# MATH 748: Algebraic Number Theory | UW–Madison [View on UW Courses](https://uwcourses.com/courses/MATH_748) ## 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 ce9c1bf590d694529405193243c6440de71ca0dd0bab9b6198604d8c1ee334ca ### course id MATH 748 ### course uid course\_eceba8534cefe7b6309329a9 ### catalog version id 3bd8beb9e2e9c15bc56859f02586b03e389baf8bfbd466efc8bad3ebfe023854 ### course number 748 ### subjects * MATH ### title ALGEBRAIC NUMBER THEORY ### description A rigorous introduction to the arithmetic of number fields; algebraic integers, geometry of numbers, Dirichlet's Unit Theorem, ideal class groups, first case of Fermat's Last Theorem; prime decompositions, Galois automorphisms. Basic graduate algebra courses (e.g.MATH 741and742) are strongly recommended. ### 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 d5755dd889851db68c3294d685df8ed66eea25eac64f571dec08478700d9fe8f ### llm model nvidia/Qwen3.6-35B-A3B-NVFP4 ### llm model revision 1355db6a052410cfd62085d94b58866fd0f2c3c5 ### llm task version 14 ### llm search status valid ### llm summary ALGEBRAIC NUMBER THEORY covers the arithmetic of number fields, including algebraic integers, Dirichlet's Unit Theorem, and ideal class groups. ### llm topics * Arithmetic of number fields and algebraic integers * Geometry of numbers * Dirichlet's Unit Theorem * Ideal class groups * First case of Fermat's Last Theorem * Prime decompositions and Galois automorphisms ### llm skills * Study of number fields, algebraic integers, and ideal class groups. * Application of Galois automorphisms and prime decomposition. ### llm assumed background * Basic graduate algebra courses (e.g.MATH 741and742) are strongly recommended. ### llm search phrases * algebraic number theory graduate * number fields arithmetic * Dirichlet Unit Theorem * ideal class groups * Fermat's Last Theorem first case ### llm requirements status valid ### llm student summary status valid ### llm experience status insufficient\_evidence ### catalog variants None recorded. ### student summary #### context hash 643f397df2bcf3ab5ac663e5107b05cf40e396567e2b0ed453f8029efe809a26 #### course id MATH 748 #### 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 — Fall 2020: 3.96 GPA, 100.0% A/AB 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"source_aliases": [ "MATH 748" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 748", "course_uid": "course_eceba8534cefe7b6309329a9", "term_id": "1232", "term_name": "Fall 2022", "instructors": [ "YOUSHENG SHI" ], "a": 24, "ab": 0, "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": 25, "source_aliases": [ "MATH 748" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 748", "course_uid": "course_eceba8534cefe7b6309329a9", "term_id": "1252", "term_name": "Fall 2024", "instructors": [ "Tonghai Yang" ], "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 748" ] } ] ``` ### statistics #### gpa 3.91 #### graded 178 #### counts * 152 * 20 * 6 * 0 * 0 * 0 * 0 ### grade conflicts None recorded. ### evidence #### history * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_eceba8534cefe7b6309329a9-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_eceba8534cefe7b6309329a9-0.json) #### traces * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_eceba8534cefe7b6309329a9-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_eceba8534cefe7b6309329a9-0.json) #### results * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_eceba8534cefe7b6309329a9-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_eceba8534cefe7b6309329a9-0.json) ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ## context ### all #### term #### gpa 3.9101123595505616 #### count 178 #### university ##### size 3411 ##### gpa Percentile 80 ##### count Percentile 59 ##### median Count 132 ##### 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 | 9 | false | | 2.8–3.2 | 306 | false | | 3.2–3.6 | 1039 | false | | 3.6–4.0 | 2057 | true | #### departments ```json [ { "subject": "MATH", "comparison": { "size": 81, "gpaPercentile": 75, "countPercentile": 45, "medianCount": 201, "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": 3, "current": false }, { "range": "2.8–3.2", "count": 29, "current": false }, { "range": "3.2–3.6", "count": 17, "current": false }, { "range": "3.6–4.0", "count": 32, "current": true } ] } } ] ``` ### terms #### 1072 ##### term 1072 ##### gpa 3.730769230769231 ##### count 26 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1092 ##### term 1092 ##### gpa 3.6153846153846154 ##### count 13 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1112 ##### term 1112 ##### gpa 3.9375 ##### count 16 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1132 ##### term 1132 ##### gpa 4 ##### count 10 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1152 ##### term 1152 ##### gpa 3.973684210526316 ##### count 19 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1172 ##### term 1172 ##### gpa 3.9545454545454546 ##### count 11 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1192 ##### term 1192 ##### gpa 4 ##### count 11 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1212 ##### term 1212 ##### gpa 3.96 ##### count 25 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1232 ##### term 1232 ##### gpa 3.96 ##### count 25 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1252 ##### term 1252 ##### gpa 4 ##### count 22 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | ### benchmarks #### all ##### school ###### size 3411 ###### gpa 3.6370674697125156 ###### top Share 80.50331745796493 ###### count 132 ##### MATH ###### size 81 ###### gpa 3.4381932444599017 ###### top Share 68.46483517511537 ###### count 201 #### terms ##### 1072 ###### school ###### size 723 ###### gpa 3.344595727439471 ###### top Share 62.012941427864526 ###### count 67 ###### MATH ###### size 21 ###### gpa 2.878188611674867 ###### top Share 40.4748751710427 ###### count 115 ##### 1092 ###### school ###### size 732 ###### gpa 3.374660709520374 ###### top Share 63.690339324346596 ###### count 70 ###### MATH ###### size 22 ###### gpa 2.8820162698417926 ###### top Share 39.71597770466243 ###### count 131 ##### 1112 ###### school ###### size 805 ###### gpa 3.3737773184830386 ###### top Share 63.91039244872789 ###### count 66 ###### MATH ###### size 26 ###### gpa 2.9941347625171355 ###### top Share 43.79682105650899 ###### count 87 ##### 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 ##### 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 ##### 1172 ###### school ###### size 991 ###### gpa 3.465129042641772 ###### top Share 69.42600667567366 ###### count 67 ###### MATH ###### size 36 ###### gpa 3.098601909983034 ###### top Share 48.67573746500224 ###### count 66 ##### 1192 ###### school ###### size 1077 ###### gpa 3.50327634323125 ###### top Share 72.44641925727845 ###### count 67 ###### MATH ###### size 39 ###### gpa 3.1003216533236415 ###### top Share 50.01588968281552 ###### count 99 ##### 1212 ###### school ###### size 1111 ###### gpa 3.5856416028074487 ###### top Share 77.58926748660845 ###### count 68 ###### MATH ###### size 41 ###### gpa 3.3211331103538813 ###### top Share 59.85093623917685 ###### count 87 ##### 1232 ###### school ###### size 1216 ###### gpa 3.575457431972425 ###### top Share 77.33712216234007 ###### count 66 ###### MATH ###### size 43 ###### gpa 3.2486774162409366 ###### top Share 56.56203211471963 ###### count 69 ##### 1252 ###### school ###### size 1333 ###### gpa 3.619494049739118 ###### top Share 79.71442190500672 ###### count 69 ###### MATH ###### size 43 ###### gpa 3.185692541204979 ###### top Share 54.14175342403773 ###### count 74 ## instructor Trends ```json [ { "uid": "instructor_91a8295117bb0ce7b172a161", "name": "TONGHAI YANG", "count": 38, "terms": [ { "term": "1112", "count": 16, "sections": 1, "gpa": 3.9375 }, { "term": "1252", "count": 22, "sections": 1, "gpa": 4 } ] }, { "uid": "instructor_87f24f0fa5dbe5bf4d4b510c", "name": "MELANIE WOOD", "count": 30, "terms": [ { "term": "1152", "count": 19, "sections": 1, "gpa": 3.973684210526316 }, { "term": "1172", "count": 11, "sections": 1, "gpa": 3.9545454545454546 } ] }, { "uid": "instructor_79caf97dfd5ee43cecb1a346", "name": "RAPHAEL F JONES", "count": 26, "terms": [ { "term": "1072", "count": 26, "sections": 1, "gpa": 3.730769230769231 } ] }, { "uid": "instructor_627bd6efdd66a1083f8cbb97", "name": "JORDAN ELLENBERG", "count": 25, "terms": [ { "term": "1212", "count": 25, "sections": 1, "gpa": 3.96 } ] }, { "uid": "instructor_98e9331ef0690b66352c0c4a", "name": "YOUSHENG SHI", "count": 25, "terms": [ { "term": "1232", "count": 25, "sections": 1, "gpa": 3.96 } ] }, { "uid": "instructor_163db9c2515680c781e5d5d1", "name": "AMANDA FOLSOM", "count": 13, "terms": [ { "term": "1092", "count": 13, "sections": 1, "gpa": 3.6153846153846154 } ] }, { "uid": "instructor_e9103eecc0b4e9d9f206ab8d", "name": "MARK SHUSTERMAN", "count": 11, "terms": [ { "term": "1192", "count": 11, "sections": 1, "gpa": 4 } ] }, { "uid": "instructor_1e425973e35e549fa9aaef2b", "name": "ZEV KLAGSBRUN", "count": 10, "terms": [ { "term": "1132", "count": 10, "sections": 1, "gpa": 4 } ] } ] ``` ## following None recorded.