[{"run_id":"20260906T231458-5fdd2fff","semester":"1272","observed_at":"2026-09-06 23:14:58.172943+00:00","record_version_id":"a2ff726b16251d9d94ca683ffc881cebda0b17e71e02211819ba7f70cc3d9169","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"20260907T155543-ce3781c4","semester":"1272","observed_at":"2026-09-07 15:55:43.033547+00:00","record_version_id":"a2ff726b16251d9d94ca683ffc881cebda0b17e71e02211819ba7f70cc3d9169","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-03b0bbb9723907cf3d1b41cf0bb34837dc398e42","semester":"1262","observed_at":"2025-04-16 05:20:33.104844+00:00","record_version_id":"55ed02cf0d0d7566f1227d445b2e617c28abafe7ea8bb110f7bf520066cee91e","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0837245627eb714ae6bb0375f7abe8f41042011f","semester":"1262","observed_at":"2025-04-16 05:20:33.104844+00:00","record_version_id":"55ed02cf0d0d7566f1227d445b2e617c28abafe7ea8bb110f7bf520066cee91e","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-08c92e359bbbc110b0778b7e0b15d6f40000e6b1","semester":"1262","observed_at":"2025-08-21 07:05:14.730696+00:00","record_version_id":"a5e995c337d3e2519b3d3c016740489f4a417a4a8b238b355e9797e3b61ef29b","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0944d76440dc778fbb89626058c10451009ce9c6","semester":"1262","observed_at":"2025-05-21 03:36:18.194118+00:00","record_version_id":"c5316b48a8395bb6f9694274fd9619a3fe1a0e27614c8bbfddd21a0abd49efac","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0a7f4bce29c816ef4d3d71b4eb8a2a3e15e33cc1","semester":"1262","observed_at":"2025-06-18 20:04:02.695444+00:00","record_version_id":"cc754faafb236ee69b002f6a9eceaee57bbbf3fbc591f16d20e9bc7485b8f4c2","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0ab917f827a7de22ebdc1087114d377a31c4687b","semester":"1262","observed_at":"2025-05-22 02:11:02.531191+00:00","record_version_id":"d22005fa90c1bc52bd11c5a3abe1798bd292c0178c1406e39f62cd88414ce317","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0c40ecab4b6db9333d1f18aef816e3ee659e300c","semester":"1262","observed_at":"2025-05-25 18:02:34.797617+00:00","record_version_id":"8a31165b9adeec562f3975d5b74e98b0341cb7d01c3e49d16d74a0128370bf4b","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-0cb4d29a588ec7f11c7e00b7cf5dc3a0d23d0349","semester":"1266","observed_at":"2026-01-22 01:00:26.555427+00:00","record_version_id":"c9038e13767beca350fb5118f04b0975953758249744faef3860004a69ea5984","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-11c30ec39e91498cbfcf3a923c53a4b03e387280","semester":"1262","observed_at":"2025-07-20 04:58:26.847117+00:00","record_version_id":"a6a358fb450c8463836aa8a09e08ad9cfe2e3d8c30d2332c875ae6f75ee398ff","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-13cd500edf2587e9a3428f326253738fbea965ea","semester":"1264","observed_at":"2025-12-14 04:50:04.653658+00:00","record_version_id":"19c09df0eec56a7dc15882c3eee320ed8675474f7aabfd581e9d4959f54a3274","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-1da08b2de39f05e6bc877c189fc2fd6eeda563f5","semester":"1262","observed_at":"2025-07-01 00:03:56.707251+00:00","record_version_id":"ee06c3c1ae30de5d8eb40f468ab7f1c3ab736d6fcdad6b6d2d13f1aee57871f7","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-2031af47efe133b0e7877f433286ff07385afc41","semester":"1262","observed_at":"2025-07-02 20:16:45.749584+00:00","record_version_id":"51bfbc9e2994d68f4b7887147424f47599822f8ea2cbe29b4f6d2d6fa3e1db1d","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-238eba6f32fbc30407f616dd0628ff02a2a824dd","semester":"1262","observed_at":"2025-08-17 