# MATH 616: Data-driven Dynamical Systems, Stochastic Modeling and Prediction | UW–Madison

[View on UW Courses](https://uwcourses.com/courses/MATH_616)

## Dataset

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

### repository

twangodev/uwcourses

### schema version

6

### importer version

7

### projection id

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### 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

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### term

1272

### departments

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| 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    |
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| 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

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### course id

MATH 616

### course uid

course\_2d244e0d230263518e578140

### catalog version id

1061ee60bc95f0ea74b48b5921cc2d62e078adb90e2bccbf5ef4fa57ae15b9a3

### course number

616

### subjects

* MATH

### title

DATA-DRIVEN DYNAMICAL SYSTEMS, STOCHASTIC MODELING AND PREDICTION

### description

An introduction to data-driven dynamical systems, including mathematical theory, methodology, numerical algorithms, applications and the use of a programming language to solve related coding problems. Topics include stochastic toolkits for dynamical systems and data science, linear Gaussian processes, nonlinear stochastic systems, elementary stochastic differential equations, data assimilation, parameter estimation, forecasting and prediction.

### requirements text

(MATH 320,340,341,345, or375) and (STAT/​MATH  309,431,STAT 311, orMATH 531) and (MATH 322,341,375,421, or467), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate)

### credit offering ids

None recorded.

### llm job id

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### llm output id

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### llm model

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

### llm model revision

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### llm task version

14

### llm search status

valid

### llm summary

Introduction to data-driven dynamical systems, stochastic modeling, and prediction using numerical algorithms and programming.

### llm topics

* Stochastic toolkits for dynamical systems and data science
* Linear Gaussian processes
* Nonlinear stochastic systems
* Elementary stochastic differential equations
* Data assimilation
* Parameter estimation
* Forecasting and prediction

### llm skills

* Programming for data-driven systems
* Numerical algorithms for dynamical systems
* Stochastic toolkits for data science
* Data assimilation and prediction

### llm assumed background

* Linear algebra and differential equations
* Probability and mathematical statistics
* Programming in Python

### llm search phrases

* data-driven dynamical systems
* stochastic modeling
* data assimilation
* parameter estimation
* linear Gaussian processes
* nonlinear stochastic systems
* stochastic differential equations
* forecasting and prediction
* numerical algorithms
* data science applications

### llm requirements status

valid

### llm student summary status

valid

### llm experience status

valid

### catalog variants

None recorded.

### student summary

#### context hash

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#### course id

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#### current instructors

None recorded.

#### difficulty workload

Historical reviews of Samuel Stechmann: The course is rated as having low difficulty, with a difficulty rating of 2.

```json
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#### errors

None recorded.

#### historical context

Historical reviews of Samuel Stechmann: Samuel Stechmann is described as an awesome professor who delivers funny, clear, and engaging lectures. Reviewers strongly recommend taking a class with him if the opportunity arises.

```json
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#### offered

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#### profile hash

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#### quick take

Historical reviews of Samuel Stechmann: Samuel Stechmann delivers funny, clear, and engaging lectures, making his course highly recommended for those who have the opportunity to take it with him.

```json
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```

Recent recorded grades — Fall 2024: 3.57 GPA, 75.7% A/AB (n=37 letter grades); Spring 2026: 4.00 GPA, 100.0% A/AB (n=40 letter grades).

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#### student experience

Historical reviews of Samuel Stechmann: Students find the lectures engaging and clear, describing the professor as funny and highly effective.

```json
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#### task hash

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#### teaching history

SAMUEL STECHMANN is recorded teaching in Fall 2024. Recorded history may be incomplete and does not establish a future schedule.

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#### term id

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#### term name

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#### version

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```

#### notes

* Fixed missing node references and updated course evidence to exact source substrings.

#### root

n0

#### status

parsed

### instructors

None recorded.

### offerings

None recorded.

### sections

None recorded.

