# MATH 635: An Introduction to Brownian Motion and Stochastic Calculus | UW–Madison

[View on UW Courses](https://uwcourses.com/courses/MATH_635)

## 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

8eaee69daab5457a2a0b3db4455c71497847218c004ad4bfe2e9e37979f08a8f

### course id

MATH 635

### course uid

course\_34ef395682f16208c88d0770

### catalog version id

cd2c2ba84c528ec91ac05fb63b7af47caab98bd785e15e3c8c7f08f532b8f031

### course number

635

### subjects

* MATH

### title

AN INTRODUCTION TO BROWNIAN MOTION AND STOCHASTIC CALCULUS

### description

Presents an introduction to Brownian motion and its application to stochastic calculus. Sample path properties of Brownian motion, Ito stochastic integrals, Ito's formula, stochastic differential equations and properties of their solutions, and various applications will be included.

### requirements text

(MATH 521andSTAT/​I SY E/​MATH/​OTM  632) or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

### credit offering ids

None recorded.

### llm job id

enrich-f516c4d3e82cfe326b4f5f54

### llm output id

30c97bd1919ebc881392edaefd302f86199bd9362b2b7eea6cfa3f85f8c232a4

### llm model

nvidia/Qwen3.6-35B-A3B-NVFP4

### llm model revision

1355db6a052410cfd62085d94b58866fd0f2c3c5

### llm task version

14

### llm search status

valid

### llm summary

An introduction to Brownian motion and stochastic calculus, covering Ito integrals, Ito's formula, and stochastic differential equations.

### llm topics

* Sample path properties of Brownian motion
* Ito stochastic integrals and Ito's formula
* Stochastic differential equations and solution properties

### llm skills

* Introduction to Brownian motion and stochastic calculus
* Analysis of sample path properties and SDE solutions

### llm assumed background

* Real analysis and stochastic processes background

### llm search phrases

* Brownian motion introduction
* stochastic calculus applications
* Ito integrals formula
* stochastic differential equations

### llm requirements status

valid

### llm student summary status

valid

### llm experience status

valid

### catalog variants

None recorded.

### student summary

#### context hash

8f9634b3c549abd1d2ad023f308b21f38a2a6b5ead25b1b0235ccab112641ff0

#### course id

MATH 635

#### current instructors

None recorded.

#### difficulty workload

Historical reviews of Hao Shen: The course is rated as difficult, requiring students to self-teach from the textbook due to ineffective lectures.

```json
{
  "citations": [
    {
      "instructor_name": "Hao Shen",
      "review_date": "2026-05-07 03:51:40 +0000 UTC",
      "review_id": "7137f25e699859b6eee3848e",
      "run_id": "20260907T155543-ce3781c4",
      "source_instructor_id": "rmp:2674823",
      "source_review_id": "UmF0aW5nLTQzMDU1ODc1",
      "source_url": "https://www.ratemyprofessors.com/professor/2674823",
      "type": "review"
    }
  ]
}
```

#### errors

None recorded.

#### historical context

Historical reviews for Hao Shen indicate poor lecture effectiveness, with one student reporting they learned nothing from his instruction. The reviewer suggests that students must rely entirely on the textbook for learning, resulting in a low quality rating for his teaching.

```json
{
  "citations": [
    {
      "instructor_name": "Hao Shen",
      "review_date": "2026-05-07 03:51:40 +0000 UTC",
      "review_id": "7137f25e699859b6eee3848e",
      "run_id": "20260907T155543-ce3781c4",
      "source_instructor_id": "rmp:2674823",
      "source_review_id": "UmF0aW5nLTQzMDU1ODc1",
      "source_url": "https://www.ratemyprofessors.com/professor/2674823",
      "type": "review"
    }
  ]
}
```

