LUMS Alumni Magazine 2008
Transcription
LUMS Alumni Magazine 2008
Message from the Alumni Relations Office Dear Alumni, The LUMS Alumni Annual is here again, with news from LUMS as well as your fellow alumni. This year’s class notes again speak of achievements and new efforts by you all despite the political upheaval in the country as well as the erratic economics of the world in general. The LUMS alumni community is now a very strong professional network the world over with numerous and varied experiences. Therefore, along with various interviews and articles, we have incorporated this year the alumni perspective of the workplace. We thought that you all can relate to what these alumni have to say about the real work environment. The year 2008 has taken LUMS through quite a few changes but one thing that stays constant is the alumni bond with the university. The Homecoming in December 2007 saw a huge audience. Similarly the chapter reunions in 2008 not only had heavy alumni participation but were also supported by volunteer alumni in terms of organization. The Islamabad Reunion was hosted by an alumnus at his own restaurant. The Alumni philanthropic efforts continue with financial contributions from various classes as well as individuals. Your ideas, feedback for improvements in systems and your participation in the LUMS projects and researches gives all these endeavors remarkable strength. We thank you all who took the time out to compile the class notes or to write articles. Like every year, this year’s issue has also been structured through your ideas and written contributions. We look forward to your feedback on Alumni Annual 2008 as well as your ideas for the next year’s issue Regards, Amna Arshad Ali Alumni Relations Office Pro-Chancellor’s Message Dear Alumni, The year 2008 sees the joining of the first batch of School of Science and Engineering, a school that aspires to provide science & engineering education that our country has not previously known. The Suleman Dawood School of Business and the School of Humanities, Social Sciences and Law are progressing with more diverse educational programmes coming up every year. The National Outreach Programme is continuing to be a source of providing quality education to talent from the underprivileged areas of the country. Like every year we hear of our Alumni reaching greater heights in their professional journeys. The achievements of our Alumni are always a source of pride for us and of course we hope that the progress of your University will be an inspiration to you. You, being Alumni are the most important stakeholders in LUMS as you, more than anyone else, can realize all what we stand for and all that we aspire for. We therefore, look towards your active involvement in the form of ideas as well as valuable feedback. I wish you another year of professional and personal achievement. Syed Babar Ali Syed Babar Ali in Nepal, February 08 Lahore University of Management Sciences has been enriched by the commitment and dedication of many people, and it is now ready to become a source of national renewal and international leadership. As we develop and implement a vision for LUMS in the 21st century, we ask alumni to help fulfill the promise inscribed in the famous LUMS insignia, “prepared for life.” You are uniquely qualified to contribute to the envisioned strengthening of this wonderful university and for improving the LUMS educational experience as a preparation for life. It is my aspiration that LUMS alumni enjoy a lifetime of networking, learning, and leadership by staying connected with their alma mater. We hope to engage you more than ever before in creating the next vision of this university. A first step towards this goal has been the formation of a dedicated office under the leadership of a very capable LUMS alumnus, Sheikh Ali Hussain, who will spearhead this renewed commitment to reach out to our alumni. I ask you to reflect on my thoughts below and suggest any new ways in which you may be able to help LUMS attain new heights. You are a source of strength and symbol of success for LUMS and I hope that we can continue to count on your unwavering support as we begin to shape LUMS as a world class university. Alumni will be vital in developing a 21st century vision for LUMS by Joining in the Focalpoint Forum programs to create a vision for the future Identifying opportunities for changes that will benefit students Participating in continuing education, mentoring students, and joining in activities such as university events, alumni lectures and alumni outreach Identifying corporate sponsors and partnership opportunities for LUMS Contributing funds for scholarships, awards and general operating money Making visible their identity as LUMS alumni in their professional, civic and personal lives For the past 26 years, I have been a professor of civil engineering, an associate dean of engineering, a researcher, and the sponsor of new initiatives in business and social entrepreneurship at one of America’s leading research universities, Rice University, in Houston, Texas. Recently I have been active in bringing together scientists, engineers, and social scientists in developing new approaches to earthquake risk mitigation in Pakistan and South Asia. I am honored and delighted to have been chosen to lead LUMS, and I deeply cherish the opportunity to contribute to higher education in the country of my birth. Dialog and discussion are crucial to achieving our goals, and alumni must have an important voice. I invite you to contribute to this exciting dialog and look forward with great expectation to your active involvement in the advancement of your alma mater. Ahmad J. Durrani, PhD, MBA Vice Chancellor, LUMS durrani@lums.edu.pk Who’s back at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“I am a local boy,” says Dr. Shaukat Ali Brah with unmistakable pride and a broad smile. The present Dean of Suleman Dawood School of Business started his academic career in Lahore - from Garrison School and Government College to the University of Engineering & Technology as a student of Mechanical Engineering. With a host of fond memories and a solid foundation in place - courtesy some of the best institutes in the country - Dr. Brah set the stage for his later successes. for a special issue of International Journal of Service Industry Management, served as an Associate Editor for Asian Case Research Journal for over five years until recently, and is a member of the editorial board of Decision Sciences Journal. To further strengthen his portfolio, there are numerous refereed papers, case studies, conference papers, etc, that Dr. Brah has contributed to. What’s more, since July 2007 he has been spending his days and often late evenings at LUMS as the Dean of SDSB. Following his scholastic ambitions, he departed to the US to add the much-coveted title of Dr. Shaukat Brah is not new to LUMS. He has been here before. Prior to his NUS experience, he Introducing well as professional lives. Moving up the academic success ladder at NUS with his refreshing demeanour and positive attitude, Dr. Shaukat Brah also kept an active interest in executive education, teaching in a broad range of open and customized executive programmes for industry leaders like, Samsung Asia, Indah Kiat Pulp and Paper Corporation and Toshiba Asia, etc. As a mature academic, he enthused a new life into the Business School with his progressive policies and a whole new set of goals…not just for the students, but also for the School. Dr. Shaukat Ali Brah Dean of SDSB ‘Doctor of Philosophy’ before his name. He completed his PhD from the University of Houston, where he was given the opportunity to work on a research project on NASA’s Space Shuttle Programme. served LUMS as an Assistant Professor for two years in the late 80s and early 90s. At that time, the school was still in the process of establishing itself and hence, there was not much emphasis on research. “I was very fortunate to get that kind of exposure and experience,” says Dr. Brah, “as it opened many doors for me.” “The motto at the time,” recalls the Dean, “was ‘Businessman’s Business School.’ “Being more research-oriented, I was looking for something more in that direction.” To name just a handful of some such opportunities: He spent 16 years as a faculty member in the National University of Singapore’s Business School – consistently ranked one of the top three schools in Asia and among the top ten outside North America. He was the Production Editor of Asia Pacific Journal of Operational Research for a number of years, worked as a guest Editor Driven by his ambition as a scholar, he eventually decided to leave LUMS with a heavy heart and accepted a position as a faculty member at the NUS Business School. Though not before getting married! Six months into the marriage and the young couple was en route to Singapore, ready for exciting new challenges, both in their personal as “I believe that in order to make your mark, it is important to bear in mind the four ‘Rs’ as the main ingredients of success– Rigour, Relevance, Reward and Recognition,” Dr. Brah enumerates with gusto. Elaborating on each, he states, “Rigour or discipline and hard work is absolutely the most essential, for it instils in the students the stamina to take on difficult challenges and deal with them unfazed in the real world. Then comes relevance, it is imperative that the institute provides the kind of education to its students, which reflects the environment the students are meant to enter as professionals. Without Relevance in coursework, there is not much merit in the education. From the point of view of the students, a relevant education enhances, in fact,confirms their success as professionals, as they are able to add more value to the industry with their hands-on knowledge. As for Reward - the education provided should have the merit to groom well-rounded individuals who become an asset to the institute’s name and integrity. On the other hand, the students would be rewarded for their hard work with success in the real world. Finally, there