By Dahua Lin
2008.07.13
杩欓噷璇磋鍑犳湰鎴戠湅杩囧悗瑙夊緱涓嶉敊鐨勬暟瀛︽暀绉戜功銆�
1. 绾挎€т唬鏁� (Linear Algebra)锛�
鎴戞兂鍥藉唴鐨勫ぇ瀛︾敓閮戒細瀛﹁繃杩欓棬璇剧▼锛屼絾鏄紝鏈繀姣忎竴浣嶈€佸笀閮借兘璐交瀹冪殑绮捐銆傝繖闂ㄥ绉戝浜嶭earning鏄繀澶囩殑鍩虹锛屽瀹冪殑閫忓交鎺屾彙鏄繀涓嶅彲灏戠殑銆傛垜鍦ㄧ澶т竴骞寸骇鐨勬椂鍊欏氨瀛︿範浜嗚繖闂ㄨ锛屽悗鏉ュ埌浜嗛娓悗锛屽張閲嶆柊鎶婄嚎鎬т唬鏁拌浜嗕竴閬嶏紝鎵€璇荤殑鏄�
Introduction to Linear Algebra (3rd Ed.) by Gilbert Strang.
杩欐湰涔︽槸MIT鐨勭嚎鎬т唬鏁拌浣跨敤鐨勬暀鏉愶紝涔熸槸琚緢澶氬叾瀹冨ぇ瀛﹂€夌敤鐨勭粡鍏告暀鏉愩€傚畠鐨勯毦搴﹂€備腑锛岃瑙ｆ竻鏅帮紝閲嶈鐨勬槸瀵硅澶氭牳蹇冪殑姒傚康璁ㄨ寰楁瘮杈冮€忓交銆傛垜涓汉瑙夊緱锛屽涔犵嚎鎬т唬鏁帮紝鏈€閲嶈鐨勪笉鏄幓鐔熺粌鐭╅樀杩愮畻鍜岃В鏂圭▼鐨勬柟娉曗€斺€旇繖浜涘湪瀹為檯宸ヤ綔涓璏ATLAB鍙互浠ｅ姵锛屽叧閿殑鏄娣卞叆鐞嗚В鍑犱釜鍩虹鑰屽張閲嶈鐨勬蹇碉細瀛愮┖闂�(Subspace)锛屾浜�(Orthogonality)锛岀壒寰佸€煎拰鐗瑰緛鍚戦噺(Eigenvalues and eigenvectors)锛屽拰绾挎€у彉鎹�(Linear transform)銆備粠鎴戠殑瑙掑害鐪嬫潵锛屼竴鏈嚎浠ｆ暀绉戜功鐨勮川閲忥紝灏卞湪浜庡畠鑳藉惁缁欒繖浜涙牴鏈蹇典互瓒冲鐨勯噸瑙嗭紝鑳藉惁鎶婂畠浠殑鑱旂郴璁叉竻妤氥€係trang鐨勮繖鏈功鍦ㄨ繖鏂归潰鏄仛寰楀緢濂界殑銆�
鑰屼笖锛岃繖鏈功鏈変釜寰楀ぉ鐙帤鐨勪紭鍔裤€備功鐨勪綔鑰呴暱鏈熷湪MIT璁叉巿绾挎€т唬鏁拌(18.06)锛岃绋嬬殑video鍦∕IT鐨凮pen courseware缃戠珯涓婃湁鎻愪緵銆傛湁鏃堕棿鐨勬湅鍙嬪彲浠ヤ竴杈圭湅鐫€鍚嶅笀鎺堣鐨勫綍鍍忥紝涓€杈瑰鐓ц鏈涔犳垨鑰呭涔犮€�
http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/CourseHome/index.htm
2. 姒傜巼鍜岀粺璁� (Probability and Statistics):
姒傜巼璁哄拰缁熻鐨勫叆闂ㄦ暀绉戜功寰堝锛屾垜鐩墠涔熸病鏈夌壒鍒殑鎺ㄨ崘銆傛垜鍦ㄨ繖閲屾兂浠嬬粛鐨勬槸涓€鏈叧浜庡鍏冪粺璁＄殑鍩虹鏁欑涔︼細