#### offered

false

#### profile hash

e59ddc7389015d0035b68cd195c939d475bf72b959b29cf12eab59b454ccaef1

#### quick take

Historical reviews for Hao Shen indicate a poor lecture experience, with students reporting they learned nothing from class and had to rely entirely on the textbook.

```json
{
  "citations": [
    {
      "instructor_name": "Hao Shen",
      "review_date": "2026-05-07 03:51:40 +0000 UTC",
      "review_id": "7137f25e699859b6eee3848e",
      "run_id": "20260907T155543-ce3781c4",
      "source_instructor_id": "rmp:2674823",
      "source_review_id": "UmF0aW5nLTQzMDU1ODc1",
      "source_url": "https://www.ratemyprofessors.com/professor/2674823",
      "type": "review"
    }
  ]
}
```

Recent recorded grades — Spring 2022: 3.38 GPA, 54.5% A/AB (n=33 letter grades); Spring 2024: 3.34 GPA, 63.6% A/AB (n=22 letter grades); Spring 2026: 3.70 GPA, 85.2% A/AB (n=27 letter grades).

```json
{
  "citations": [
    {
      "course_id": "MATH 635",
      "run_id": "20260907T155543-ce3781c4",
      "source_record": {
        "entity_id": "9b913c4f-cfd2-320c-8c89-6646485e7808",
        "file": "tables/observations.parquet",
        "kind": "grades",
        "source": "madgrades"
      },
      "table": "grades_latest",
      "term_id": "1224",
      "type": "grade"
    },
    {
      "course_id": "MATH 635",
      "run_id": "20260907T155543-ce3781c4",
      "source_record": {
        "entity_id": "9b913c4f-cfd2-320c-8c89-6646485e7808",
        "file": "tables/observations.parquet",
        "kind": "grades",
        "source": "madgrades"
      },
      "table": "grades_latest",
      "term_id": "1244",
      "type": "grade"
    },
    {
      "course_id": "MATH 635",
      "run_id": "20260907T155543-ce3781c4",
      "source_record": {
        "entity_id": "9b913c4f-cfd2-320c-8c89-6646485e7808",
        "file": "tables/observations.parquet",
        "kind": "grades",
        "source": "madgrades"
      },
      "table": "grades_latest",
      "term_id": "1264",
      "type": "grade"
    }
  ]
}
```

#### student experience

Historical reviews of Hao Shen: Students found the lectures unhelpful and frustrating, feeling forced to learn the material independently rather than through instruction.

```json
{
  "citations": [
    {
      "instructor_name": "Hao Shen",
      "review_date": "2026-05-07 03:51:40 +0000 UTC",
      "review_id": "7137f25e699859b6eee3848e",
      "run_id": "20260907T155543-ce3781c4",
      "source_instructor_id": "rmp:2674823",
      "source_review_id": "UmF0aW5nLTQzMDU1ODc1",
      "source_url": "https://www.ratemyprofessors.com/professor/2674823",
      "type": "review"
    }
  ]
}
```

