The Matrix Calculus You Need For Deep Learning
Terence Parr and Jeremy Howard (Terence is a tech lead at Google and ex-Professor of computer/data science in University of San Francisco's MS in Data Science program. You might know Terence as the creator of the ANTLR parser generator. For more material, see Jeremy's fast.ai courses and University of San Francisco's Data Institute in-person version of the deep learning course.) Please send commen
245A: Problem solving strategies
245A: Problem solving strategies 21 October, 2010 in 245A - Real analysis, math.CA, math.GM, tricks | Tags: measure theory, problem solving | by Terence Tao This is going to be a somewhat experimental post. In class, I mentioned that when solving the type of homework problems encountered in a graduate real analysis course, there are really only about a dozen or so basic tricks and techniques that
よãã‚ã‹ã‚‹æ¸¬åº¦è«–ã¨ãƒ«ãƒ™ãƒ¼ã‚°ç©åˆ†ã€‚ - ã¹ã£ã日記
今日ã¯ã¨ã¦ã‚‚寒ãã€ç§‹ã‚‰ã—ã„天気ã 。一般ã«ç§‹ã«ãªã‚‹ã¨ã€ã€Œã€‡ã€‡ã®ç§‹ã€ã¨ã„ã†è¨€è‘‰ã‚’èžãã‘ã‚Œã©ã‚‚ã€ã€‡ã€‡ã«å¥½ããªè¨€è‘‰ã‚’入れれã°ç§‹ã‚‰ã—ããªã‚‹ã®ã§ä¸æ€è°ã§ã‚る。 ã•ã¦ã€è¶£å‘³ã®Twitterを眺ã‚ã¦ã„ã‚‹ã¨ã€æ¸¬åº¦è«–ãŒã‚ã‹ã‚‰ãªã„ã¨ã„ã†ãƒ„イートを見ãŸã€‚ç§ã¯ä¸€å¿œæ¸¬åº¦è«–ã®TAã‚’ã‚„ã£ã¦ã„ã‚‹ã®ã§ã€ä»Šå›žã¯æ¸¬åº¦è«–ã‚’ã–ã£ãã‚Šã‚ã‹ã‚Šã‚„ã™ãã¾ã¨ã‚ã‚‹ã“ã¨ã«ã—ãŸã€‚測度論ã¯è§£æžç³»ã‚„統計系ã§ã¯å¿…é ˆã®é“å…·ã§ã‚る。ç§ã¯è§£æžç³»ã®äººé–“ãªã®ã§ã€ä»Šå›žã¯ãƒ«ãƒ™ãƒ¼ã‚°ç©åˆ†ã®åŸºæœ¬ã§ã‚ã‚‹Fubiniã®å®šç†ã‚„å˜èª¿åŽæŸå®šç†ã€ãƒ«ãƒ™ãƒ¼ã‚°ã®åŽæŸå®šç†ã€ç©åˆ†è¨˜å·ä¸‹ã§ã®å¾®åˆ†ã‚’ゴールã«è§£èª¬ã‚’ã™ã‚‹ã“ã¨ã«ã—ãŸã€‚ 以下ã€ã“ã®è¨˜äº‹ã®ãƒ¡ãƒ‹ãƒ¥ãƒ¼ã§ã‚る。 ï¼ï¼Žæ¸¬åº¦è«–ã®å¿ƒ １．測度ã®å®šç¾© １-ï¼‘ï¼Žå®Œå…¨åŠ æ³•æ— ï¼‘-２．測度 １-３．測度空間 １-４．測度ã®æ€§è³ª ２．ルベーグç©åˆ†ã®å®šç¾© ï¼’-１．特性関数 ï¼’-２．階段関数 ï¼’-３．ルベーグç©åˆ†ã®å®šç¾© ï¼’-４．リーマンç©åˆ†ã¨ãƒ«ãƒ™ãƒ¼ã‚°ç©åˆ†ã¨ã®é–¢ä¿‚ ï¼’-
The Principles of Deep Learning Theory
This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are
Online texts
