#中央社外文新聞中心FocusTaiwan徵才 Focus Taiwan
中央社外文新聞中心誠徵全職【英文編輯】和【英文改稿顧問】,歡迎對英文新聞有熱情的你,加入FocusTaiwan團隊!
履歷請寄:cnafnc2@gmail.com
薪資:4萬以上,面議
福利:比照勞基法規定
上班時段:日班/晚班/假日班,需輪班
上班地點:台北市中山區松江路209號7樓
其他:通過第一階段履歷篩選者,我們會以email通知筆試時間。
【徵才職位】
🔵英文編輯Writer
語言能力:精通中、英文,英文聽說讀寫能力近母語。
學歷要求:大學以上畢業,新聞系、外文科系尤佳。
工作經驗:具有英文新聞工作至少1年經驗者優先考慮。
工作內容:英文編輯需將中文新聞編譯成英文新聞,並撰寫圖說、替英文影音新聞過音、製作圖表,並協助管理FocusTaiwan網站後台及社群媒體平台。
工作要求:英文編輯須具備求證與求知的精神,除了編譯中文稿之外,也願意花心思查證新聞訊息,包括做電話採訪,或是上官方網站查詢數據或資料,以充實稿子內容。通訊社的發稿步調快速,英文編輯必須在短時間內掌握新聞重點,以外國讀者感興趣的角度撰寫文章。
🔵英文改稿顧問Copy Editor
語言能力:精通中、英文。以英語為母語的(外籍)人士,通曉中文,居住台灣者優先考慮。
學歷要求:大學以上畢業,新聞科系尤佳。
工作經驗:具有英文新聞工作至少3年經驗者優先考慮。
工作內容:英文改稿顧問主要負責編審英文編輯的稿件,包括檢查文法、拼字、標點符號和文章結構等。改稿顧問也需編審每日新聞頭條、圖說新聞和影音稿。
工作要求:英文改稿顧問需熟悉中央社英文新聞寫作體例和頭條寫作規則,確保文章使用正確的文法、拼字和標點符號,結構完整、內容詳實和平衡。
A. Writer Position:
Requirements:
-- Native or near native English and Chinese proficiency
-- A bachelor’s degree or higher in journalism, foreign languages or a related field
-- Experience writing English news stories
-- Willing to work night shifts and on weekends
-- Able to work in a fast-paced newsroom and meet tight deadlines.
The job:
The writer will be assigned Chinese news stories by the shift leaders and are required to rewrite the stories in English.
He/she will also be asked to write captions, do voiceovers for videos, create graphics, and manage the FocusTaiwan website’s backend and social media accounts.
The writer will specifically be expected to:
-- Ensure that all news stories have proper structure, content, clarity, accuracy and balance
-- Research and fact-check the information in the Chinese news stories by sometimes making calls, conducting interviews, or sifting through official information on government websites
B.Copy Editor Position:
Requirements:
-- A bachelor’s degree or higher in journalism or a related field
-- A background in English news writing and editing, preferably with some experience editing the work of non-native English writers.
-- Native English speaker; Chinese language proficiency a plus
-- Able to function efficiently under time and deadline pressure
-- Willing to work late night shifts and on some weekends
-- Flexible with regard to work hours and days off
-- Able to work as a team with shift leaders and other copy editors to ensure quality content
The job:
The editor will be required to edit news stories in the English language department, checking the grammar, punctuation, and structure and making other changes where necessary.
He/she will also be asked to write and edit headlines for the news stories, edit captions, and occasionally check video scripts.
The copy editor will specifically be expected to:
-- Become familiar with the style rules of CNA, as well as with the rules and restrictions associated with headline writing.
-- Ensure that all news stories have proper grammar, punctuation, structure, content, clarity, accuracy and balance.
-- Answer questions by writers and shift leaders about style, grammar and other aspects of English news writing.