05:15:07.788352+00:00","record_version_id":"537eae202965ec110449a795926a82a89354312e9a4ea6ac46c03d3a793f4a8a","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-25f0ff56bc4d80f8a8afa1a0bcce8dae6fddb5e5","semester":"1262","observed_at":"2025-05-25 17:20:25.942090+00:00","record_version_id":"a9a25b554ee51543f7941e744354a64a7a2d0f94be87879ab8dfbfbe551b92a1","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-2923f91826ce253b7aeefa9f75b4a39fe4c80ff0","semester":"1262","observed_at":"2025-08-10 05:10:25.938416+00:00","record_version_id":"2454574a2a1f432e1f8cc890442db18ab171f5dd1942972914be945aae3ca615","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-2a05214a4023e0157fa6f7d188c85308f714176c","semester":"1262","observed_at":"2025-09-07 04:56:38.255315+00:00","record_version_id":"db4f6889c52b36f79f3af62b509ce701bd00e27a27e96a27bf4fc54f0dc2bccb","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-2b1b8e39131de92b94620b25c5bbb25690efed4c","semester":"1262","observed_at":"2025-06-01 07:54:53.913454+00:00","record_version_id":"b4dd25fb4fbd633dec20c9d1c69bb23886494f195d4233c8eb207b1306a74cee","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-33a1225644e5a5855d60f66e65413946e72fedf4","semester":"1262","observed_at":"2025-06-22 01:52:05.152650+00:00","record_version_id":"d9439139f997930b50e4a5a7f8c13421acb787743131fbc5dbffcb5e4346cfcb","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-3b89c83dbf5208e13756184de1f2b2d0c09af35f","semester":"1262","observed_at":"2025-06-30 06:40:10.235522+00:00","record_version_id":"8cd6e57caa3aa6481812d16ae94d7f4f1f5894cb82812c0f491cc0cd6d6615c3","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-3c3eebf7f35c39364b445a2fa5a112ce28dbb4a1","semester":"1262","observed_at":"2025-06-01 17:03:59.062985+00:00","record_version_id":"259a70fdd10f22d1f4c7db309a512aa0420a7140f5d135357931b340714899ae","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-3fa4dd71391f1c9cf4ab2216680bbc428689f92d","semester":"1262","observed_at":"2025-05-25 01:15:58.180530+00:00","record_version_id":"77bf730ebc225b3369f4ad0023c3391798a8c7f94ef11cbc37f8f3275a2373b2","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-4040aa216da722a34483f68fc1e129ea571ae08d","semester":"1262","observed_at":"2025-06-01 07:27:39.695506+00:00","record_version_id":"7a5e7efbfec8edbcfb050e127d4bc724b1beece15eeffba2a808ad9cc491900a","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-454d53cd690294459f8ad0793cc3ed562060e56c","semester":"1262","observed_at":"2025-05-25 01:34:00.536004+00:00","record_version_id":"be9fd1ec278b6905b775798a06fbe3b04555245ae2290a834a0cbe329a1d8f45","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-486f091e051fdb4ccdb80ee7b4fb0a5814510324","semester":"1264","observed_at":"2025-11-16 05:32:31.273726+00:00","record_version_id":"bf34021fa4d4e10e2094926b71df93114c8c786ec8b7086fcf3bbe77c2e6798c","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-50393cfc5fd5598d4f4731ef1919f2ff53af07d9","semester":"1262","observed_at":"2025-06-30 06:05:57.438846+00:00","record_version_id":"f53e95951310ed76992b7e03e6a97ba2311c35b08c9648094a1dfd01a655ce3e","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-50f6947786b208c800db8bbd0cec84a8f0f187d2","semester":"1262","observed_at":"2025-06-02 03:49:42.915428+00:00","record_version_id":"1ef49e4c909a1c60f563a0d9d802fa6c7975f25cecb5a109e1b2fc3f0b73dc6f","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-51d86ed4082dced3803c295419b0ec8440942016","semester":"1264","observed_at":"2025-11-12 04:50:41.141307+00:00","record_version_id":"5094db341d2a07354fa62650a2bdde792988b0ad3245e8ea9a9be90f75d078dc","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-53101bd1c10db0d00d094e4c9154d4c244ff23d9","semester":"1262","observed_at":"2025-10-05 