is the final R – Recognition. It is the ‘WOW factor’ inspired in others that is the real proof of recognition for both, the institute and the student.” Incidentally, the four Rs have now found a new home in LUMS, along with several initiatives that the new Dean has introduced. His pride in his work and his unabated enthusiasm is infectious. Perhaps that is what is generating a whole lot of energy in the Business School these days with a flurry of activities all around. There is a new building for SDSB in the offing, expected to be occupied and fully functional by December 2009, while structural changes within the administration are keeping everyone on their toes. “I have just one goal,” declares the Dean, “and that is to make SDSB an internationally recognized school of global standing.” Considering the distinguished history that LUMS enjoys, he has complete faith that the university will achieve this goal sooner than anticipated. “In 22 years, LUMS is probably the only university that has established itself as the best in the country and one of the top institutes in the region,” he states indulgently, “In such a short span, it has grown considerably with 3 schools already in place and maybe more on the way. It is truly dynamic; in fact, I really think that there is no other place like LUMS.” According to him, LUMS is now moving from the initial, creative phase, which he describes as being “entrepreneurial” to a more mature stage that will allow for the building of a sound structure. Presently, the university follows a mix of both, North American and British models, but the Dean is in favour of implementing the former in its entirety. Being a true democrat at heart, he claims, “My task is to introduce policies, but it’s up to my team to approve or disapprove. There is no moving forward without that.” Encouraging his colleagues, faculty and staff members alike, in the decision-making process through participation, he aims to create an environment of mutual trust and gratification. He has identified a few things that need fine tuning in the administrative departments, like more specialized training for areas like Corporate Communications and Advertising, but on the whole the new Dean is appreciative of the staff and considers them to be “very skilled and a great support” to the university. One aspect that the Dean especially feels strongly about is research and is enthusiastic about the fact that there is considerably more emphasis on it in this second, more mature phase of LUMS. In keeping with the former Vice Chancellor, Dr. Syed Zahoor Hassan’s vision of making LUMS a leading research institute, Dr. Brah is designing definitive policies for SDSB with his team of esteemed faculty members to realize this goal. Regarding plans for the future, he states that at present the main focus is on inducting more students for the undergraduate as well as postgraduate programmes. “The more competitive students we have, the more SDSB will flourish,” he beams. He believes in the uninhibited creative energy of the young students as being the driving force behind any prominent educational institute. “If you get the cream of the crop and nurture them without restraint, then you are bound to get the best results. I follow this philosophy and often tell my stu- dents that I’m not here to put road blocks in front of their ambition and energy, for it is this energy that will take the school forward.” In the same vein, moving from the present and potential students to the former ones, he applauds the alumni for their successes and for making SDSB and indeed LUMS proud. “We are proud of the alumni,” he says, “and hope they are proud of their alma mater and that they keep giving their valuable time, energy and contributions as always.” "*#( (( LUMS School of Science and Engineering (SSE) aims to provide a world-class education to the best students in Pakistan, independent of their financial background. Starting fall 2008, SSE will be the first private research school for science and engineering in Pakistan, providing an environment comparable to the best research universities of the world. SSE aims to (i) set a new standard for science and engineering education in Pakistan, (ii) produce technically competent graduates and innovative problem-solvers, (iii) create useful knowledge that can help address pressing local and global issues, and (iv) provide an opportunity to students from less-privileged backgrounds who would otherwise have little chance of obtaining a world-class education. It takes five things to create a world-class research school: a rigorous well-designed curriculum, excellent research-active faculty, world-class infrastructure, rigorous but need-blind admissions process and very strong financial foundations. SSE’s curriculum is as rigorous as that at the world's best universities. It has recruited some of the best available faculty, trained at places like MIT, Caltech, A Doorway to Opportunity Berkeley, Stanford, Oxford, Cambridge, Harvard, Princeton, Imperial and Yale. Its infrastructure and laboratories have been designed using global best practices. It has created an admissions process modeled on the best research universities; and it is raising resources to build a sustainable science and engineering research infrastructure, as well as to offer truly need-blind admissions. SSE is premised on a hope; that by getting the best minds of Pakistan and providing them with world-class education, it can influence the destiny of this nation. SSE hopes that its graduates will be change-agents who will contribute to the frontiers of knowledge and transform life as we know it. The school is committed to locating the best students in Pakistan from every section of society and from every socioeconomic background. As admission to SSE is need-blind, applicants are admitted based on their academic qualification without regard to their financial circumstances. If a student is admitted and the Financial Aid Committee determines that he/she cannot afford to pay, a customized financial aid package is created to enable that student to complete her/his education. SSE’s inaugural admissions cycle has received an overwhelming response with around 7500 students applying for 200 seats. Because of the limited opportunities in quality science and engineering education, and because of SSE’s need-blind admissions pol- icy, the demographics of this extremely competitive applicant pool includes people from widely varying backgrounds and financial circumstances. The final admitted students are some of the best in Pakistan. The quality of their interviews has been excellent and their performance on the SSE Admissions Test, impressive. Around 70-80% of the admitted students have indicated a need for financial aid. In keeping with its promise of need blind admissions, SSE has been exceedingly careful to make sure no one who was admitted and deserved financial aid has been denied assistance. Though the SSE has successfully catered to the financial needs of its first batch, there is a pressing need to raise funds for future batches so that the promise of need-blind admissions is honored. For this purpose the school is trying to establish an endowment for scholarships. Current SSE tuition is set at approximately 60% of what it costs the school to educate a student, so in a sense all students receive a significant subsidy. However, for less-privileged students, that subsidy is not enough. The school needs to fund their entire education. In this endeavor SSE needs societal, governmental and corporate support to build a large scholarship endowment, and to offer scholarships which would have reasonable certainty of continuity. Alumni support is essential to SSE’s vision of building a suc- cessful research school in Pakistan. By contributing to this endowment fund you have the chance to touch a life and make a difference for the better. By investing in the future of these children you are essentially investing in the future of Pakistan, helping make SSE a Doorway to Opportunity which will allow our deserving youth to take our country forward. := -9D 501-> 2110.-/6 -90 >@; ;:=? ;71->1 /:9?-/? @> -? (/4::7 :2 (/519/1 935911=593 (1/?:= * "-4:=1 -9?? &-65>?-9 )17 -C 8-57 >>10:9-?5:9 7@8> 10@ ;6 4??; >>1 7@8> 10@ ;6 By Uzair Haroon Moosa BSc 2004 After graduating from LUMS, I had the opportunity to spend a year at the Cisco Sales Associate Program (SAP), a year long training program in Amsterdam where candidates were imparted with sales and technical knowledge after which they were sent back to their home countries. The best way to describe this experience would be to walk you through a typical day. 6:00 am: “Trinnnng!!! Triinnnggg!!! Triiiiiinngggg!!!!” Damn I hate these alarm clocks. 6:15 am: I still hate these alarm clocks. 6:30 am: I get out of bed despite hating these alarm clocks. 7:30 am: I walk out of the house and prepare myself for the challenging day that would begin at 8:30 am sharp. I look at my watch and realize that the challenge might be beginning a little earlier; in order to catch the last tram to reach work on time I would have to cover the 10 minute walk to the tram station in just 5 minutes. What a start to the day! 8:27 am: I arrive at the office with three minutes to spare. Just enough time to grab a quick cup of hot warm cappuccino. I think about the week that lies ahead. We have an IT Network Troubleshooting exam, a product presentation to give and a commit meeting with the sales team all in the space of a mere 5 days. I take a deep breath and mutter, “It is going to be a typical week at Cisco.” 