#### task hash

74fb0997943e888960bbc9e47db8c4fd12e4292d55c20509d8d89db6a9910f68

#### teaching history

HAO SHEN is recorded teaching in Spring 2020, Spring 2022, Spring 2024, Spring 2026. Recorded history may be incomplete and does not establish a future schedule.

```json
{
  "citations": [
    {
      "course_id": "MATH 635",
      "run_id": "20260907T155543-ce3781c4",
      "section_number": 1,
      "source_course_id": "9b913c4f-cfd2-320c-8c89-6646485e7808",
      "source_record": {
        "entity_id": "9b913c4f-cfd2-320c-8c89-6646485e7808",
        "file": "tables/observations.parquet",
        "kind": "grades",
        "source": "madgrades"
      },
      "table": "section_grades_latest",
      "term_id": "1204",
      "type": "grade"
    },
    {
      "course_id": "MATH 635",
      "run_id": "20260907T155543-ce3781c4",
      "section_number": 1,
      "source_course_id": "9b913c4f-cfd2-320c-8c89-6646485e7808",
      "source_record": {
        "entity_id": "9b913c4f-cfd2-320c-8c89-6646485e7808",
        "file": "tables/observations.parquet",
        "kind": "grades",
        "source": "madgrades"
      },
      "table": "section_grades_latest",
      "term_id": "1224",
      "type": "grade"
    },
    {
      "course_id": "MATH 635",
      "run_id": "20260907T155543-ce3781c4",
      "section_number": 1,
      "source_course_id": "9b913c4f-cfd2-320c-8c89-6646485e7808",
      "source_record": {
        "entity_id": "9b913c4f-cfd2-320c-8c89-6646485e7808",
        "file": "tables/observations.parquet",
        "kind": "grades",
        "source": "madgrades"
      },
      "table": "section_grades_latest",
      "term_id": "1244",
      "type": "grade"
    },
    {
      "course_id": "MATH 635",
      "run_id": "20260907T155543-ce3781c4",
      "section_number": 1,
      "source_course_id": "9b913c4f-cfd2-320c-8c89-6646485e7808",
      "source_record": {
        "entity_id": "9b913c4f-cfd2-320c-8c89-6646485e7808",
        "file": "tables/observations.parquet",
        "kind": "grades",
        "source": "madgrades"
      },
      "table": "section_grades_latest",
      "term_id": "1264",
      "type": "grade"
    }
  ]
}
```

#### term id

1272

#### term name

2026 Fall

#### version

2

### requirements

#### nodes

```json
[
  {
    "children": [
      "n1",
      "n2",
      "n3"
    ],
    "condition": null,
    "course": null,
    "evidence": "(MATH 521andSTAT/I SY E/MATH/OTM 632) or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program",
    "id": "n0",
    "kind": "any"
  },
  {
    "children": [],
    "condition": null,
    "course": {
      "course_number": 521,
      "minimum_grade": null,
      "subjects": [
        "MATH"
      ],
      "timing": "prior"
    },
    "evidence": "MATH 521",
    "id": "n1",
    "kind": "course"
  },
  {
    "children": [],
    "condition": null,
    "course": {
      "course_number": 632,
      "minimum_grade": null,
      "subjects": [
        "ISYE",
        "MATH",
        "OTM",
        "STAT"
      ],
      "timing": "prior"
    },
    "evidence": "STAT/I SY E/MATH/OTM 632",
    "id": "n2",
    "kind": "course"
  },
  {
    "children": [],
    "condition": "graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program",
    "course": null,
    "evidence": "graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program",
    "id": "n3",
    "kind": "condition"
  }
]
```

#### notes

* The text 'STAT/I SY E/MATH/OTM 632' is parsed as a single course reference to ISYE/MATH/OTM/STAT 632 based on linked\_courses.

#### root

n0

#### status

parsed

### instructors

None recorded.

### offerings

None recorded.

### sections

None recorded.

