    apply for an overload during PhaseII, the rst question we are going toask you is why you didnt registeras soon as your time ticket opened

    in Phase I. Like guring skating, wewill grade your response on bothtechnical and artistic merit.

    The stories you may have heardabout graduating senior priority ingetting into any class you need are

    just that urban legends. Your timeticket is your priority. If you have

    the hours to graduate, you likely wilhave one of the earliest time ticketsUse that priority or risk losing yourseat to an underclassman. If youcome to us at the end of Phase Ifor a seat in a required course thatphysically is full, you better start

    It seems that just as you get into

    the groove of a new semester andare starting to feel comfortablewith at least some of your courses,its times to start planning for theNEXT semester a life-time away!

    Well, Spring semester starts in lessthan three months, and registrationis even closer November 1st-19th and that will be here in aheartbeat.

    6 october 2010the firewall

    Registration got youStressed?

    http://scrapetv.com/News

    Academic Darwinism

    by Tom Pilsch

    Registration 101:Overloads

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    getting your story together totell your parents why you will bearound for yet another semester.There is not much we can do for

    you at that point.

    If you are not a senior, chances areyou are not a degree candidate.Please dont claim that you are. Itdenitely will not help you chancesto get an overload.

    The worksheet sheet you receive

    from your advisor is not anacademic contract. That term isreserved for those returning from

    drop, and we know who they are.You may think the worksheet is abinding agreement, but it is justadvice on what you need to progresstoward graduation. It is up to you

    to register as soon as you are able.Your overload request comes witha time stamp, and we do comparethis with you time ticket and when

    the class lled.

    If we tell you that all overloads areprocessed via OSCAR, we actually

    mean it. The constant emails, ofce

    visits, and phone calls from you willnot change our minds, but you mayremain on them for some time tocome.

    No, your professor cannot grantyou an overload. Please read theprevious paragraph again.

    Spring 2011Registration:

    November

    1st - 19th

    If you dont believe what we telyou and decide to escalate yourissue to the highest levels of theInstitute, please have the forsight

    to include your GD ID# and thecourse(s) you are having difculty

    with. The people on The Hill wiljust send your e-mail back to us forresolution. We are up to our armpitsin alligators during registration, andif we have to do a lot of digging tond who you are, we just might notget to your problem as quickly asyou would like.

    Remember that having to requestan overload is like an encounterwith the law. It is there to help youbut is best avoided. And you canavoid that pain by planning aheadand registering early.

    If you nd yourself in the position

    where you need to ask the systemfor help via an overload, rememberthe advice your parents gave you ifyou ever get stopped by the policeStay Cool! You can help us do thatby not generating any more heatthan necessary. We really do haveyour best interests at heart.

    One last thing:

    Remember the First Law ofAcademic Darwinism:

    The Seats Go to the Swift

    7registration 101: overloads

    TicketImage:1.bp.b

    logspot.com

    Monkey Image: www.lydiadeniz.com/

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    A deranged algorithms professor has devised a terriblenal exam: he throws his students into a strange mazeformed entirely of linear and circular paths, with linesegment endpoints and object intersections forming the

    junctions of the maze. The professor gives his studentsa map of the maze and a xed amount of time to nd theexit before he oods the maze with xerobiton particles,causing anyone still in the maze to be immediatelyinverted at the quantum level. Students who escapepass the course; those who dont are trapped forever ina parallel universe where the grass is blue and the skyis green.

    The entrance and the exit are always at a junction asdened above. Knowing that clever ACM programmingstudents will always follow the shortest possible path

    between two junctions, he chooses the entrance andexit junctions so that the distance that they have totravel is as far as possible. That is, he examines all pairsof junctions that have a path between them, and selectsa pair of junctions whose shortest path distance is thelongest possible for the maze (which he rebuilds everysemester, of course, as the motivation to cheat on this

    exam is very high).

    The joy he derives from quantumly inverting themajority of his students is marred by the tedium ofcomputing the length of the longest of the shortest paths(he needs this to know to decide how much time to put

    on the clock), so he wants you to write a program todo it for him. He already has a program that generatesthe mazes, essentially just a random collection of linesegments and circles. Your job is to take that collectionof line segments and circles, determine the shortestpaths between all the distinct pairs of junctions, andreport the length of the longest one.

    The input to your program is the output of the programthat generates his mazes. That program was written byanother student, much like yourself, and it meets a fewof the professors specications: 1) No endpoint of a

    line segment will lie on a circle; 2) No line segment willintersect a circle at a tangent; 3) If two circles intersectthey intersect at exactly two distinct points; 4) Everymaze contains at least two junctions; that is, a minimummaze is either a single line segment, or two circles thatintersect. There is, however, one bug in the program(He would like to have it xed, but unfortunately thestudent who wrote the code never gave him the sourceand is now forever trapped in a parallel universe.) That

    bug is that the maze is not always entirely connectedThere might be line segments or circles, or both, off

    by themselves that intersect nothing, or even littlsubmazes composed of intersecting line segmentsand circles that as a whole are not connected to the restof the maze. The professor insists that your solutionaccount for this! The length that you report must be fora path between connected junctions!

