【國立臺灣大學109學年度畢業典禮 致詞代表 資訊工程學系韓哈斯】
Student Address, National Taiwan University Commencement 2021
International student Seth Austin Harding from Department of Computer Science and Information Engineering
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校長、教授、以及在螢幕前的各位同學，大家好。非常感謝臺大給我這個機會。我是韓哈斯，來自美國華盛頓特區。我會以自身的真實經驗出發，來跟大家分享臺大帶給我的收穫。
我當初為什麼選擇來台灣求學呢？我小時候非常喜歡看武打片，然後我十歲的時候去看了一部電影叫做「功夫熊貓」。這部電影成為了我最喜歡的電影，主角「阿波」的故事跟我的故事很像。我看完了之後就決定要開始學功夫，所以去了「美國武術學院」。那個時候我每天都聽旁邊的人講中文，到了高中我就決定開始學中文。當時我遇到了一位貴人，她是從台北到美國來教書的中文老師，她教的課是我當時最喜歡的課，我每天去她的教室跟好朋友練習。到了高中畢業時，我是全高中中文最好的非母語人士。同時，我第二喜歡的課程是電腦科學，那時候我是程式能力數一數二的學生。後來在成功錄取夢寐以求的學校：臺灣大學之後，我感到雀躍不已，因為我既可以繼續學習中文，也可以持續在世界頂尖的學府中，往電腦科學的方向精進自我。
不過老實說，當我回顧大一的時期，我也曾迷失自我。雖然我修了很多很多的中文課，但是我那時只聽得懂大概一半的課程內容。跟大家對美國人的印象不同，我其實很害羞，也很害怕舉手提問，我甚至不太敢參與社交，所以當時朋友也很少。我開始想家，也變得有一點憂鬱。那時籃球是我唯一的紓壓方式。
但更不幸的是，我在打籃球時弄傷了我的前十字韌帶，做了兩次手術，需要一年半才能恢復。許多的負面情緒壓得我喘不過氣。我被困在人生的低谷，不知如何是好。我覺得我的中文不夠好，我也被診斷出失眠跟ADHD，另外，美國高中的數學太簡單了，來這邊不夠用。種種壓力讓我足不出戶，找不到自己的人生方向。後來，我向臺大心輔中心以及我的心理醫師尋求協助，然後我也開始跟系上有更多互動。有一位教授叫徐宏民跟我說，"Never give up"，雖然那時候我覺得這句話太過於簡化了我的問題，不過，在我仔細思考了一個禮拜之後，我下定決心，發誓不讓自己被這些事擊敗。我決定要克盡全力，認真做好每件事。這是我人生的轉捩點，我開始變得異常自律。當時廖世偉教授和洪士灝系主任帶我進入它們的研究室鑽研學術。這重燃了我對資訊工程的熱忱，提醒了我當初會愛上這個領域的原因。我開始研究人工智慧以及區塊鏈，也開始跟其他系上同學交朋友，一起成立臺大人工智慧應用社NTUAI。NTUAI現在是校內頗具規模的技術研究社團，致力於推廣人工智慧給任何對該領域有熱忱的學生。歡迎加入NTUAI，可以掃描我們的QR CODE。
最近，由於疫情的緣故，我已經一年半沒回美國了。但是沒關係，因為我已經找到了我第二個家。我很愛臺大，以及台灣的人事物。雖然我經歷了人生的低潮，但這裡的一切總是給我滿滿的祝福與協助。最後，我想送給大家「功夫熊貓」裡的一句台詞： "You just need to believe"。只要用樂觀的態度去面對困難，就有能力改變自己，甚至改變身旁所愛的人。就像阿波的父親說的，"心誠則靈，只要你相信，點石就能成金。根本沒有什麼秘笈。只有你。"謝謝大家。
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President, professors, and classmates, I'm very honored to be here. Thank you to NTU for giving me this opportunity. My name's Seth Austin Harding, and I'm from the D.C. metropolitan area. I'm going to tell a real story that's personal but that's relatable and what I see as the real me.
What motivated and guided me to take my undergraduate studies in Taiwan? When I was very young, I really loved watching kung fu movies, and when I was 10 years old, I went to the theater to watch "Kung Fu Panda". This became my favorite movie as I felt like the story of the main character Po was one to which I could very much relate. After watching this movie, I decided that I wanted to start learning kung fu, so I went to the United States Wushu Academy. At the time, I began hearing Mandarin on a daily basis, so when I was in high school, I decided to begin formally studying Chinese. It ended up being my Chinese teacher from Taipei who was my favorite teacher who taught my favorite class, so I decided I'd hang out in the Chinese classroom every day and practice lots. By the time graduation came around, I had attained the highest proficiency in Chinese among any non-native speaker in my school. My second favorite class was computer science, and I ended up attaining among the best coding skills in my school. After getting accepted to the school of my dreams -- National Taiwan University -- I felt honored, humbled, and excited; I could now spend time at among the world's finest universities studying Chinese and at the same time advancing my knowledge of computer science.