04:58:05.366968+00:00","record_version_id":"e367f32505ad3f9d975812e24fc12dbe07b671d4223f49139e7e2a96087a4d24","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-58751151c564e11c5cb8aedd3a2d3527c22f73eb","semester":"1262","observed_at":"2025-06-01 06:59:01.536576+00:00","record_version_id":"ec59bc3630773a0cf9b876a385aad1d8441d50f042d970f4d2cab625fd43a799","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-5c4c8d3701a333ba4ddadef7d0b5dde8440fcdf0","semester":"1262","observed_at":"2025-06-01 01:57:51.256704+00:00","record_version_id":"8231f62991b85303997ee0313a1eaf019c834afd0f4770d27b46eebd3ea69d37","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-5d20d9f81651d3c83fcaa2fd10870ce6e5d5a685","semester":"1262","observed_at":"2025-05-21 16:48:48.484741+00:00","record_version_id":"a6b5c6530f47e06e1f05586f592d9ed426fb56f54d791a22d9a332b144eef78f","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-5feaebf2ab37051c86ad360cc0fa0d7e0e2ea295","semester":"1262","observed_at":"2025-05-24 15:58:23.378859+00:00","record_version_id":"a900d240fd4362c686d02072e267153354ce8831fa9ee5640ac0814b348a80eb","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-60949965544fce098cc006354e201149005fb77b","semester":"1264","observed_at":"2025-10-26 05:07:14.077864+00:00","record_version_id":"dabeb8422d250a30ea292e632def85ba0e689ede7ff6d1365d63f52d1fdf5fdc","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-639225ac3addf8522f1d30cb4fe26054ea7f8c49","semester":"1262","observed_at":"2025-06-01 08:14:42.497608+00:00","record_version_id":"dc1928857334bac244248a9930d91b2af96d120ee131109f51bd765fcd845197","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-64093b17b3a9c67a41aa33eb37adb53ec38df714","semester":"1262","observed_at":"2025-05-22 02:11:02.531191+00:00","record_version_id":"6159b6463b041ec3e69835774f7b280de91a34fe9dc0ea914411eea17cbbb277","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-6885b56099f55e08aa0205546369fb0381d50e13","semester":"1262","observed_at":"2025-07-13 04:59:22.367394+00:00","record_version_id":"feed385810d089ab779fe4e3ce0440895354804c8278bac8090f210b4bb5cdfe","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-69d4b2b16e8268f75b6390b3a0e2ce8bf73999da","semester":"1262","observed_at":"2025-06-30 03:21:29.925498+00:00","record_version_id":"dd147ab49f3ab0bcb236cedd688289729f2af7ccdab44f6e8a04c285863aa610","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-6b29c3e0673b2f9a736d2363db5409e03d5b3ed4","semester":"1264","observed_at":"2025-12-03 12:33:41.418072+00:00","record_version_id":"36e319063c344d9139869498dda9ac4b4abba1ade4c7a2deb33340292d275ffa","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-73259984748de484976ef2ad56ad7ab3d4cb4518","semester":"1262","observed_at":"2025-06-26 08:27:56.461216+00:00","record_version_id":"c49ca3374ddadc7293597ed64d317f4cc690792d6b1f7d1954daadb677be093b","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-741602fbc6252c232a0b9e6bc1a9ae3101625f5a","semester":"1262","observed_at":"2025-06-30 22:49:32.522034+00:00","record_version_id":"0dae27342ebe96535cbb0b30fa401332258c07cffa605dd6574fa1cc8d7aa7c6","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-7774f45558276ec29bf626e58fffb4a27bdbb2a9","semester":"1264","observed_at":"2025-11-01 11:49:36.359151+00:00","record_version_id":"bf34021fa4d4e10e2094926b71df93114c8c786ec8b7086fcf3bbe77c2e6798c","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-7ab7c5e783fc8ebef8b8ee8cea019ee37a72ce74","semester":"1262","observed_at":"2025-09-28 