# MATH 758: Introduction to Ergodic Theory and Dynamics | UW–Madison [View on UW Courses](https://uwcourses.com/courses/MATH_758) ## 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 | | 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| 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 9e930b574967c1761505b5a0609b6df8111378834d8478e70f894c3e20e942e9 ### course id MATH 758 ### course uid course\_e02dda0c80f5eb64763f2690 ### catalog version id 8b869e9600a8668a81bd4fd329dd96816d40c9082f0fc9f3fe5cdc17c16cec0e ### course number 758 ### subjects * MATH ### title INTRODUCTION TO ERGODIC THEORY AND DYNAMICS ### description An introduction to ergodic theory and dynamics covering fundamental theorems of ergodic theory, classical examples of one and two dimensional dynamics as well as applications to study of group actions. ### requirements text Graduate/professional standing ### credit offering ids None recorded. ### llm job id enrich-8b774950c2b6adfdc46d1b82 ### llm output id cc859a35a441d9c7948331616c8441f2debd8ae776c48eb51bec8fafefea0aff ### llm model nvidia/Qwen3.6-35B-A3B-NVFP4 ### llm model revision 1355db6a052410cfd62085d94b58866fd0f2c3c5 ### llm task version 14 ### llm search status valid ### llm summary Introduction to ergodic theory and dynamics, covering fundamental theorems, classical examples, and applications to group actions. ### llm topics * Ergodic theory * Dynamics * One and two dimensional dynamics * Group actions ### llm skills * Understanding fundamental theorems of ergodic theory * Analyzing classical examples of one and two dimensional dynamics * Applying ergodic theory to the study of group actions ### llm assumed background * Graduate or professional student standing ### llm search phrases * ergodic theory introduction * dynamics group actions * one two dimensional dynamics * graduate ergodic theory ### llm requirements status valid ### llm student summary status valid ### llm experience status insufficient\_evidence ### catalog variants None recorded. ### student summary #### context hash f25b2ef412cf7727da8c24f0c0e703973e9c01fdb92f4a079bf403d92a7d5c6b #### course id MATH 758 #### current instructors None recorded. #### difficulty workload None recorded. #### errors None recorded. #### historical 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[ "MATH 758" ] } ] ``` ### statistics #### gpa 3.972 #### graded 108 #### counts * 107 * 0 * 0 * 0 * 0 * 1 * 0 ### grade conflicts None recorded. ### evidence #### history * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_e02dda0c80f5eb64763f2690-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_e02dda0c80f5eb64763f2690-0.json) #### traces * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_e02dda0c80f5eb64763f2690-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_e02dda0c80f5eb64763f2690-0.json) #### results * [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_e02dda0c80f5eb64763f2690-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_e02dda0c80f5eb64763f2690-0.json) ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ## context ### all #### term #### gpa 3.9722222222222223 #### count 108 #### university ##### size 2961 ##### gpa Percentile 89 ##### count Percentile 57 ##### 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 | 1 | false | | 2.4–2.8 | 14 | false | | 2.8–3.2 | 195 | false | | 3.2–3.6 | 783 | false | | 3.6–4.0 | 1968 | true | #### departments ```json [ { "subject": "MATH", "comparison": { "size": 79, "gpaPercentile": 90, "countPercentile": 53, "medianCount": 99, "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": 23, "current": false }, { "range": "3.2–3.6", "count": 26, "current": false }, { "range": "3.6–4.0", "count": 26, "current": true } ] } } ] ``` ### terms #### 1234 ##### term 1234 ##### gpa 4 ##### count 23 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1244 ##### term 1244 ##### gpa 4 ##### count 34 ##### university ###### size 1241 ###### gpa Percentile 95 ###### count Percentile 9 ###### median Count 65 ###### 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 | 2 | false | | 2.4–2.8 | 9 | false | | 2.8–3.2 | 151 | false | | 3.2–3.6 | 373 | false | | 3.6–4.0 | 706 | true | ##### departments ```json [ { "subject": "MATH", "comparison": { "size": 43, "gpaPercentile": 98, "countPercentile": 10, "medianCount": 68, "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": 2, "current": false }, { "range": "2.4–2.8", "count": 2, "current": false }, { "range": "2.8–3.2", "count": 20, "current": false }, { "range": "3.2–3.6", "count": 11, "current": false }, { "range": "3.6–4.0", "count": 8, "current": true } ] } } ] ``` #### 1254 ##### term 1254 ##### gpa 4 ##### count 14 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1262 ##### term 1262 ##### gpa 3.918918918918919 ##### count 37 ##### university ###### size 1320 ###### gpa Percentile 82 ###### count Percentile 14 ###### median Count 70 ###### 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 | 8 | false | | 2.8–3.2 | 133 | false | | 3.2–3.6 | 381 | false | | 3.6–4.0 | 797 | true | ##### departments ```json [ { "subject": "MATH", "comparison": { "size": 43, "gpaPercentile": 95, "countPercentile": 19, "medianCount": 81, "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": 18, "current": false }, { "range": "3.2–3.6", "count": 16, "current": false }, { "range": "3.6–4.0", "count": 6, "current": true } ] } } ] ``` ### benchmarks #### all ##### school ###### size 2961 ###### gpa 3.675002446012273 ###### top Share 82.84369387140099 ###### count 91 ##### MATH ###### size 79 ###### gpa 3.411109970124529 ###### top Share 66.33347869437824 ###### count 99 #### terms ##### 1234 ###### school ###### size 1188 ###### gpa 3.5799441677552393 ###### top Share 77.18256448537606 ###### count 65 ###### MATH ###### size 41 ###### gpa 3.178489266862151 ###### top Share 56.06874885619616 ###### count 67 ##### 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 ##### 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 ##### 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_aa08ce380e5560c2bd8d8883", "name": "PAUL APISA", "count": 71, "terms": [ { "term": "1244", "count": 34, "sections": 1, "gpa": 4 }, { "term": "1262", "count": 37, "sections": 1, "gpa": 3.918918918918919 } ] }, { "uid": "instructor_18ef1d7d9b98466965984778", "name": "CAGLAR UYANIK", "count": 23, "terms": [ { "term": "1234", "count": 23, "sections": 1, "gpa": 4 } ] }, { "uid": "instructor_09b1c1be00e1b7fd397c55cf", "name": "CHENXI WU", "count": 14, "terms": [ { "term": "1254", "count": 14, "sections": 1, "gpa": 4 } ] } ] ``` ## following None recorded.