### grade instructors

```json
[
  {
    "instructor_uid": "instructor_0eef5fd9bbc2212e9f6abe3b",
    "source": "madgrades",
    "source_instructor_id": "2601039",
    "identity_basis": "source_id",
    "identity_status": "source_identified",
    "name": "THOMAS G. KURTZ",
    "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": 2.973,
      "graded": 165,
      "counts": [
        41,
        24,
        44,
        15,
        35,
        3,
        3
      ],
      "sections": 19
    },
    "instructor_url": "/instructors/THOMAS_G_KURTZ"
  },
  {
    "instructor_uid": "instructor_cda4aae4567f70b662d00163",
    "source": "madgrades",
    "source_instructor_id": "4538519",
    "identity_basis": "source_id",
    "identity_status": "source_identified",
    "name": "BENEDEK VALKO",
    "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": 4.07,
      "difficulty": 3.25,
      "quality_count": 28,
      "difficulty_count": 28,
      "profile_id": "rmp:1566085",
      "source_url": "https://www.ratemyprofessors.com/professor/1566085",
      "match_basis": "exact_name",
      "observed_at": "2026-09-07 16:52:13.892497+00:00",
      "courses": {
        "course_c602622d732dbbc9aceeeddf": {
          "review_count": 1,
          "quality": 4,
          "difficulty": 3,
          "quality_count": 1,
          "difficulty_count": 1
        },
        "course_dcdb624e3fb8cbaf9a557ab9": {
          "review_count": 13,
          "quality": 4.08,
          "difficulty": 3.46,
          "quality_count": 13,
          "difficulty_count": 13
        },
        "course_436b4b4087325a19ccd87bd6": {
          "review_count": 3,
          "quality": 4.67,
          "difficulty": 2.33,
          "quality_count": 3,
          "difficulty_count": 3
        },
        "course_e0a93fa3466c39b6802e52a7": {
          "review_count": 2,
          "quality": 5,
          "difficulty": 2,
          "quality_count": 2,
          "difficulty_count": 2
        },
        "course_8634dde81cc95f6c58014087": {
          "review_count": 3,
          "quality": 4,
          "difficulty": 3.33,
          "quality_count": 3,
          "difficulty_count": 3
        }
      },
      "bayesian_quality": 3.899035743144415,
      "prior_mean": 3.6596857835465957,
      "prior_weight": 20
    },
    "grade_statistics": {
      "gpa": 3.153,
      "graded": 1160,
      "counts": [
        502,
        118,
        253,
        66,
        128,
        57,
        36
      ],
      "sections": 57
    },
    "instructor_url": "/instructors/BENEDEK_VALKO--instructor_cda4aae4567f70b662d00163"
  },
  {
    "instructor_uid": "instructor_74c5f2722d98d13de18c1d20",
    "source": "madgrades",
    "source_instructor_id": "4308515",
    "identity_basis": "source_id",
    "identity_status": "source_identified",
    "name": "DAVID ANDERSON",
    "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": 3.068,
      "graded": 1195,
      "counts": [
        473,
        139,
        243,
        78,
        151,
        62,
        49
      ],
      "sections": 36
    },
    "instructor_url": "/instructors/DAVID_ANDERSON--instructor_74c5f2722d98d13de18c1d20"
  },
  {
    "instructor_uid": "instructor_bec15c77aa953cbac45042f2",
    "source": "madgrades",
    "source_instructor_id": "3374880",
    "identity_basis": "source_id",
    "identity_status": "source_identified",
    "name": "TIMO SEPPALAINEN",
    "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": 22,
      "quality": 5,
      "difficulty": 3.32,
      "quality_count": 22,
      "difficulty_count": 22,
      "profile_id": "rmp:1006782",
      "source_url": "https://www.ratemyprofessors.com/professor/1006782",
      "match_basis": "exact_name",
      "observed_at": "2026-09-07 16:01:48.471263+00:00",
      "courses": {
        "course_b533f0f6b5fef2c11c4fa06c": {
          "review_count": 2,
          "quality": 5,
          "difficulty": 3,
          "quality_count": 2,
          "difficulty_count": 2
        },
        "course_c602622d732dbbc9aceeeddf": {
          "review_count": 6,
          "quality": 5,
          "difficulty": 3.33,
          "quality_count": 6,
          "difficulty_count": 6
        },
        "course_dcdb624e3fb8cbaf9a557ab9": {
          "review_count": 13,
          "quality": 5,
          "difficulty": 3.46,
          "quality_count": 13,
          "difficulty_count": 13
        },
        "course_364c50303ed83d1234b4ea51": {
          "review_count": 1,
          "quality": 5,
