# MATH 825: Selected Topics in Functional Analysis | UW–Madison [View on UW Courses](https://uwcourses.com/courses/MATH_825) ## 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 975d9ab21bb307ce46b84c4e75851d6b5de5432e0139450e62cd1ce7cabf440f ### course id MATH 825 ### course uid course\_a88d8bc7da942a242ead59e7 ### catalog version id 096f319317a86a05de960ea5b3dd5f036403ad84ff753a78081803104dc18a3a ### course number 825 ### subjects * MATH ### title SELECTED TOPICS IN FUNCTIONAL ANALYSIS ### description Topics will vary and may include spectral theory, nonlinear functional analysis or abstract harmonic analysis. ### requirements text Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program ### credit offering ids None recorded. ### llm job id enrich-8b774950c2b6adfdc46d1b82 ### llm output id ce53aa8896f91ddd31eef6fd58f256a763ba6219aee64fdfd7c35c912904b9dd ### llm model nvidia/Qwen3.6-35B-A3B-NVFP4 ### llm model revision 1355db6a052410cfd62085d94b58866fd0f2c3c5 ### llm task version 14 ### llm search status valid ### llm summary MATH 825 covers selected topics in functional analysis, potentially including spectral theory, nonlinear functional analysis, or abstract harmonic analysis. ### llm topics * Spectral theory * Nonlinear functional analysis * Abstract harmonic analysis ### llm skills None recorded. ### llm assumed background None recorded. ### llm search phrases * spectral theory * nonlinear functional analysis * abstract harmonic analysis * graduate functional analysis ### llm requirements status valid ### llm student summary status valid ### llm experience status insufficient\_evidence ### catalog variants None recorded. ### student summary #### context hash bf4db7ab7ce45fd55a9fc49c66b6c88a218a22d173bb2598fd2875825718f2e4 #### course id MATH 825 #### current instructors None recorded. #### difficulty workload None recorded. #### errors None recorded. #### historical context None recorded. #### message No course-specific reviews available #### offered false #### profile hash 5cb4dabf887cdbcd8c00d5a1312e10828b95c63f30bc3ea76aea199565390d02 #### quick take Recent recorded grades — Spring 2019: 4.00 GPA, 100.0% A/AB (n=11 letter grades); Fall 2019: 4.00 GPA, 100.0% A/AB (n=9 letter grades); Fall 2025: 3.67 GPA, 83.3% A/AB (n=6 letter grades). ```json { "citations": [ { "course_id": "MATH 825", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "03cb34a3-4302-3985-8963-3ec9724792e3", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1194", "type": "grade" }, { "course_id": "MATH 825", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "03cb34a3-4302-3985-8963-3ec9724792e3", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1202", "type": "grade" }, { "course_id": "MATH 825", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "03cb34a3-4302-3985-8963-3ec9724792e3", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1262", "type": "grade" } ] } ``` #### student experience None recorded. #### task hash 74fb0997943e888960bbc9e47db8c4fd12e4292d55c20509d8d89db6a9910f68 #### teaching history None recorded. #### 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 None recorded. #### root n0 #### status parsed ### instructors None recorded. ### offerings None recorded. ### sections None recorded. ### grade instructors ```json [ { "instructor_uid": "instructor_f00d358fd7c1650bfb3e8b33", "source": "madgrades", "source_instructor_id": "2600167", "identity_basis": "source_id", "identity_status": "source_identified", "name": "ALEXANDER NAGEL", "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": 45, "quality": 4.8, "difficulty": 2.69, "quality_count": 45, "difficulty_count": 45, "profile_id": "rmp:314655", "source_url": "https://www.ratemyprofessors.com/professor/314655", "match_basis": "exact_name", "observed_at": "2026-09-07 16:56:55.504552+00:00", "courses": { "course_6bc496e4640fd08f71e1b041": { "review_count": 6, "quality": 4.83, "difficulty": 2.5, "quality_count": 6, "difficulty_count": 6 }, "course_eec4aae06b946a73f1878be4": { "review_count": 2, "quality": 4, "difficulty": 1.5, 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0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 11, "source_aliases": [ "MATH 825" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 825", "course_uid": "course_a88d8bc7da942a242ead59e7", "term_id": "1194", "term_name": "Spring 