8:30 am: The day begins. Our managers, Chris and Jochen walk in and greet us. We are to begin the day with an impromptu hot spot role play exercise. Our managers lower the projector and we have five minutes to read through a scenario. “Oh my God, it is about ISDN and Frame Relay connections, my weakest topics” The managers are eyeing the room to pick one out of the 30 of us. They look around the room, their eyes freeze on me. I put on the most innocent look I can but it seems as if a miracle is far away. I walk up to the front of the room. My task is to obtain additional customer requirements, and based on these requirements come up with a customized Cisco solution all within the space of 20 minutes. The role of the customer will be played by the audience. I look at my audience; 29 exceptionally motivated Engineers, 3 highly experienced managers and 2 well qualified technical trainers. It is not going to be an easy task. As I present the Cisco solution, I am constantly questioned as to why I have chosen a particular product family,, why the particular product within that family, what value added features does this product have which competition does not provide. With the wide portfolio of products that Cisco offers, the dynamically changing nature of the technology market and the technical adeptness of my audience I have to leverage my technical and soft skills to the best of my abilities. Chris, our manager calls, “Time!” and we move into the feed back session. Feedback from 34 people; 34 people who have been making detailed notes on how I have conducted myself during the role play, 34 people representing 16 different countries - each bringing a unique perspective on the role play, 34 people who really want to see me grow!!! I pick up my notebook and start making notes of the constructive feedback that I am receiving. I marvel at the ability of my colleagues who are able to pick even very minute details, those details that would enable me, a good presenter, to become an effective presenter. 9:00 am: Technical training starts. Today, we are covering the troubleshooting course material. Tom, our technical trainer is explaining the Cisco best practices to troubleshoot a problem. “It is always good to isolate a network problem into a particular OSI layer before applying either the topdown, bottom-up or divide and conquer approach.” he explains. 12:00 pm: Lunch break. I just grab a quick salad and join my colleagues at the lunch table. I look around and notice that not two people at my table are from the same country. Such cultural variety is very enriching. 1:00 pm: Back in class and ready to do some of my own trouble shooting 5:30 pm: Still deeply involved in the trouble shooting exercises. Hmm…the access router can ping the core router. However, a telnet to the core router fails. The network, data link and physical layer must be working fine. I decide to apply the top down approach to troubleshoot the network problem further. 6:30 pm: I pack up and leave for home. The walk to the tram station is really nice. I can feel the spring wind blow gently on my face and at this point in time it makes me forget about all other worries that I have. 8:00: Have just had a nice dinner of chicken curry with some freshly baked chapatti. That should give me enough energy to start studying! 11:00: Decide to call it a day. Reflect back on the previous 5 months. I could have never imagined that my skill set would improve this drastically in such a short time span. At Cisco, there was guidance at each step – guidance to help us overcome our weaknesses; guidance allowing us to grow and yet be ourselves; guidance that served to maintain the uniqueness that makes us who we are. I look at the future that lay ahead. I had come a long way, but the journey was far from over. At Cisco, I learned that it is about continuous improvement. There is no denying that overwhelming challenges lay ahead – yet the resources available to overcome those challenges congruent. It is up to each individual how he/she decides to utilize the unprecedented resources at his/her disposal in overcoming those challenges. The Ayesha Ali Khan and Nabeeha Qazi BSc 2007 Graduation from one’s Alma Mater marks the end of one’s infant years and begins a new chapter in their lives. For many, this brings an unraveling of their dreams. For us, it meant making the giant leap into the corporate pool. From time in memorial, people have dreamt of the glorified corporate world. It is a land of opportunity. It is where young guns like us are meant to rise to the occasion and take on the corporations for all they’ve got. So with high hopes, we burst into the corporate arena. Yes indeed, this corporate world was ‘way cooler’ than those dorky deputy student years. Previously we had gaped in awe at the lavish lifestyle which had become a code of young budding executives. Now we were proud members of the same clan we had so idolized. Life was indeed good. We were attending high profile meetings. We formulated strategic business growth models. We had our gourmet breakfast meetings. We had our mobiles configured to receive critical emails at any time of the day. We were right up there. This Corporate Illusion corporate image was catching on to us real fast. But then, the second week of our induction began. The corporate cloud began to clear slowly and we were able to see our true relativity. Our crucial role in these high profile meetings, revolved around taking minutes and a few nods. Our contribution remained vital to the formulation of strategic business growth models in the back end market research support we provided. Our gourmet breakfast meetings involved daily congregations at the water cooler. Finally we eventually learnt modern mobile communication was not a blessing but a deterrent to an unavailable status. And where was the high powered, high cultured Wall Street executive disappearing to? Was it not about talking the talk and walking the walk anymore? Was it not about flying the corporate jet and having team building sessions in the Maldives? Was it not about watching the cricket final sitting in the VIP box sipping cocktails? No it wasn’t. The hyped up corporate arena slowly revealed its true colors. You eventually realize you never did take that giant leap into the corporate pool. In fact it seems you never left high school. Everyday as you enter, you see the arena so passively categorized. You see the corner reserved for the jocks, the table occupied by the cheerleaders, the hunched away nerds and techies, the swaying of the hippies and the lurking of the bad boys. They all come together working whilst remaining loyal to their alias. Just like in high school, one person would rule the most likely to succeed category. Perhaps the corporate world was a glass house effect or perhaps it was something for us to shape up. Our peers have risen to the challenge and have proven their worth. Many have gone places worthy of their potential. Perhaps eventually everybody will be classified under the most likely to succeed category. It is just a matter of how one defines their success. The LUMS MBA Methods and Memories By Saroop Gul MBA 2006 The beauty of the LUMS MBA case method of study is that it gives you a good feel of the real work environment. This is in contrast to the lecture method, where the frameworks and methodologies narrated by the professor are forgotten as soon as the students leave the classroom. In the case method since the frameworks are applied on real life scenarios, the retention levels rise exponentially. However, this you do not realize till you enter the real work environment. I think the most valuable lesson I learnt is that every situation is unique. ItÊs funny; back in class it seemed that only certain courses were very important, the rest were nice-to-haves. This might sound cliché but, it is really true that each module teaches something significant. I have lost count of the number of times when I have mentally referred back to cases while dealing with a situation on the job. For example, some of the aspects, which we tend to overlook but which, if properly understood, give you that extra edge, are: Culture and norms (religious, traditional etc.) are very important. I remember this case from China where the narrative about the central character in the situation marrying a local Chinese girl was ten pages long. (I agree, that was stretching it a bit too far). In todayÊs global village more and more of us are working abroad or have regional reporting lines. Even if most Gen-Y consumers watch the same sitcoms and movies, at the core they are all dif ferent. So while deciding to launch a new product you have to be sensitive to local needs. The general impression was that HR and OB courses were „dabba‰. You understand their relevance when these „dabbas‰ fall on your head, initially when you have to „manage your boss‰ and later when you have to „manage your reportees‰. Everyone has their unique style of working, the key lies in understanding and exploiting this uniqueness. Forcing your reportee to work late when he has a family to take care of, can wreak havoc with both his professional/ personal life. „Know the resistance point‰, a key takeaway which has helped me in not just business negotiations but also in other dealings. The tendency to do all your student projects with friends also backfires. Not working outside your core group ef fects your team building skills. In real life, you have to work with all sorts of people. The irony is that usually you end up working with those you donÊt like. True you canÊt like everyone and there are times when you have to stand up for what you believe in. Still you have to learn to keep your professional and personal lives separate. To excel, you have to have a working relationship with everyone. Very easy to preach, very dif ficult to follow but these are the rules of the game. You canÊt run away from numbers. Usually a CP based on number analysis to justif y your decision was highly regarded. Same is the case in real life. If you know how to use data to deduce meaningful information, people will regard you highly. ItÊs a myth that by not working in a bank you will be able to avoid Finance. At the end of the day profits rule. DoesnÊt matter which business or department you end up working for, there will be a time when you will be pulling your hair out while reconciling numbers. So its better not to avoid taking that Corporate Finance course because trust me it comes in handy. „So what have you decided?