          "difficulty": 2,
          "quality_count": 1,
          "difficulty_count": 1
        }
      },
      "bayesian_quality": 4.361755135022189,
      "prior_mean": 3.6596857835465957,
      "prior_weight": 20
    },
    "grade_statistics": {
      "gpa": 3.109,
      "graded": 882,
      "counts": [
        352,
        85,
        221,
        47,
        104,
        48,
        25
      ],
      "sections": 50
    },
    "instructor_url": "/instructors/TIMO_SEPPALAINEN--instructor_bec15c77aa953cbac45042f2"
  },
  {
    "instructor_uid": "instructor_0a9a7c5c9ed52646788c2132",
    "source": "madgrades",
    "source_instructor_id": "3620114",
    "identity_basis": "source_id",
    "identity_status": "source_identified",
    "name": "JUN YIN",
    "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": 15,
      "quality": 3.87,
      "difficulty": 2.27,
      "quality_count": 15,
      "difficulty_count": 15,
      "profile_id": "rmp:1699172",
      "source_url": "https://www.ratemyprofessors.com/professor/1699172",
      "match_basis": "exact_name",
      "observed_at": "2026-09-07 16:29:28.164446+00:00",
      "courses": {
        "course_c602622d732dbbc9aceeeddf": {
          "review_count": 2,
          "quality": 4.5,
          "difficulty": 3,
          "quality_count": 2,
          "difficulty_count": 2
        },
        "course_b533f0f6b5fef2c11c4fa06c": {
          "review_count": 1,
          "quality": 3,
          "difficulty": 4,
          "quality_count": 1,
          "difficulty_count": 1
        },
        "course_6bc496e4640fd08f71e1b041": {
          "review_count": 8,
          "quality": 3.62,
          "difficulty": 1.5,
          "quality_count": 8,
          "difficulty_count": 8
        }
      },
      "bayesian_quality": 3.749820447740912,
      "prior_mean": 3.6596857835465957,
      "prior_weight": 20
    },
    "grade_statistics": {
      "gpa": 3.052,
      "graded": 716,
      "counts": [
        226,
        122,
        138,
        111,
        59,
        45,
        15
      ],
      "sections": 15
    },
    "instructor_url": "/instructors/JUN_YIN"
  },
  {
    "instructor_uid": "instructor_5088fbe0824eddc6e8e0f351",
    "source": "madgrades",
    "source_instructor_id": "4434130",
    "identity_basis": "source_id",
    "identity_status": "source_identified",
    "name": "WAI TONG FAN",
    "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": 3.093,
      "graded": 388,
      "counts": [
        110,
        67,
        92,
        65,
        38,
        11,
        5
      ],
      "sections": 12
    },
    "instructor_url": "/instructors/WAI_TONG_FAN"
  },
  {
    "instructor_uid": "instructor_a3ba606a773db62292d9f2ac",
    "source": "madgrades",
    "source_instructor_id": "4431741",
    "identity_basis": "source_id",
    "identity_status": "source_identified",
    "name": "HAO SHEN",
    "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": 25,
      "quality": 3.16,
      "difficulty": 3.24,
      "quality_count": 25,
      "difficulty_count": 25,
      "profile_id": "rmp:2674823",
      "source_url": "https://www.ratemyprofessors.com/professor/2674823",
      "match_basis": "exact_name",
      "observed_at": "2026-09-07 16:37:11.740384+00:00",
      "courses": {
        "course_34ef395682f16208c88d0770": {
          "review_count": 1,
          "quality": 1,
          "difficulty": 3,
          "quality_count": 1,
          "difficulty_count": 1
        },
        "course_b533f0f6b5fef2c11c4fa06c": {
          "review_count": 1,
          "quality": 2,
          "difficulty": 4,
          "quality_count": 1,
          "difficulty_count": 1
        },
        "course_6bc496e4640fd08f71e1b041": {
          "review_count": 20,
          "quality": 3.2,
          "difficulty": 3.25,
          "quality_count": 20,
          "difficulty_count": 20
        },
        "course_dcdb624e3fb8cbaf9a557ab9": {
          "review_count": 2,
          "quality": 5,
          "difficulty": 2.5,
          "quality_count": 2,
          "difficulty_count": 2
        }
      },
      "bayesian_quality": 3.3820825704651534,
      "prior_mean": 3.6596857835465957,
      "prior_weight": 20
    },
    "grade_statistics": {
      "gpa": 3.268,
      "graded": 723,
      "counts": [
        386,
        64,
        126,
        17,
        69,
        36,
        25
      ],
      "sections": 17
    },
    "instructor_url": "/instructors/HAO_SHEN--instructor_a3ba606a773db62292d9f2ac"
  }
]
```