#國際影音串流平台徵才 6/28更新
文化部補助、中央社承辦的國際影音串流平台誠徵以下職位專業人才,有志者請依以下徵才內容需求附上所需資料與我們聯繫。
請注意:來函應徵時,請在電郵主旨欄註明應徵類別,例如「應徵D1 社群媒體內容製作人」、「應徵E3 網路平台技術主管」或「應徵E5 數據工程師」
履歷請寄: personnel-video@mail.cna.com.tw
薪資:4萬以上,面議
福利:均比照勞基法規定
【公司介紹】
Taiwan Plus (Taiwan+) 國際影音串流平台,是台灣第一個以全球為目標族群的全英語新聞、節目平台。
本平台希望在全球舞台上呈現台灣觀點與聲音,同時在國際社會中提升台灣的能見度與影響力。我們將提供與台灣相關,以及超越一般視野的新聞與節目。無論是與台灣相關議題或是區域情勢,以及台灣高舉的普世價值:民主、人權、開放、創新等等,我們都期待在該領域的全球對話中成為最具影響力媒體。
我們以全球為範圍尋覓專業人才,希望打造一支世界級水準的團隊。如果您是專長領域的頂尖人才,同時堅信台灣所代表的多重價值,希望促成改變,您將是Taiwan Plus需要的夥伴。
【徵才職位】
🔵 B1 節目製作人
工作內容:
網路影音節目企劃規劃統籌,能產製外國受眾感興趣的網路影音內容。
1. 節目預算規劃與成本管控。
2. 節目主題發想與設定、外部資源整合洽談。
3. 影音節目行銷及文字撰寫。
4. 透過數據分析及判讀,並與社群數據相關部門緊密合作
學歷要求:大學以上畢業,不限科系,大眾傳播相關科系尤佳。
工作經驗:具網路影音相關節目製作5年以上工作經驗,熟悉新媒體作業。
工作技能:Office文書軟體,了解後製剪接、轉檔、字幕、ES、音效、配樂、調色等工作流程。
語言能力:精通中、英文。
其他條件:1、對台灣題材具熱情,可協調完成節目前製、後製工作。
2、請提供先前製作之節目連結。
🔵 B2 編導人員
工作內容:
1、網路節目發想/拍攝/製作。
2、協助主視覺及鏡面效果包裝設計。
3、短片內容拍攝。
4、其他主管交辦事項。
學歷要求:大學以上畢業,大眾傳播相關科系尤佳。
工作經驗:具節目製作3年以上工作經驗、網路影片拍攝、非線性剪輯3年以上經驗。
工作技能:Office文書軟體、After Effect、Final Cut、Premiere,會3D軟體尤佳。
語言能力:精通國台語、英語中等以上。
其他條件:
1. 對台灣題材有興趣、可以獨立完成節目前製與後製工作。
2. 請提供3∼5分鐘自製的影音作品及連結。
🔵 B3 節目企畫
工作內容:
1. 影音節目相關版權及IP洽談業務
2. 影音節目採購標案撰寫、執行與驗收
3. 重製影音節目發想、洽談與流程管控
4. 自製網路影音節目發想、規劃與執行
5. 密切與社群部門溝通,以利節目內容產生有效的國際傳播
學歷要求:大專以上畢業,不限科系。
工作經驗: 具2年以上傳播行銷、節目授權、專案開發等相關工作經驗。
工作技能:Office文書軟體
語言能力:精通中、英文。
其他條件:熟悉著作權相關法律,具備採購專業人員基本資格或進階資格者尤佳
🔵 D1 社群媒體內容製作人
工作內容:
1. 經營Facebook、YouTube、Instagram、Twitter等社群平台,以及
Line、What’s App等等通訊軟體。負責所有社群活動,包括內容排程、社群管理,以及最佳化貼文使用者互動經驗與搜尋。
2. 發想與製作能夠引起高度共鳴的社群圖文,同時密切與內容產製部門合作,達成內容傳遞最佳效益,將台灣題材透過創意社群轉譯給國際觀眾。
3. 管理全站及跨平台數位內容產品,包括主網站與手機應用程式(APP),主責新聞推播與電子報策略。
4. 監測互動與流量表現,並提出內容策略建議。
學歷要求:大學以上畢業,不限科系
工作經驗:具3年以上實際社群經營經驗(請提供相關工作經驗與成功案例)。
工作技能:具備影片、圖片製作思維與能力;社群平台數據分析、Google Analytics分析能力。
語言能力:精通中、英文。
🔵 E3 網路平台技術主管 Platform Technology Manager
工作內容:
1. 帶領並管理技術團隊,以充分掌握技術並達成產品開發或專案交付目標。
2. 依據專案需求,主導或協助專案管理。包含直接或協助專案經理帶領與管理技術團隊,能有效解決專案技術相關問題,確保專案如期如質交付。
3. 依據公司發展需求,負責建立開發技術團隊。內容包含人員面試、考核、技術帶領與管理等。
4. 針對新技術導入與知識管理需求,建立技術評估、技術分享辦法,協助團隊提升技術能力。
5. 其他主管交辦事項。
學歷要求:大學以上畢業,資訊或理工相關科系畢。
工作經驗:具備7年以上開發團隊主管經驗,5年以上C#、Python紮實技術基礎與開發經驗,具大型網路服務系統規畫建置經驗。
工作技能:熟悉C#/.net or Python/Django任一開發技術,熟悉AWS、GCP等雲端平台。具影音串流經驗尤佳。
語言能力:具備中等以上英語聽說讀寫能力。
其他條件:良好的溝通、團隊合作能力。
🔵 E4 DevOp工程師 DevOps Engineer
工作內容:
1. 負責內外部系統發佈、部署、調優、監控、日誌等系統和流程的維護和優化,確保系統的高可用性。
2. 負責雲端系統執行環境的建置與維護。
3. 負責突發問題處理並進行定位和處理。
4. 探索新的運維技術方向。
5. 其它主管交辦事項。
學歷要求:大學以上畢業,理工相關科系畢。
工作經驗:3年以上系統、應用運維經驗。
工作技能:熟悉linux系統,瞭解網路基本技術,熟悉TCP/IP協定原理,具AWS、GCP等雲端平台與服務維運經驗。熟悉網路安全者佳。
其他條件:良好的溝通、團隊合作、獨立作業的能力。
🔵 E5 數據工程師 Data Engineer
工作內容:
1. 執行資料處理、資料分析以及data lake、data mart的建立與維護。
2. 使用BI工具建立報表分析及數據探勘。
3. 因應業務需求,持續優化資料平台架構。
學歷要求:大學以上畢業,資訊或理工相關科系畢。
工作經驗:具備專案管理經驗,熟悉Agile軟體開發流程者佳。