    Line segments only. The large dots arethe junction pair whose shortest path isthe longest possible.

    (See File1.in)

    Note that in this case there is alsoanother pair of junctions with the samelength longest possible shortest path.

    (See File2.in)

    The line segments are connected bya circle, allowing for a longer shortestpath.

    (See File4.in)

    byThe Programming Team

    8 october 2010the firewall

    ProgrammingPuzzler()

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    Input

    An input test case is a collection of line segments and circles. A line segment is specied as "L X1 Y1 X2Y2" where "L" is a literal character, and (X1,Y1) and (X2,Y2) are the line segment endpoints. A circle ispecied by "C X Y R" where "C" is a literal character, (X,Y) is the center of the circle, and R is its radiusAll input values are integers, and line segment and circle objects are entirely contained in the rsquadrant within the box dened by (0,0) at the lower left and (100,100) at the upper right. Each testcase will consist of from 1 to 20 objects, terminated by a line containing only a single asterisk. Followingthe nal test case, a line containing only a single asterisk marks the end of the input.

    OutputFor each input maze, output "Case N: ", where N is the input case number starting at one (1), followed

    by the length, rounded to one decimal, of the longest possible shortest path between a pair of connectedjunctions.

    File1.in

    L 10 0 50 40

    L 10 40 50 0

    L 10 10 60 10

    L 0 30 50 30

    Outputs: 68.3

    File2.in

    C 25 25 25

    C 50 25 25

    C 25 50 25

    C 50 50 25

    Outputs: 78.5

    File3.in

    L 0 0 80 80

    L 80 100 100 80

    Outputs: 113.1

    File4.in

    L 0 0 80 80

    L 80 100 100 80

    C 85 85 10

    Outputs: 140.8

    Please send solutions to w. Good luck!

    9programming puzzler

    details

    examples

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    Vinay Deolalikar, Principal Research ScientistSource: HP Labs (hpl.hp.com)

    10 october 2010the firewall

    If you are an algorithms enthusiast, you havedoubtlessly heard about the latest proof from VinayDeolalikar of HP labs which claimed PNP. It tookthe academic community less than 2 months tond fundamental aws within the proof, but manyexpressed hope that this is a good rst draft to a nalsolution.

    wBut what is P and NP? And why is it important forcomputing?

    P and NP both describe a general set of problemsthat describe what a Deterministic Turing Machine(a computer) can and can not accomplish. The set'P' denes all problems that can be solved in a setpolynomial time. Algorithms that are solved in O(n),

    O(n2) are all in P. An example of a problem within Pis, determine the greatest common denominator ofintegers a and b. There is a simple algorithm we canfollow to determine the factors of our variables, andthe number of computations we must run is bounded

    by the size of the integers, so clearly a computer cansolve this problem.

    (To P=NP) OR (To P=NPverify, but hard to derive is the basis for algorithmsthat ensure secure encoding of messages, and the

    birth of computer security as we know it today.

    One of the earliest encryption algorithms is theRivest-Shamir-Adleman algorithm (RSA), whichuses encryption and decryption keys for sendingsecure messages. If we have person A, Alice, how

    do send a message to person B, Bob, without havingperson C, Charlie intercept and read the message?Each person has a public encryption key, whicheveryone can use to encrypt a message to that userEveryone also has a private decryption key that eachspecic person can use to decrypt messages sent tothem. So all Alice has to do is use Bob's encryptionkey on her message, and send it to Bob. If Charliereads it, then all he sees is garbage. But Bob has his

    by Michael Riley

    'NP' problems however, have a much greater rangeof complexity, and cannot be solved by a Turingmachine. They generally have an exponentialcomplexity, such as O(2n), or O(nn). A famous exampleof an NP problem is the traveling salesman problem.The problem is easy to explain: Given a set of cities,come up with the shortest tour around each city.Interestingly, the traveling salesman problem could

    be solved if you had many computers all calculatingthe shortest tour from a given path, but you wouldneed a theoretically innite number of machine tocalculate the exact answer. So the problem falls inthe realm of 'NP'. We have algorithms that can comeup with good answers , but they are not alwayscorrect. An interesting side effect of NP problemsis that verifying the correct answer can actually fall

    within the realm of P. Problems that are easy to

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    private decryption key, only he can use it to get backthe original message. As long as it's really hard toderive the decryption key given the encryption key,the system is secure.