Applied Multivariate Statistical Analysis (5th Ed.) by Richard A. Johnson and Dean W. Wichern
杩欐湰涔︽槸鎴戝湪鍒氭帴瑙﹀悜閲忕粺璁＄殑鏃跺€欑敤浜庡涔犵殑锛屾垜鍦ㄩ娓椂鍋氱爺绌剁殑鍩虹灏辨槸浠庢鎵撲笅浜嗐€傚疄楠屽鐨勪竴浜涘悓瀛︿篃鍊熺敤杩欐湰涔﹀涔犲悜閲忕粺璁°€傝繖鏈功娌℃湁鐗瑰埆杩芥眰鏁板涓婄殑娣卞害锛岃€屾槸浠ラ€氫織鏄撴噦鐨勬柟寮忚杩颁富瑕佺殑鍩烘湰姒傚康锛岃璧锋潵寰堣垝鏈嶏紝鍐呭涔熷緢瀹炵敤銆傚浜嶭inear regression, factor analysis, principal component analysis (PCA), and canonical component analysis (CCA)杩欎簺Learning涓殑鍩烘湰鏂规硶涔熷睍寮€浜嗗垵姝ョ殑璁鸿堪銆�
涔嬪悗灏卞彲浠ヨ繘涓€姝ユ繁鍏ュ涔犺礉鍙舵柉缁熻鍜孏raphical models銆備竴鏈悊鎯崇殑涔︽槸
Introduction to Graphical Models (draft version). by M. Jordan and C. Bishop.
鎴戜笉鐭ラ亾杩欐湰涔︽槸涓嶆槸宸茬粡鍑虹増浜嗭紙涓嶈鍜孡earning in Graphical Models娣锋穯锛岄偅鏄釜璁烘枃闆嗭紝涓嶉€傚悎鍒濆锛夈€傝繖鏈功浠庡熀鏈殑璐濆彾鏂粺璁℃ā鍨嬪嚭鍙戜竴鐩存繁鍏ュ埌澶嶆潅鐨勭粺璁＄綉缁滅殑浼拌鍜屾帹鏂紝娣卞叆娴呭嚭锛宻tatistical learning鐨勮澶氶噸瑕佹柟闈㈤兘鍦ㄦ涔︽湁娓呮璁鸿堪鍜岃缁嗚瑙ｃ€侻IT鍐呴儴鍙互access锛岃嚦浜庡闈紝濂藉儚涔熸槸鏈夌數瀛愮増鐨勩€�
3. 鍒嗘瀽 (Analysis)锛�
鎴戞兂澶у鍩烘湰閮藉湪澶у灏卞杩囧井绉垎鎴栬€呮暟瀛﹀垎鏋愶紝娣卞害鍜屽箍搴﹀垯闅忓悇涓鏍¤€屽紓浜嗐€傝繖涓鍩熸槸寰堝瀛︾鐨勫熀纭€锛屽€煎緱鎺ㄨ崘鐨勬暀绉戜功鑾繃浜�
Principles of Mathematical Analysis, by Walter Rudin
鏈夌偣鑰侊紝浣嗘槸缁濆缁忓吀锛屾繁鍏ラ€忓交銆傜己鐐瑰氨鏄瘮杈冭壈娣扁€斺€旇繖鏄疪udin鐨勪功鐨勪竴璐鏍硷紝閫傚悎浜庢湁涓€瀹氬熀纭€鍚庡洖澶村幓鐪嬨€�
鍦ㄥ垎鏋愯繖涓柟鍚戯紝鎺ヤ笅鏉ュ氨鏄硾鍑藉垎鏋�(Functional Analysis)銆�
Introductory Functional Analysis with Applications, by Erwin Kreyszig.