‰ A line oft repeated in every class, at the end of each case. You have to go this way or that. There is no in-bet w een.Int er es tingl y there is no one particular answer. Each option has its pros and cons but the most optimal has to be chosen. You have to use your judgment knowing that even after all the analysis, if that one assumption goes wrong, it will all fall down like a house of cards. In class it was just your CP on the line. In real life the stakes are much higher. Timing is the key. In class you have to think on your feet and tailor your CP as the discussion progresses, likewise on the job you have to decide to launch the product at the right time lest the competition takes advantage and becomes the leader. The two years of the LUMS MBA just fly away but they arm you with all the skills required to excel in the real world. The added bonus is the ton of cherished memories to keep you going through the harsh realities of real life. Thriller Night A happening year with the LUMS Music Society By Mohammad Hassaan Aslam The Music Society has always been committed to providing great exposure to musical entertainment at LUMS. The current Society President, Shibli Mansuri and Vice President Ammar Rashid, both from the Batch of 2008, along with their team took newer and bolder steps in the year 2007-08, resulting in the attainment of newer heights for the society, as well as for the music loving LUMS community. The year started like any other, with an unplugged gig for the new batch of 2011, where new and budding musicians were encouraged to perform without any restrictions on songs or the number of songs. During the autumn quarter, The Music Society hosted one of the most innovative and exhilarating internal events ever witnessed at LUMS. Held late in October, the concert, known as the “Thriller Night” was based along the lines of Halloween, where not only the performers, but also the crowd was asked to dress up in costumes. It was quite a sight in LUMS with people dressed as scarily as they could. Prizes were given out for the best costumes. The Music Society then hosted one of the biggest external concerts in the history of LUMS. In collaboration with The Music, the concert was known as the “Rock Drive”, and it included a number of famous performers and bands from Pakistan, including Siege, Akash, Annie, Shafqat Amanat Ali, Roxen and Call. The concert was an instant hit, drawing a large crowd. Highlights of the night were Shafqat’s classical solos without music and Call who not only did their famous numbers but also covered Bon Jovi’s “It’s My Life.” The Music Society also collaborated with the LUMS Entrepreneurial Society and helped them organize the YLES ’08 concert in the Sports Complex. This was another huge event, featuring bands like Mauj, Noori and Josh, drawing a crowd of more than 3000. After “recuperating” from all the excitement, the Music Society took stage again in spring, where they hosted another ground-breaking event, the “Maula-Jutt Rock.” It was an internal event which catered only to Pakistani music, themed around our very own Lollywood, where the backdrop included a picture of Maula Jutt holding a guitar. It was a new tradition, catering only to Urdu s o n g s , vowed to be continued over the years. The year-end was marked by another internal unplugged gig held in the new student lounge. It featured mostly the 2008’s, the graduating batch, a perfect goodbye to them. Apart from these events, other positive steps include improvement in the new music room, which has been shifted to the sports complex and purchase of new equipment particularly guitars. The Music Society is now looking towards the next year, with plans to hold panel discussions as well as instrument (guitar, drums as well as tabla) lessons. A new recording studio is being set up so that the musicians may record their originals in LUMS itself. All in all, The Music Society plans to continue with their efforts for promoting music within LUMS and also motivating the talented aspiring musicians here. Josh - Rocking the YLES Concert DRAMALINE The Dramatics Society at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ports at LUMS By Umair Rao Sports at LUMS (SLUMS) is one of the most active societies at LUMS and believes in providing opportunities to the student body that ensues to inculcate a sense of sportsman spirit, discipline and responsibility during all sporting events. Sports at LUMS is the largest society in LUMS which caters to approximately 60 % of the entire student body. Comprising of 17 different sports (Athletics, Badminton, Basketball, Cricket, Football, Hockey, Netball, Rugby, Snooker, Squash, Table Tennis, Tennis ,Softball, Swimming, Weightlifting, Boxing and Vol- leyball), it caters to the entire LUMS student body as it renders to be a platform to challenge one’s athletic abilities and provide the opportunity to pursue a sport one already knows or yearns to learn. SLUMS successfully manages to host various inter and intra university tournaments every academic year. These entail annual fixtures with various universities, participation in the large scale annual Higher Education Commission (HEC) Sports tournaments and participation in All-Pakistan sports tournaments. The highlights for the last year were two international trips. The first one was the result of the proactive Rugby team that participated in the International 7s Rugby tournament in Dubai where they played the best teams and faced tough competition. The Basketball, Volleyball, Football, Table Tennis, Tennis and Badminton teams participated in the International Sports Festival in Turkey held at and hosted by Bogazici University in Istanbul. Our claim to fame was our tennis team; the final was played between Muteeb Pasha and Said Khan (both LUMINITES) and won by Muteeb Pasha. Shaza Fatima and Zainul Abideen won the third position in mixed doubles in badminton, whereas Misha Rehman bagged the third position in Tennis. SLUMS last year had the honor to host and organize the biggest ever National Inter-University Table Tennis Tournament in which 40 universities from all over Pakistan participated. This tournament was held over a period of four days and Karachi University emerged as the champion after beating Punjab University in the final. The society also hosted the Nirala Futsal Challenge that attracted 32 teams, both university and school level, to play “6 a side” football matches. There were three fields where matches took place at one time, attracting loads of students, teachers and supporters for external teams. This first of its kind tournament was very successful. The Clash of the Volley bulls was also another huge event which took place at the beach court and in which approximately 16 teams participated. Sponsored by Red bull, this three day tournament ended with a celebrity match in which cricketers, models and athletes were invited. Here the girls’ teams also participated and that was indeed a boost to their sporting abilities and interest. For all other sports; namely tennis, cricket, squash, hockey, badminton, basketball and rugby, a number of regional and national levels inter university fixtures were organized and played with great vigor, enthusiasm and sportsman spirit. SLUMS hopes and aims to take all the sports to new heights in the next year by providing training sessions for aspiring sportspersons and organizing all sorts of tournaments to encourage participation. Warid Telecom sponsored most of the events organized by SLUMS thus helping to promote sports at the university level. Their support is highly appreciated. The Passion for Volleyball A message from the volleyball representatives By Anum Basir & Qasim Hasnain All night All right-Happening Music-Interesting food- In the heat of August and the winds of December - Students across the batches are seen at no place other than the Volleyball Courts. Introducing to you our "Claim to Fame" for the term 07-08 and our love of life: VOLLEYBALL. Volleyball at LUMS is not just a mere sport; it's a sport which involves excitement, passion, and enthusiasm and most importantly the love for the game. We invite you to come and witness this passion and excitement directly live from LUMS volley courts (Beach court and Hard court). These are the courts where we have learned to enjoy play and play, where many have learnt after us in awe, inspiration, imitation and most importantly mere interest and passion. Thus we proudly claim that Volleyball is currently one of the most famous sports here at LUMS with the highest turnout in tournaments and the biggest support base. We had a number of tournaments during the last year; including a 3 on 3, 6 on 6, an Intersociety Volleyball tournament and Valentines Volleyball tournament. We participated in the annual HEC tournaments where both the boys and girls teams performed really well .The LUMS Boys Volleyball team even attended the Turkey sports festival hosted by Bogazici University. As reps for this year we hosted the Redbull "CLASH of the Volley bulls 07." It was a unique and exciting festival, as it was the only Beach (Sand) volleyball tournament to be held in Pakistan, which featured, both male and female teams playing simultaneously. We tried our best to take Volleyball to new heights this year and we'd like the new sports representatives to work harder on the popularity and skill of the sport by conducting more training sessions and encouraging those individuals to play who are interested but currently don't have the skill or incentive to play. t n e m it m m Co to c i t s a l o h Sc pursuits 0+ @ "(04669 !/(/ <905. 3(:; @,(9 ;/, # ! 0;,9(9@ !6*0,;@ /6:;,+ :,=,9(3 >,33 (;;,5+,+ ,=,5;: 5 *633()69(;065 >0;/ ;/, !6*0(3 !*0,5*,: , 7(9;4,5; 6- # ! ! :;(9;,+ ( :,90,: 6- 3,*;<9,: )@ 79640 5,5; 30;,9(9@ -0.<9,: 05 (20:;(5 "/, :,90,: :;(9;,+ >0;/ ( =,9@ >,33 9,*,0=,+ ,=,505. >0;/ -;02/(9 90- ( =,9@ :,5069 76,; 6(20:;(5 >/6 *(4, 05 -964 :3(4 ()(+ (5+ /(+ ;>6 :,7( 9(;, :,: :065: (; # ! "/, -09:; +0: *<::065 >(: -63 36>,+ )@ ( ),(<;0-<3 9,5+0;065 6- /0: =,9:,: , (3:6 ;9,(;,+ ;/, (<+0,5*, ;6 :64, 6- /0: <57<)30:/,+ >692: 90+(@ "04,: *6=,9,+ ;/, >/63, ,=,5; (5+ 9,4(92,+ ;/(; D -;02/(9 90-C: 3,*;<9,: (; # ! 