工作技能:熟悉Python 或 Java,熟悉 Power BI或其他BI軟體工具,熟悉SQL。具數據分析與統計經驗。熟悉GCP者佳。
語言能力:具備基本英語溝通能力。
其他條件:良好的溝通協調能力。
🔵 E6 資訊安全暨系統維護主管 Information Security & System Maintenance Manager
工作內容:
1. 統籌公司內部資訊相關系統整合、部署、營運及維護 。
2. 確保資訊設備的可用性,因應公司營運發展所需改善現有資訊系統並預先規劃所需資源。
3. 機房規畫及運營。
4. 規劃辦公室網路環境。
5. 訂立資訊體制,改善資訊安全規範,落實資訊安全控管機制。
6. 定期對資訊風險進行評估以合乎公司安全策略及必要法規(包含ISO),確保系統運營的持續性與可回復。
7. 協助主管其他資訊專案推動。
學歷要求:大學以上畢業,資訊或理工相關科系畢。
工作經驗:7年以上資訊領域工作經驗,具資安經驗者佳。
工作技能:具軟體或平台開發經驗。具備資安相關證照者佳,具有導入ISO經驗者佳。
語言能力:具備中等英語聽說讀寫能力。
其他條件:良好的溝通協調能力。
🔵 E7 資訊安全主管 Information Security Lead
工作內容:
1. 帶領資安團隊、規劃與推動整體資安之目標與計畫。
2. 規劃/制定/執行整體資安治理流程管理。
3. 認證、稽核協調與管理。
4. 資安情資收集與資安事件應變處理。
5. 服務平台資安檢測、諮詢,與規範,持續強化系統資訊安全強度。
6. 辦公室資訊安全防禦建置與監控。
7. 研究與採購建置資安產品。
8. 對內對外資訊安全教育訓練規劃與推動。
學歷要求:大學以上畢業,資訊或理工相關科系畢。
工作經驗:3年以上資安工作經驗,具資安主管經驗者佳。
工作技能:具有AWS、GCP 等雲端環境經驗。具備OSCP,CEH等資安相關證照者佳。具有導入 ISO 經驗者佳。
語言能力:具備中等英語聽說讀寫能力。
其他條件:良好的溝通協調能力。
🔵 E8 資安工程師 Information Security Engineer
工作內容:
1. 協助資訊安全專案執行與維護工作。
2. 資訊安全解決方案(資安系統)專案規劃及建置、維護。
3. 週期性確認相關紀錄(Log),確認相關控制措施有效。
4. 研究資訊安全技術,如重大系統漏洞或惡意程式。
學歷要求:專科或大學以上,理工相關科系畢。
工作經驗:2年以上系統、應用開發或運營經驗。
工作技能:熟悉linux、windows系統,瞭解網路基本技術。具AWS等雲端平台與服務經驗者佳。具備OSCP,CEH等資案相關證照者佳。
其他條件:良好的溝通能力。
🔵 E9 網路暨維護主管/工程師 Network & System Maintenance Lead / Engineer
工作內容:
1. 負責公司與IDC 網路之規劃、建置、管理及維護。
2. 網路設備安裝、設定、管理及維護等。
3. 與分析網路資料傳輸與網路安全架構等特性,以設計、發展及維護網際網路系統之正常運作。
4. 網路解決方案研究與導入。
5. 網路系統進行監控與告警處理。
6. 一般告警處理流程、重大網路障礙排除。工作內容:
7. 機房監控、管理與一般障礙排除與處理。
8. 協助公司其他單位,提供相關的系統操作與技術支援。包含一般員工以及影音編輯人員的電腦故障排除,軟體安裝、設定、系統操作等。
9. 對突發狀況的緊急應變處理。
學歷要求:專科或大學以上,理工相關科系畢。
工作經驗:網管工作2年以上相關經驗。
工作技能:熟悉linux、windows系統。了解OSI架構、HTTP、TCP/IP、DNS、SMTP、CDN。具備Load-balancer/ Firewall/ Switch操作
經驗。具備CCNA優先考慮。
其他條件:能配合公司輪班制度者優先考慮。
🔵 E10 產品管理師
工作內容:
1. 負責OTT影音平台相關的產品功能設計、UI/UX設計。
2. 內部使用單位訪談及需求分析,協助提供內容部門產品端的解決方案。
3. 撰寫商業需求文件及負責產品UAT,執行產品功能上線前驗收測試。
4. 持續優化平台功能與使用者體驗。
學歷要求:大學以上畢業。
工作經驗:具備3年以上網路服務或者to-c系統運營經驗,對產品設計流程和解決問題抱有高度熱情及興趣。
工作技能:熟悉Web、App開發流程。具備專案管理方法以及流程設計的經驗。具UX思維規劃功能,改善使用者體驗。
語言能力:具備基本英語溝通能力。
其他條件:良好的溝通協調能力,個性耐心且細心者為佳。
🔵 E11 軟體開發主管 Software Development Lead
工作內容:
1. 負責影音平台網站、後台與API等相關功能開發。
2. 負責優化與維護既有網站與後台功能。
學歷要求:大學或專科以上畢業,理工相關科系畢。
工作經驗:具備5年以上C#.NET or Python開發經驗。具人員管理經驗。
工作經驗:
1. 具備5年以上C#.NET or Python開發經驗。
2. 具人員管理經驗。
工作技能:
1. http://xn--pcu439a.net/.net core 或 Django、Flask framework。
2. 熟悉JavaScript/CSS/HTML5。
3. 熟悉mySQL、PostgreSQL與mongo DB。
4. 熟悉版控軟體,如Git。
5. 熟悉CI/DC流程。
6. 熟悉Vue.js或React者佳。
其他條件:工作認真仔細,具良好的溝通、團隊合作、獨立作業的能力。
🔵 E12 軟體開發工程師 Software Development Engineer
工作內容:
1. 負責影音平台網站、後台與會員中心等相關功能開發。
2. 負責優化與維護既有網站與後台功能。
學歷要求:大學或專科以上畢業,理工相關科系畢。
工作經驗:具備3年以上C#.NET or Python開發經驗。
工作技能:
1. http://xn--pcu439a.net/.net core 或 Django、Flask framework。
2. 熟悉JavaScript/CSS/HTML5。