    Both the encryption and decryption keys are justinteger values. The process for generating the keys(D and E respectively), relies on the NP problem ofprime factorization. It is really hard to derive primefactorization for really big composite numbers. So aslong as you cannot efciently factorize, then RSA issecure. In order to generate the keys, you must:Pick 2 unique prime numbers: p and q. For thisexample, I will use 7 and 13, but the algorithmrecommends picking 100 digit decimal numbers.Calculate n = pq, and calculate = (p-1)(q-1). Our n

    is equal to 91, our is equal to 72.Choose an integer e between 1 and exclusive.This is our encryption key value. The algorithmrecommends picking large values for e, but our rangeis relatively small anyways. I go with 5.Calculate another integer d such that(d e) % = 1. You can easily write this as gcd(d,)=1, and use a reversed Euclids algorithm to solvefor d. Clearly, your decryption key is depended on

    your encryption key. Our lowest possible d for thisproblem is 29. We can verify this by the algorithm

    above: (29 5) % 72 = 1.

    Now that we have both of the keys how do we actuallyencode a message? If someone wanted to send usthe message hello mike, they would rst have toencoded the message into numbers, and block eachsection into message chunk. For this example I'lluse a small, simple alphabet. A = 1, B = 2, C =3, etc. We'll also just make whitespace = 99 just forthis example hello mike, when blocking into 2 digit

    blocks, would look like: 08 05 12 12 15 99 13 09 11 05.

    Then to encode, you take each message block, raiseto a power of e (your encryption key), and mod by n.In algorithm form, it reads as Me(mod n). Using oure from above, the rst block becomes (85) % 91 = 8.The next block is (55) % 91 = 31. The entire encryptedmessage reads as 08 29 00 00 63 27 61 09 59 29.To decrypt, you run the same algorithm, with yourdecryption key instead. If you run the algorithm, youcan see that the original message returns: 08 05 1212 15 00 13 09 11 05.

    In this example, our n was comparably small, soour message chunks were one character eachHowever, this means that each character hashed outto a certain value, and all Charlie has to do is keyeach character with an encrypted value. In practice

    your end up grouping many characters at a timeso that keying each possible value quickly becomesinfeasible. An encoding method that more complexthan simple substitution is more than sufcientlyencoded. Of course, this encryption method is also

    broken the moment that Charlie is able to gureout d. Fortunately, in order to gure out d, Charliemust gure out p and q. Since factorization is an NPproblem, choosing a really large p and q means thatit would take the best known computer algorithm

    years to calculate. The record for highest numbe

    factored on a computer was 768 digits long, andmost keys today are at least 1024 digits.

    But what if Vinay Deolalikar is wrong, and P=NP?Then suddenly all of these problems thought to beimpossible for computers to solve efciently wouldnow, by denition, have a solution. Factorizing a largenumber would suddenly be solvable in polynomialtime, and RSA encryption would no longer be secureIn fact, most modern day cryptography wouldno longer work, as they rely on the fact that some

    problems are easy to verify, but hard to computeFortunately, mathematicians are skeptical that a P= NP proof can even exist, and most believe that P NP is much more likely to be true.

    Err, what is this P=NP?- P represents all problems whose solution can be found

    in polynomial time.

    -NP represents all problems whose solutions can be

    veried in polynomial time.-Polynomial time just means that the time to nd the

    solution has a polynomial relationship with the sizeof the problem. For instance, a particularly terrible

    sorting algorithm may take n2 seconds to sort anarbitrary list of names, where n is the number ofnames in the list. This is a second-order polynomial ofthe form (a+b)(n+c)(n2), where a = b = 0, and c = 1.

    -And nally, does P=NP?

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    by Jamie Crabb and Jessica Crabb

    The Grace Hopper Celebrationof Women in Computing (GHC),named in honor of one of the veryrst computer programmers, washeld from 9/28 -10/2 in Atlanta thisyear. It was the largest GHC so farwith 2,147 attendees representing29 countries and 280 schools.Georgia Tech had the largest

    group with 69 women attending.The conference provided a uniqueopportunity for the women atGeorgia Tech as well as the rest ofthe women in the technical eld tomeet with companies, have theirrsums critiqued, network witheach other, display their research,

    learn about new opportunities,and get inspired by the successfulwomen already working in the eld.

    The career fair allowed for studentsto meet with 75 notable companies,including Adobe, Amazon, Apple,AT&T, Cisco, Comcast, Facebook,Google, HP, IBM, Intel, Microsoft,

    and Yahoo!. The poster sessionallowed students to highlight theirresearch; Georgia Tech presentedtwo posters. How to Attract

    Students to Computing? presentedby Barbara Ericson featured ways toattract students (especially femalesand underrepresented minorities)

    from the fourth to twelfth gradesto computing. Her poster was a bighit with attendees in part becauseit showcased the adorable Pleorobotic dinosaurs.