9, 405+,+ 4(5@ 6- (20:;(5C: 90*/ /0:;69@ (5+ 30;,9(9@ ;9(+0;065E <:/;(8 /4,+ &<:<-0 >(: 05=0;,+ -964 (9(*/0 05 ( *65;05< (;065 6- ;/0: :,90,: ;/0: :,::065 (3:6 -,(;<9,+ 05 ;/, 90+(@ "04,: , 9,(+ /0: >692: ;6 ( -<33 /6<:, 05 !(,,+ !(0.63 ;/, 3(9.,:; (<+0;690<4 (; # ! 69 ;>6 /6<9: ;/, (<+0,5*, >/0*/ 05*3<+,+ 796405,5; 30;,9(9@ -0.<9,: :<*/ (: 41(+ :3(4 14(+ 96-,::69 /<9:/0+ 0A=0 ;;0@( !(@@,+ (5+ 6;/,9: >(: (4<:,+ >0;/ /0: >65+,9-<33@ >0;;@ (5+ /03(906<: >90;05.: 69 ;/, 5,?; 3,*;<9, 05 ;/, :,90,: ',/9( 0.(/ >(: 05=0;,+ -964 (9(*/0 >/6 ;(32,+ ()6<; /,9 ,?7,90,5*,: (: ( -,4(3, 76,; ), -69, ),(<;0-<3 9,5+0;065 6- /,9 76,;9@ $,9@ 9,*,5;3@ ( :,::065 >(: *65+<*;,+ 65 *65;,4769(9@ 9,5*/ 30;,9(;<9, )@ 9,5*/ !*/63(9 (90, ,:*(: ,*69+05.: 6- (33 ;/,:, :,::065: (9, (=(03 ()3, 05 ;/, # ! 0)9(9@ "/, :6*0,;@ *,3,)9(;,+ (0A /4,+ (0AC: )09;/+(@ 65 ;/, ;/ 6- ,)9<(9@ 5 ;/0: 6**(:065 ( 5,> >692 65 (0A /4,+ (0A )@ ( :;<+,5; 6- # ! >(: 79,:,5;,+ (5+ /0./3@ (779,*0(;,+ ;,,) <3 79,7(9,+ ( *6473,;, *65*69+(5*, 6- (0AC: >692 >/0*/ /, 79,:,5;,+ ;6 ;/, (<+0,5*, :0403(9 >692 65 /(30) *64 73,;, *65*69+(5*, 6- /(30)C: 76,;9@ 79,7(9,+ )@ "(04669 !/(/0+ >(: (3:6 79,:,5;,+ 65 ;/, 6**(:065 5;,9,:;05.3@ ,56<./ ;/0: 205+ 6- >692 /(+ 56; ),,5 (;;,47;,+ :6 -(9 05 #9+< *90; 0*0:4 ;/, 0965@ 6- >/6:, 796+<*;065 05 (5 5.30:/ :7,(205. <50 =,9:0;@ 0: 40;0.(;,+ 653@ )@ ;/, +,=6;065 6- 0;: (<;/69: (5+ ;/, 05:70905. :<7,9=0:065 6- 30;,9(9@ .0(5; 9 64(5<3 (8 90 +(@ "04,: *644,5;,+ 5 ;/0: 6**(:065 (0AC: +(<./;,9 !(3,,4( (:/40 9,*633,*;,+ :64, 63+ 4,4690,: (5+ ;63+ (5,* +6;,: -964 /0: 30-, ;6 ;/, (<+0,5*, (990: /(308<, >/6 *(4, ,:7,*0(33@ -964 :3(4()(+ (3:6 9,*0;,+ (0AC: 76,;9@ ;6 ;/, (< +0,5*, 9 64(5<3 (8 >/6 0: (3:6 ;/, 7(;965 6- ! ;(32,+ ()6<; ;/, ),(<;0-<3 4,;(7/69: 05 (0AB: 76,;9@ >/03, 9 %(:,,4 ;(32,+ ()6<; ;/, 9,3,=(5*, 6- /0: 76,;9@ ;6 *65;,4769(9@ ;04,: "/0: ,=,5; >(: -6336>,+ )@ ( /(A(3 50./; >/0*/ >(: 69 .(50A,+ 05 *633()69(;065 >0;/ ;/, # ! 644<50;@ !,9=0*, !6 *0,;@ "/, -09:; /6<9 6- ;/0: 50./; >(: +,+0*(;,+ ;6 (0AC: 76,;9@ !;<+,5;: 6- # ! :<7769;,+ )@ ;9(05,+ 4<:0*0(5: 05 *3(::0*(3 .,59, :(5. ),(<;0-<3 ./(A(3: "/0: >(: ( */(90;@ ,=,5; (5+ ;/, -<5+: ;/<: 9(0:,+ >,9, <:,+ ;6 /,37 ;/, :<7769; :;(-- (; # ! ! (3:6 *65+<*;,+ ( ;/9,, /6<9 365. *(330.9(7/@ >692:/67 -69 ;/, :;<+,5;: 6- # ! :;<+,5;: (;;,5+,+ ;/0: >692 :/67 *65+<*;,+ )@ 796405,5; *(330.9(7/,9 !(11(+ /(30+ >/6 /(: :;<+0,+ -964 (5+ 0: 05 (2 0:;(5C: (330.9(7/,9C: <03+ "/, :6 *0,;@ 73(5: ;6 *65+<*; ( :0403(9 >692:/67 05 ;/, 5,(9 -<;<9, ! (:709,: ;6 *65;05<, >0;/ ;/,:, ,=,5;: (5+ /(: :,=,9(3 6;/,9 <7*6405. 73(5: :<*/ (: ( )0 >,,23@ 9,(+05. *09*3, )<03+ 05. <7 ( 30)9(9@ 6- 30;,9(9@ ;(32: (5+ ,=,5;: *65+<*;05. ( 4<:/(09( (; # ! (5+ 7<)30:/05. ( 30;,9(9@ :<773,4,5; ,=,9@ 465;/ Some Achievements… il Compiled by Rabia Roha LUMUN Wins World Championship LUMUN has done it again! We take pride in the fact that the LUMUN team has been declared World Champion for the third consecutive year. This year Harvard WorldMUN or World Model United Nations was held at Puebla in Mexico. There were 1600 delegates from all over the world and top class Universities like Oxford, MIT, William and Mary, West Point, Berkley, and Princeton etc. were competing for the Outstanding Delegation Award. It is very significant that this year all eight delegates of the LUMS team won individual Outstanding Diplomacy Awards which is a rare happening in the history of Harvard WorldMUN. Collectively the LUMUN team was awarded the coveted Outstanding Delegation Award. This year’s achievement of the LUMUN team is indeed a tremendous performance by the students. Laurels in Floriculture & Horticulture LUMS stood first in the gardens category of the universities in the 150th Annual Flower Show Competition organized by the Horticulture Society of Pakistan at Bagh – i- Jinnah. The Gardeners and their Supervisors, Mr. Altaf & Mr. Kabir & lawn mower technician Mr. Muzaffar deserve special praise for their untiring and concerted efforts. LUMS T20 - Stars swarm to the LUMS Cricket Ground LUMS cricket club organized a match including real cricket stars of the Pakistani Team. Watching Imran Nazir, Shabbir Ahmad along with Junaid Zia and Abdul Rehman playing at LUMS cricket ground was exhilarating for many. LUMS Alumna wins Fellowship The Woodrow Wilson National Fellowship Foundation announced the selection of 29 Charlotte W. Newcombe Doctoral Dissertation Fellows for 2008. Among them is LUMS alumna Nosheen Ali, now a Ph.D. candidate in sociology at Cornell University. The 2008 Newcombe Fellowship, a highly competitive national award, provides $23,000 for 12 months of work on a dissertation in the humanities or social sciences that addresses questions of religious or ethical value. National Outreach Programme Donors Acknowledgement Event On June 14, 2008, LUMS NOP team arranged a special event to acknowledge the generous support of the LUMS National Outreach Programme. This event, hosted at LUMS, was sponsored by Zong (China Mobile Pakistan) and had participation of more than 200 socially responsible guests including representatives of corporate identities, individuals, alumni, students and colleagues. This was the 5th Donor’s Acknowledgment Event organized in honor of supporters of the National Outreach Programme. The evening started with a welcome address by Sheikh Ali Hussain, Director Resource Development and Alumni Affairs followed by a presentation overview on the National Outreach Programme by Dr Syed Zahoor Hassan (former Vice Chancellor, LUMS). Dr Hassan emphasized on how LUMS had, in the last twenty three years, managed to establish itself as an institution of repute by adhering to its core values of merit, diversity and excel- lence. He also shared the rationale behind need-blind admission policy of LUMS and future aspirations of the National Outreach Programme. Mr Abdul Razak Dawood, the Rector of LUMS then shared with the audience, his thought that went into setting up the university and the dire need of programmes like the National Outreach Programme for Pakistan. The event ended with a spectacular performance by the legendary Tina Sani. Making LUMS Accessible to All! The LUMS National Outreach Programme (NOP) has continued to make a difference in the higher education sector of Pakistan by providing a unique educational opportunity to the brilliant yet financially disadvantaged students of Pakistan. Since inception, the National Outreach Programme has been successful in inducting 190 students in LUMS at undergraduate level through the NOP stream; this includes the 83 NOP scholars inducted this year as well as the students currently at various stages in their 4 year programme. 13 NOP Scholars have graduated to date, 3 of which received Fulbright Scholarship and joined top universities such as Harvard, Cornell and Columbia. 3 are enrolled in National University of Singapore, Lake- head University and Pantheon Sorbonne University respectively on fellowships while those who opted to work have joined leading organizations such as Unilever, Standard Chartered Bank, Colony Group, Al-Ghanim Industries Kuwait, Habib Bank AG Zurich and Habib Bank Limited. In the year 2008, 7500 highly talented students from across Pakistan applied for admission into LUMS through the NOP. After conducting the evaluation test in 16 cities, 700 candidates were shortlisted for LUMS Admission Tests coaching. The coaching sessions were arranged at 9 different centers such as Lahore, Rawalpindi, Peshawar, Multan, Kohat, Attock, Sahiwal, Faisalabad and Karachi. These remote coaching sessions were made possible through the support of our partner institutions, current students and alumni. The candidates coached in these sessions would be eligible to join LUMS from Fall 2009. At least 100 of these students are expected to be inducted at LUMS at that time. It is re- ally encouraging to receive such exceptional results, which would not have been possible without the persistent efforts of the NOP team and support of the LUMS family including alumni, faculty, staff and a large number of well-wishers. The growing population of NOP scholars requires greater support from the LUMS family as well as socially responsible citizens. It has become necessary to generate sufficient funds to sustain this noble initiative and meet educational expenses of young men and women of Pakistan. BSc graduates of 2002 came forward to set up an endowment fund to sponsor two NOP Scholars. BSc Class of 2006 graduates have sponsored the tuition fee of a NOP Scholar for the second year in 2008. The generosity of these alumni and their support toward the LUMS vision shows that the LUMS spirit stays with the alumni at all times. We are truly grateful to the alumni for contributing their time in our identification process for brilliant and needy students as well as for helping us financially in this endeavor. Future plans include inducting students in graduate programmes through the National Outreach Programme stream. We look forward to your help in turning this dream into reality. It is only with your support and encouragement that we have been able to change lives and will continue to do so in the future as well. : 9 ? = 5 ( #" . @ ? 5 : 9 )(& ? : ? 4 &# & !! $-81 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 1>539-?5:9 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, :8;-9D ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, @>591>> 00=1>> ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 5?D ,,,,,,,,,,,,,,,,,,,,,,,, )17 ,,,,,,,,,,,,,,,,,,,,,,,,, :@9?=D ,,,,,,,,,,,,,,,,,,,, 8-57 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, -C ,,,,,,,,,,,,,,,,,,,,,,,,,, 177 ,,,,,,,,,,,,,,,,,,,,,,,,,,,, '1>5019?5-7 00=1>> ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 5?D ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, :@9?=D ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, )17 ,,,,,,,,,,,,,,,,,,,,,,,,, -C ,,,,,,,,,,,,,,,,,,,, 8-57 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ! #D :8;-9D B:@70 7561 ?: /=1-?1 - 9-810 190:B819? 2:= ?B: $%& >/4:7-=> 59 ;1=;1?@5?D 1912-/?:= 90:B819? 2:= ?B: >?@019?