# MATH 716: Ordinary Differential Equations | UW–Madison [View on UW Courses](https://uwcourses.com/courses/MATH_716) ## Dataset ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ### repository twangodev/uwcourses ### schema version 6 ### importer version 7 ### projection id 52a78527ff09011d88cb04c7d43867d9fbfec2930bf1dd2ec359ebd2844e0b07 ### observed at 2026-09-07T15:55:43.033547+00:00 ### built at 2026-09-10T19:50:42.743001+00:00 ### courses 8951 ### current instructors 5754 ### limited false ### terms * 1272 * 1264 * 1262 * 1254 * 1252 * 1244 * 1242 * 1234 * 1232 * 1224 * 1222 * 1212 * 1204 * 1202 * 1194 * 1192 * 1184 * 1182 * 1174 * 1172 * 1164 * 1162 * 1154 * 1152 * 1144 * 1142 * 1134 * 1132 * 1124 * 1122 * 1114 * 1112 * 1104 * 1102 * 1094 * 1092 * 1084 * 1082 * 1074 * 1072 ### term 1272 ### departments | subject | count | | --------- | ----- | | AAE | 90 | | ABT | 20 | | ACCTIS | 36 | | ACTSCI | 14 | | AFAERO | 10 | | AFRICAN | 87 | | AFROAMER | 71 | | AGROECOL | 21 | | AMERIND | 53 | | ANAT\&PHY | 7 | | ANATOMY | 2 | | ANESTHES | 8 | | ANSCI | 57 | | ANTHRO | 95 | | ART | 125 | | ARTED | 10 | | ARTHIST | 121 | | ASIALANG | 129 | | ASIAN | 109 | | ASIANAM | 28 | | ASTRON | 38 | | ATMOCN | 69 | | BIOCHEM | 51 | | BIOCORE | 10 | | BIOLOGY | 14 | | BIOMDSCI | 18 | | BME | 66 | | BMI | 41 | | BMOLCHEM | 10 | | BOTANY | 69 | | BSE | 44 | | C\&ESOC | 73 | | CBE | 48 | | CHEM | 101 | | CHICLA | 52 | | CIVENGR | 133 | | CLASSICS | 47 | | CNP | 10 | | CNSRSCI | 50 | | COMARTS | 137 | | COMPBIO | 15 | | COMPLIT | 11 | | COMPSCI | 138 | | COUNPSY | 78 | | CRB | 19 | | CS\&D | 71 | | CSCS | 40 | | CURRIC | 193 | | DANCE | 93 | | DERM | 8 | | DS | 88 | | DYSCI | 35 | | ECE | 155 | | ECON | 145 | | EDPOL | 114 | | EDPSYCH | 97 | | ELPA | 70 | | EMA | 53 | | EMERMED | 17 | | ENGL | 206 | | ENTOM | 40 | | ENVIRST | 148 | | EP | 15 | | EPD | 67 | | ESL | 16 | | F\&WECOL | 60 | | FAMMED | 22 | | FINANCE | 50 | | FOLKLORE | 40 | | FOODSCI | 43 | | FRENCH | 63 | | GEN\&WS | 145 | | GENBUS | 72 | | GENECSLR | 17 | | GENETICS | 60 | | GEOG | 113 | | GEOSCI | 83 | | GERMAN | 82 | | GLE | 48 | | GNS | 38 | | GREEK | 27 | | HDFS | 41 | | HEBR-BIB | 13 | | HEBR-MOD | 10 | | HISTORY | 233 | | HISTSCI | 56 | | HONCOL | 13 | | ILS | 43 | | INFOSYS | 9 | | INTEGART | 7 | | INTEGSCI | 22 | | INTER-AG | 18 | | INTER-HE | 11 | | INTER-LS | 22 | | INTEREGR | 16 | | INTLBUS | 21 | | INTLST | 50 | | ISYE | 83 | | ITALIAN | 53 | | JEWISH | 56 | | JOURN | 88 | | KINES | 128 | | LACIS | 26 | | LANDARC | 61 | | LATIN | 24 | | LAW | 120 | | LEGALST | 48 | | LINGUIS | 35 | | LIS | 89 | | LITTRANS | 78 | | LSC | 52 | | M\&ENVTOX | 7 | | MARKETNG | 62 | | MATH | 153 | | MDGENET | 8 | | ME | 130 | | MEDHIST | 43 | | MEDICINE | 60 | | MEDIEVAL | 32 | | MEDPHYS | 39 | | MEDSC-M | 29 | | MEDSC-V | 41 | | MHR | 68 | | MICROBIO | 45 | | MILSCI | 16 | | MM\&I | 22 | | MOLBIOL | 6 | | MS\&E | 59 | | MUSIC | 165 | | MUSPERF | 126 | | NAVSCI | 20 | | NE | 44 | | NEURODPT | 11 | | NEUROL | 7 | | NEURSURG | 4 | | NTP | 11 | | NURSING | 111 | | NUTRSCI | 65 | | OBS\&GYN | 18 | | OCCTHER | 39 | | ONCOLOGY | 14 | | OPHTHALM | 5 | | OTM | 43 | | PATH | 34 | | PATH-BIO | 29 | | PEDIAT | 26 | | PHARMACY | 31 | | PHILOS | 77 | | PHMCOL-M | 11 | | PHMPRAC | 45 | | PHMSCI | 60 | | PHYASST | 37 | | PHYSICS | 88 | | PHYSIOL | 3 | | PHYTHER | 37 | | PLANTSCI | 52 | | PLPATH | 35 | | POLISCI | 192 | | POPHLTH | 58 | | PORTUG | 33 | | PSYCH | 101 | | PSYCHIAT | 22 | | PUBAFFR | 54 | | PUBLHLTH | 23 | | RADIOL | 11 | | REALEST | 41 | | RELIGST | 90 | | RHABMED | 9 | | RMI | 24 | | RP\&SE | 102 | | S\&APHM | 17 | | SCANDST | 73 | | SLAVIC | 89 | | SOC | 149 | | SOCWORK | 87 | | SOILSCI | 46 | | SPANISH | 83 | | SRMED | 21 | | STAT | 94 | | STDYABRD | 52 | | STS | 8 | | SURGERY | 25 | | SURGSCI | 33 | | THEATRE | 91 | | URBRPL | 60 | | UROLOGY | 5 | | ZOOLOGY | 89 | ## course ### run id 20260907T155543-ce3781c4 ### semester 1272 ### observed at 2026-09-07 15:55:43.033547+00:00 ### record version id 89896d2a286d0e18c5eb204d18493b195b5100562d863c19f71b9f32c8c11638 ### course id MATH 716 ### course uid course\_7ca9a6429350e4d5fc31a8fe ### catalog version id c8704b426b9a07b73f1e65fba271ad98cadcdf198990c01116a05be86a45a843 ### course number 716 ### subjects * MATH ### title ORDINARY DIFFERENTIAL EQUATIONS ### description Existence, uniqueness, and continuous dependence theorems, linear systems, stability, singular points, and boundary value problems. Qualitative behavior of nonlinear equations, stability, Lyapunov functions, invariant manifolds, bifurcation theory, periodic orbits, and connecting orbits. ### requirements text Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program ### credit offering ids None recorded. ### llm job id enrich-f516c4d3e82cfe326b4f5f54 ### llm output id 039f13c4b6ec0b6b4c0ecdbb297a13ba4d967955895cb2f286d2f099e365c276 ### llm model nvidia/Qwen3.6-35B-A3B-NVFP4 ### llm model revision 1355db6a052410cfd62085d94b58866fd0f2c3c5 ### llm task version 14 ### llm search status valid ### llm summary Covers existence, uniqueness, stability, and qualitative behavior of nonlinear ordinary differential equations including bifurcation theory. ### llm topics * Linear systems, stability, singular points, and boundary value problems * Qualitative behavior of nonlinear equations * Lyapunov functions and invariant manifolds * Bifurcation theory, periodic orbits, and connecting orbits ### llm skills * Apply existence, uniqueness, and continuous dependence theorems * Analyze qualitative behavior of nonlinear equations * Use Lyapunov functions and invariant manifolds for stability analysis * Apply bifurcation theory to identify periodic orbits and connecting orbits ### llm assumed background None recorded. ### llm search phrases * ordinary differential equations graduate * Lyapunov stability bifurcation * nonlinear systems qualitative analysis * boundary value problems MATH 716 ### llm requirements status valid ### llm student summary status valid ### llm experience status valid ### catalog variants None recorded. ### student summary #### context hash 8cb9fd7cfba05cb7e6a0ced50873248e6193b015fbbbdd7e965b490657a7f02b #### course id MATH 716 #### current instructors None recorded. #### difficulty workload Historical reviews of Sigurd Angenent: The course is rated as difficult, with homework assignments delayed until the final three weeks of the term. ```json { "citations": [ { "instructor_name": "Sigurd Angenent", "review_date": "2021-11-06 18:42:00 +0000 UTC", "review_id": "3527fae6f20ac91d22114692", "run_id": "20260907T155543-ce3781c4", "source_instructor_id": "rmp:262518", "source_review_id": "UmF0aW5nLTM1MjAwMzE0", "source_url": "https://www.ratemyprofessors.com/professor/262518", "type": "review" } ] } ``` #### errors None recorded. #### historical context Historical reviews of Sigurd Angenent: Sigurd Angenent provides clear, intuitive explanations supported by good visuals. However, he delays assigning homework until the final three weeks of the term, leading to requests for more consistent assignment schedules. ```json { "citations": [ { "instructor_name": "Sigurd Angenent", "review_date": "2021-11-06 18:42:00 +0000 UTC", "review_id": "3527fae6f20ac91d22114692", "run_id": "20260907T155543-ce3781c4", "source_instructor_id": "rmp:262518", "source_review_id": "UmF0aW5nLTM1MjAwMzE0", "source_url": "https://www.ratemyprofessors.com/professor/262518", "type": "review" } ] } ``` #### offered