The writing of textbooks and making them freely available on the web is an idea whose time has arrived. Most college mathematics textbooks attempt to be all things to all people and, as a result, are much too big and expensive. This perhaps made some sense when these books were rather expensive to produce and distribute--but this time has passed. Professor Jim Herod and I have written Multivariabl
Oliver-Soundararajanã®ãƒ—レプリントã«ã¤ã„㦠- INTEGERS
3/11ã«arXivã«æŠ•ç¨¿ã•ã‚ŒãŸãƒ—レプリント R. J. L. Oliver, K. Soundararajan, Unexpected biases in the distribution of consecutive primes, preprint. ãŒFields賞å—賞者ã§ã‚ã‚‹Terence Taoã®ãƒ–ãƒã‚°ã§å–り上ã’られãŸã‚Š("very nice"ã¨æ›¸ã„ã¦ã‚ã‚‹ï¼)ã€natureã§è¨˜äº‹ãŒæ›¸ã‹ã‚ŒãŸã‚Šã™ã‚‹ãªã©ã—ã¦æ³¨ç›®ã‚’æµ´ã³ã¾ãã£ã¦ã„ã¾ã™ã€‚ ç§è‡ªèº«ã¯é¡Œåã ã‘見ã¦ä¸èº«ã¯è¦‹ã¦ã„ãªã‹ã£ãŸã®ã§ã™ãŒã€å…ˆã»ã©*1twitterã§æƒ…å ±ãŒæµã‚Œã¦ãã‚‹ã®ã‚’見ã¦æ°—ã«ãªã£ãŸã®ã§è©±é¡Œã®ãƒ—レプリントを少ã—眺ã‚ã¦ã¿ã¾ã—ãŸã€‚ ã—ã£ã‹ã‚Šè¨ˆç®—ã¯è¿½ãˆã¦ã„ã¾ã›ã‚“ã—ã€ç†è§£ã§ãã¦ã„ãªã„部分も多ã„ã§ã™ãŒã€ç¾æ®µéšŽã«ãŠã‘ã‚‹ç†è§£ã‚’ã¾ã¨ã‚ã¦ã¿ãŸã„ã¨æ€ã„ã¾ã™(ã¾ã ã€å°‚門家ã«ã‚ˆã‚‹æŸ»èªã‚’å—ã‘ã¦ã„ãªã„プレプリントã®ãŸã‚ã€å†…容を全é¢çš„ã«ä¿¡ç”¨ã™ã‚‹ã“ã¨ã¯ã§
SageMath - Wikipedia
ウィリアム・スタイン（2011å¹´6月） SageMath（セイジã€ä»¥å‰ã¯Sageã€SAGEã¨è¨˜ã—ãŸï¼‰ã¯æ•°å¦ã®å¹…広ã„処ç†ã‚’扱ã†ã‚½ãƒ•ãƒˆã‚¦ã‚§ã‚¢ã§ã‚る。扱ã†å‡¦ç†ã¯è¨ˆç®—機代数ã€çµ„ã¿åˆã‚ã›ã€æ•°å€¤è¨ˆç®—ãªã©å¤šå²ã«åŠã¶ã€‚å·¥å¦çš„応用ã«åŠ ãˆåŸºç¤Žç§‘å¦ã®ç ”究も対応ã—ã¦ã„る。 SageMathã¯2005å¹´2月24æ—¥ã«ãƒ•ãƒªãƒ¼ã‚½ãƒ•ãƒˆã‚¦ã‚§ã‚¢ã¨ã—ã¦GNU General Public Licenseã®å…ƒã§åˆç‰ˆãŒå…¬é–‹ã•ã‚ŒãŸã€‚ãã®é–‹ç™ºç›®çš„ã¯Magmaã€Mapleã€Mathematica（ã„ãšã‚Œã‚‚計算機代数ソフトウェア）ã€MATLABã®ä»£æ›¿ã¨ãªã‚‹ãƒ•ãƒªãƒ¼ã‹ã¤ã‚ªãƒ¼ãƒ—ンソースãªã‚½ãƒ•ãƒˆã‚¦ã‚§ã‚¢ã‚’æä¾›ã™ã‚‹ã“ã¨ã§ã‚ã£ãŸ[3]。開発ã¯ã€ç±³ãƒ¯ã‚·ãƒ³ãƒˆãƒ³å¤§å¦ã®æ•°å¦å‡†æ•™æŽˆã®ã‚¦ã‚£ãƒªã‚¢ãƒ ・スタイン (William Stein) ãŒä¸»å°Žã—ã¦å§‹ã¾ã£ãŸã€‚ SageMathã¯Pythonプãƒã‚°ãƒ©ãƒŸãƒ³ã‚°è¨€èªžã‚’使用ã—ã¦ãŠã‚Šã€æ‰‹ç¶šã型・関数型・オブジェクト指å‘ã«ã‚ˆã‚‹ãƒ—ãƒ
åŒå€¤ - Wikipedia