3. 熟悉mySQL、PostgreSQL與mongo DB。
4. 熟悉Vue.js或React者佳。
其他條件:工作認真仔細,具良好的溝通、團隊合作、獨立作業的能力。
同時也有280部Youtube影片,追蹤數超過2萬的網紅數學老師張旭,也在其Youtube影片中提到,【摘要】 這是張旭微積分的第一個篇章,極限篇;極限篇是微分和積分的根本,要有極限的觀念與計算能力,才能進入微分和積分的世界,因此是要學微積分絕不可或缺的一個篇章 【加入會員】 歡迎加入張旭老師頻道會員 付費訂閱支持張旭老師,協助本頻道發展並獲得會員專屬福利 👉 https://www.youtub...
log function 在 TPIsoftware Global Facebook 的最讚貼文
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log function 在 Taipei Ethereum Meetup Facebook 的最佳貼文
📜 [專欄新文章] Uniswap v3 Features Explained in Depth
✍️ 田少谷 Shao
📥 歡迎投稿: https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium
Once again the game-changing DEX 🦄 👑
Image source: https://uniswap.org/blog/uniswap-v3/
Outline
0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion
0. Intro
The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥
While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.
Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅
Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊
If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏
There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!
1. Uniswap & AMM recap
Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.
Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.
Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:
AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.
Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².
Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.
In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP
¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity
² the range is in fact [-∞,∞], while a price in most cases won’t be negative
³ AMM of constant sum does not have price slippage
2. Tick
The whole innovation of Uniswap v3 starts from ticks.
For those unfamiliar with what is a tick:
Source: https://www.investopedia.com/terms/t/tick.asp
By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:
The price range of each tick is predefined by the system instead of being proposed by users.
Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.
Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.
With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯
So, how is the price range of a tick decided?
This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.
The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.
Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.
However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.
This is how price ranges of ticks are decided⁴:
Image source: https://uniswap.org/whitepaper-v3.pdf
With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.