2019", "instructors": [ "Brian Street" ], "a": 11, "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": 11, "source_aliases": [ "MATH 825" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 825", "course_uid": "course_a88d8bc7da942a242ead59e7", "term_id": "1202", "term_name": "Fall 2019", "instructors": [ "Brian Street" ], "a": 9, "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": 9, "source_aliases": [ "MATH 825" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 825", "course_uid": "course_a88d8bc7da942a242ead59e7", "term_id": "1262", "term_name": "Fall 2025", "instructors": [ "Brian Street" ], "a": 5, "ab": 0, "b": 0, "bc": 0, "c": 1, "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": 6, "source_aliases": [ "MATH 825" ] } ] ``` ### statistics #### gpa 3.946 #### graded 37 #### counts * 36 * 0 * 0 * 0 * 1 * 0 * 0 ### grade conflicts None recorded. ### evidence #### history * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_a88d8bc7da942a242ead59e7-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_a88d8bc7da942a242ead59e7-0.json) #### traces * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_a88d8bc7da942a242ead59e7-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_a88d8bc7da942a242ead59e7-0.json) #### results * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_a88d8bc7da942a242ead59e7-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_a88d8bc7da942a242ead59e7-0.json) ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ## context ### all #### term #### gpa 3.945945945945946 #### count 37 #### university ##### size 2778 ##### gpa Percentile 88 ##### count Percentile 10 ##### median Count 85 ##### 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 | 1 | false | | 2.4–2.8 | 14 | false | | 2.8–3.2 | 332 | false | | 3.2–3.6 | 839 | false | | 3.6–4.0 | 1592 | true | #### departments ```json [ { "subject": "MATH", "comparison": { "size": 70, "gpaPercentile": 88, "countPercentile": 7, "medianCount": 103, "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": 4, "current": false }, { "range": "2.8–3.2", "count": 28, "current": false }, { "range": "3.2–3.6", "count": 15, "current": false }, { "range": "3.6–4.0", "count": 23, "current": true } ] } } ] ``` ### terms #### 1152 ##### term 1152 ##### gpa 4 ##### count 11 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1194 ##### term 1194 ##### gpa 4 ##### count 11 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1202 ##### term 1202 ##### gpa 4 ##### count 9 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1262 ##### term 1262 ##### gpa 3.6666666666666665 ##### count 6 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | ### benchmarks #### all ##### school ###### size 2778 ###### gpa 3.6096456096665084 ###### top Share 78.84121524939202 ###### count 85 ##### MATH ###### size 70 ###### gpa 3.3552115759463406 ###### top Share 64.07867272072603 ###### count 103 #### terms ##### 1152 ###### school ###### size 918 ###### gpa 3.408733538594633 ###### top Share 66.06693005846735 ###### count 65 ###### MATH ###### size 34 ###### gpa 3.0803080141506425 ###### top Share 49.72677618758506 ###### count 82 ##### 1194 ###### school ###### size 1040 ###### gpa 3.4906527436719808 ###### top Share 71.74728845515045 ###### count 67 ###### MATH ###### size 38 ###### gpa 3.133406260873163 ###### top Share 53.17595010634325 ###### count 71.5 ##### 1202 ###### school ###### size 1102 ###### gpa 3.5102605987403313 ###### top Share 72.78244569053733 ###### count 68 ###### MATH ###### size 40 ###### gpa 3.1467748801316944 ###### top Share 52.57847974231038 ###### count 90.5 ##### 1262 ###### school ###### size 1320 ###### gpa 3.628825763035853 ###### top Share 80.21118846327654 ###### count 70 ###### MATH ###### size 43 ###### gpa 3.2481769276584003 ###### top Share 56.325967864851854 ###### count 81 ## instructor Trends ```json [ { "uid": "instructor_c0289d403f78c76ec800e7ea", "name": "BRIAN STREET", "count": 26, "terms": [ { "term": "1194", "count": 11, "sections": 1, "gpa": 4 }, { "term": "1202", "count": 9, "sections": 1, "gpa": 4 }, { "term": "1262", "count": 6, "sections": 1, "gpa": 3.6666666666666665 } ] }, { "uid": "instructor_f00d358fd7c1650bfb3e8b33", "name": "ALEXANDER NAGEL", "count": 11, "terms": [ { "term": "1152", "count": 11, "sections": 1, "gpa": 4 } ] } ] ``` ## following None recorded.