閫傚悎浣滀负娉涘嚱鐨勫熀纭€鏁欐潗锛屽鏄撳垏鍏ヨ€屼笉澶卞叏闈€€傛垜鐗瑰埆鍠滄瀹冨浜庤氨璁哄拰绠楀瓙鐞嗚鐨勭壒鍒叧娉紝杩欏浜庡仛learning鐨勭爺绌舵槸鐗瑰埆閲嶈鐨勩€俁udin涔熸湁涓€鏈叧浜巉unctional analysis鐨勪功锛岄偅鏈功鍦ㄦ暟瀛︿笂鍙兘鏇翠负娣卞埢锛屼絾鏄笉鏄撲簬涓婃墜锛屾墍璁插唴瀹瑰拰learning鐨勫垏鍚堝害涓嶅姝や功銆�
鍦ㄥ垎鏋愯繖涓柟鍚戯紝杩樻湁涓€涓噸瑕佺殑瀛︾鏄祴搴︾悊璁�(Measure theory)锛屼絾鏄垜鐪嬭繃鐨勪功閲岄潰鐩墠杩樻病鏈夋劅瑙夋湁鐗瑰埆鍊煎緱浠嬬粛鐨勩€�
4. 鎷撴墤 (Topology)锛�
鍦ㄦ垜璇昏繃鐨勫熀鏈嫇鎵戜功鍚勬湁鐗硅壊锛屼絾鏄患鍚堣€岃█锛屾垜鏈€鎺ㄥ磭锛�
Topology (2nd Ed.) by James Munkres
杩欐湰涔︽槸Munkres鏁欐巿闀挎湡鎵ф暀MIT鎷撴墤璇剧殑蹇冭鎵€鍑濄€傚浜庝竴鑸嫇鎵戝(General topology)鏈夊叏闈粙缁嶏紝鑰屽浜庝唬鏁版嫇鎵�(Algebraic topology)涔熸湁閫傚害鐨勬帰璁ㄣ€傛涔︿笉闇€瑕佺壒鍒殑鏁板鐭ヨ瘑灏卞彲浠ュ紑濮嬪涔狅紝鐢辨祬鍏ユ繁锛屼粠鏈€鍩烘湰鐨勯泦鍚堣姒傚康锛堝緢澶氫功涓嶅睉璁茶繖涓級鍒癗agata-Smirnov Theorem鍜孴ychonoff theorem绛夎緝娣辩殑瀹氱悊锛堝緢澶氫功閬垮紑浜嗚繖涓級閮借鐩栦簡銆傝杩版柟寮忔€濇兂鎬у緢寮猴紝瀵逛簬寰堝瀹氱悊锛岄櫎浜嗙粰鍑鸿瘉鏄庤繃绋嬪拰寮曞浣犳€濊€冨叾鑳屽悗鐨勫師鐞嗚剦缁滐紝寰堝浠や汉璧炲徆鐨勪寒鐐光€斺€旀垜甯歌寰楀繕鍗撮ゥ楗匡紝涓嶆効閲婃墜銆傚緢澶氫範棰樺緢鏈夋按骞炽€�
5. 娴佸舰鐞嗚 (Manifold theory)锛�
瀵逛簬鎷撴墤鍜屽垎鏋愭湁涓€瀹氭妸鎻℃椂锛屾柟鍙紑濮嬪涔犳祦褰㈢悊璁猴紝鍚﹀垯鎵€瀛﹀彧鑳芥祦浜庢诞娴呫€傛垜鎵€浣跨敤鐨勪功鏄�
Introduction to Smooth Manifolds. by John M. Lee