04:58:07.340658+00:00","record_version_id":"5094db341d2a07354fa62650a2bdde792988b0ad3245e8ea9a9be90f75d078dc","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-7b2f22d83ea05055ab90dcb77dc802382cccc6f7","semester":"1262","observed_at":"2025-05-21 17:56:46.096741+00:00","record_version_id":"2add24bfa63c0500b832687c0459079a669971288bde37e980165537e373ee61","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-7ca1175502be18eb51f7b016818a884a43fd4ebb","semester":"1262","observed_at":"2025-07-29 06:28:23.644795+00:00","record_version_id":"cd95363ae910647001a40c165f5f6922ad12bbebc762f256b422c977c27f0b5b","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-7d8cee5e42602ad9ba5dc0322085af2fa0dffaac","semester":"1262","observed_at":"2025-05-22 01:15:19.291664+00:00","record_version_id":"00b9acf42a8edff3d4a3332c11b3f5ceab6d7553a83b769fc8cbda345c09ef9a","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-81a0d6a7f668c98c59bd05fa988aa079c5ad1f68","semester":"1262","observed_at":"2025-05-31 07:49:50.419452+00:00","record_version_id":"fad680e462ac22387a191d010adf352c00b3ed5421726df83bbcf38a95e00e70","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-82f31c08c746a214872494cde6ecaeb9330441b4","semester":"1262","observed_at":"2025-06-17 21:26:08.547156+00:00","record_version_id":"7a5e7efbfec8edbcfb050e127d4bc724b1beece15eeffba2a808ad9cc491900a","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-84c248343c5a99ab42c5616c594812a5e3e31cbb","semester":"1262","observed_at":"2025-07-04 06:00:07.487827+00:00","record_version_id":"74e33fd4ad5c49bee61c3d82fe1af1e6ad1f82d69c66a24fb69c53a4695071d8","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-86334e7275e315853287e8580c35456c68df800b","semester":"1262","observed_at":"2025-05-22 06:53:03.336354+00:00","record_version_id":"a6b5c6530f47e06e1f05586f592d9ed426fb56f54d791a22d9a332b144eef78f","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-8686dc1664f93a6c05f50321410961b39b12f91b","semester":"1262","observed_at":"2025-05-28 10:17:41.595894+00:00","record_version_id":"af6960965728da9c3bb57014fd5f73760642ea7cc5143de986f5a466e5cde6b5","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-86d941366886c9a14a2581c04e20d0bdd25e1b02","semester":"1262","observed_at":"2025-08-31 04:54:14.656039+00:00","record_version_id":"78b7ed0e678766a7da5db2ae024a3b06babe2486cec51250eec8e613e34e7f1c","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-8ba1d2e6cfbb1525b4f9f769ec164fb6ad0f237a","semester":"1262","observed_at":"2025-06-02 05:22:45.010398+00:00","record_version_id":"f44ee995c4bf157c445b2fea91d7be256a537bd8c07b1525d3c86b710f11f06f","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-90e5aa456689a3b222016c05c319bbcd0bddd453","semester":"1262","observed_at":"2025-05-25 02:00:10.037905+00:00","record_version_id":"6f71287ec5287f7ff59017c18dc32e7f7f7fe41aa3a17fff1a3bd8f845362893","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-92d960aa7e4cd6e4c9ac8b2e232092904038e9e4","semester":"1262","observed_at":"2025-06-08 01:50:46.451351+00:00","record_version_id":"2df1b952f84d4766d4e50d5e8252b1d4f996e098393d91cbd2967537aa2ea0c7","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-94002ae588a8f71eca6d64105f2e603e8587293b","semester":"1262","observed_at":"2025-05-21 09:01:16.021508+00:00","record_version_id":"4df0f6e6ca264e638aecc229be326734f56c61ae56d2efb7bd83178723a1074d","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-9dd575e013c5c6e000ab3ad2d1288cc1dd9c96dc","semester":"1264","observed_at":"2025-12-21 04:47:46.589081+00:00","record_version_id":"2d47f06f32fea1d6baaf052ad4bd10697141433e19c706a19c9163f11c4e508a","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-a1ea26ed78cbd6e94bc3221e50a6ed9b6bf43871","semester":"1262","observed_at":"2025-05-25 