false #### profile hash e59ddc7389015d0035b68cd195c939d475bf72b959b29cf12eab59b454ccaef1 #### quick take Historical reviews of Sigurd Angenent: Sigurd Angenent provides clear, intuitive explanations with helpful visuals, though the lack of early homework assignments is a notable drawback. ```json { "citations": [ { "instructor_name": "Sigurd Angenent", "review_date": "2021-11-06 18:42:00 +0000 UTC", "review_id": "3527fae6f20ac91d22114692", "run_id": "20260907T155543-ce3781c4", "source_instructor_id": "rmp:262518", "source_review_id": "UmF0aW5nLTM1MjAwMzE0", "source_url": "https://www.ratemyprofessors.com/professor/262518", "type": "review" } ] } ``` Recent recorded grades — Spring 2020: 4.00 GPA, 100.0% A/AB (n=22 letter grades); Spring 2025: 3.97 GPA, 100.0% A/AB (n=18 letter grades); Spring 2026: 3.93 GPA, 96.3% A/AB (n=27 letter grades). ```json { "citations": [ { "course_id": "MATH 716", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "2ec9c86c-b527-3b8b-82a7-901d96805089", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1204", "type": "grade" }, { "course_id": "MATH 716", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "2ec9c86c-b527-3b8b-82a7-901d96805089", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1254", "type": "grade" }, { "course_id": "MATH 716", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "2ec9c86c-b527-3b8b-82a7-901d96805089", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1264", "type": "grade" } ] } ``` #### student experience Historical reviews of Sigurd Angenent: Reviewers appreciate the clear teaching style but express frustration with the inconsistent assignment schedule. ```json { "citations": [ { "instructor_name": "Sigurd Angenent", "review_date": "2021-11-06 18:42:00 +0000 UTC", "review_id": "3527fae6f20ac91d22114692", "run_id": "20260907T155543-ce3781c4", "source_instructor_id": "rmp:262518", "source_review_id": "UmF0aW5nLTM1MjAwMzE0", "source_url": "https://www.ratemyprofessors.com/professor/262518", "type": "review" } ] } ``` #### task hash 74fb0997943e888960bbc9e47db8c4fd12e4292d55c20509d8d89db6a9910f68 #### teaching history SIGURD ANGENENT is recorded teaching in Spring 2020. Recorded history may be incomplete and does not establish a future schedule. ```json { "citations": [ { "course_id": "MATH 716", "run_id": "20260907T155543-ce3781c4", "section_number": 1, "source_course_id": "2ec9c86c-b527-3b8b-82a7-901d96805089", "source_record": { "entity_id": "2ec9c86c-b527-3b8b-82a7-901d96805089", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "section_grades_latest", "term_id": "1204", "type": "grade" } ] } ``` #### term id 1272 #### term name 2026 Fall #### version 2 ### requirements #### nodes ```json [ { "children": [ "n1", "n2" ], "condition": null, "course": null, "evidence": "Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program", "id": "n0", "kind": "any" }, { "children": [], "condition": "Graduate/professional standing", "course": null, "evidence": "Graduate/professional standing", "id": "n1", "kind": "condition" }, { "children": [], "condition": "member of the Pre-Masters Mathematics (Visiting International) Program", "course": null, "evidence": "member of the Pre-Masters Mathematics (Visiting International) Program", "id": "n2", "kind": "condition" } ] ``` #### notes * Graduate/professional standing is a program status condition, not a specific course node. #### root n0 #### status parsed ### instructors None recorded. ### offerings None recorded. ### sections None recorded. ### grade instructors ```json [ { "instructor_uid": "instructor_d6ae5bf489a32285b7c8c1c7", "source": "madgrades", "source_instructor_id": "3126228", "identity_basis": "source_id", "identity_status": "source_identified", "name": "SERGEY BOLOTIN", "email": null, "first_observed_at": "2026-09-06 23:14:58.172943+00:00", "last_observed_at": "2026-09-07 15:55:43.033547+00:00", "ratings": { "review_count": 41, "quality": 3.27, "difficulty": 3.41, "quality_count": 41, "difficulty_count": 41, "profile_id": "rmp:1929872", "source_url": 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"source_aliases": [ "MATH 716" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 716", "course_uid": "course_7ca9a6429350e4d5fc31a8fe", "term_id": "1114", "term_name": "Spring 2011", "instructors": [ "SERGEY BOLOTIN" ], "a": 16, "ab": 0, "b": 3, "bc": 1, "c": 0, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 20, "source_aliases": [ "MATH 716" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 716", "course_uid": "course_7ca9a6429350e4d5fc31a8fe", "term_id": "1132", "term_name": "Fall 2012", "instructors": [ "SERGEY BOLOTIN" ], "a": 5, "ab": 4, "b": 1, "bc": 0, "c": 0, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 10, "source_aliases": [ "MATH 716" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 716", "course_uid": "course_7ca9a6429350e4d5fc31a8fe", "term_id": "1204", "term_name": "Spring 2020", "instructors": [ "Sigurd Angenent" ], "a": 22, "ab": 0, "b": 0, "bc": 0, "c": 0, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 22, "source_aliases": [ "MATH 716" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 716", "course_uid": "course_7ca9a6429350e4d5fc31a8fe", "term_id": "1254", "term_name": "Spring 2025", "instructors": [ "Chanwoo Kim" ], "a": 17, "ab": 1, "b": 0, "bc": 0, "c": 0, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 1, "no_work": 0, "not_reported": 0, "other": 0, "total": 19, "source_aliases": [ "MATH 716" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 716", "course_uid": "course_7ca9a6429350e4d5fc31a8fe", "term_id": "1264", "term_name": "Spring 2026", "instructors": [ "Chanwoo Kim" ], "a": 24, "ab": 2, "b": 1, "bc": 0, "c": 0, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 27, "source_aliases": [ "MATH 716" ] } ] ``` ### statistics #### gpa 3.871 #### graded 112 #### counts * 93 * 12 * 5 * 1 * 1 * 0 * 0 ### grade conflicts None recorded. ### evidence #### history * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_7ca9a6429350e4d5fc31a8fe-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_7ca9a6429350e4d5fc31a8fe-0.json) #### traces * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_7ca9a6429350e4d5fc31a8fe-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_7ca9a6429350e4d5fc31a8fe-0.json) #### reviews * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course\_7ca9a6429350e4d5fc31a8fe-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course_7ca9a6429350e4d5fc31a8fe-0.json) #### results * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_7ca9a6429350e4d5fc31a8fe-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_7ca9a6429350e4d5fc31a8fe-0.json) ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ## context ### all #### term #### gpa 3.8705357142857144 #### count 112 #### university ##### size 3270 ##### gpa Percentile 73 ##### count Percentile 56 ##### median Count 91 ##### histogram | range | count | current | | ------- | ----- | ------- | | 0.0–0.4 | 0 | false | | 0.4–0.8 | 0 | false | | 0.8–1.2 | 0 | false | | 1.2–1.6 | 0 | false | | 1.6–2.0 | 0 | false | | 2.0–2.4 | 0 | false | | 2.4–2.8 | 17 | false | | 2.8–3.2 | 293 | false | | 3.2–3.6 | 918 | false | | 3.6–4.0 | 2042 | true | #### departments ```json [ { "subject": "MATH", "comparison": { "size": 