### grades

```json
[
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 635",
    "course_uid": "course_34ef395682f16208c88d0770",
    "term_id": "1074",
    "term_name": "Spring 2007",
    "instructors": [
      "THOMAS G. KURTZ"
    ],
    "a": 5,
    "ab": 6,
    "b": 3,
    "bc": 0,
    "c": 0,
    "d": 0,
    "f": 1,
    "satisfactory": 0,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 15,
    "source_aliases": [
      "MATH 635"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 635",
    "course_uid": "course_34ef395682f16208c88d0770",
    "term_id": "1104",
    "term_name": "Spring 2010",
    "instructors": [
      "Benedek Valko"
    ],
    "a": 14,
    "ab": 3,
    "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": 18,
    "source_aliases": [
      "MATH 635"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 635",
    "course_uid": "course_34ef395682f16208c88d0770",
    "term_id": "1124",
    "term_name": "Spring 2012",
    "instructors": [
      "David Anderson"
    ],
    "a": 13,
    "ab": 5,
    "b": 3,
    "bc": 0,
    "c": 0,
    "d": 0,
    "f": 0,
    "satisfactory": 1,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 22,
    "source_aliases": [
      "MATH 635"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 635",
    "course_uid": "course_34ef395682f16208c88d0770",
    "term_id": "1144",
    "term_name": "Spring 2014",
    "instructors": [
      "Timo Seppalainen"
    ],
    "a": 13,
    "ab": 3,
    "b": 8,
    "bc": 1,
    "c": 2,
    "d": 0,
    "f": 0,
    "satisfactory": 0,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 1,
    "not_reported": 0,
    "other": 0,
    "total": 28,
    "source_aliases": [
      "MATH 635"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 635",
    "course_uid": "course_34ef395682f16208c88d0770",
    "term_id": "1164",
    "term_name": "Spring 2016",
    "instructors": [
      "JUN YIN"
    ],
    "a": 5,
    "ab": 3,
    "b": 4,
    "bc": 0,
    "c": 2,
    "d": 1,
    "f": 0,
    "satisfactory": 0,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 15,
    "source_aliases": [
      "MATH 635"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 635",
    "course_uid": "course_34ef395682f16208c88d0770",
    "term_id": "1184",
    "term_name": "Spring 2018",
    "instructors": [
      "WAI TONG FAN"
    ],
    "a": 13,
    "ab": 4,
    "b": 3,
    "bc": 1,
    "c": 0,
    "d": 0,
    "f": 0,
    "satisfactory": 1,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 22,
    "source_aliases": [
      "MATH 635"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 635",
    "course_uid": "course_34ef395682f16208c88d0770",
    "term_id": "1204",
    "term_name": "Spring 2020",
    "instructors": [
      "Hao Shen"
    ],
    "a": 15,
    "ab": 7,
    "b": 3,
    "bc": 0,
    "c": 0,
    "d": 1,
    "f": 0,
    "satisfactory": 7,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 33,
    "source_aliases": [
      "MATH 635"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 635",
    "course_uid": "course_34ef395682f16208c88d0770",
    "term_id": "1224",
    "term_name": "Spring 2022",
    "instructors": [
      "Hao Shen"
    ],
    "a": 15,
    "ab": 3,
    "b": 12,
    "bc": 0,
    "c": 2,
    "d": 1,
    "f": 0,
    "satisfactory": 2,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 35,
    "source_aliases": [
      "MATH 635"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 635",
    "course_uid": "course_34ef395682f16208c88d0770",
    "term_id": "1244",
    "term_name": "Spring 2024",
    "instructors": [
      "Hao Shen"
    ],
    "a": 13,
    "ab": 1,
    "b": 4,
    "bc": 0,
    "c": 3,
    "d": 0,
    "f": 1,
    "satisfactory": 1,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 1,
    "other": 0,
    "total": 24,
    "source_aliases": [
      "MATH 635"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 635",
    "course_uid": "course_34ef395682f16208c88d0770",
    "term_id": "1264",
    "term_name": "Spring 2026",
    "instructors": [
      "Hao Shen"
    ],
    "a": 18,
    "ab": 5,
    "b": 2,
    "bc": 1,
    "c": 1,
    "d": 0,
    "f": 0,
    "satisfactory": 2,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 29,
    "source_aliases": [
      "MATH 635"
    ]
  }
]
```