> '> %' ! #D :8;-9D B:@70 7561 ?: >;:9>:= -9 $%& >/4:7-= -> &-?=:9 2:= 2@77 ;=:3=-8 @-=05-9 2:= D1-=> (@;;:=?1= 2:= D1-= '> '> '> =5190 9D -8:@9? )41 ;-D819? 5> .1593 8-01 ?4=:@34 "*#( +1.>5?1 -96 =-2? 41<@1 +5=1 )=-9>21= )=-9>-/?5:9 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,, -96,,,,,,,,,,,,,,,,,,, ,,,,,,,,,,, -96,,,,,,,,,,,,,,,,,,, -96 01?-57> ,,,,,,,,,,,,,,,,,,,,,,,,, &71->1 9:?1 /:8;71?1 2:=8 >4:@70 .1 >19? ?: "*#( 2:= =121=19/1 )41 ;-D819? /-9 .1 8-01 59 4-72 D1-=7D 59>?-7819?> 1 #" ( " " * ' '( & & $& && #$( #" !3-)9- .6336= :0- 9:-79 ) &191: % # =-* 91:- === 3;49 -,; 72 * #-3-+: C!)? 5315-D 3152 + 5 9:-7 +0669- A 65689 ! 65):1659 65):1659 .68 #+063)89017 ;5, :0-8 65):1659 B , 5 9:-7 4)2- :0- 8-3-<)5: +061+- .68 ?6; C % # 8),;):-9D 68 C :0-8 65689D 5 :0- 5->: 9+8--5 6. 9:-7 .133 6;: ?6;8 ,-:)139 )4- 8/)51@):165 -:+ )5, :0- )46;5: .68 ?6;8 +65:81*;:165 15 !)2 ";7--9 . 5 :0- C!;8769- 6. 65):165D *6> *- 9;8- :6 4-5:165 A ! #+063)89017B / 5 9:-7 +65.184 ?6;8 ,-:)139 0 5 9:-7 73-)9- -5:-8 ?6;8 +8-,1: +)8, ,-:)139 %) ' " " & (' & (# *#)& # "'(&) ( #"' #& ! & "' & :==1>;:90593 -96 , (# #)"( ")! & #)( " ")! & + ( # E"-4:=1 *95A1=>5?D :2 #-9-31819? (/519/1>F )5, 9-5: :6 :0- ),,8-99 /1<-5 *-36= $-?5:9-7 %@?=1-/4 &=:3=-881 %225/1 #"( " )52 -= '682 %# " "-4:=1 *95A1=>5?D :2 #-9-31819? (/519/1> %;;:>5?1 (1/?:= * &4->1 "-4:=1 -9?? &-65>?-9 )17 C? -C 8-57 9:; 7@8> 10@ ;6 #-5168 & &, " $0- "6?)3 )52 6. #+6:3)5, 141:-, #=1.: 6,! 15)3 -5-.1+1)8? #)"( #)"( & '' ( )! ( & )068- %51<-891:? 6. )5)/-4-5: #+1-5+-9 )<)38? 86;5, 8)5+0 )068- )5:: &'#" 9 ()15)* 418 ..1+-8 ):165)3 ;:8-)+0 !86/8)44!0 >: -33 ALUMNI EVENTS The Alumni Office, like every year, hosted a number of events to strengthen the alumni bond and further this network. Homecoming 2007 The Alumni Annual Homecoming 2007 was hosted at the LUMS grounds on Saturday December 15, 2007. Alumni from various years gathered to meet their friends and teachers. The evening started with a brief welcome from the Alumni Office followed by addresses by Pro Chancellor Syed Babar Ali, First Vice Chancellor Dr. Syed Zahoor Hassan, Dean of Business School Dr. Shaukat Brah and Dr. Jamshed H. Khan. Alumni Irfan Khan and Sheikh Muhammad Ali also exchanged their views with the audience. A scrumptious dinner was followed by a swinging concert by none other than Strings. The support of generous sponsors contributed a lot towards the success of the evening. The next afternoon, the alumni were invited to the Homecoming Sunday Sports at the sports centre. The current sports society competed with the previous popular sportspersons of LUMS at various sports, during the afternoon. The day ended with tea for all participants at the executive dining hall. 2008 Batch Alumni Orientation The MBA 2008 graduating batch was welcomed to the alumni world on April 03, 2008. The LUMS Alumni Relations Department hosted the event at the LUMS Executive Dining Hall with a presentation focused on the role of an alumnus in the growth of a university and benefits of being in the LUMS Alumni Network, followed by tea. Dr. Syed Zahoor Hassan and Dr. Shaukat Ali Brah also talked to the batch about their upcoming professional lives. The rationale of this forum was to enhance the involvement of these soon to be alumni in the university activities and most importantly, develop a life long relationship with their alma mater. Similarly the BSc 2008 batch was welcomed to the alumni world on May 14, 2008. These prospective alumni were given details of all the benefits and responsibilities of being LUMS alumni. Dr. Syed Zahoor Hassan in his talk emphasized on the importance of maintaining a strong link with the university even after leaving the campus with their degrees. The evening ended with tea in the central courtyard. LUMS Alumni UAE Chapter Reunion 2008 The UAE Alumni had a reunion at Al Dhiyafah Ball Room, Crowne Plaza on April 25, 2008. Syed Babar Ali and Dr. Syed Zahoor Hassan attended this event. The alumni gave ideas for the development of the university and discussed various issues with each other as well as the LUMS team over dinner. Karachi Alumni Chapter Reunion 2008 LUMS hosted the Karachi Alumni Chapter Reunion at the Karachi Sheraton, Ballroom on May 31, 2008. A large number of Alumni attended the event including many young professionals as well as high profile corporate entities. Dr. Syed Zahoor Hassan gave an update about the growth and changes in LUMS over the years. He also highlighted the importance of alumni participation for the advancement of LUMS and how their contributions can make a big difference in helping the National Outreach Programme students. He discussed some future projects and plans regarding LUMS and its different schools. Dr. Shaukat Ali Brah then talked about the Suleman Dawood School of Business and the new SDSB Building that is being constructed. Thereafter Muhtashim Ashai, an alumnus from MBA 1992 shared his experiences at and since LUMS. Muhammad Yaqoob Baqapuri, an alumnus of MBA 1988, the first batch of LUMS, also said a few words, reminiscing about his days at his Alma Mater The evening proceeded with stand-up comedy improvisation by Saad Haroon and Danish Ali who kept the audience entertained with their hilarious performance. A lavish dinner concluded this fun filled evening. Islamabad Alumni Chapter Reunion 2008 The Islamabad Annual City Chapter Reunion was hosted at The Monal Restaurant, on June 29, 2008. The beautiful location in the Daman-e-Koh Mountains added to the evening of meeting friends and renewing old ties. Dr. Syed Zahoor Hassan and Dr. Shaukat Brah addressed the alumni with updates on the university followed by Alumni Salman Abdul Wassay and Luqman Ali Afzal’s expression of their bond with LUMS. The event was successful due to the generous support and hosting at the Monal by Alumnus Luqman Ali Afzal. Mark Saturday December 20, 2 008 on your calend ar Cancel All Appoin tments.......... RSVP all family engag ements........ LUMS Alumni Annual Homecoming 2 0 0 8 Strings Performance at Homecoming 2007 &/ Class notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes I<JK F= FLI 98K:? 0?@J G<IG<KL@KP =LE; ;FE8K<; 9P 8CC F= LJ @J 8EK@:@ G8K<; KF GIFM@;< K?< J:?FC8IJ?@G F= 8 ;<J<IM@E> :8E;@;8K< 8K (1)/ <M<IP P<8I 8E; =FI<M<I 0?@J @J 8E 8:?@<M< D<EK K?8K JLI<CP ;F<J LJ GIFL; 8CJF D8IBJ P<8IJ J@E:< N< 8CC =@IJK D<K <8:? FK?<I $<I<YJ =@E;@E> FLK N?8K K?< C8JJ F= ?8J 9<<E LG KF K?@J G8JK P<8I 4?-: -B10 45?4@E ?8J DFM<; 8>8@E 3<CC DFI< C@B< DFM<; 98:B KF ) 8G@K8C N?<I< ?< @J EFN @E :?8I>< F= K?< @EK<IE8K@FE8C <HL@KP J8C<J ;<JB J G8IK F= 8 :I8:B K<8D F= J8C<JD8E KI8;<IJ ?< JG<E;J ?@J DFIE@E>J 8=K<IEFFEJ 8E; <M<E@E>J :FEM@E:@E> FM<IJ<8J @EM<JKFIJ N?F 8I< :I8:B @E 8 ;@==<I<EK J<EJ< 89FLK K?< GFK<EK@8C @E ,8B@JK8E <HL@K@<J +E K?< G<IJFE8C =IFEK ?< ?8J GIFM<; ;FFD J8P<IJ NIFE> I<8; $8J8E .8?@D 8E; ?8J D8E8><; KF I<D8@E D8II@<; =FI P<8IJ +E 8 ;@==<I<EK EFK< ?< @EM@K<J ?@J =<CCFN 8CLDE@ KF @>EFI< K?FJ< C8NP<IJ 8E; :FD< @EM<JK @E ,8B@JK8E *F J<I@FLJCP @KYJ JK@CC 8 >I<8K :FLEKIP >?-8-: 6-F :C1> >FK D8II@<; @E <: $8J ?8; 8 M<IP 9LJP N@K? 8 E<N C@=< 8K ?FD< 8E; E<N<I :?8CC<E><J 8K *@I8C8 N?<I< ?< N8J 9LJP J<KK@E> LG 8 E<N 9LJ@E<JJ LE@K =K<I JL::<JJ=LC P<8IJ 8K *@I8C8 JK8IK@E> &LCP ?< N@CC 9< J?@=K@E> KF =LCC K@D< :FEJLCK@E> N@K? /8GG?@I< 0<OK@C<J (K; 9<@E> ?@J E<OK D8AFI :C@<EK $< 8CJF GC8EJ KF DFM< KF K?< 1' <8ICP E<OK P<8I @5=A1 A> %-49-: 8=K<I JC8M@E> 8N8P =FI KNF 8E; ?8C= P<8IJ 8K 1"FE< @J 98:B 8K (1)/ GLIJL@E> ?@J ) ;<>I<< 0?@J GC8:< ?8J :?8E><; 8 CFK J@E:< /: 8E; @ D@JJ DP 98K:? E1?4- ?8-9 ?8J 9I<8K?<; 8 J@>? F= I<C@<= J@E:< ?<I JFE !@J8 KLIE@E> @E &LCP %EJ?8CC8? JK8IK<; >F@E> KF J:?FFC 8E; @J EFN NFIB@E> G8IK K@D< =FI 9FLK1J FI> 8J 8 FEK<EK !;@KFI @E K?<@I (8?FI< F==@:< -5?-8 45?4@E :FEK@EL<J KF JC8M< 8N8P 8K ',)# @E F? JF ?8GG<E@E> /8L;@ I89@8 @E K?< ?FG< K?8K K?<P NFLC; I<:F>E@Q< ?@J KIL< K8C<EKJ 8E; G8P ?@D KF ALJK :FD< KF K?< F==@:< <M<IP;8P +E K?< G<I JFE8C =IFEK "8@J8C ?8J =@E8CCP >@M<E LG K?< I<@>EJ F= ?@J =I<<;FD KF 8 D<D 9<I F= K?< =8@I<I JG<:@<J 8E; :FEK<D GC8K<J 8KK<E;@E> 9LJ@E<JJ J:?FFC N@K? ?<I %K ?8J 9<<E 8 :I8QP P<8I =FI ,8B @JK8E 8E; "8@J8C ?FG<J <M<IPFE< 8E; K?<@I =8D@C@<J 8I< ;F@E> N<CC ->-F &4-450 4-: @J NFIB@E> 8K <CF@KK< 0FL:?< ,?@C8;<CG?@8 8J 8 K<8D C<8;<I $< 9<:8D< K?< GIFL; =8K?<I KF 8 989P 9FP C8K< C8JK P<8I $@J E8D< @J 68@E "8I8Q '?8E ->-F &41574 K?@EBJ ?< ?8J ?8; 8 M<IP <O:@K@E> P<8I 9LK >@M<E K?8K ?< ?8J JG<EK DFJK F= ?@J K@D< =@E@J?@E> ?@J ,? :FLIJ<NFIB @E .<C@>@FLJ /KL;@<J 8K %E;@8E8 1E@M<IJ@KP CFFD@E>KFE @K ;F<J GLK 8 JKI8@E FE K?< NFI; <O:@K@E> $< ?FG<J KF K8B< ?@J ,? FDG <O8DJ @E <: =@E@J? NI@K@E> ?@J K?<J@J @E 8 P<8I FI KNF 8E; =@E8CCP LEC<8J? ?@J CFE> JLGGI<JJ<; G<;8>F>@:8C K8C<EKJ LGFE K?< LEJLJ G<:K@E> LE;<I>I8;L8K< JKL;<EKJ @E D<I@:8 <E:FLI8><; 8J ?< @J 9P K?< 8::FDGC@J?D<EK F= 8E 8E8CF>FLJ =<8K 9P ?@J N@=< <8IC@<I K?@J P<8I $< J<E;J AFP G<8:< =I@<E;J?@G CFM< 8E; 9C<JJ@E>J KF PFL 8CC -??-: %-459 @J <O8:KCP K?< J8D< J8D< AF9 J8D< :@KP J8D< JK8KLJ =K<I CFE> P<8IJ N@K? K?< KC8J #IFLG -C-0 -8119 ?8J AF@E<; (@M< /<:LI@K@<J 8J $<8; F= !HL@KP .< J<8I:? )8II@<; EFN =FI P<8IJ ?@J JFE J :IFJJ<; DFEK?J 8E; N?F C@B< =8K?<I ;F<JE K 9C@EB 8E <P< N?<E K?< C@B<J F= @J? /LJ? '8K ,I@ 8P8EB8 <K: 8I< FE K?< K<C<M@ J@FE /F =<CCFN :FCC<8>L<J N@K? 9<8LK@=LC ;8L>? K<IJ <N8I< F= K?@J ;L;< +E 8 DFI< J<I@FLJ EFK< &8N8; :FDGC<K<CP J<: FE;J ?J8E ?@J?KP J GF@EK F= M@<N K?@J @J JK@CC 8 >I<8K :FLEKIP A8?A9 ..-?5 @J GI8:K@J@E> !:FE GI<J<EK8K@FE JB@CCJ FE LEJLJG<:K@E> # ! :8E;@;8K<J 'LCJLD JK@CC =<<CJ PFLE> 8K ?<8IK 9LK I<>LC8I :FEK8:K N@K? 8;FC<J:<EKJ GLKJ ?<I @E ?<I GC8:< -45>- 8E-? 8J GIFD@J<; ?8; D8;< :?8E><J @E ?<I C@=< /?< DFM<; 98:B KF ,8B@JK8E @E L>LJK 8E; AF@E<; 48MFI FEJLCK@E> /?< @J <E AFP@E> ?<I NFIB 8J 8 /F=KN8I< !E>@ E<<I 8E; C@B<J K?< GC8:< 8E; G<FGC< KFF /?< ?8J 8CJF =@E8CCP >FKK<E ?<I N@J? F= ;F@E> ) 8E; N@CC 9< AF@E @E> K?< ) GIF>I8DD< 8K (1)/ JK8IK@E> @E L>LJK /?< GI8PJ K?8K 8CC JK8PJ N<CC @E ,8B@JK8E 8E; J?< @J 89C< GLIJL< ?<I ) N@K? <8J< %EJ?8CC8? +E K?< G<IJFE8C =IFEK J?< N<EK =FI $8AA @E <:<D9<I 8E; ?8; 8 >I<8K <OG<I@<E:< 8E; I<:FDD<E;J 8CC KF >F =FI @K / , =K<I JG<E;@E> 8 P<8I 8K 10 LJK@E -:?;;> -2>E ;IFGG<; FLK F= K?