As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.
For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.
p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001
See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?
Image source: https://tenor.com/view/coin-master-cool-gif-19748052
But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?
Price range: max & min
To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.
Image source: https://uniswap.org/whitepaper-v3.pdf
The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.
24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:
1.0001 ^ (2¹⁸) = 242,214,459,604.341
1.0001 ^ -(2¹⁷) = 0.000002031888943
I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌
⁴ For implementation concern, however, a square root is added to both sides of the equation.
How about finding out which tick does a price belong to?
Tick index from price
The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:
Image source: https://www.codecogs.com/latex/eqneditor.php
Let’s try this out, say we wanna find out the tick index of 1000000.
Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm
Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!
⁵ This formula is also slightly modified to fit the real implementation usage.
3. Concentrated liquidity
Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.
Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.
As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!
Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/
Mmm… examples are always helpful for abstract descriptions 😂
Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].
If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.
The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.
However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).
We can observe the following two points from the above example:
Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.
√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.
What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!
Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!
Image source: https://uniswap.org/blog/uniswap-v3/
It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵
⁶ Thanks to Yenwen Feng for the information.
4. Range orders: reversible limit orders
As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:
current price < the targeted price range
current price > the targeted price range
current price belongs to the targeted price range
The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.
The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).
There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!
In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.
Range orders
To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.
The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.
For the price of X to go up, y has to increase and x decrease.
With this pricing mechanism in mind, it’s example time!
Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).
The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.
The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.
If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.
Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.
What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].
This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.
…wut? 🤔
Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!
What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.
The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.
Image source: https://uniswap.org/blog/uniswap-v3/
Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.
To wrap up such an interesting feature, we know that:
Only one token is required for range orders.
Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯
I will be discussing more the impacts of v3 in 5. Impacts of v3.
⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.
Reversible limit orders