### statistics

#### gpa

3.536

#### graded

225

#### counts

* 124
* 40
* 43
* 3
* 10
* 3
* 2

### grade conflicts

None recorded.

### evidence

#### history

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_34ef395682f16208c88d0770-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_34ef395682f16208c88d0770-0.json)

#### traces

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_34ef395682f16208c88d0770-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_34ef395682f16208c88d0770-0.json)

#### reviews

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course\_34ef395682f16208c88d0770-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course_34ef395682f16208c88d0770-0.json)

#### results

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_34ef395682f16208c88d0770-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_34ef395682f16208c88d0770-0.json)

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

## context

### all

#### term



#### gpa

3.5355555555555553

#### count

225

#### university

##### size

3636

##### gpa Percentile

30

##### count Percentile

68

##### median Count

120.5

##### 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 | 295   | false   |
| 3.2–3.6 | 1030  | true    |
| 3.6–4.0 | 2299  | false   |

#### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 93,
      "gpaPercentile": 52,
      "countPercentile": 65,
      "medianCount": 149,
      "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": 5,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 25,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 21,
          "current": true
        },
        {
          "range": "3.6–4.0",
          "count": 42,
          "current": false
        }
      ]
    }
  }
]
```

### terms

#### 1074

##### term

1074

##### gpa

3.3333333333333335

##### count

15

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1104

##### term

1104

##### gpa

3.861111111111111

##### count

18

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1124

##### term

1124

##### gpa

3.738095238095238

##### count

21

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1144

##### term

1144

##### gpa

3.4444444444444446

##### count

27

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1164

##### term

1164

##### gpa

3.1666666666666665

##### count

15

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1184

##### term

1184

##### gpa

3.6904761904761907

##### count

21

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1204

##### term

1204

##### gpa

3.6346153846153846

##### count

26

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1224

##### term

1224

##### gpa

3.378787878787879

##### count

33

##### university

###### size

1171

###### gpa Percentile

28

###### count Percentile

9

###### median Count

64

###### 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 | 3     | false   |
| 2.4–2.8 | 21    | false   |
| 2.8–3.2 | 173   | false   |
| 3.2–3.6 | 358   | true    |
| 3.6–4.0 | 616   | false   |

##### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 34,
      "gpaPercentile": 79,
      "countPercentile": 3,
      "medianCount": 87.5,
      "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": 2,
          "current": false
        },
        {
          "range": "2.4–2.8",
          "count": 4,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 12,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 12,
          "current": true
        },
        {
          "range": "3.6–4.0",
          "count": 4,
          "current": false
        }
      ]
    }
  }
]
```

