# MATH 718: Randomized Linear Algebra and Applications | UW–Madison [View on UW Courses](https://uwcourses.com/courses/MATH_718) ## 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 5ef8fe7b9a2fd26f32db90bdab88adcc266317127d664b0e4ce293e4cd77b735 ### course id MATH 718 ### course uid course\_4c518c7aee577750986dc7c8 ### catalog version id 6abd77afa0c5cc2fb52089990f2a655229eb67f24bcc7121e0cd542d31bdf6a8 ### course number 718 ### subjects * MATH ### title RANDOMIZED LINEAR ALGEBRA AND APPLICATIONS ### description Random solvers have been playing increasingly crucial roles in the modern computational tasks. The recent breakthroughs in applied and computational linear algebra that incorporate techniques of randomization have proven to be of great importance in modern applied math, computational sciences and data science, such as inverse problems, machine learning and scientific computing. The guiding principle is that one may greatly reduce computational and storage expenses at the cost of a small probability of failure. Systematic study of these modern methods of randomized linear algebra solvers will be provided, presenting mathematical backgrounds, algorithms, and concrete applications. Core theoretical topics include randomized Kaczmarz and its generalization to stochastic gradient descent, randomized singular value decomposition, random sketching, matrix completion, and compressive sensing, and corresponding applications. ### requirements text Graduate/professional standing or declared in Mathematics VISP (graduate or dissertator) ### credit offering ids None recorded. ### llm job id enrich-8b774950c2b6adfdc46d1b82 ### llm output id 1699be0093a28903b5d01e84eac887f607cab522a19d56fac3bb4fd1311c9cb7 ### llm model nvidia/Qwen3.6-35B-A3B-NVFP4 ### llm model revision 1355db6a052410cfd62085d94b58866fd0f2c3c5 ### llm task version 14 ### llm search status valid ### llm summary MATH 718 covers randomized linear algebra solvers, algorithms, and applications including Kaczmarz, SVD, and sketching. ### llm topics * Randomized Kaczmarz and stochastic gradient descent * Randomized singular value decomposition * Random sketching, matrix completion, and compressive sensing * Applications in inverse problems, machine learning, and scientific computing ### llm skills * Study of randomized linear algebra solvers, algorithms, and applications * Understanding core theoretical topics in randomized linear algebra ### llm assumed background None recorded. ### llm search phrases * randomized linear algebra * randomized Kaczmarz * stochastic gradient descent * randomized SVD * matrix completion * compressive sensing * random sketching * inverse problems * scientific computing ### llm requirements status valid ### llm student summary status valid ### llm experience status insufficient\_evidence ### catalog variants None recorded. ### student summary #### context hash 7345a1322e1af335d58d62a9e43e21bddb6ad34753a8bc0c431f5a16f3b1c1e0 #### course id MATH 718 #### 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 2024: 3.83 GPA, 100.0% A/AB (n=23 letter grades); Spring 2026: 3.69 GPA, 88.5% A/AB (n=26 letter grades). ```json { "citations": [ { "course_id": "MATH 718", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "83307b03-51e0-31a1-a5ba-40c4ba2ab211", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1252", "type": "grade" }, { "course_id": "MATH 718", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "83307b03-51e0-31a1-a5ba-40c4ba2ab211", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1264", "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 declared in Mathematics VISP (graduate or dissertator)", "id": "n0", "kind": "any" }, { "children": [], "condition": "Graduate/professional standing", "course": null, "evidence": "Graduate/professional standing", "id": "n1", "kind": "condition" }, { "children": [], "condition": "declared in Mathematics VISP (graduate or dissertator)", "course": null, "evidence": "declared in Mathematics VISP (graduate or dissertator)", "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_11da40ed2a2bb6d06bf52104", "source": "madgrades", "source_instructor_id": "6398400", "identity_basis": "source_id", 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"quality": 3.56, "difficulty": 3.06, "quality_count": 16, "difficulty_count": 16 } }, "bayesian_quality": 3.7357024098110814, "prior_mean": 3.6596857835465957, "prior_weight": 20 }, "grade_statistics": { "gpa": 3.072, "graded": 1421, "counts": [ 489, 237, 270, 133, 178, 82, 32 ], "sections": 44 }, "instructor_url": "/instructors/QIN_LI--instructor_6cee1ae6c2c6ae042c8870e4" } ] ``` ### grades ```json [ { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "MATH 718", "course_uid": "course_4c518c7aee577750986dc7c8", "term_id": "1252", "term_name": "Fall 2024", "instructors": [ "HANBAEK LYU" ], "a": 15, "ab": 8, "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": 23, "source_aliases": [ "MATH 718" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": 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departments ```json [ { "subject": "MATH", "comparison": { "size": 55, "gpaPercentile": 89, "countPercentile": 28, "medianCount": 97, "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": 6, "current": false }, { "range": "2.8–3.2", "count": 20, "current": false }, { "range": "3.2–3.6", "count": 19, "current": false }, { "range": "3.6–4.0", "count": 10, "current": true } ] } } ] ``` ### terms #### 1252 ##### term 1252 ##### gpa 3.8260869565217392 ##### count 23 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | #### 1264 ##### term 1264 ##### gpa 3.6923076923076925 ##### count 26 ##### departments | subject | comparison | | ------- | ---------- | | MATH | | ### benchmarks #### all ##### school ###### size 2124 ###### gpa 3.654433279098965 ###### top Share 81.90118684490442 ###### count 72 ##### MATH ###### size 55 ###### gpa 3.247873874239582 ###### top Share 57.639013141414146 ###### count 97 #### terms ##### 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 ##### 1264 ###### school ###### size 1283 ###### gpa 3.6229729166451925 ###### top Share 80.13669149396227 ###### count 66 ###### MATH ###### size 42 ###### gpa 3.13598176627681 ###### top Share 52.25969905887213 ###### count 80 ## instructor Trends ```json [ { "uid": "instructor_6cee1ae6c2c6ae042c8870e4", "name": "QIN LI", "count": 26, "terms": [ { "term": "1264", "count": 26, "sections": 1, "gpa": 3.6923076923076925 } ] }, { "uid": "instructor_11da40ed2a2bb6d06bf52104", "name": "HANBAEK LYU", "count": 23, "terms": [ { "term": "1252", "count": 23, "sections": 1, "gpa": 3.8260869565217392 } ] } ] ``` ## following None recorded.