As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.
We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].
Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.
The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.
As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:
When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸
When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸
A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!
⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.
5. Impacts of v3
Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:
Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.
The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.
LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏
In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.
After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔
Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!
6. Conclusion
That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂
There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅
If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!
Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟
Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.
👏 歡迎轉載分享鼓掌
log function 在 數學老師張旭 Youtube 的最佳貼文
【摘要】
這是張旭微積分的第一個篇章,極限篇;極限篇是微分和積分的根本,要有極限的觀念與計算能力,才能進入微分和積分的世界,因此是要學微積分絕不可或缺的一個篇章
【加入會員】
歡迎加入張旭老師頻道會員
付費訂閱支持張旭老師,協助本頻道發展並獲得會員專屬福利
👉 https://www.youtube.com/channel/UCxBv4eDVLoj5XlRKM4iWj9g/join
【勘誤】
無,有任何錯誤歡迎留言告知
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👉 https://www.facebook.com/changhsumath/reviews
【習題】
重點一:https://drive.google.com/file/d/1YLFYLH96IZyPos_ampP60r4_55jW2mnd/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXiyPrttGXSTluVRga7c5ec2
重點二:https://drive.google.com/file/d/1-A6rc8K3Y6CgAS9awQJh1L0fqiy-1hQD/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXgGS-Bt28sC-i0QZDBcLddi
重點三:https://drive.google.com/file/d/1PQNL-IJRN2ulePKRuQTXofgZ05SzocLW/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXh8HQQbJ4h2CEdwy-YWEipO
重點四:https://drive.google.com/file/d/1S91OWZBh2OCpc8fdCJR0g99LpDP7fXJ2/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXjNO4nC3eIEcq0F4SNAL7hR
重點五:https://drive.google.com/file/d/1NDlpvtxhkQX47p_7o8TWdkmSPPwfx7AD/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXg0cOhjFarM56LcjU87xtdB
重點六:https://drive.google.com/file/d/1IwJPyiGPmG6nTu1xuLY-RWYu7yC--rzh/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXjnSHFVNhM9j1aIG3dvYLyU
重點七:https://drive.google.com/file/d/1HcKh_LVuX-WVwQ_sFaVFQKNsouOGShWx/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXgWMZtWu77QzGIfbTKLHoLk
重點八:https://drive.google.com/file/d/15JjGfobYehx_Zz9DHeFCWIsnB3QoNVEs/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXiiIEiKwpg2qru9zqNxurgx
重點九:https://drive.google.com/file/d/1cVqiS6pLMeHbjmXQIAJNzNO6eMNrhg71/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXiEkmV5qYcyp_-yB_30fcZW
重點十之一:https://drive.google.com/file/d/1O2hcZgPw87gFClgabCwuO-CMVIPPEw9g/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXih3a_3DDXOUk0hRHMfg53_
重點十之二:https://drive.google.com/file/d/1O2hcZgPw87gFClgabCwuO-CMVIPPEw9g/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXih3a_3DDXOUk0hRHMfg53_
重點十之三:https://drive.google.com/file/d/1O2hcZgPw87gFClgabCwuO-CMVIPPEw9g/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXih3a_3DDXOUk0hRHMfg53_
重點十一:https://drive.google.com/file/d/19m9ss4eVSTQxTa3p9wKOtTeUrPAIkMI9/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXi9a02MYJJadw5sMIqoII-T
重點十二:https://drive.google.com/file/d/1D8R-DA-7epAyFnVqNqPrR0Kgjiy14NKO/view?usp=sharing
偶數題講解影片:https://www.youtube.com/playlist?list=PLKJhYfqCgNXhWs16FYbGx5HTe2QdPwBqD
簡答:https://www.facebook.com/groups/changhsumath666.calculus/files
微積分討論群:https://www.facebook.com/groups/changhsumath666.calculus
【附註】
重點十之一~十之三作業皆為同一個檔案
【學習地圖】
【極限篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXjkwxSf-xDV47b9ZXDUkYiN)
重點一:極限的直觀定義 (https://youtu.be/hZT2fOcxSJw)