### grade instructors

```json
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          "difficulty_count": 4
        },
        "course_0002a781bc9543f3a2ac1a94": {
          "review_count": 2,
          "quality": 4.5,
          "difficulty": 3.5,
          "quality_count": 2,
          "difficulty_count": 2
        },
        "course_dcdb624e3fb8cbaf9a557ab9": {
          "review_count": 3,
          "quality": 4,
          "difficulty": 3.33,
          "quality_count": 3,
          "difficulty_count": 3
        },
        "course_346ab4e00def5d21d922d818": {
          "review_count": 1,
          "quality": 5,
          "difficulty": 1,
          "quality_count": 1,
          "difficulty_count": 1
        }
      },
      "bayesian_quality": 3.8483081504104293,
      "prior_mean": 3.6596857835465957,
      "prior_weight": 20
    },
    "grade_statistics": {
      "gpa": 2.978,
      "graded": 1527,
      "counts": [
        490,
        177,
        383,
        117,
        213,
        100,
        47
      ],
      "sections": 53
    },
    "instructor_url": "/instructors/SAMUEL_STECHMANN--instructor_e8033b131444ac21313c075f"
  },
  {
    "instructor_uid": "instructor_1227fa1f8db520a460645e3f",
    "source": "madgrades",
    "source_instructor_id": "4891217",
    "identity_basis": "source_id",
    "identity_status": "source_identified",
    "name": "NAN CHEN",
    "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": 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
    },
    "grade_statistics": {
      "gpa": 3.633,
      "graded": 654,
      "counts": [
        452,
        76,
        58,
        32,
        19,
        10,
        7
      ],
      "sections": 32
    },
    "instructor_url": "/instructors/NAN_CHEN--instructor_1227fa1f8db520a460645e3f"
  }
]
```

### grades

```json
[
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 616",
    "course_uid": "course_2d244e0d230263518e578140",
    "term_id": "1252",
    "term_name": "Fall 2024",
    "instructors": [
      "SAMUEL STECHMANN"
    ],
    "a": 15,
    "ab": 13,
    "b": 8,
    "bc": 1,
    "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": 37,
    "source_aliases": [
      "MATH 616"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 616",
    "course_uid": "course_2d244e0d230263518e578140",
    "term_id": "1264",
    "term_name": "Spring 2026",
    "instructors": [
      "Nan Chen"
    ],
    "a": 40,
    "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": 40,
    "source_aliases": [
      "MATH 616"
    ]
  }
]
```

### statistics

#### gpa

3.792

#### graded

77

#### counts

* 55
* 13
* 8
* 1
* 0
* 0
* 0

### grade conflicts

None recorded.

### evidence

#### history

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_2d244e0d230263518e578140-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_2d244e0d230263518e578140-0.json)

#### traces

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_2d244e0d230263518e578140-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_2d244e0d230263518e578140-0.json)

#### reviews

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course\_2d244e0d230263518e578140-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course_2d244e0d230263518e578140-0.json)

#### results

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_2d244e0d230263518e578140-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_2d244e0d230263518e578140-0.json)

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

## context

### all

#### term



#### gpa

3.792207792207792

#### count

77

#### university

##### size

2124

##### gpa Percentile

60

##### count Percentile

52

##### median Count

72

##### 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 | 16    | false   |
| 2.8–3.2 | 156   | false   |
| 3.2–3.6 | 599   | false   |
| 3.6–4.0 | 1353  | true    |

#### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 55,
      "gpaPercentile": 93,
      "countPercentile": 41,
      "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

3.5675675675675675

##### count

37

##### university

###### size

1333

###### gpa Percentile

39

###### count Percentile

15

###### median Count

69

###### 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 | 14    | false   |
| 2.8–3.2 | 115   | false   |
| 3.2–3.6 | 431   | true    |
| 3.6–4.0 | 773   | false   |

##### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 43,
      "gpaPercentile": 95,
      "countPercentile": 12,
      "medianCount": 74,
      "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": 20,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 16,
          "current": true
        },
        {
          "range": "3.6–4.0",
          "count": 2,
          "current": false
        }
      ]
    }
  }
]
```

#### 1264

##### term

1264

##### gpa

4

##### count

40

##### university

###### size

1283

###### gpa Percentile

95

###### count Percentile

21

###### median Count

66

###### 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 | 20    | false   |
| 2.8–3.2 | 130   | false   |
| 3.2–3.6 | 343   | false   |
| 3.6–4.0 | 789   | true    |

##### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 42,
      "gpaPercentile": 100,
      "countPercentile": 17,
      "medianCount": 80,
      "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": 1,
          "current": false
        },
        {
          "range": "2.4–2.8",
          "count": 7,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 17,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 11,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 6,
          "current": true
        }
      ]
    }
  }
]
```

### 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_1227fa1f8db520a460645e3f",
    "name": "NAN CHEN",
    "count": 40,
    "terms": [
      {
        "term": "1264",
        "count": 40,
        "sections": 1,
        "gpa": 4
      }
    ]
  },
  {
    "uid": "instructor_e8033b131444ac21313c075f",
    "name": "SAMUEL STECHMANN",
    "count": 37,
    "terms": [
      {
        "term": "1252",
        "count": 37,
        "sections": 1,
        "gpa": 3.5675675675675675
      }
    ]
  }
]
```

## following

None recorded.
