# MATH 717: Stochastic Computational Methods | UW–Madison

[View on UW Courses](https://uwcourses.com/courses/MATH_717)

## Dataset

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## course

### run id

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### semester

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### catalog version id

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### course number

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### subjects

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### title

STOCHASTIC COMPUTATIONAL METHODS

### description

Introduction to computational methods that use stochastic algorithms and/or methods that are applied to random or stochastic mathematical problems. The main emphasis will be placed on learning practical tools, while some aspects of theoretical foundations will also be covered (e.g., basic error analysis for numerical solution of stochastic differential equations (SDEs), and basic convergence of Monte Carlo methods). Topics include Monte Carlo methods, Bayesian inference and Bayesian sampling, simulation of Markov chains, numerical analysis for SDEs, data assimilation / state estimation, stochastic optimization methods and random sketching. Applications to science, engineering, finance, data science, and other practical problems also included.

### requirements text

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### llm summary

MATH 717 introduces computational methods using stochastic algorithms for random mathematical problems, covering Monte Carlo, Bayesian inference, and SDEs.

### llm topics

* Monte Carlo methods
* Bayesian inference and sampling
* Markov chain simulation
* Numerical analysis for Stochastic Differential Equations
* Data assimilation and state estimation
* Stochastic optimization and random sketching

### llm skills

* Application of practical computational tools
* Error analysis for numerical solutions of SDEs
* Analysis of Monte Carlo method convergence
* Simulation of Markov chains
* Data assimilation and state estimation
* Stochastic optimization and random sketching

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#### root

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          "quality": 3.17,
          "difficulty": 2.83,
          "quality_count": 6,
          "difficulty_count": 6
        },
        "course_f237678d9fac59631b4aa4ff": {
          "review_count": 6,
          "quality": 5,
          "difficulty": 3.5,
          "quality_count": 6,
          "difficulty_count": 6
        },
        "course_0002a781bc9543f3a2ac1a94": {
          "review_count": 16,
          "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"
  },
  {
    "instructor_uid": "instructor_eed27452237c073abcf30787",
    "source": "enrollment",
    "source_instructor_id": "nchen29",
    "identity_basis": "netid",
    "identity_status": "source_identified",
    "name": "Nan Chen",
    "email": "CHENNAN@MATH.WISC.EDU",
    "first_observed_at": "2026-09-07 15:55:43.033547+00:00",
    "last_observed_at": "2026-09-07 15:55:43.033547+00:00",
    "ratings": {
      "review_count": 29,
      "quality": 4.59,
      "difficulty": 3.1,
      "quality_count": 29,
      "difficulty_count": 29,
      "profile_id": "rmp:2402431",
      "source_url": "https://www.ratemyprofessors.com/professor/2402431",
      "match_basis": "exact_name",
      "observed_at": "2026-09-07 16:14:47.792861+00:00",
      "courses": {
        "course_6bc496e4640fd08f71e1b041": {
          "review_count": 3,
          "quality": 3.67,
          "difficulty": 3.67,
          "quality_count": 3,
          "difficulty_count": 3
        },
        "course_346ab4e00def5d21d922d818": {
          "review_count": 1,
          "quality": 5,
          "difficulty": 4,
          "quality_count": 1,
          "difficulty_count": 1
        },
        "course_8634dde81cc95f6c58014087": {
          "review_count": 21,
          "quality": 4.86,
          "difficulty": 2.95,
          "quality_count": 21,
          "difficulty_count": 21
        }
      },
      "bayesian_quality": 4.210279911651671,
      "prior_mean": 3.6596857835465957,
      "prior_weight": 20
    },
    "instructor_url": "/instructors/NAN_CHEN"
  }
]
```

### grades