< ,? GIF>I8D 8E; :8E F==@:@8CCP 9< :FEJ@;<I<; 8 :FIGFI8K< J<CC FLK $< EFN NFIBJ 8K )@:IFJF=K 8J 8 ,IF>I8D )8E8><I @E 3@E;FNJ )F9@C< 14> -6C- ?8J >FKK<E <E>8><; @J JK@CC NFIB@E> @E K?< ;<M<CFGD<EK J<:KFI @E (8?FI< 9LK ?8J J?@=K<; =IFD K?< )@E @JKIP F= %E;LJKI@<J KF 1/ % 8K 8 D8E 8><D<EK :FEJLCK8E:P & ! LJK@E JJF:@8K<J %E: 8E; :8E K 9<C@<M< @K N@CC 9< P<8IJ J@E:< <M<IPFE< =@IJK D<K <8:? FK?<I 8K (1)/ ;.11: +-=A. ?8J 9<<E C@M@E> @E I@K8@E =FI K?< C8JK =@M< P<8IJ 8E; @J K?< DFK?<I F= 8 =FLI P<8I FC; =K<I 8 GFJK >I8;L8K< ;<>I<< @E !:FEFD@: ,FC@:P J?< J NFIB@E> =FI 8 C@KKC< N?@C< @E (FE;FE 8E; NFE;<I@E> N?<I< C@=< N@CC K8B< ?<I E<OK ;95:- #5>-/4- @J K?< DFK?<I F= KNF 9<8LK@=LC B@;J "8@Q88E 8E; )8?LD 8E; <EAFP@E> <M<IP JK8>< F= K?<@I >IFNK? /K@CC C@M@E> @E /FLK?<IE 8C@=FIE@8 8E; <EAFP@E> K?< 89LE;8E:< F= G8IBJ 8E; 9<8:?<J J?< :8E K ;<:@;< N?<K?<I KF KLIE @EKF 8 JF::<I DFD FI >F 98:B KF >I8;L8K< JKL;@<J A4-9 9-0 *-=-? ?52 *E:1 @J ;F@E> 8E Class notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes *% +, @< =LKLI< >F@E> 89IF8; @E E<8I A4-99-0 -4519 (88-4 ?8J K8B<E ?@J =I<<C8E:@E> KF K?< E<OK C<M<C 8E; ?8J JK8IK<; ?@J FNE JF=KN8I< :FD G8EP $FI@QFE 0<:?EFCF>@<J N?<I< ?< J 9L@C;@E> GIF;L:KJ 8J N<CC 8J :LJ KFD@Q<; JFCLK@FEJ A4-99-0 ?4-= ?8J >FE< D@JJ@E>T I<G<8K<; <D8@CJ J<EK KF (FJK "FLE; 8K (1)/ KLIE<; FLK =IL@KC<JJ A4-99-0 ?59 %-25=A1 ?8J C<=K K?< ,? GIF >I8D 8K (1)/ 8E; @J EFN DFM@E> KF 38I@; FE>F U 5<J 0?8K J =I@:8 A4-99-0 .0A8 %149-: 7.-> 4-: 8 B 8 )8E@ @J ?8GG@CP <E>8><; KF $@E8 .8A8 8E; @J EFN NFIB@E> 8K * . N@K? K?< I<JGFEJ@9@C@KP F= ;8K8 D@E@E> N<@I; E@:BE8D<J =FI ?@J %)J A4-99-0 4?A: 85 @J NFIB@E> 8J 8 /F=KN8I< !E>@E<<I 8K )F9@C< 3<8M<I %JC8D898; A4-99-0 85 &4-2=-@ ;@; JFD<K?@E> K?8K EF J8E< D8E NFLC; <M<I ;F ?< @EK<EK@FE 8CCP D@JJ<; ?@J :FEMF:8K@FE <M<E K?FL>? ?< C@M<J FECP 8 :FLGC< F= 9CF:BJ 8N8P =IFD (1)/ .LDFIJ JL> ><JK K?8K ?< N8J E<:B ;<<G @E GC8P@E> M@;<F >8D<J FE ?@J ,/ 8E; FI 49FO 3?<E EFK GC8P@E> M@;<F >8D<J 8K ?FD< ?< :8E 9< =FLE; ;L <C@E> 8>8@EJK ?@J NFIB :FCC<8>L<J 8K / 8K % 3" N?<I< ?@J F==@:@8C ;<J@> E8K@FE @J /<E@FI /F=KN8I< !E>@E<<I 9LK @J LEF==@:@8CCP BEFNE 8J ?@<= #8D@E> +==@:<I A4-99-0 ?59 -B10 ;LDG<; ?@J GC8EJ =FI 8 ,? =FI 8E FGGFIKLE@KP KF NFIB 8K /:IP9< %E: %JC8D898; 3?<E EFK 8K NFIB ?< :8E 9< =FLE; GIFM@;@E> =I<< :FEJLCK@E> J<IM@:<J KF (1)/ ?FJK<C@K<J @E =@E;@E> 8E; ;FNE CF8;@E> JKL== F== (1)/ ?FJK<C ( * A4-99-0 9>-: :?->5 8=K<I 9<@E> 8JJF:@8K<; N@K? ()'. =FI 8 :FLGC< F= P<8IJ @J EFN <E>8><; N@K? 8 E<N K<:? :FDG8EP @E %JC8D898; @ < C<L .@;<I 8J 8 (<8; <M<CFG<I A4-99-0 -9>-: !5?4-@ 8 B 8 '8D@ @J ?8GG@CP D8II@<; 8E; DFM<; FLK F= (1)/ ?FJK<C $< J JK<8;@CP 8; M8E:@E> KFN8I;J ?@J ,? A4-9 9-0 -?452 F4-> A>2 -/44A AC->5E- J?FLC; M< 9<<E 8 GFB<I ;<8C<I @E JFD< LE;<I>IFLE; :CL9 9LK @EJK<8; @J NFIB@E> 8J 8 /F=KN8I< !E>@E<<I A4-99-0 "91> %-22-@ 8 B 8 +D<I DFM<; KF 2@I>@E@8 1/ N?<I< ?< J NFIB@E> 8J 8 FEJLCK8EK 8K ):"8;P<E /FCLK@FEJ A4-99-0 &4;-5. -?-: @J :LII<EKCP NFIB@E> @E )F9@C@EB $< ?8J 9<<E FE 8 :<IK@=@:8 K@FEJ JGI<< K?@J G8JK FE< P<8I 8E; EFN =<<CJ ?< J FM<I HL8C@=@<; =FI K?< AF9 ?< J ;F@E> A4-99-0 (9-5> 4-: 8 B 8 L;;P @J NFIB@E> @E 8 JF=KN8I< ?FLJ< @E '8I8:?@ 8E; ;F@E> N<CC $@J JK8KLJ @J J@E>C< JF =8I 9LK CFFB@E> J<I@FLJCP ><EL@E<CP 9LK EFK ;<JG<I8K<CP LEC@B< JFD< FK?<I G<FGC< =FI ?@J 9<KK<I ?8C= A4-99-0 (9-> ->;;= KFF @J NFIB@E> 8K U 8EFK?<I :C@:?R U 0<I8 ;8K8 %JC8D898; A4-99-0 ,-450 85 8 B 8 ?8KK@ K?< >LP N?F LJ<; KF 9< D@JK8B<E 8J K?< =@IJK ,? F= (1)/ ?8; ?@J ;I<8D D8K<I@8C@Q<; 8E; DFM<; FLK F= ,8B@JK8E $< J EFN @E ?@:8>F N?<I< ?< J NFIB@E> =FI 8 K<:?EFCF>P =@ID 8E; K8B@E> ?@J G@: KLI<J N@K? K?< /<8IJ 0FN<I @E K?< 98:B>IFLE; =IFD <M<IP GFJJ@9C< 8E>C< A4-99-0 &41>-F &4->52 @J NFIB@E> 8J 8 /F=KN8I< !E>@E<<I 8K %E K<IE8K@FE8C 0LIEB<P /FCLK@FEJ %0/ (8 ?FI< A:-FF-4 .0A8 4-22-> @J ?8GG@CP D8II@<; KF 8 JN<<K CFM@E> ?<CG=LC CFP8C >LP E8D<; )L?8DD8; $8JJ8E )/ /?< @J EFN C@M@E> @E (8?FI< 8E; K?<J< ;8PJ J?< @J N8K:? @E> DFM@<J 8K $ :@E<D8 8KK<E;@E> =8D@CP <M<EKJ 8E; @EM@K@E> =I@<E;J KF ?<I GC8:< !-@-?4- $-5?-> EFN *8K8J?8 1JD8E LKK @J ?8GG@CP D8II@<; J<K KC<; @E K?< 1' 8E; @J CFM@E> <M<IP 9@K F= ?<I E<N C@=< =K<I JG<E;@E> 8 NFE;<I=LC M8:8K@FE @E L98@ J?< @J N8@K@E> =FI ?<I E<OK KI@G KF PGILJ 9LK :LII<EKCP J?< @J KIP@E> M<IP ?8I; KF ><K 8 AF9 8E; @= J?< @J EFK JL::<JJ =LC J?< @J >FEE8 KIP 8>8@E !-B110 4910 9<:8D< K?< GIFL; ;8; F= 8 :LK< C@KKC< 989P >@IC /?LD8@D $< N8J 8 C<:KLI<I 8K *1 " /0 9LK K?<E ;< :@;<; KF DFM< KF @E;LJKIP 8E; @J EFN NFIB@E> 8K ' * $< J @E 'FE;LQ =>?8E@JK8E K?<J< ;8PJ FE 8 NFIB I< C8K<; KI@G N<CC K?8K J 8 =@IJK $-?59 85 AF@E<; 0<:?CF>@O JFFE 8=K<I C<8M @E> (1)/ 8E; @J GIF989CP JK@CC K?<I< ?41> 9@5-F @J ?8GG@CP LED8II@<; 9LK CFFB@E> <8;C@E< KF :FEK8:K ?@D =FI K?< GLIGFJ< @J <: E; "5% 8=K<I ><KK@E> ?8GG@CP D8II@<; ?< GC8EJ KF JG<E; 8 NFE;<I=LC M8:8K@FE @E L98@ LK PGILJ @JE K @E GC8E $< @J K<8:?@E> 8K " =LCC K@D< 8E; 8CJF NFIB@E> =FI 8 E<N JK8IKLG 2<IJFE@: 8K (8?FI< =LCC K@D< 8E; ;FE K =FI><K ?< @J JK@CC <EIFCC<; @E )/ C<8; @E> KF ,?; 8K (1)/ =LCC K@D< JKL;<EK %119- '->5= EFN BEFNE 8J .<<D8 1J8D8 ?8J DFM<; 98:B KF %JC8D 898; N@K? ?<I ?LJ98E; /?< @J KIP@E> KF D8B< K?< NFIC; 9<KK<I 9P K<8:?@E> @E FDJ8KJ /?< @J :FEK<DGC8K@E> FE N8PJ KF >F =FI 8 ,? 89IF8; %149-: 4A34@-5 ?8J D8;< 8 E8D< =FI ?@DJ<C= 8J 8 :8D<I8 KFKK@E> 8EK@ D8IK@8C C8N 8:K@M@JK 8K (1)/ $@J G?F KF>I8G?J N<I< N@;<CP GL9C@J?<; @E M8I@FLJ E8K@FE8C 8E; @EK<IE8K@FE8C E<NJG8G<IJ U 8CK?FL>? N@K?FLK 8EP ;L< :I<;@KJ &--05- A9@-F 8=K<I ><KK@E> ?<I )/ ;FE< NFIB<; @E 0<:?CF>@O 8J 8 /F=KN8I< !E>@E<<I /?< N8J 8 G8IK F= 8 K<8D NFIB@E> FE GIF M@;@E> !., JFCLK@FEJ 9LK D8E8><; KF =C<< 8E; ALJK =FI K?< J8B< F= K8B@E> 8 9I<8B =IFD ?<:K@: J:?<;LC< F= J?< JK8IK<; K<8:?@E> LII<EKCP J?< @J ;<C@M<I@E> C<:KLI<J @E # 1E@M<IJ@KP 8E; >I@:LCKLI< 1E@M<IJ@KP "8@J8C898; /?< @J JK@CC :FE=LJ<; N?<K?<I KF GLI JL< 0<8:?@E> 8J ?<I :8I<<I K?FL>? J?< ?8J =FLE; @K DFJK I<N8I;@E> /?< @J 8CJF 8KK<E;@E> N<;;@E>J F= =I@<E;J 8E; J@E>@E> JFE>J FE K?88G F= ;?FC8B 8E; D@JJ<J K@D<J E =I@<E;J 8K (1)/ &-0-2 4910 @J 98:B @E %JC8D898; 8E; ALJK AF@E<; " /0 %JC8D898; 8J 8 .<J<8I:? !E>@E<<I NFIB@E> FE 8E % 0 GIFA<:K /?< GC8EJ KF JN@K:? ?<I AF9 8J J?< ;F<JE K I<8CCP C@B< K?< AF9 8E; K?< GC8:< /?< N8EKJ KF ;F JFD< K?@E> DFI< @EK<I<JK@E> 8E; J8K@J=P@E> C@B< =8:LCKP 8K JFD< LE@M<IJ@KP @E %JC8D 898; &-05- &-8119 K?< LCK@D8K< =LE CFM<I <EAFPJ K?< 9LJP NFIB Class notes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lass notes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lass notes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lass notes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lass notes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lass notes 336(-2%836 0- %=-8-&%2/ %0- /%=- '-8- '31 !-8, 7944368 *631 %-6% %8%7,% 2%1 ),1-2% 001%//< 1%6 %1)) %&-& ,3%6 %97))* %2( 396 '0%771%8)7> %')&33/ 463*-0)7 %K J EFK 9<<E <8JP KI8:B@E> ;FNE 8CC F= FLI :C8JJD8K<J K?FL>? HL@K< 8 =<N 8I< FE "8:<9FFB U N?<I< 0<?D@E8 ?8J ;FE< 8 >I<8K AF9 9P J<K K@E> LG 8 (1)/ ) >IFLG U GC<8J< AF@E @K @= PFL ?8M<EYK 8CI<8;P /F JFD< F= K?< XJG@:<Y @E K?@J NI@K< LG @J K?8EBJ KF PFLI FNE " GIF=@C<J 8I<<IJ N@J< % EFK< K?8K FLI :C8JJ @J FM<IN?<CD<; N@K? 98EB<IJ J<M<I8C D8IB<K<IJ 8 JD8KK<I@E> F= GIF=<JJFIJ K<8:?<IJ <;L:8K@FE@JKJ 8E; 8E @E :I<8J@E> ELD9<I F= :FEJLCK8EKJ : :FI;@E>CP K?< :C8JJ J<<DJ N<CC ;@JG<IJ<; 8:IFJJ 98EB@E> ?L9J JL:? 8J L98@ (FE;FE *5 8J N<CC 8J '8I8:?@ K?FL>? K?<I< @J 8 JKIFE> 98J< F= EFE 98EB<IJ @E (8?FI< ;:0;: ( !-A9-: 96-0 @J GLKK@E> ;FNE IFFKJ @E (FE;FE $< ?8J ALJK DFM<; @EKF 8E 8G8IKD<EK @E /K &F?E J 3FF; 8CFE> N@K? *8;@8 8E; K?<@I P<8I FC; JFE 68@E *8LD8E 8E; *8;@8 9FK? >F KF F==@:< @E 8E8IP 3?8I= *8LD8E 8K @K@>IFLG N?@C< *8;@8 NFIBJ E<OK ;FFIJ 8K $/ !-59- 8CFE> N@K? ?<I ?LJ98E; D@E K?<@I KNF JFEJ 8E; 989P ;8L>?K<I ?8M< J<KKC<; @EKF K?<@I E<N ?FD< @E (FE;FE J $8DG JK<8; #8I;<E 8I<8 /?< @J 8E <OG<IK EFN @E ?FD< I<EFM8K@FE 8E; PFL D8P :FEK8:K ?<I =FI 8;M@:< 99-> 85 $A>1?45 @J NFIB@E> 8J 8 LJ@E<JJ <M<CFGD<EK )8E8><I N@K? 8I9FE .<JFLI:< )8E8><D<EK % K?@EB ?< N@CC ?<CG KF J8M< K?< GC8E<K $@J I<C8 K@FEJ?@G JK8KLJ @J /@E>C< 8E; ?< J<<DJ C@B< 8E 8:K@M< "8:<9FFB D<D 9<I GIF=@C< I<GC<K< N@K? 9FFBJ NI@K <IJ 8E; G?@CFJFG?<IJ 8J N<CC 8J <EK<IK8@ED<EK < > 3?8K "C8MFI I< 5FL ->411: 49-0 @J 8CJF @E (FE;FE N@K? ?<I ?LJ98E; /?8?Q8; 8E; K?<@I KNF ;8L>?K<IJ ?<I " GIF =@C< N@CC C<K PFL =@E; FLK ?<I =8MFI@K< PF>8 GFJ< "9-> ->;;= NFIBJ N@K? $/ CJF @E K?< 1' N< ?<8I 8I< -5F- ->50 N?F ?8; 8 989P C8JK *FM<D9<I 8E; I<D8@EJ M<IP <CL J@M< 8E; (9-> 5@/481C N?F ?8J ALJK I<:<EKCP ;<:@;<; 8CFE> N@K? ?@J N@=< $<EE8 8E; K?<@I KNF JFEJ KF DFM< FE =IFD .8N8CG@E;@ 8E; D8B< K?<@I E<N ?FD< @E K?< :?8ID@E> :@KP F= !;@E9LI>? !+ %1?@ ;2 !;>@4 91>5/- *<N 5FIB<IJ 8K K?< :<EK<I F= K?< =@ E8E:@8C LE@M<IJ< % K?@EB N< J?FLC; >I@CC 8CC F= K?<J< >LPJ 89FLK K?<@I IFC< @E K?< JL9 GI@D< D<JJ &;4-58 4-: /KIL:KLI<; I<;@K @K@>IFLG ?8J KNF B@;J .88@; 8E; ?D<I 8E; 8J G<I " ?8J M@J@K<; :@K@<J @E :FLEKI@<J 85 89-77E /KI8K<>P LJ@E<JJ < M<CFGD<EK =FI "@O<; %E:FD< )<II@CC (PE:? U :8E PFL 9<C@<M< ?< ?8J DFI< K?8E =I@<E;J FE " ,->5:- C@YJ 8::FDGC@:< @J ;<MFK<; KF 8;8D 8E; C@E8 8E; C@ N?<E ?<YJ ?FD< !-A9-: AF-22-> 8G@K8C /KIL:KLI< ;M@JFIP /FCLK@FEJ &, )FI>8E @J EFN P<8IJ @E *5 8E; @J 9I@E>@E> LG :?@C;I<E N@K? ?@J N@=< $A9.1> -??-: @J KI8;@E> JKI8K<>@JK :FM<I@E> DFIK>8>< 98:B<; J<:LI@K@<J 8EB F= D<I@:8 $@J <C;<I JFE @J >F@E> KF :FCC<>< E<OK P<8I 8E; PFLE><I JFE J<<J K?< N@J;FD @E 9<@E> @EJG@I<; JFD<N?<I< FK?<I K?8E 38CC /KI<<K &-8119 49-0 T /8C<<D ?D8; =I@<E;J FE " N?F ?8J 9<<E @EMFCM<; N@K? GI@M8K< <HL@KP 8E; 8 ELD9<I F= C8I>< C<M<I8><; 9LPFLKJ @E ?@J FNE NFI;J M<IP C@>?KCP <;@K<; VM<IP J@E>C< 8E; <EAFP@E> C@=< @EMFCM<; N@K? 8 9LE:? F= ,8B@JK8E I<C8K<; @E@K@8K@M<J GI@D8I@CP F= 8 JF:@F <:FEFD@: E8KLI< /K@CC B<<ECP @EK<I<JK<; @E 8E; @EMFCM<; @E 8 =<N D@:IF=@E8E:< 8E; C@K<I8:P I<C8K<; GIF>I8DJ /GFEJFI@E> 8 =<N B@;J K?IFL>? ?@>? J:?FFC ?<I< ;8LEK@E> 9LK >I8K@=P@E> :K@M<CP G8IK@:@G8K< N@K? 8 *5 98J<; =FI<@>E I<C8 K@FEJ K?@EB K8EB CJF FE <O<:LK@M< :FDD@KK<< F= 8 1/ 98J<; FI>8E@Q8 K@FE =F:LJ<; FE GIFDFK@E> <EKI<GI< E<LIJ?@G 8DFE>JK D<I@:8EJ F= ,8B@JK8E@ ;<J:<EK (FM< K?< 8IK 8E; K?<8K<I J:<E< @E *5 8E; K?< LE;<I >IFLE; DLJ@: <JK89C@J?D<EKJ W .50 ,-505 8E; ?@J N@=< 8I< 9FK? NFIB@E> N@K? )@:IFJF=K 8E; J<KKC<; @E /<8KKC< N@K? K?