# MATH 845: Class Field Theory | UW–Madison [View on UW Courses](https://uwcourses.com/courses/MATH_845) ## 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 9d43ed5d79acb72a89a912c53eb7778ec858fdfe88d33dd07e86d170ba1742cc ### course id MATH 845 ### course uid course\_2f67171e98d0175542979e4a ### catalog version id 2db24b81eb7bbc7fdc1ac679bd18eeb4142a5e8b6ba158561e1acf3df2b48bd0 ### course number 845 ### subjects * MATH ### title CLASS FIELD THEORY ### description Introduction to local and global class field theory. Theory of local fields; local and global class field theory; complex multiplication, adeles, ideles, idele class characters, Tchebotarev's Density Theorem, CM elliptic curves, construction of class fields of imaginary quadratic fields. ### 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 e62e52b7cd8ce3c6f6404184218b7bbcc34787c52b10724b0789df73855d6257 ### llm model nvidia/Qwen3.6-35B-A3B-NVFP4 ### llm model revision 1355db6a052410cfd62085d94b58866fd0f2c3c5 ### llm task version 14 ### llm search status valid ### llm summary MATH 845 introduces local and global class field theory, covering adeles, ideles, and CM elliptic curves. ### llm topics * Theory of local fields * Local and global class field theory * Complex multiplication * Adeles, ideles, and idele class characters * Tchebotarev's Density Theorem * CM elliptic curves * Construction of class fields of imaginary quadratic fields ### llm skills * Understanding local and global class field theory * Analyzing adeles, ideles, and idele class characters * Applying Tchebotarev's Density Theorem * Constructing class fields of imaginary quadratic fields ### llm assumed background None recorded. ### llm search phrases * class field theory graduate course * local and global class field theory * adeles ideles number theory * complex multiplication elliptic curves ### llm requirements status valid ### llm student summary status valid ### llm experience status insufficient\_evidence ### catalog variants None recorded. ### student summary #### context hash 6a7c7939d55b5e2cae12436ad2f0c6ea9f2c9f16abde4f319d05ca13f60676a2 #### course id MATH 845 #### current instructors None recorded. #### difficulty workload None recorded. #### errors None recorded. #### historical context None recorded. #### message No course-specific reviews available #### offered 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"term_name": "Spring 2015", "instructors": [ "Tonghai Yang" ], "a": 24, "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": 24, "source_aliases": [ "MATH 845" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 845", "course_uid": "course_2f67171e98d0175542979e4a", "term_id": "1174", "term_name": "Spring 2017", "instructors": [ "NIGEL BOSTON" ], "a": 10, "ab": 4, "b": 2, "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": 16, "source_aliases": [ "MATH 845" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 845", "course_uid": "course_2f67171e98d0175542979e4a", "term_id": "1194", "term_name": "Spring 2019", "instructors": [ "SIMON MARSHALL" ], "a": 8, "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": 8, "source_aliases": [ "MATH 845" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 845", "course_uid": "course_2f67171e98d0175542979e4a", "term_id": "1244", "term_name": "Spring 2024", "instructors": [ "BRIAN LAWRENCE" ], "a": 17, "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": 17, "source_aliases": [ "MATH 845" ] } ] ``` ### statistics #### gpa 3.929 #### graded 113 #### counts * 103 * 6 * 3 * 0 * 1 * 0 * 0 ### grade conflicts None recorded. ### evidence #### history * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_2f67171e98d0175542979e4a-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_2f67171e98d0175542979e4a-0.json) #### traces * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_2f67171e98d0175542979e4a-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_2f67171e98d0175542979e4a-0.json) #### results * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_2f67171e98d0175542979e4a-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_2f67171e98d0175542979e4a-0.json) ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ## context ### all #### term #### gpa 3.9292035398230087 #### count 113 #### university ##### size 2933 ##### gpa Percentile 84 ##### count Percentile 53 ##### median Count 103 ##### 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 | 24 | false | | 2.8–3.2 | 320 | false | | 3.2–3.6 | 934 | false | | 3.6–4.0 | 1654 | true | #### departments ```json [ { "subject": "MATH", "comparison": { "size": 79, "gpaPercentile": 77, "countPercentile": 47, "medianCount": 122, "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": 1, "current": false }, { "range": "2.4–2.8", "count": 8, "current": false }, { "range": "2.8–3.2", "count": 25, "current": false }, { "range": "3.2–3.6", "count": 12, "current": false }, { "range": "3.6–4.0", "count": 33, "current": true } ] } } ] ``` ### terms #### 1074 ##### term 1074 ##### gpa 4 ##### count 11 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1094 ##### term 1094 ##### gpa 4 ##### count 20 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1114 ##### term 1114 ##### gpa 3.764705882352941 ##### count 17 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1154 ##### term 1154 ##### gpa 4 ##### count 24 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1174 ##### term 1174 ##### gpa 3.75 ##### count 16 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1194 ##### term 1194 ##### gpa 4 ##### count 8 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1244 ##### term 1244 ##### gpa 4 ##### count 17 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | ### benchmarks #### all ##### school ###### size 2933 ###### gpa 3.6032196701769106 ###### top Share 78.47718527704623 ###### count 103 ##### MATH ###### size 79 ###### gpa 3.394885046645041 ###### top Share 67.36340770839756 ###### count 122 #### terms ##### 1074 ###### school ###### size 695 ###### gpa 3.3616924722887376 ###### top Share 63.22509110105764 ###### count 69 ###### MATH ###### size 17 ###### gpa 2.821339129045922 ###### top Share 38.66654769268061 ###### count 133 ##### 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 ##### 1154 ###### school ###### size 935 ###### gpa 3.4282378385810093 ###### top Share 67.66674668721691 ###### count 63 ###### MATH ###### size 33 ###### gpa 2.9834698949629033 ###### top Share 46.71989715257013 ###### count 69 ##### 1174 ###### school ###### size 955 ###### gpa 3.4597947384071412 ###### top Share 69.5290038366363 ###### count 69 ###### MATH ###### size 32 ###### gpa 2.992971960864239 ###### top Share 44.393513280464695 ###### count 89 ##### 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 ##### 1244 ###### school ###### size 1241 ###### gpa 3.5975573126929192 ###### top Share 78.29036874847135 ###### count 65 ###### MATH ###### size 43 ###### gpa 3.228240949537157 ###### top Share 55.86451059486035 ###### count 68 ## instructor Trends ```json [ { "uid": "instructor_247d961acdc61511ccc819c5", "name": "NIGEL BOSTON", "count": 33, "terms": [ { "term": "1114", "count": 17, "sections": 1, "gpa": 3.764705882352941 }, { "term": "1174", "count": 16, "sections": 1, "gpa": 3.75 } ] }, { "uid": "instructor_91a8295117bb0ce7b172a161", "name": "TONGHAI YANG", "count": 24, "terms": [ { "term": "1154", "count": 24, "sections": 1, "gpa": 4 } ] }, { "uid": "instructor_627bd6efdd66a1083f8cbb97", "name": "JORDAN ELLENBERG", "count": 20, "terms": [ { "term": "1094", "count": 20, "sections": 1, "gpa": 4 } ] }, { "uid": "instructor_8e516e076f29ce5d673213e8", "name": "BRIAN LAWRENCE", "count": 17, "terms": [ { "term": "1244", "count": 17, "sections": 1, "gpa": 4 } ] }, { "uid": "instructor_2526da1b4d60f44a1bea00f0", "name": "YANNAN QIU", "count": 11, "terms": [ { "term": "1074", "count": 11, "sections": 1, "gpa": 4 } ] }, { "uid": "instructor_8779cbf2cbe1e0b379b7d322", "name": "SIMON MARSHALL", "count": 8, "terms": [ { "term": "1194", "count": 8, "sections": 1, "gpa": 4 } ] } ] ``` ## following None recorded.