79, "gpaPercentile": 82, "countPercentile": 53, "medianCount": 108, "histogram": [ { "range": "0.0–0.4", "count": 0, "current": false }, { "range": "0.4–0.8", "count": 0, "current": false }, { "range": "0.8–1.2", "count": 0, "current": false }, { "range": "1.2–1.6", "count": 0, "current": false }, { "range": "1.6–2.0", "count": 0, "current": false }, { "range": "2.0–2.4", "count": 0, "current": false }, { "range": "2.4–2.8", "count": 5, "current": false }, { "range": "2.8–3.2", "count": 24, "current": false }, { "range": "3.2–3.6", "count": 18, "current": false }, { "range": "3.6–4.0", "count": 32, "current": true } ] } } ] ``` ### terms #### 1094 ##### term 1094 ##### gpa 3.7 ##### count 15 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1114 ##### term 1114 ##### gpa 3.775 ##### count 20 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1132 ##### term 1132 ##### gpa 3.7 ##### count 10 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1204 ##### term 1204 ##### gpa 4 ##### count 22 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1254 ##### term 1254 ##### gpa 3.9722222222222223 ##### count 18 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1264 ##### term 1264 ##### gpa 3.925925925925926 ##### count 27 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | ### benchmarks #### all ##### school ###### size 3270 ###### gpa 3.6436182459559805 ###### top Share 80.84155795518713 ###### count 91 ##### MATH ###### size 79 ###### gpa 3.4193516771417682 ###### top Share 68.18361593738798 ###### count 108 #### terms ##### 1094 ###### school ###### size 758 ###### gpa 3.3891454428111527 ###### top Share 64.36369814389255 ###### count 71 ###### MATH ###### size 19 ###### gpa 2.861322177541941 ###### top Share 40.26350030907326 ###### count 108 ##### 1114 ###### school ###### size 804 ###### gpa 3.3696004653806844 ###### top Share 64.0389334741844 ###### count 68 ###### MATH ###### size 26 ###### gpa 2.9090822348911582 ###### top Share 41.14706210117883 ###### count 83.5 ##### 1132 ###### school ###### size 851 ###### gpa 3.391128778809763 ###### top Share 64.69509437122704 ###### count 66 ###### MATH ###### size 25 ###### gpa 2.9605395515107897 ###### top Share 42.794601137643824 ###### count 108 ##### 1204 ###### school ###### size 1012 ###### gpa 3.703747431523761 ###### top Share 84.59811226304916 ###### count 65.5 ###### MATH ###### size 29 ###### gpa 3.478717830475146 ###### top Share 69.61236805388549 ###### count 83 ##### 1254 ###### school ###### size 1289 ###### gpa 3.6126423469389106 ###### top Share 79.48050408754871 ###### count 66 ###### MATH ###### size 39 ###### gpa 3.180435541912479 ###### top Share 53.878371816747475 ###### count 89 ##### 1264 ###### school ###### size 1283 ###### gpa 3.6229729166451925 ###### top Share 80.13669149396227 ###### count 66 ###### MATH ###### size 42 ###### gpa 3.13598176627681 ###### top Share 52.25969905887213 ###### count 80 ## instructor Trends ```json [ { "uid": "instructor_6015ff78a76a4e4bf9ce2581", "name": "CHANWOO KIM", "count": 45, "terms": [ { "term": "1254", "count": 18, "sections": 1, "gpa": 3.9722222222222223 }, { "term": "1264", "count": 27, "sections": 1, "gpa": 3.925925925925926 } ] }, { "uid": "instructor_d6ae5bf489a32285b7c8c1c7", "name": "SERGEY BOLOTIN", "count": 45, "terms": [ { "term": "1094", "count": 15, "sections": 1, "gpa": 3.7 }, { "term": "1114", "count": 20, "sections": 1, "gpa": 3.775 }, { "term": "1132", "count": 10, "sections": 1, "gpa": 3.7 } ] }, { "uid": "instructor_679f753cde11c003a592a1a8", "name": "SIGURD ANGENENT", "count": 22, "terms": [ { "term": "1204", "count": 22, "sections": 1, "gpa": 4 } ] } ] ``` ## following None recorded.