#### 1244

##### term

1244

##### gpa

3.340909090909091

##### count

22

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1264

##### term

1264

##### gpa

3.7037037037037037

##### count

27

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

### benchmarks

#### all

##### school

###### size

3636

###### gpa

3.655101919875121

###### top Share

81.60501306643062

###### count

120.5

##### MATH

###### size

93

###### gpa

3.4660056669689197

###### top Share

70.64863927393316

###### count

149

#### 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

##### 1104

###### school

###### size

793

###### gpa

3.384661458923085

###### top Share

64.6614752434143

###### count

66

###### MATH

###### size

23

###### gpa

2.9531575824731964

###### top Share

43.549837152646596

###### count

98

##### 1124

###### school

###### size

821

###### gpa

3.406589342026613

###### top Share

66.35774230127205

###### count

67

###### MATH

###### size

28

###### gpa

2.9109864595893504

###### top Share

42.40580272314707

###### count

75

##### 1144

###### school

###### size

878

###### gpa

3.4092443327803017

###### top Share

65.95978235963416

###### count

64

###### MATH

###### size

30

###### gpa

2.926152797086596

###### top Share

42.17363619414386

###### count

79

##### 1164

###### school

###### size

965

###### gpa

3.46491230798535

###### top Share

69.92376287143657

###### count

68

###### MATH

###### size

32

###### gpa

2.995223360849456

###### top Share

46.38098813836469

###### count

83

##### 1184

###### school

###### size

1010

###### gpa

3.47925290354517

###### top Share

70.86270937115944

###### count

68

###### MATH

###### size

36

###### gpa

3.0650838986714333

###### top Share

47.42689290604571

###### count

83.5

##### 1204

###### school

###### size

1012

###### gpa

3.703747431523761

###### top Share

84.59811226304916

###### count

65.5

###### MATH

###### size

29

###### gpa

3.478717830475146

###### top Share

69.61236805388549

###### count

83

##### 1224

###### school

###### size

1171

###### gpa

3.5627882428500937

###### top Share

76.37271640560496

###### count

64

###### MATH

###### size

34

###### gpa

3.1555898753466907

###### top Share

53.444319815085976

###### count

87.5

##### 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

##### 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_a3ba606a773db62292d9f2ac",
    "name": "HAO SHEN",
    "count": 108,
    "terms": [
      {
        "term": "1204",
        "count": 26,
        "sections": 1,
        "gpa": 3.6346153846153846
      },
      {
        "term": "1224",
        "count": 33,
        "sections": 1,
        "gpa": 3.378787878787879
      },
      {
        "term": "1244",
        "count": 22,
        "sections": 1,
        "gpa": 3.340909090909091
      },
      {
        "term": "1264",
        "count": 27,
        "sections": 1,
        "gpa": 3.7037037037037037
      }
    ]
  },
  {
    "uid": "instructor_bec15c77aa953cbac45042f2",
    "name": "TIMO SEPPALAINEN",
    "count": 27,
    "terms": [
      {
        "term": "1144",
        "count": 27,
        "sections": 1,
        "gpa": 3.4444444444444446
      }
    ]
  },
  {
    "uid": "instructor_5088fbe0824eddc6e8e0f351",
    "name": "WAI TONG FAN",
    "count": 21,
    "terms": [
      {
        "term": "1184",
        "count": 21,
        "sections": 1,
        "gpa": 3.6904761904761907
      }
    ]
  },
  {
    "uid": "instructor_74c5f2722d98d13de18c1d20",
    "name": "DAVID ANDERSON",
    "count": 21,
    "terms": [
      {
        "term": "1124",
        "count": 21,
        "sections": 1,
        "gpa": 3.738095238095238
      }
    ]
  },
  {
    "uid": "instructor_cda4aae4567f70b662d00163",
    "name": "BENEDEK VALKO",
    "count": 18,
    "terms": [
      {
        "term": "1104",
        "count": 18,
        "sections": 1,
        "gpa": 3.861111111111111
      }
    ]
  },
  {
    "uid": "instructor_0a9a7c5c9ed52646788c2132",
    "name": "JUN YIN",
    "count": 15,
    "terms": [
      {
        "term": "1164",
        "count": 15,
        "sections": 1,
        "gpa": 3.1666666666666665
      }
    ]
  },
  {
    "uid": "instructor_0eef5fd9bbc2212e9f6abe3b",
    "name": "THOMAS G. KURTZ",
    "count": 15,
    "terms": [
      {
        "term": "1074",
        "count": 15,
        "sections": 1,
        "gpa": 3.3333333333333335
      }
    ]
  }
]
```

## following

None recorded.