铏界劧涔﹀悕鏈塱ntroduction杩欎釜鍗曡瘝锛屼絾鏄疄闄呬笂姝や功娑夊叆寰堟繁锛岄櫎浜嗚鎺堜簡鍩烘湰鐨刴anifold, tangent space, bundle, sub-manifold绛夛紝杩樻帰璁ㄤ簡璇稿绾茬悊璁�(Category theory)锛屽痉鎷夊涓婂悓璋�(De Rham cohomology)鍜岀Н鍒嗘祦褰㈢瓑涓€浜涙瘮杈冮珮绾х殑涓撻銆傚浜庢潕缇ゅ拰鏉庝唬鏁颁篃鏈夌浉褰撳鐨勮璁恒€傝鏂囬€氫織鑰屽張涓嶅け涓ヨ皑锛屼笉杩囧鏌愪簺璁板彿鏂瑰紡闇€瑕佺啛鎮変竴涓嬨€�
铏界劧鏉庣兢璁烘槸寤哄熀浜庡钩婊戞祦褰㈢殑姒傚康涔嬩笂锛屼笉杩囷紝涔熷彲鑳戒粠鐭╅樀鍑哄彂鐩存帴瀛︿範鏉庣兢鍜屾潕浠ｆ暟鈥斺€旇繖绉嶆柟娉曞浜庢€ラ渶浣跨敤鏉庣兢璁鸿В鍐抽棶棰樼殑鏈嬪弸鍙兘鏇村姞瀹炵敤銆傝€屼笖锛屽浜庝竴涓棶棰樹粠涓嶅悓瑙掑害鐪嬪緟涔熷埄浜庡姞娣辩悊瑙ｃ€備笅闈竴鏈功灏辨槸杩欎釜鏂瑰悜鐨勫吀鑼冿細
Lie Groups, Lie Algebras, and Representations: An Elementary Introduction. by Brian C. Hall
姝や功浠庡紑濮嬪嵆浠庣煩闃靛垏鍏ワ紝浠庝唬鏁拌€岄潪鍑犱綍瑙掑害寮曞叆鐭╅樀鏉庣兢鐨勬蹇点€傚苟閫氳繃瀹氫箟杩愮畻鐨勬柟寮忓缓绔媏xponential mapping锛屽苟灏辨寮曞叆鏉庝唬鏁般€傝繖绉嶆柟寮忔瘮璧蜂紶缁熺殑閫氳繃鈥滃乏涓嶅彉鍚戦噺鍦�(Left-invariant vector field)鈥滅殑鏂瑰紡瀹氫箟鏉庝唬鏁版洿瀹规槗涓轰汉鎵€鎺ュ彈锛屼篃鏇村鏄撴彮绀烘潕浠ｆ暟鐨勬剰涔夈€傛渶鍚庯紝涔熸湁涓撻棬鐨勮杩版妸杩欑鏂扮殑瀹氫箟鏂瑰紡鍜屼紶缁熸柟寮忚仈绯昏捣鏉ャ€�
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鏃犺鏄爺绌禫ision, Learning杩樻槸鍏跺畠鍒殑瀛︾锛屾暟瀛︾粓绌舵槸鏍瑰熀鎵€鍦ㄣ€傚濂芥暟瀛︽槸鍋氬ソ鐮旂┒鐨勫熀鐭炽€傚濂芥暟瀛︾殑鍏抽敭褰掓牴缁撳簳鏄嚜宸辩殑鍔姏锛屼絾鏄€夋嫨涓€鏈ソ鐨勪功杩樻槸澶ф湁鐩婂鐨勩€備笉鍚岀殑浜烘湁涓嶅悓鐨勭煡璇嗚儗鏅紝鎬濈淮涔犳儻鍜岀爺绌舵柟鍚戯紝鍥犳涔︾殑閫夋嫨涔熷洜浜鸿€屽紓锛屽彧姹傞€傚悎鑷繁锛屼笉蹇呭己姹備竴鑷淬€備笂闈㈢殑涔︿粎浠呮槸浠庢垜涓汉瑙掑害鐨勫嚭鍙戜粙缁嶇殑锛屾垜鐨勯槄璇荤粡鍘嗗疄鍦ㄩ潪甯告湁闄愶紝寰堝彲鑳借繕鏈夋瘮瀹冧滑鏇村ソ鐨勪功锛堜笉濡ㄤ篃鍛婄煡鎴戜竴澹帮紝鍏堣澹拌阿璋簡锛夈€