重點二:極限的嚴格定義 (https://youtu.be/gCkhy0aODZk)
重點三:一些基本函數的極限 (上集) (https://youtu.be/qoIOFz1D_W4)
重點四:極限運算定理 (四則運算篇) (https://youtu.be/d6PzP8ApFgk)
重點五:極限運算定理 (合成篇) (https://youtu.be/h2X2yyGyWHQ)
重點六:去零因子求極限 (https://youtu.be/vqoc59G-gRI)
重點七:去絕對值求極限 (https://youtu.be/PYzasrBZWWA)
重點八:高斯符號求極限 (https://youtu.be/EXKQQS17k2Y)
重點九:含無窮符號之極限 (https://youtu.be/RhKkx7DO_kM)
重點十之一:老大比較法 (上):多項式分式 (https://youtu.be/Wr6rkCa1Neo)
重點十之二:老大比較法 (中):指數函數多項式 (https://youtu.be/FYGzcSw0U0s)
重點十之三:老大比較法 (下):叉叉接旨刺 log (https://youtu.be/YbvXCZmmff4)
重點十一:夾擠定理 (https://youtu.be/sTvtt4K85s0)
重點十二:lim_(x→0) sin(x) / x 專論 (https://youtu.be/sVohBWF-6ww)
【連續篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXgntIXH9Jrpgo5O6y_--58L)
【微分篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXiPgR9GLKtro3CTr6OIgdMg)
【微分應用篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXjNzXUa9hI2IfknA8Q7iSwE)
【積分前篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXikxrvbQAnPa_l3nFh5m9XK)
【積分後篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXhFI6OnDy0la5MqPOnWtoU7)
【數列與級數】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXjcv6ChH_w0Y0WRkdbiP6xY)
【多變數函數的微積分】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXhoWH8tB00L6d3tWMV1l_o8)
【向量微積分】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXhVcuTj1IoCcYsRhJqoHN-y)
【附註】
1. 積分前篇和後篇自 2021 年 5 月起改成買張旭微積分上學期講義解鎖影片
2. 數列與級數以後的章節為下學期內容,為付費課程,購買後在張旭無限教室線上課程平台觀看
張旭微積分上學期講義購買頁面
👉 https://www.changhsumath.cc/calculusBook
張旭微積分下學期課程影片將不會在 YouTube 頻道上免費公開
若你覺得我的課程適合你,且你下學期也有微積分要修
可以參考購課頁面 👉 https://www.changhsumath.cc/calculus2nd
【張旭無限教室線上課程平台】
2021 年年初,我建置了一個線上課程平台
除了放我的線上課程以外
也有其他與我合作的老師們的課程
👉 https://changhsumath.com
【版權宣告】
本影片版權為張旭 (張舜為) 老師所有
嚴禁用於任何商業用途⛔
如果有學校老師在課堂使用我的影片的話
請透過以下聯絡方式通知我讓我知道,謝謝
FB:https://www.facebook.com/changhsumath
IG:https://www.instagram.com/changhsumath
log function 在 數學老師張旭 Youtube 的最佳解答
【摘要】
透過解釋有理數和無理數在實數上的分布狀況,探討了 Dirichlet function 的極限存不存在這個問題
【加入會員】
歡迎加入張旭老師頻道會員
付費訂閱支持張旭老師,協助本頻道發展並獲得會員專屬福利
👉 https://www.youtube.com/channel/UCxBv4eDVLoj5XlRKM4iWj9g/join
【勘誤】
無,有任何錯誤歡迎留言告知
【講義】
請到張旭老師臉書粉專評論區留下你的評論
然後私訊張旭老師臉書粉專索取講義,通過審核即可獲得講義連結
👉 https://www.facebook.com/changhsumath/reviews
【習題】
重點一習題請點選連結下載
👉 https://drive.google.com/file/d/1YLFYLH96IZyPos_ampP60r4_55jW2mnd/view?usp=sharing
偶數題講解影片
👉 https://www.youtube.com/playlist?list=PLKJhYfqCgNXiyPrttGXSTluVRga7c5ec2
簡答:https://www.facebook.com/groups/changhsumath666.calculus/files
微積分討論群:https://www.facebook.com/groups/changhsumath666.calculus
【附註】
本影片適合理、工學院學生觀看
商學院學生可作為補充教材
【學習地圖】
【極限篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXjkwxSf-xDV47b9ZXDUkYiN)
重點一:極限的直觀定義 (https://youtu.be/hZT2fOcxSJw)
├ 精選範例 1-1 👈 目前在這裡
└ 精選範例 1-2 (https://youtu.be/Ks8BPRYcrKs)
重點二:極限的嚴格定義 (https://youtu.be/gCkhy0aODZk)
重點三:一些基本函數的極限 (上集) (https://youtu.be/qoIOFz1D_W4)
重點四:極限運算定理 (四則運算篇) (https://youtu.be/d6PzP8ApFgk)
重點五:極限運算定理 (合成篇) (https://youtu.be/h2X2yyGyWHQ)
重點六:去零因子求極限 (https://youtu.be/vqoc59G-gRI)
重點七:去絕對值求極限 (https://youtu.be/PYzasrBZWWA)
重點八:高斯符號求極限 (https://youtu.be/EXKQQS17k2Y)
重點九:含無窮符號之極限 (https://youtu.be/RhKkx7DO_kM)
重點十之一:老大比較法 (上):多項式分式 (https://youtu.be/Wr6rkCa1Neo)
重點十之二:老大比較法 (中):指數函數多項式 (https://youtu.be/FYGzcSw0U0s)
重點十之三:老大比較法 (下):叉叉接旨刺 log (https://youtu.be/YbvXCZmmff4)
重點十一:夾擠定理 (https://youtu.be/sTvtt4K85s0)
重點十二:lim_(x→0) sin(x) / x 專論 (https://youtu.be/sVohBWF-6ww)
【連續篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXgntIXH9Jrpgo5O6y_--58L)
【微分篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXiPgR9GLKtro3CTr6OIgdMg)
【微分應用篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXjNzXUa9hI2IfknA8Q7iSwE)
【積分前篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXikxrvbQAnPa_l3nFh5m9XK)
【積分後篇】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXhFI6OnDy0la5MqPOnWtoU7)
【數列與級數】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXjcv6ChH_w0Y0WRkdbiP6xY)
【多變數函數的微積分】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXhoWH8tB00L6d3tWMV1l_o8)
【向量微積分】(https://www.youtube.com/playlist?list=PLKJhYfqCgNXhVcuTj1IoCcYsRhJqoHN-y)