09:16:55.180581+00:00","record_version_id":"10f3d99710921135a9fb54c1e6bade339bc9435174cc2b5dc51554aa47f8b735","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-a76a3505853d5ea9c13bb98472b87361d469e2ee","semester":"1262","observed_at":"2025-05-28 18:03:41.793846+00:00","record_version_id":"e6a982200eadad9e630b99f997f9bd9438a900887e5cb4dd9e7eec1b91be0be0","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-b285d591f6acf3aa1910e02edc297664db86eb8c","semester":"1262","observed_at":"2025-06-10 22:48:22.460295+00:00","record_version_id":"b4dd25fb4fbd633dec20c9d1c69bb23886494f195d4233c8eb207b1306a74cee","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-b79af756e4f00ba98231feb859ed8e98239eb811","semester":"1262","observed_at":"2025-05-22 02:47:56.931581+00:00","record_version_id":"0e337b8bfa8b374d25a294919178ede5819e6857172e2df5eb9041cb8e29392d","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-b89e05b94730c6471439082d9279c0a834a4aeec","semester":"1262","observed_at":"2025-08-26 20:25:42.325239+00:00","record_version_id":"af9d2246e278acbd1bd056c5bcfcb399ec7303a12c1825722be1b397d6fca5f8","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-b9279a12d1f2688df9e556183c94d41a89e431dc","semester":"1262","observed_at":"2025-07-06 01:49:47.203835+00:00","record_version_id":"8cb7f9742e24c18c3d545cde1bce9919304c943e7ce472619754fad547812e1b","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-bbdc905e96cc681a5e9a8b02c795b682206e36d1","semester":"1262","observed_at":"2025-06-25 08:02:45.445730+00:00","record_version_id":"a59703bf97eaf523bee64355961f49af97cae03ff08fd02374889adc7ef3b2b8","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-bde225b5243a13d81827aa173e39c78a652b54a0","semester":"1262","observed_at":"2025-05-23 07:22:33.219345+00:00","record_version_id":"804325a41285cfa2a93e3828c33244e8daf62dd2ee185e51a623bc2e7259ecfc","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-c1fac4cbfde737f4f4ac02cdf15e6f5a9b5b676d","semester":"1262","observed_at":"2025-05-22 01:15:19.291664+00:00","record_version_id":"00b9acf42a8edff3d4a3332c11b3f5ceab6d7553a83b769fc8cbda345c09ef9a","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-c6b62be45f8a13cba109ef2a7741b9cd9a6b8272","semester":"1262","observed_at":"2025-08-24 08:48:09.035112+00:00","record_version_id":"a58377349b5ac24cb1e127f90037f2718bc6ea1d7fc609cbaf48dff828cce0fe","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-cc83f62cb6db61f39320916d819ad48ce55cd96d","semester":"1262","observed_at":"2025-05-22 00:45:35.735230+00:00","record_version_id":"4662878c4247bcd78fc5d91a123b3389e136f596d87f6afd12597e2d03fa2470","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-d33818a01b6b4c5e2902e704da6e5b713742d4dc","semester":"1262","observed_at":"2025-10-13 10:46:24.251475+00:00","record_version_id":"522b1915db42617698e5de7237742e78923a01921493ca0ec77153c922446963","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-d3c17db9832d3064916046caf891dd23f10b1bb9","semester":"1262","observed_at":"2025-08-26 11:30:42.288639+00:00","record_version_id":"a110d6944ff9a476685cb066cb45efae3452beb6945f1cfca6b1e25ad9410118","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-d4ee226dc44268e9b6767fb9f5f20343322f494b","semester":"1262","observed_at":"2025-06-15 01:52:23.911697+00:00","record_version_id":"259a70fdd10f22d1f4c7db309a512aa0420a7140f5d135357931b340714899ae","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-d8f9fc7f136e2033556d9d65bbdbdf33425dbdc9","semester":"1262","observed_at":"2025-05-28 