# MATH 848: Advanced Topics in Number Theory | UW–Madison [View on UW Courses](https://uwcourses.com/courses/MATH_848) ## Dataset ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ### repository twangodev/uwcourses ### schema version 6 ### importer version 7 ### projection id 94468b7d4154126ca413937bb4738a6d21e0c2277f6fa397a6078ad80a32384f ### observed at 2026-09-07T15:55:43.033547+00:00 ### built at 2026-09-10T23:19:01.870283+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 d47961d3e7639c3a7ee15b1ce69993c528a3daaa6eb8d54d7a63e38ae6cfa242 ### course id MATH 848 ### course uid course\_b2cc5d7ed9882287cd8e7c03 ### catalog version id a36e7b93185127befd726b5695315bfffbdc8282d52cf32835ec78b8e84a8a7b ### course number 848 ### subjects * MATH ### title ADVANCED TOPICS IN NUMBER THEORY ### description This is an advanced graduate topic course in number theory. Topics will vary. Target audience: Advanced graduate students in number theory, representation theory, and algebraic geometry. ### 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 b0ef97af9ae70eae2ca01a35c05f12ad87b2d4c78e273312167005da5d7f67b6 ### llm model nvidia/Qwen3.6-35B-A3B-NVFP4 ### llm model revision 1355db6a052410cfd62085d94b58866fd0f2c3c5 ### llm task version 14 ### llm search status valid ### llm summary An advanced graduate course in number theory covering varying topics for students in number theory, representation theory, and algebraic geometry. ### llm topics * Advanced number theory topics (variable). ### llm skills None recorded. ### llm assumed background * Background in number theory, representation theory, and algebraic geometry. ### llm search phrases * advanced number theory * graduate algebraic geometry * representation theory topics * MATH 848 number theory ### llm requirements status valid ### llm student summary status valid ### llm experience status insufficient\_evidence ### catalog variants None recorded. ### student summary #### context hash 5e7799c2f8cdfaf6d28be4454de17c9e489c2192353f35b7a7c12e6f47a5ce0f #### course id MATH 848 #### 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=7 letter grades); Fall 2021: 4.00 GPA, 100.0% A/AB (n=17 letter grades); Fall 2025: 4.00 GPA, 100.0% A/AB (n=19 letter grades). ```json { "citations": [ { "course_id": "MATH 848", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": 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```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_91a8295117bb0ce7b172a161", "source": "madgrades", "source_instructor_id": "3230527", "identity_basis": "source_id", "identity_status": "source_identified", 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3.248, "graded": 2472, "counts": [ 1217, 198, 495, 118, 292, 103, 49 ], "sections": 63 }, "instructor_url": "/instructors/TONGHAI_YANG--instructor_91a8295117bb0ce7b172a161" }, { "instructor_uid": "instructor_5b47ad9775f570fe5fcf848a", "source": "madgrades", "source_instructor_id": "5846697", "identity_basis": "source_id", "identity_status": "source_identified", "name": "NASER TALEBIZADEH SARDARI", "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", "grade_statistics": { "gpa": 3.017, "graded": 362, "counts": [ 126, 33, 80, 49, 47, 16, 11 ], "sections": 11 }, "instructor_url": "/instructors/NASER_TALEBIZADEH_SARDARI" }, { "instructor_uid": "instructor_627bd6efdd66a1083f8cbb97", "source": "madgrades", "source_instructor_id": "3921210", "identity_basis": "source_id", "identity_status": "source_identified", "name": "JORDAN ELLENBERG", "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": 28, "quality": 4.46, "difficulty": 3.36, "quality_count": 28, "difficulty_count": 28, "profile_id": "rmp:1012704", "source_url": "https://www.ratemyprofessors.com/professor/1012704", "match_basis": "exact_name", "observed_at": "2026-09-07 16:30:34.696141+00:00", "courses": { "course_364c50303ed83d1234b4ea51": { "review_count": 8, "quality": 5, "difficulty": 3.62, "quality_count": 8, "difficulty_count": 8 }, "course_72733c94bb8725b969d3e958": { "review_count": 1, "quality": 5, "difficulty": 3, "quality_count": 1, "difficulty_count": 1 }, "course_9a1a7bf1933981bcbaca47ac": { "review_count": 19, "quality": 4.21, "difficulty": 3.26, "quality_count": 19, "difficulty_count": 19 } }, "bayesian_quality": 4.126535743144415, "prior_mean": 3.6596857835465957, "prior_weight": 20 }, "grade_statistics": { "gpa": 3.415, "graded": 1050, "counts": [ 497, 179, 215, 74, 61, 19, 5 ], "sections": 70 }, "instructor_url": "/instructors/JORDAN_ELLENBERG--instructor_627bd6efdd66a1083f8cbb97" }, { "instructor_uid": "instructor_87f5de61e3e2a0faa6fbddb7", "source": "madgrades", "source_instructor_id": "4598048", "identity_basis": "source_id", "identity_status": "source_identified", "name": "YINGKUN