But when I look back at my freshman year, to be honest with you, I didn't know what I was doing. Despite having taken very many Chinese classes, when I went to the NTU lectures, I understood only about half of what the teachers were saying. Contrary to most people's impressions of an American, I was actually too shy to raise my hand, to ask questions, or to even meet with teachers after class, so I had very few friends at the time. I started to become homesick and depressed. At that time, I found that basketball was the only way I knew of relieving my stress. However, while playing basketball, I had torn my ACL and it would take two surgeries and a year and a half in time to fully recover. At this point, I felt caught between a rock and a hard place. In fact, this was the lowest point of my life, and I didn't know what to do. I felt like my Chinese wasn't good enough, I had been diagnosed with insomnia and ADHD, and I felt like the math taught in America was too simple to allow for me to keep up with my classmates. I was under immense pressure, and at this time, I lost any sense of purpose or direction. Later on, I went to seek help from NTU counseling, from my psychiatrist, and from my department. I reached out to Professor Winston Hsu from CSIE, and he told me this: "Never give up"; it was such an oversimplified way to approach such a complex series of problems, I had thought. However, I pondered these words intensely for one week, and by the end of that week, I had made a firm decision. This would NOT be another example of me giving up. I decided to go all out, to work diligently and passionately on all tasks at hand. This was the turning point of my life; I started to discipline myself to a very high degree. At this time, I met my then-to-become advisors Professor Shih-Wei Liao and Professor Shih-Hao Hung and entered their labs to begin research. Finally, the passion that I had for computer science that I had previously held in high school was kindled again, and I was finally reminded why I loved this field. I began my research life in blockchain and AI, and at the time I entered the lab, I also began creating NTUAI. NTUAI is now a large and highly successful NTU club that is dedicated to the research and public understanding of AI. Welcome one and all to join us; please scan our QR code here.
For a year and a half I haven't returned to America because of covid. But not to worry; I have found my second home, away from home. I love it here in NTU and I cherish all of the things I've had the privilege to experience in Taiwan. I've gone through the most difficult of struggles in my life here, but I've also had the most fortunate and blessed of experiences. To conclude, I'd like to quote a line from "Kung Fu Panda": "You just need to believe". As long as you are willing to adopt an optimistic attitude in facing challenges and hardships, you may become a positive force in changing the lives of those around you as well as your own life. It all depends on how you view it; just like what Po's father says, "there is no secret ingredient. It's just you." Thank you, everyone.
詳見：
https://www.facebook.com/NTUCommencement/posts/2718185771805180
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#臺灣大學 #畢業典禮 #NTUCommencement2021 #學生致詞代表 #臺大資訊工程學系 #韓哈斯 #SethAustinHarding
field數學 在 Re: [其他] 代數結構的體(fields)跟場論的場一樣嗎? - 看板Math 的推薦與評價
數學中的field指的是某種代數結構.他是群(group)跟環(ring)概念的延伸.
所以先講群比較簡單
群是在一個集合內賦予他運算.會滿足三個原則 1-結合律2-單位元素 3-反元素
最簡單的例子比如x^4=1的解1,-1,i,-i在乘法下就是群.你可以動手畫個4x4表格看看
並觀察,在對角線上下有對稱性,把這種對群內都滿足a*b=b*a稱為交換群(abelian)
note:不可交換群的標準範例Dihedral Groups.有興趣可谷歌 .接著
把10以下跟10互質的數字找出來有: 1,3,7,9 在 mod10 的乘法下也會形成群,稱U10
有沒發現上面這個表格跟你之前畫的很像呢?這種很像,用數學語言說法,叫做同構
(isomorphic),事實上,這兩個都叫做循環群cyclic group,顧名思義就是這個群可以
僅用一個元素並對自己一直做運算去生成,而這元素就稱為生成子(generator)
比如用i去乘法自己四次.就是你的表格 或用 3去乘法自己四次(mod 10).形成U10
事實上這兩種群都跟Z_4同構.
有個有趣的問題,n在那些值時.使Un是循環群呢? 高斯給了答案:
研究群的主題很多,比如subgroup/permutation/homomorphism/automorphism/
coset/factor group/simple group 等等.
再來對 環+體 做個定義:
簡言之就是這個群他本身加法下可交換.成為了abelian.並且乘法下有結合律跟分配律的
話.他就進化了.變成Ring.而體(field)就是Ring在乘法裡補上那些abelian在加法下
有的性質,在乘法下也來一套,進化成最完美的情況.也就是加入:
乘法單元+乘法反元素+乘法交換律.
總結一下體(field)滿足在加法與乘法下有:
結合律: (a*b)*c = a*(b*c)
交換律: a*b=b*a
單位元素: 存在e使a*e=e*a=a {若*是加法則e=0,反之若*是乘法則e=1}
反元素: 對任意非0的a.存在b使a*b=b*a = e {類上有a+(-a) = 0 或axa^-1 = 1}
最後補上分配律.大功告成
要問-那體的樣子是怎樣?就像上述.在加法表跟乘法表下有雙abelian的樣子.
最早發現有限體內元素個數是p^n的有兩位(p is prime)分別是Gauss跟Galois,為了紀念
Galois所發現Field.後世都簡稱GF(p^n).而n=2或以上都是用factor poly-ring去切出來的.
想知道的話.歡迎進入抽象代數的世界.
而n=1就簡單多了.就是上面說的Up.比如把U3,U5,U7,U11....分別列出加法跟乘法表.
你就得到Field了
補充-下面是GF(9)在乘法下的樣子.(加法easy就不列)
至於物理中的場?我想你可先把微積分+工程數學中的向量分析看看.就會瞭.
版上高手頗多.這就不介紹.
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※ 編輯: coolbetter33 (123.193.47.189 臺灣), 06/15/2020 00:28:19
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