```json
[
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 717",
    "course_uid": "course_6b1402df5d4cb88b5d36366c",
    "term_id": "1232",
    "term_name": "Fall 2022",
    "instructors": [
      "Nan Chen"
    ],
    "a": 18,
    "ab": 1,
    "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 717"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 717",
    "course_uid": "course_6b1402df5d4cb88b5d36366c",
    "term_id": "1244",
    "term_name": "Spring 2024",
    "instructors": [
      "Nan Chen"
    ],
    "a": 37,
    "ab": 1,
    "b": 2,
    "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": 40,
    "source_aliases": [
      "MATH 717"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 717",
    "course_uid": "course_6b1402df5d4cb88b5d36366c",
    "term_id": "1254",
    "term_name": "Spring 2025",
    "instructors": [
      "Qin Li"
    ],
    "a": 25,
    "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": 25,
    "source_aliases": [
      "MATH 717"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 717",
    "course_uid": "course_6b1402df5d4cb88b5d36366c",
    "term_id": "1262",
    "term_name": "Fall 2025",
    "instructors": [
      "Nan Chen"
    ],
    "a": 34,
    "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": 34,
    "source_aliases": [
      "MATH 717"
    ]
  }
]
```

### statistics

#### gpa

3.975

#### graded

118

#### counts

* 114
* 2
* 2
* 0
* 0
* 0
* 0

### grade conflicts

None recorded.

### evidence

#### history

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_6b1402df5d4cb88b5d36366c-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_6b1402df5d4cb88b5d36366c-0.json)

#### traces

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_6b1402df5d4cb88b5d36366c-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_6b1402df5d4cb88b5d36366c-0.json)

#### meetings

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/meetings/course\_6b1402df5d4cb88b5d36366c-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/meetings/course_6b1402df5d4cb88b5d36366c-0.json)

#### results

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_6b1402df5d4cb88b5d36366c-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_6b1402df5d4cb88b5d36366c-0.json)

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

## context

### all

#### term



#### gpa

3.9745762711864407

#### count

118

#### university

##### size

3107

##### gpa Percentile

89

##### count Percentile

61

##### median Count

83

##### 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 | 17    | false   |
| 2.8–3.2 | 198   | false   |
| 3.2–3.6 | 805   | false   |
| 3.6–4.0 | 2087  | true    |

#### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 86,
      "gpaPercentile": 89,
      "countPercentile": 62,
      "medianCount": 75.5,
      "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": 25,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 24,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 33,
          "current": true
        }
      ]
    }
  }
]
```

### terms

#### 1232

##### term

1232

##### gpa

3.973684210526316

##### count

19

##### departments

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

#### 1244

##### term

1244

##### gpa

3.9375

##### count

40

##### university

###### size

1241

###### gpa Percentile

87

###### count Percentile

22

###### 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": 95,
      "countPercentile": 24,
      "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

25

##### departments

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

#### 1262

##### term

1262

##### gpa

4

##### count

34

##### university

###### size

1320

###### gpa Percentile

95

###### count Percentile

8

###### 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": 98,
      "countPercentile": 12,
      "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

3107

###### gpa

3.6753731957792684

###### top Share

82.95049894654645

###### count

83

##### MATH

###### size

86

###### gpa

3.450161104669193

###### top Share

68.58299792804891

###### count

75.5

#### terms

##### 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

##### 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_1227fa1f8db520a460645e3f",
    "name": "NAN CHEN",
    "count": 93,
    "terms": [
      {
        "term": "1232",
        "count": 19,
        "sections": 1,
        "gpa": 3.973684210526316
      },
      {
        "term": "1244",
        "count": 40,
        "sections": 1,
        "gpa": 3.9375
      },
      {
        "term": "1262",
        "count": 34,
        "sections": 1,
        "gpa": 4
      }
    ]
  },
  {
    "uid": "instructor_6cee1ae6c2c6ae042c8870e4",
    "name": "QIN LI",
    "count": 25,
    "terms": [
      {
        "term": "1254",
        "count": 25,
        "sections": 1,
        "gpa": 4
      }
    ]
  }
]
```

## following

None recorded.