LI", "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", "grade_statistics": { "gpa": 3.812, "graded": 32, "counts": [ 25, 6, 0, 0, 0, 1, 0 ], "sections": 5 }, "instructor_url": "/instructors/YINGKUN_LI--instructor_87f5de61e3e2a0faa6fbddb7" } ] ``` ### grades ```json [ { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 848", "course_uid": "course_b2cc5d7ed9882287cd8e7c03", "term_id": "1172", "term_name": "Fall 2016", "instructors": [ "Tonghai Yang" ], "a": 19, "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": 19, "source_aliases": [ "MATH 848" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 848", "course_uid": "course_b2cc5d7ed9882287cd8e7c03", "term_id": "1194", "term_name": "Spring 2019", "instructors": [ "NASER TALEBIZADEH SARDARI" ], "a": 7, "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": 7, "source_aliases": [ "MATH 848" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 848", "course_uid": "course_b2cc5d7ed9882287cd8e7c03", "term_id": "1222", "term_name": "Fall 2021", "instructors": [ "Jordan Ellenberg" ], "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 848" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 848", "course_uid": "course_b2cc5d7ed9882287cd8e7c03", "term_id": "1262", "term_name": "Fall 2025", "instructors": [ "Yingkun Li" ], "a": 19, "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": 19, "source_aliases": [ "MATH 848" ] } ] ``` ### statistics #### gpa 4 #### graded 62 #### counts * 62 * 0 * 0 * 0 * 0 * 0 * 0 ### grade conflicts None recorded. ### evidence #### history * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_b2cc5d7ed9882287cd8e7c03-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_b2cc5d7ed9882287cd8e7c03-0.json) #### traces * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_b2cc5d7ed9882287cd8e7c03-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_b2cc5d7ed9882287cd8e7c03-0.json) #### results * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_b2cc5d7ed9882287cd8e7c03-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_b2cc5d7ed9882287cd8e7c03-0.json) ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ## context ### all #### term #### gpa 4 #### count 62 #### university ##### size 2795 ##### gpa Percentile 94 ##### count Percentile 35 ##### median Count 86 ##### 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 | 12 | false | | 2.8–3.2 | 283 | false | | 3.2–3.6 | 820 | false | | 3.6–4.0 | 1680 | true | #### departments ```json [ { "subject": "MATH", "comparison": { "size": 72, "gpaPercentile": 92, "countPercentile": 30, "medianCount": 97.5, "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": 24, "current": false }, { "range": "3.2–3.6", "count": 22, "current": false }, { "range": "3.6–4.0", "count": 22, "current": true } ] } } ] ``` ### terms #### 1172 ##### term 1172 ##### gpa 4 ##### count 19 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1194 ##### term 1194 ##### gpa 4 ##### count 7 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1222 ##### term 1222 ##### gpa 4 ##### count 17 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1262 ##### term 1262 ##### gpa 4 ##### count 19 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | ### benchmarks #### all ##### school ###### size 2795 ###### gpa 3.62789630005738 ###### top Share 79.97803653231934 ###### count 86 ##### MATH ###### size 72 ###### gpa 3.383329863458626 ###### top Share 65.44508516905073 ###### count 97.5 #### terms ##### 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 ##### 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 ##### 1222 ###### school ###### size 1157 ###### gpa 3.563052311875811 ###### top Share 76.64869058732418 ###### count 64 ###### MATH ###### size 39 ###### gpa 3.2083447119296955 ###### top Share 56.75007696473496 ###### count 63 ##### 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_87f5de61e3e2a0faa6fbddb7", "name": "YINGKUN LI", "count": 19, "terms": [ { "term": "1262", "count": 19, "sections": 1, "gpa": 4 } ] }, { "uid": "instructor_91a8295117bb0ce7b172a161", "name": "TONGHAI YANG", "count": 19, "terms": [ { "term": "1172", "count": 19, "sections": 1, "gpa": 4 } ] }, { "uid": "instructor_627bd6efdd66a1083f8cbb97", "name": "JORDAN ELLENBERG", "count": 17, "terms": [ { "term": "1222", "count": 17, "sections": 1, "gpa": 4 } ] }, { "uid": "instructor_5b47ad9775f570fe5fcf848a", "name": "NASER TALEBIZADEH SARDARI", "count": 7, "terms": [ { "term": "1194", "count": 7, "sections": 1, "gpa": 4 } ] } ] ``` ## following None recorded.