åŒå€¤ï¼ˆã©ã†ã¡ï¼‰ã¾ãŸã¯ç‰ä¾¡ï¼ˆã¨ã†ã‹ï¼‰ã¨ã¯ã€2ã¤ã®å‘½é¡ŒãŒå…±ã«çœŸã¾ãŸã¯å…±ã«å½ã®ã¨ãã«çœŸã¨ãªã‚‹è«–ç†æ¼”ç®—ã§ã‚る。 英語ã§ã¯equivalence (EQ)。「if and only if（～ã®ã¨ãã€ã‹ã¤ãã®ã¨ãã«é™ã‚‹ï¼‰ã€ã‚’ç•¥ã—ã¦ã€iff ã¨ã‚‚ã„ã†ã€‚å¦å®šæŽ’ä»–çš„è«–ç†å’Œ (XNOR) ã«ç‰ã—ã„。 演算å記å·ã¯ ⇔ã€â†”ã€â‰¡ã€=ã€EQ ãªã©ãŒä½¿ã‚れる。
PhotoMath uses your phone's camera to solve equations
Need a little help getting through your next big math exam? MicroBlink has an app that could help you study more effectively -- perhaps too effectively. Its newly unveiled PhotoMath for iOS and Windows Phone (Android is due in early 2015) uses your smartphone's camera to scan math equations and not only solve them, but show the steps involved. Officially, it's meant to save you time flipping throu
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エルデシュ数 - Wikipedia
ãƒãƒ¼ãƒ«ãƒ»ã‚¨ãƒ«ãƒ‡ã‚·ãƒ¥ エルデシュ数（エルデシュã™ã†ã€ErdÅ‘s number）ã¾ãŸã¯ã‚¨ãƒ«ãƒ‡ã‚·ãƒ¥ç•ªå·ã¨ã¯ã€æ•°å¦è€…åŒå£«ã€ã‚ã‚‹ã„ã¯ã‚‚ã£ã¨åºƒã科å¦è€…åŒå£«ã®ã€å…±è‘—è«–æ–‡ã«ã‚ˆã‚‹çµã³ä»˜ãã«ãŠã„ã¦ã€ãƒãƒ³ã‚¬ãƒªãƒ¼å‡ºèº«ã®æ•°å¦è€…ãƒãƒ¼ãƒ«ãƒ»ã‚¨ãƒ«ãƒ‡ã‚·ãƒ¥ã¨ã©ã‚Œã ã‘è¿‘ã„ã‹ã‚’表ã™æ¦‚念ã§ã‚る。エルデシュã«å…±è‘—è«–æ–‡ãŒéžå¸¸ã«å¤šã„ã“ã¨ã‹ã‚‰ã€ãã®å‹äººãŸã¡ã«ã‚ˆã£ã¦ã€æ•¬æ„ã¨ãƒ¦ãƒ¼ãƒ¢ã‚¢ã‚’è¾¼ã‚ã¦è€ƒãˆå‡ºã•ã‚ŒãŸã€‚今日ã§ã¯ç§‘å¦è€…ã®ã‚³ãƒŸãƒ¥ãƒ‹ãƒ†ã‚£ã«ãŠã„ã¦ã‚ˆã知られã¦ãŠã‚Šã€ã‚¨ãƒ«ãƒ‡ã‚·ãƒ¥ã¨è¿‘ã„ã“ã¨ãŒå誉ã§ã‚ã‚‹ã‹ã®ã‚ˆã†ã«åŠã°å†—談ã‚ã„ã¦èªžã‚‰ã‚Œã‚‹ã€‚ アリスã¯ã‚¨ãƒ«ãƒ‡ã‚·ãƒ¥ã¨å…±è‘—ã§è«–文を書ãã€ãƒœãƒ–ã¨ã‚‚共著ã§è«–文を書ã„ã¦ã„ã‚‹ã¨ã™ã‚‹ã€‚ãã—ã¦ã€ãƒœãƒ–ã¨ã‚¨ãƒ«ãƒ‡ã‚·ãƒ¥ã«ã¯ç›´æŽ¥ã®å…±è‘—è«–æ–‡ãŒãªã„ã¨ã™ã‚‹ã€‚ボブãŒå…±è‘—論文をãŸã©ã£ã¦ã‚¨ãƒ«ãƒ‡ã‚·ãƒ¥ã«è¡Œãç€ããŸã‚ã«ã¯2回ã®ã‚¹ãƒ†ãƒƒãƒ—ãŒå¿…è¦ã§ã‚ã‚‹ãŸã‚ã€ãƒœãƒ–ã«ã¯ã‚¨ãƒ«ãƒ‡ã‚·ãƒ¥æ•°2ãŒä¸Žãˆã‚‰ã‚Œã‚‹ã€‚ ã‚る者ãŒæ–°ãŸã«ã‚¨ãƒ«ãƒ‡ã‚·ãƒ¥æ•°ã‚’å¾—ã‚‹ãŸã‚ã«ã¯ã€ã™ã§ã«ã‚¨ãƒ«ãƒ‡ã‚·ãƒ¥æ•°ãŒä¸Žãˆã‚‰ã‚Œã¦
www.sagemath.org
SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers. Mission: Creating a viable free open source alternative to Magma, Maple, Mathematic
Essential Math for Games Programmers