16:48:12.400438+00:00","record_version_id":"0eaa6c276556b4a52bac938e89a9f6d322ef816358db8933c0854f8d7f50c247","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-dbbc9739c616c3846b2e796e00a36fa41225f7d8","semester":"1262","observed_at":"2025-06-01 17:47:19.325144+00:00","record_version_id":"b925a4353282ada4d7fd97f367359a769c97944228765325ff3fdc352b68a028","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-dbe5f2d24b48c3177297a3d69c553cc9d1194bac","semester":"1262","observed_at":"2025-09-14 05:00:27.366070+00:00","record_version_id":"d2f4bb02e85c40f33068b27637698bd2a435130db1eafeeadf4191417fc502f8","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-dd357dc2758e9e282c30988a527ce37de92593b9","semester":"1264","observed_at":"2025-10-19 01:39:41.951404+00:00","record_version_id":"b9b57702b3190e9171d477f1bc98add62abff28d97d448c908c85cae384ab427","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-de74de559e409a3fe668685e28043b888d2e6841","semester":"1262","observed_at":"2025-06-27 07:38:50.882897+00:00","record_version_id":"1920672c01c0f21af90b6e5577ed7a5f5bf906c02f7c33c883fa1933ab14de6d","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-deca7188cf536ade3203cd88b52a45e92a059617","semester":"1262","observed_at":"2025-06-27 00:37:46.087071+00:00","record_version_id":"78fd6df39c5e0e2ed11f8e825653c741155b010577e5a41e2cb1dd8e922aa76b","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-df60fa9ac3931c5612b0fa641b7a6f5fbec86fab","semester":"1262","observed_at":"2025-05-24 06:36:37.554678+00:00","record_version_id":"1057ddc2f076a47a204362dfe9223cf458ae28298757f9efeb2c9c272f983c64","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-e339da2d849aaf8bb4dceca07a84728af23cf755","semester":"1262","observed_at":"2025-07-23 08:49:22.748925+00:00","record_version_id":"87a1560b2efacd30d887f3bd132e15eb181cb8fc9ed5e986b36e0ecb7d85bd64","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-e934b1784835f5d36ae9b7ef0992b11e72c39142","semester":"1262","observed_at":"2025-06-01 06:21:25.219533+00:00","record_version_id":"ff348a99330c097b54b3d2a052436dd424113070823ba3f32280b75e9f5300ec","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-ef471690c082448deebd2687eab84b0b78813c36","semester":"1262","observed_at":"2025-06-29 01:47:56.317645+00:00","record_version_id":"b357d49abe306b865ea274ab951120f44b2616fb96bd5c523be278f0615b5cef","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-efc4e8e2cd7c3f68e059a308990c00c77c7611eb","semester":"1264","observed_at":"2025-10-16 05:48:13.935141+00:00","record_version_id":"3ac1fa664e0fcb7210c49a8344994c88b56a8b333c97ab7cb5bdbc8234bc486c","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"},{"run_id":"legacy-f18b7749725097d41f69c60779ff38cf073b93b3","semester":"1262","observed_at":"2025-05-21 19:52:03.259353+00:00","record_version_id":"e37b31ff3f171c36312878644daf5ee36f909f762bd619661a5724d2d6437933","course_id":"MATH 747","course_uid":"course_34ae84cc48e70d6fce6b838b","catalog_version_id":"7c279427689995b09a5df63bc317a3d6cef3a085d779395ed91153d53987415a","course_number":747,"subjects":["MATH"],"title":"LIE ALGEBRAS","description":"Lie algebras and matrix groups. Topics: tangent spaces; exponentials; Baker-Campbell-Hausdorff formula; (nilpotent, solvable, semisimple) Lie algebras; Engel's and Lie's theorems; Levi decomposition; Killing form; sl(2)-representations; root systems; Dynkin diagrams; Weyl groups; Cartan and Borel subalgebras; Serre's theorem. Basic graduate algebra courses (e.g.MATH 541and542orMATH 741and742) are strongly recommended.","requirements_text":"Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program"}]