    Victoria Ayo posing holding a Pleo, with

    Barbara Ericson and her poster in thebackground.

    Inspiration came to the audienceof technical women in the formof panels, sessions, and keynoteaddresses. A record 630 speakersattended this years GHC. One

    notable keynote speaker was CarolBartz, CEO of Yahoo! and one

    of two female CEOs of Fortune500 companies. She spoke of theimportance of embracing change,standing up for yourself andstanding up to the guys. In her mostmemorable quote she said Itsvery easy to get put into rolestonot let our stars shine. Sometimesyou have to be [aggressive]. Stand

    up for yourself. You have to manageyour own career. After her speech,awards were given to inspiringwomen in technology - those whohave used technology to impactthe lives of other women in theircommunities and around the world.

    Sometimesyou have to be

    [agressive]. Standup for yourself. Youhave to manage

    your own career.

    Carol Bartz, CEO of Yahoo!, inserting

    some sass into her speech.

    12 october 2010the firewall

    Computer EngineerBarbieThe popular doll Barbie willbe adding Computer Engineerto her long resume thanks

    to online voters. She will bewearing a binary code tee,

    comfortable wedges and a hotpink laptop. This will hopefullybe a positive inuence for younggirls interested in computing.

    Grace Hopper ConferenceCelebrates Women in Computing

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    W@CC members at the Georgia Tech

    sponsored Dance Party.

    Georgia Techs GHC shirt in front of aBeluga Whale at the Aquarium party.

    Women enjoying dinner at the dance

    party at the Georgia Aquarium,sponsored by Google and Microsoft.

    Poken

    Poken is a social business cardthat automatically transfers yourinformation to a new contact. It

    features a USB, a hand for virtualhandshakes and an online locationfor contact information. Studentswere given pokenSparks free. The

    pokenSpark showcases a cutedesign with easy functionalityand was the primary way toconnect with other attendees andpresenters at GHC.

    When 2,000 women come togetherfor one cause, there is sure to be agood time had by all. One of those

    good times was the Georgia Techsponsored DJ Dance Party, which

    allowed the women in technologyto let loose, have fun, and get toknow the other attendees. Anothermemorable highlight was GHCSponsor Night at the GeorgiaAquariumsponsored by Microsoft and Google.(Dont worry; there werent any

    Bing vs. Google ghts.)The music, food, free t-shirts, viewsof Beluga whales and chance tomeet smart, successful womendenitely made for an unforgettablecombination.

    The Grace Hopper Conferencewas a truly unique and amazing

    experience for women incomputing, and reportedly thelargest gathering to date of womenin technology. Every year the GraceHopper Celebration of Women inComputing grows as the inclusionof more women in the computingeld becomes a more widespread

    goal. This winter a sister GraceHopper Conference will be heldin India to grow its community offemale computer scientists. Nextyears conference will be held inNovember in Portland, Oregon.

    All pictures by Jamie Crabb and Jessica Crabb,except for the following:Barbie: mattel.comPoken: pokenlive.com

    The ofcial poster for the 2010 GHCexemplies this years motto:Collaborating across Boundaries.

    13grace hopper conference 2010

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    October

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    firgen

    Hungry HungryHackers

    Saturday, October 23rd10 AM - MidnightGTRI Conference Center

    ESP Smash Brothers TournamentSaturday, October 30th5-11PMPiedmont room, Student Success Center

    Entrants must bring own controllers.

    W@CC Disney KaraokeNight

    6-7pmEVERYMonday

    Friday, October 22nd

    5 PMKlaus 1116W

    Enjoy an evening singing Disney songs and

    meeting new people!

    uPComing events

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    November

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    Microsoft College PuzzleChallenge

    Saturday, November 6th12 PM - 11 PM

    Save the world from the Apocalypse on a SaturdayRegister online at www.collegepuzzlechallenge.com

    Upsilon Pi Epsilon Interview FairTuesday, November 9th11-2PMKlaus 1116

    Come talk to others who have done internships invarious companies (and get swag!)

    Turkey Ball

    Saturday, November 20th8 PM - 1AM

    Klaus 1116

    Conjured up by Minorities@CC in collaboration w

    Hispanics@CC, Women@CC, and other studentorganizations, the Turkey Ball will serve as a fundraievent for unprivileged families. Want to dance, eatdelicious food, have an awesome evening, and helpdonate to charities on November 20th? Simply brin

    canned food (at least two) to be admitted.

    College of Computing

    3rd Floor Room 347WaLLmeetings

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