As the quality of games has improved, more attention has been given to all aspects of a game to increase the feeling of reality during gameplay and distinguish it from its competitors. Mathematics provides much of the groundwork for this improvement in realism. And a large part of this improvement is due to the addition of physical simulation. Creating such a simulation may appear to be a daunting
Reverse Mathematics in Coq
This is a Korea-France research project on reverse mathematics. It is part of the STAR Project sponsored by the National Research Foundation on the Korean side and Ministry of Foreign and European Affairs on the French side. Besides two leaders of the project, Gyesik Lee on the Korean side and Hugo Herbelin on the French side, more researchers are involved, above all Laurent Bienvenu, Sungwoo Park
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オンラインã§å…¥æ‰‹ã§ãã‚‹æ•°ç†è«–ç†å¦ãƒ»æ•°å¦åŸºç¤Žè«–ã®ãƒ†ã‚スト æ•°ç†è«–ç†å¦ã€æ•°å¦åŸºç¤Žè«–ã®æ•™ç§‘書的ã«ä½¿ãˆã‚‹ãƒ†ã‚スト（講義ノートã€ã‚µãƒ¼ãƒ´ã‚§ã‚¤ã€ãƒ¢ãƒŽã‚°ãƒ©ãƒ•ç‰ï¼‰ã®ã†ã¡ã€ã‚ªãƒ³ãƒ©ã‚¤ãƒ³ã§å…¥æ‰‹ã§ãã‚‹ã‚‚ã®ã‚’集ã‚ã¾ã—ãŸã€‚ 入門的概説 è«–ç†ä¸€èˆ¬ 高階論ç†ã¨åž‹ç†è«– ç›´è¦³ä¸»ç¾©è«–ç† ã‚³ãƒ³ãƒ“ãƒãƒ¼ã‚¿ã¨ãƒ©ãƒ ダ計算 時相論ç†ãŠã‚ˆã³æ™‚åˆ¶è«–ç† æ§˜ç›¸è«–ç† é©åˆ‡ã•ã®è«–ç† è‡ªç„¶è¨€èªžã®è«–ç† ç©ºé–“è«–ç† ãƒ¢ãƒ‡ãƒ«ç†è«– 安定性ç†è«– ç„¡é™è«–ç† è¨ˆç®—å¯èƒ½æ€§ç†è«–ãŠã‚ˆã³å†å¸°ç†è«– 集åˆè«– pcfç†è«– 記述集åˆè«– 実数ã®é›†åˆè«– é¸æŠžå…¬ç† 強制法ã¨å†…部モデル 連続体仮説 NF 証明論ã¨æ§‹æˆçš„æ•°å¦ é †åºæ•°è§£æž ç®—è¡“ã®ä½“ç³»ã¨ä¸å®Œå…¨æ€§ 証明å¯èƒ½æ€§è«–ç† ç·šå½¢è«–ç† æ§‹æˆçš„æ•°å¦ ä»£æ•°çš„è«–ç†ã¨åœè«– ブール代数 æ™®é代数 é‡åè«–ç† åœè«– æ´å² 入門的概説 [â–²] åŠ èŒ‚é™å¤«ï¼Œã€Œæ•°ç†è«–ç†å¦ï¼ˆå‘½é¡Œè«–ç†ã¨è¿°èªžè«–ç†ï¼‰ã€ï¼Ž[PDF] 嘉田å‹ï¼Œã€Œæ•°ç†è«–ç†å¦ 講義ノート（2013年度版）ã€ï¼Ž St
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What does "curly (curved) less than" sign $\succcurlyeq$ mean?
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Visually stunning math concepts that are easy to explain
Sysquake
Quaternion to Euler - Qiita
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