<@I K?I<< :?@C;I<E @E :CL;@E> KN@EJ &--05- A:5> -9 9-0 @J J<KKC<; @E KC8EK8 #<FI>@8 N?<I< J?< @J 9LJP I8@J@E> ?<I K?I<< JFEJ '1495:- &4-4 @J 98J<; @E 0FIFEKF N?<I< J?< NFIBJ @E % 8J 8 LJ@E<JJ %EK<CC@><E:< D8E8><I 5FL :8E =@E; '?8C@C #@9I8E 8E; &<C8CL;;@E .LD@ FE ?<I " GIF=@C< 4A>>-9 4A@@- @J 98J<; @E K?<EJ +?@F N@K? ?@J B@;J 8E; @J 8E JJF:@8K< ,IF=<J JFI 8K +?@F 1E@M<IJ@KP 69-8 &-110 @J @E /8:I8D<EKF 8C@=FIE@8 NFIB@E> =FI 8 LK@C@KP :FDG8EP $< ?8J K?I<< B@;J 8><J 8E; $< D<EK@FEJ K?8K 9@; 8CF:? 8E; D@I '?8E :8D< KF M@J@K K?@J P<8I 8E; K?<P N<EK KF /8E "I8E:@J:F 8E; (8B< 08?F< KF ><K?<I -?452 &->2>-F K@CC I<:<EKCP @E (FJ E><C<J 8C@=FIE@8 ?8J ALJK I< KLIE<; KF 0FIFEKF JK@CC NFIB@E> =FI &F?EJFE &F?EJFE $< ?8J =FLI B@;J EFN 8=K<I K?< "<9IL8IP 8;;@ K@FE F= KN@E >@ICJ E; =IFD C8JK P<8IYJ LG;8K< -C-0 %-FF-=A1 @J ?8GG@CP D8II@<; KF 68I8 '?8E 8E; K?<P ?8M< 8 JFE )FD@E P<8IJ 0?<P :LII<EKCP C@M< @E K?< /<8KKC< 8I<8 N?<I< ?< @J NFIB@E> 8J 8 .<J<8I:? E8CPJK 8K .LJ J<CC %EM<JKD<EK #IFLG 8 >CF98C C<8;<I @E DLCK@ D8E8><I @EM<JK@E> -95> 4-: 8CDFJK D8E8><; KF ;@J8GG<8I ?FN<M<I N< I<:<@M<; 8 C8JK D@ELK< LG;8K< K?8K ?< ?8J 9<<E @E $FLJKFE =FI K?I<< P<8IJ EFN NFIB@E> =FI K?< !E<I>P 8E; %E=I8JKIL: KLI< ;M@JFIP >IFLG N@K? * EFN . / .50 -8;/4 ?8J 8CJF 9<<E KI8:<; KF K?< 38J?@E>KFE Class notes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lass notes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lass notes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lass notes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lass notes N@K? , # 8E8;8 8E; K?8KYJ 8CC % BEFN 89FLK ?@D I@>?K EFN '->5= %-F5 @J ?<8;@E> LEJ<:LI<; =@E8E:@E> 8K L98@ %JC8D@: 8EB C@M@E> @E L98@ B@;J ?FLJ<J N@=< 08I@H :8IJ 8E; @D8>@E8IP ;F>JT K?@J :FD GC<K<J K?< <HL8K@FE F= 8 KIL< 9I8E; 8D98JJ8;FI =FI L98@ 0. ) 8E; /?<IIP ) D8B< FE< F= K?< DFJK ?FJG@K89C< 8E; =LE :FLGC< @E K?< M@:@E@K@<J F= 1 ! '->5= ,-9-: 06 @J AL>>C@E> 8IFLE; N@K? D8EP GIF=<JJ@FEJ K<OK@C< <D 9IF@;<IP 9LJ@E<JJ K?< LJL8C 8E; 8 I<:<EKCP JK8IK<; FI>8E@: ;8@IP =8ID@E> GIFA<:K K?< LELJL8C J 06 GLKJ @K V%KYJ JK@CC @E K?< G@CFK JK8><J 9LK K?< I< JGFEJ< 8E; K?< GFK<EK@8C J<<D KF 9< M<IP >FF;W N?@C< 8J ?@J N@=< 1QD8 <OGC8@EJ V$< @J K?< GIFL; FNE<I F= 9L==8CF<J EFNTW 06YJ 8EFK?<I D8AFI GIF=<JJ@FE @J K?8K F= B<<G@E> LJ 8DLJ<; N@K? ?@J 89JFCLK<CP 9I@CC@8EK :FCC<:K@FE F= AFB<J @E:CL;@E> K?< FE< K?8K LJ<J ;@==<I<EK K<ID@EFCF>@<J KF ;<J:I@9< 8 :<IK8@E GF@EK F= M@<N (91> &4-95 @J FLK F= KFL:? N@K? D8EP @E K?< :C8JJ 8CK?FL>? % JLGGFJ< ?< NFLC; 9< 9LJP D8E8>@E> K?< E<NJG8G<I N@K? KIL< Q<8C 8E; Q<JK F= 8E LG:FD@E> D<;@8 >LIL (?9-: %-?A8 ?8J JK8IK<; ?@J FNE M<EKLI< "FF;J %EK N@K? 8 =I@<E; "IFD :8E;P KF =IFQ<E J<8 =FF; 8E; =IFQ<E GFK8KF JE8:BJ J<M<E P<8IJ F= ?8GG@CP D8I I@<; C@=< FE< ;8L>?K<I 8E; 8J 1JD8E GLKJ @K V@KYJ 9<<E K<E P<8IJ 8CI<8;PW (F9- $-5?1> A@@ @J K?< ?<8; F= $. 8K *<JKC< ,8B@JK8E /F @= *<JKC<JY E<OK 8EEL8C ><E<I8C D<<K@E> ?8GG<EJ KF 9< ?<C; @E 68EQ@98I PFL NFLC; BEFN N?P 1QD8 @J D8II@<; KF 08I@H 68D8E 8E; K?<P C@M< @E (8?FI< *-?119 4910 @J D8E8>@E> ?@J FNE 9LJ@ E<JJ "8@IN8P /<:LI@K@<J @E (8?FI< $< @J D8II@<; 8E; ?8J KNF B@;J FE< ;8L>?K<I 8E; 8 JFE +;A?A2 +-=A. ?8J =@E8CCP 9@; =8I<N<CC KF K?< :@KP F= (8?FI< KF I<CF:8K< KF 9L ?89@ N?<I< ?< @J JK@CC I<=<II<; KF 8J &FJ<G? &8:BF9 $< ?8J AF@E<; 8J $<8; F= /8C<J 8K /K8E;8I; ?8IK<I<; 8EB 9L ?89@ $< @J D8II@<; 8E; ?8J 8 JFE %E K?< <E; 8E; 9<=FI< 8EPFE< GF@EKJ @K FLK C<K D< :FE=<JJ K?8K % ?8M< D@JJ<; JFD< G<FGC< % NFLC; ?8M< C@B<; KF :FDG<EJ8K< =FI @K 9P 8;;@E> JFD< FK?<I G<FGC< 9LK 8GG8I<EKCP K?< NFIC; ;F<JEYK NFIB K?8K N8P 3?F<M<I % ?8M< D@JJ<; % NFLC; C@B< KF F==<I J@E:<I< 8GFCF>@<J =FI EFK B<<G@E> DPJ<C= LG;8K<; N@K? K?<@I N?<I<89FLKJ LI@E> K?< C8JK @:< 8>< :C8JJ EFK<J N<I< K?< FECP N8P F= B<<G@E> <M<IPFE< @E=FID<; 8E; LG ;8K<; 89FLK <8:? FK?<I (L:B@CP N< EFN ?8M< "8:<9FFB E; =@E8CCP ?FG< KF J<< PFL 8CC 8K K?< P<8I I<LE@FE @E (8?FI< N?<I< @= N< 8I< CL:BP N< N@CC 9< @EM@K@E> V9IF8;98E;W KF GC8P VK?< D<CF;P F= 9L==8CF<JW 08B< :8I< <M<IPFE< 336(-2%836 %0%0 %,19( 8%2(%6( ,%68)6)( %2/ %0%0 %,19( 78%2(%6(',%6 8)6)( '31 .0A88-4 -C-50 ALJK 9IFB< K?< I<:FI; F= CFE><JK J<IM@E> ) <I 8K *<JKC< 8=K<I C@ LKK I<J@>E<; $< @J JK@CC @E L98@ 8J ,IFA<:K )8E8><I @E :?8I>< F= J<KK@E> LG 8 E<N 9LJ@E<JJ @E K?< )@;;C< !8JK I<>@FE <EAFP@E> L98@ N@K? 8CC @KJ GIFJ 8E; :FEJ 8CFE> N@K? ?@J N@=< )8I@P8D 8CJF =IFD (1)/ /: )/: 22-: 4-: @J JK@CC JKL:B N@K? 8 M<IP ;P E8D@: 0<C<:FD %E;LJKIP ?< 8K K@D<J K?@EBJ FE ?@J :?F@:< F= @E;LJKIP 8E; @J @E GIF:<JJ F= ;<=@E@E> 8 CFE> K<ID :8I<<I ?<I< P<8IJ @J EFK I<8CCP CFE> %K NFLC; 9< @;<8C @= ?< :8E 8:?@<M< 8CC ?@J GIF=<JJ@FE8C >F8CJ @E %J C8D898; 8J C@=< FLKJ@;< K?@J :@KP J<<DJ KFF :LD9<IJFD< 0?<I< 8I< GC8EJ KF 9<:FD< 8E <EKI<GI<E<LI <M<EKL8CCP I<C8K<; KF 0<C<:FD FI D8P9< FLKJ@;< K?@J ;FD8@E 0?< FECP =FI<J<<89C< GIF9C<D @J 8 ;8P ?8J FECP ?FLIJ (@=< FK?<IN@J< @J M<IP >FF; #F@E> 98:B ?FD< @J FE< F= K?< ?8GG@<JK DFD<EKJ F= ?@J ;8@CP IFL K@E< 0?< K@D< JG<EK N@K? K?< N@=< 8E; ;8L>?K<I 8K ?FD< @J GLI< HL8C@KP C @Q<? F::LG@<J DFJK F= ?@J K@D< 8E; J?< 8CDFJK ;8@CP 8D8Q<J ?@D N@K? E<N NFI;J 8E; G?I8J<J 4-. 5:4-? @J JK@CC C@M@E> @E /8L;@8 9LJP I8@J@E> K?I<< B@;J 8E; NFIB@E> 8K #LC= %EK<IE8K@FE8C 8EB 8J 2@:< ,I<J@;<EK F= FIGFI8K< "@E8E:< (FFBJ C@B< 85 A@@ @J >F@E> KF CFFJ< K?< I8:< =FI K?< CFE><JK K@D< @E K?< =@IJK AF9 KF ?<8MP N<@>?KJ C@B< 9 ;LCC8? &8M8@; )8EB8E@ /?<I8Q <K: 8J ?< @J >F@E> KF C<8M< *<JKC< 8=K<I 8C DFJK P<8IJ C@ LKK NFLC; C@B< KF C<8M< 9<=FI< K?< B@;J N?F N<I< @E B@E;<I>8IK<E 8K K?< K@D< F= ?@J AF@E@E> *<JKC< J@K =FI K?<@I + C<M<C <O8DJ C@ LKK N@CC 9< AF@E@E> #@M8L;8E K?< =C8 MFIJ 8E; =I8>I8E:<J :FDG8EP 8J "+ =FI K?<@I %E;FE<J@8E FG<I8K@FEJ .8@P8E @J EFN 8CDFJK P<8IJ FC; 8E; CFFB@E> =FIN8I; KF K?< 8II@M8C F= ?@J J@9C@E> @E L>LJK $< @J GC8EE@E> KF =<<; ?@J J@9C@E> CFKJ F= *@;F 8E; GLK ?@D LE;<I K?< JLE KF D8B< ?@D >IFN HL@:BCP KF ?@J FNE J@Q< JF K?8K K?<P :8E GC8P KF><K?<I 91> 4-: C<=K 0< C<EFI ,8B@JK8E @E *FM 8E; AF@E<; 38K<<E 0<C<:FD @E (8?FI< $< @J NFIB@E> 8J )8E8><I )8IB<K@E> 8K 38K<<E 8E; C8LE:?<; 38K<<E K<C< :FD @E <:<D9<I :C--> &4-9@ @J EFN FE< F= K?< M<K<I8EJ =IFD (1)/ ) KF ?8M< JK8P<; K?@J CFE> @E K?< J8D< FI>8E@ Q8K@FE $< @J NFIB@E> 8K /?<CC @E 8 #CF98C )8IB<K@E> JJ@>ED<EK N@K? I< JGFEJ@9@C@K@<J :FM<I@E> %E;@8 /@E>8 GFI< )8C8PJ@8 %E;FE<J@8 8E; ,8B@JK8E 8J FE< F= K?< C<8;J @E %E;@ I<:K ?8EE<C <M<CFGD<EK EN88I @J CFFB@E> =FIN8I; KF 9LDG@E> @EKF JFD<FE< =IFD K?< :C8JJ FE ?@J =I< HL<EK KI8M<C KI@GJ @E J@8 ,8:@=@: ?-0 5> @J JK@CC @E L98@ NFIB@E> =FI 8 K<C:F 8E; CFFB@E> 8=K<I K?< Class notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes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lass notes F99P 8 B 8 .A.-7-> &5005=A1 @J NFIB@E> FE JFD< KFG J<:I<K I<K8@C :<EJLJ GIFA<:K 3FIB@E> KF><K?<I @E 8E; .8Q8 ?8M< 8CJF :?8E><; K?<@I 98:?<CFI JK8KLJ N?@C< F99P @EK<E;J KF JK8P J@E>C< =FI K?< K@D< 9<@E> 8E .0A8 %149-: 8E; A4-99-0 !5-F5 -857 8I< NFIB @E> =FI / ) %KYJ 8 98EB 8E; EFK 8 ;8E:< ELD9<I V IFW @J GC8:<; @E '8I8:?@ 8E; K8B<J K@D< FLK KF M@J@K ?@J =8D@CP @E 8E8;8 N?@C< *@8Q@ NFIBJ =IFD K?< (8?FI< F==@:< J@E:< >I8;L8K@FE +LI MFCC<P98CC NFE;<I 9FP -0>5 !-@4 >FK D8I I@<; <8IC@<I K?@J P<8I $<YJ NFIB@E> =FI JFD< GFN<I GIF;L:K@FE ?FLJ< GIFM@;@E> K?<D =@E8E:@8C :FEJLC K8E:P &4A4>-@ N8J C8JK J<<E @E ?@J ?FD<KFNE NFIB@E> =FI JFD< =@E8E :@8C :FE:<IE &A>1?4 &4>1?@4JG<E;J ?@J K@D< J<<@E> ?@J KNF B@;J >IFN@E> LG $< @J CFFB@E> =FIN8I; KF K8B@E> LG 8 B<P GFJ@K@FE @E F==@:< C8K<I K?@J P<8I 0?< 1E@C<M<I #IFLG JL: :<JJ=LCCP N<EK K?IFL>? K?<@I P<8I CFE> D8E8>< D<EK KI8@E<< GIF>I8D 8E; ?8J JK8IK<; KF J<KKC< ;FNE @E ;@==<I<EK 8I<8J 8E +A?A2 NFIBJ FE ALJK@=P @E> K?< =@E8E:@8C ;<:@J@FEJ F= KFG D8E8><D<EK =FI K?< @:< :I<8D :8K<>FIP &-59- :?->5 @J NFIB@E> =FI K?< V/LI=W 9I8E; 8E; JG<E;J ?<I /LE;8PJ ;F@E> K?< N<<B<E; C8LE;IP :?FI<J N@K? ?<I ?LJ98E; ID8E (91> ->>A74 8 B 8 ' YJ <E<I><K@: G<IJFE8C@KP C8E;<; ?@D @EKF K?< V!E<I>@C<W 9I8E; =K<I DL:? ;<C@9<I8K@FE =IFD FK?<IJ ?< =@E8CCP >FK 8 ?8@I :LK <8IC@<I K?@J P<8I CJF ?< ?8J I< :<EKCP J?@=K<; KF 8 E<N 8G8IKD<EK N@K? /G@B<P CJF 'EFNE 8J (91> 149;;0 9P JFD< /G@B<P @J @E K<8 :8K<>FIP NFIB@E> =FI 9I8E; IFFB< FE; '8I8B ?8@ @J:F #@IC 14@-. -?4->51 JG<EK DFJK F= ?<I C8JK P<8I 8K DJK<I;8D /?< N8J C8JK J<<E ;@E@E> FLK N@K? ?<I FC; =I@<E;J @E I@QFE8 #I@CC (8?FI< /?< GC8EJ KF :FD< 98:B KF (8?FI< G<ID8E<EKCP K?@J JLDD<I A4-99-0 85 9-9 @J 8G GCP@E> ?@J + +, 8E; ?8E>< )8E8><D<EK DF;<CJ 8K !E>IFYJ $. $< N8J 9C<JJ<; N@K? 8 J<:FE; :?@C; K?@J P<8I 8 989P >@IC E8D<; 68@E89 A4-99-0 4910 %-6 @J 8CJF NFIB@E> = F I !E>IF 8E; ?8J 9<<E LE ;<I>IFLE; J@E:< ?@J ?<8; HL8IK<I F==@:< @E '8I8:?@ >FK 9LIEK 3< ?FG< KF ?<8I =IFD ?@D JFFE EFK?<I FE< F= FLI PFLE> <EKI<GI<E<LI A4-99-0 &4-450 -?45> @J ?8M @E> JL::<JJ J<CC@E> !K?8EFC D8;< =IFD /L>8I:8E< KF GIFJG<:K@M< CF:8C 8J N<CC 8J =FI<@>E :C@<EKJ $8G G@CP D8II@<; A4-99-0 (?9-: J<CCJ /8=<>L8I; JF8G =FI , # +LI FE F= '8I8:?@ '-59A> ->59 8 B 8 /FD< F= FLI =FI<@>E =I@<E;J ?8M< 8CJF 9<<E =FLE; D@JJ@E> @E 8:K@FE 0@D@ NFIBJ =FI $/ FIGFI8K< ,11?4-: &-8119 4A@@- KI@<J KF J<CC K?< VI<8C E<NJW K?IFL>? K?< 8@CP 0@D<J ,1:A.5- $A>1?45 C<=K % % 8E; @J EFN NFIB@E> =FI %E9FO E; C8JKCP PFLI :C8JJ EFK< :FFI;@ E8KFI 4910 &45>-F A@@ @J 8K 38 K<<E J<IM@E> K?< 0<C<:FD J<:KFI N?<I< ?< ?8J D8E8><; KF @DGI<JJ ?@J JLG<I@FIJ K?IFL>? ?@J <OHL@J@K< ,FN<I,F@EK JB@CCJ K?8K ?< GFC@J?<; ;LI@E> ?@J (1)/ ;8PJ $<YJ NFIB@E> FE 9I@E>@E> @E K?< ;@>@K8C 02 I<MFCL K@FE @E ,8B@JK8E K 38K<<E ?< ?8J =FLE; KNF E<N G8JJ@FEJ @E ?@J C@=< N?@:? 8I< D8B@E> 8 2 C@9I8IP :FCC<:K@FE :LII<EKCP JK8E; 8K :FLEK 8E; GC8P@E> )+$ 'EFNE 8J V)<I:?8EK F= <8K?W 9P ?@J )+$ FDI8;<J ?@J <M<I @E:I<8J@E> 9<CCP @J =8JK 9<:FD@E> 8 JFLI:< F= F9 JKIL:K@FE KF ?@J ;8@CP C@=< IFLK@E< %E J?FIK D8EP F= LJ ?8M< 8CI<8;P JK8IK<; KF C@M< K?IFL>? K?< ?FG<J 8E; ;I<8DJ K?8K N< ?8; N?<E N< N<I< 89FLK KF C<8M< (1)/ J N< DFM< FE KF :FEK@EL< N@K? FLI C@M<J 8CC F= LJ JK@CC ?8M< ?@>? ?FG<J 8E; ;I<8DJ E; N?@C< JFD< FI@>@E8C 8D9@K@FEJ D8P EFK ?8M< JLIM@M<; FLI ;<K<ID@ E8K@FE JK@CC I<D8@EJT
Similar documents
here - AL.com
of the track will flow in both directions. Any traffic approaching the superspeedway at this time will have to do so from the east. Sunday, traffic on the boulevard will be one-way outbound.
More information