【附註】
1. 積分前篇和後篇自 2021 年 5 月起改成買張旭微積分上學期講義解鎖影片
2. 數列與級數以後的章節為下學期內容,為付費課程,購買後在張旭無限教室線上課程平台觀看
張旭微積分上學期講義購買頁面
👉 https://www.changhsumath.cc/calculusBook
張旭微積分下學期課程影片將不會在 YouTube 頻道上免費公開
若你覺得我的課程適合你,且你下學期也有微積分要修
可以參考購課頁面 👉 https://www.changhsumath.cc/calculus2nd
【張旭無限教室線上課程平台】
2021 年年初,我建置了一個線上課程平台
除了放我的線上課程以外
也有其他與我合作的老師們的課程
👉 https://changhsumath.com
【版權宣告】
本影片版權為張旭 (張舜為) 老師所有
嚴禁用於任何商業用途⛔
如果有學校老師在課堂使用我的影片的話
請透過以下聯絡方式通知我讓我知道,謝謝
FB:https://www.facebook.com/changhsumath
IG:https://www.instagram.com/changhsumath
log function 在 賭Sir【杜氏數學】HermanToMath Youtube 的最讚貼文
?《我要數學大翻身》 4合1全套DSE速效課程:
https://hermantomath.skx.io/courses/6328693527937024
?優惠限定,敬請留意❗
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#我要數學大翻身
#4合1全套DSE速效課程
#優惠限定
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杜氏數學 官方網站: http://www.HermanToMath.com
賭Sir 幫你急救 DSE 數學: https://HermanToMath.skx.io
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?️賭Sir是杜氏數學Herman To Math的始創人
?全港唯一「完爆」【DSE Core+M1+M2】、【IAL 12科Maths】、【AL Pure+Applied】、【CE Maths+A.Maths】的數學導師
?全港第一最多訂閱粉絲的數學教育YouTuber
?YouTube觀看次數超越700萬、訂閱粉絲超過50000人
?著作:《YouTuber新手到網紅》、《5**數學男人嫁得過》、《碌葛男人嫁得過》、《賭波男人嫁得過》(獲Google嚴選2018年度50大最佳書籍)
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賭Sir收集著數派街坊:
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賭Sir考試戰績:
新制中六DSE: (2016 M2 + 2017 M1)
?數學必修 (Mathematics) 一take過 奪5**
?數學延伸M1 (Calculus and Statistics) 一take過 奪5**
?數學延伸M2 (Algebra and Calculus) 一take過 奪5**
國際高考International Advanced Level: (2017 + 2018)
?Core Math 1 2 一take過 奪A
?Core Math 3 4 一take過 奪A
?Further Pure Math 1 一take過 奪A
?Further Pure Math 2 一take過 奪A
?Further Pure Math 3 一take過 奪A
?Mechanics 1 一take過 奪A
?Mechanics 2 一take過 奪A
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舊制中七高考: (2011)
?純粹數學 (Pure Mathematics) 一take過 奪A
?應用數學 (Applied Mathematics) 一take過 奪A
舊制中五會考: (2009)
?數學 (Mathematics) 一take過 奪A
?附加數學 (Additional Mathematics) 一take過 奪A
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DSE精選系列:
《DSE數學短片 之 發憤學生必看!》系列
https://www.youtube.com/watch?v=1mVTSqpY-9Q&list=PL_CM4U5au2k1xNBwQFtwjDGYHKvI6LkEe&index=5
《攞分唔使識得計 奇技淫巧》系列
https://www.youtube.com/watch?v=u9lM-7a4ivQ&list=PL_CM4U5au2k1xdQroee0QXyNUJ3n5QE6L&index=1
《DSE FINAL TIPS》系列
https://www.youtube.com/watch?v=TWTdj3tEdsQ&list=PL_CM4U5au2k1vvZ8QqzeattYEDD31wzwy&index=2
《DSE十大最常遺忘CONCEPT》系列
https://www.youtube.com/watch?v=jMbWMO7yn3U&list=PL_CM4U5au2k2Ywgjnm60vzEkSU3NgcWl5&index=2
《講大 Stand Talks》系列
https://www.youtube.com/watch?v=FthGljfW03g&list=PL_CM4U5au2k3zc32MEpb6nQiVq40GDpEE&index=2
《名校試題》系列
https://www.youtube.com/watch?v=UY8pxw-OC4E&index=1&list=PL_CM4U5au2k1n86kvgdkPBDqchYdsciCs
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賭Sir精選系列:
《賭Sir數學戒賭》糸列
https://www.youtube.com/watch?v=dhL-dRcIN5I&index=1&list=PL_CM4U5au2k1cfK2zSph8XOLqIjOPQmvo
《賭史數學戒賭》系列
https://www.youtube.com/watch?v=zL1AEoT4meM&list=PL_CM4U5au2k1SkRXo2ZEmgSmpJoPs49-p&index=2
《賭博數學入門》系列(一連5集)
https://www.youtube.com/watch?v=QLE4keUg1Qo&list=PL_CM4U5au2k0cFDn4QKXmi-1e4VNjs0fO&index=2
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過癮精選系列:
《賭Sir數學界女》系列
https://www.youtube.com/watch?v=iEBXiT8rXqs&list=PL_CM4U5au2k3-qH1PFosfFyQy5Z0JMzLy&index=2
《大眾數學娛樂台》系列
https://www.youtube.com/watch?v=99hEaM0xAZo&list=PL_CM4U5au2k1RcJWYRnSbfo9SQ6V6GjnU&index=6
log function 在 Algebra - Logarithm Functions - Pauls Online Math Notes 的相關結果
First, the “log” part of the function is simply three letters that are used to denote the fact that we are dealing with a logarithm. They are ... ... <看更多>
log function 在 Logarithmic Function Reference - Math is Fun 的相關結果
In general, the logarithmic function: · is always on the positive side of (and never crosses) the y-axis · always intersects the x-axis at x=1 ... in other words ... ... <看更多>
log function 在 對數- 維基百科,自由的百科全書 的相關結果
在數學中,對數(英語:Logarithm)是冪運算的逆運算。 ... the Three and Four Place Tables of Logarithmic and Trigonometric Functions, by James Mills Peirce, ... ... <看更多>