# MATH/STAT 734: Theory of Probability II | UW–Madison

[View on UW Courses](https://uwcourses.com/courses/MATH_STAT_734)

## Dataset

### revision

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## 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/STAT 734

### course uid

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### catalog version id

064473efc0774593b61b2d8ecdbc597b1f027f6af43cb9c0c7641678d6742c75

### course number

734

### subjects

* MATH
* STAT

### title

THEORY OF PROBABILITY II

### description

Possible topics include martingales, weak convergence of measures, introduction to Brownian motion.

### requirements text

Graduate/professional standing

### credit offering ids

None recorded.

### llm job id

enrich-f516c4d3e82cfe326b4f5f54

### llm output id

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### llm model

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### llm model revision

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### llm task version

14

### llm search status

valid

### llm summary

Theory of Probability II covers advanced topics including martingales, weak convergence of measures, and Brownian motion.

### llm topics

* Martingales
* Weak convergence of measures
* Brownian motion

### llm skills

* Understanding martingales and weak convergence of measures.
* Introduction to Brownian motion.

### llm assumed background

* Assumes completion of Theory of Probability I or equivalent graduate-level probability foundation.

### llm search phrases

* martingales
* weak convergence of measures
* Brownian motion
* advanced probability theory
* graduate probability

### 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

MATH/STAT 734

#### current instructors

None recorded.

#### difficulty workload

Historical reviews of Benedek Valko: Homework is reported as too easy and infrequent, with one reviewer wishing for greater difficulty and more frequent weekly assignments.

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```

#### errors

None recorded.

#### historical context

Historical reviews of Benedek Valko: Benedek Valko is described as an amazing and highly recommended professor who provides clear explanations and discusses interesting materials beyond the textbook. However, one reviewer notes that he skips careful treatments found in standard texts like Durrett and assigns homework that is too easy and infrequent.

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#### quick take

Historical reviews of Benedek Valko: Benedek Valko is highly recommended by students, with reviews describing him as an amazing and favorite professor who provides clear explanations.

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Recent recorded grades — Spring 2024: 3.66 GPA, 73.7% A/AB (n=38 letter grades); Spring 2025: 3.96 GPA, 96.4% A/AB (n=28 letter grades); Spring 2026: 3.45 GPA, 84.2% A/AB (n=19 letter grades).

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#### student experience

Historical reviews of Benedek Valko: Students appreciate interesting materials outside textbooks, though some find the treatment of measure-theoretic concepts insufficient compared to standard texts like Durrett.

```json
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```

#### task hash

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#### teaching history

BENEDEK VALKO is recorded teaching in Spring 2014, Spring 2026. Recorded history may be incomplete and does not establish a future schedule.

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#### term id

1272

#### term name

2026 Fall

#### version

2

### requirements

#### nodes

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#### notes

None recorded.

#### root

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#### status

parsed

### instructors

None recorded.

### offerings

None recorded.

### sections

None recorded.

### grade instructors

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```

### grades

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]
```

### statistics

#### gpa

3.704

#### graded

253

#### counts

* 163
* 45
* 37
* 5
* 2
* 0
* 1

### grade conflicts

None recorded.

### evidence

#### history

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_436b4b4087325a19ccd87bd6-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_436b4b4087325a19ccd87bd6-0.json)

#### traces

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_436b4b4087325a19ccd87bd6-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_436b4b4087325a19ccd87bd6-0.json)

#### reviews

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course\_436b4b4087325a19ccd87bd6-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course_436b4b4087325a19ccd87bd6-0.json)

#### results

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_436b4b4087325a19ccd87bd6-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_436b4b4087325a19ccd87bd6-0.json)

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

## context

### all

#### term



#### gpa

3.7035573122529644

#### count

253

#### university

##### size

3857

##### gpa Percentile

46

##### count Percentile

65

##### median Count

147

##### 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 | 11    | false   |
| 2.8–3.2 | 261   | false   |
| 3.2–3.6 | 1029  | false   |
| 3.6–4.0 | 2556  | true    |

#### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 101,
      "gpaPercentile": 60,
      "countPercentile": 59,
      "medianCount": 173,
      "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": 26,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 22,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 47,
          "current": true
        }
      ]
    }
  },
  {
    "subject": "STAT",
    "comparison": {
      "size": 61,
      "gpaPercentile": 58,
      "countPercentile": 50,
      "medianCount": 253,
      "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": 0,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 8,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 22,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 31,
          "current": true
        }
      ]
    }
  }
]
```

### terms

#### 1144

##### term

1144

##### gpa

3.4

##### count

10

##### departments

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

#### 1154

##### term

1154

##### gpa

3.423076923076923

##### count

13

##### departments

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

#### 1164

##### term

1164

##### gpa

3.7

##### count

10

##### departments

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

#### 1174

##### term

1174

##### gpa

3.629032258064516

##### count

31

##### university

###### size

955

###### gpa Percentile

63

###### count Percentile

3

###### 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 | 1     | false   |
| 2.4–2.8 | 29    | false   |
| 2.8–3.2 | 224   | false   |
| 3.2–3.6 | 332   | false   |
| 3.6–4.0 | 369   | true    |

##### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 32,
      "gpaPercentile": 94,
      "countPercentile": 0,
      "medianCount": 89,
      "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": 9,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 15,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 5,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 3,
          "current": true
        }
      ]
    }
  },
  {
    "subject": "STAT",
    "comparison": {
      "size": 22,
      "gpaPercentile": 81,
      "countPercentile": 5,
      "medianCount": 71.5,
      "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": 0,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 8,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 9,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 5,
          "current": true
        }
      ]
    }
  }
]
```

#### 1184

##### term

1184

##### gpa

4

##### count

34

##### university

###### size

1010

###### gpa Percentile

96

###### count Percentile

7

###### median Count

68

###### 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 | 26    | false   |
| 2.8–3.2 | 210   | false   |
| 3.2–3.6 | 355   | false   |
| 3.6–4.0 | 418   | true    |

##### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 36,
      "gpaPercentile": 100,
      "countPercentile": 0,
      "medianCount": 83.5,
      "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": 1,
          "current": false
        },
        {
          "range": "2.4–2.8",
          "count": 7,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 18,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 7,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 3,
          "current": true
        }
      ]
    }
  },
  {
    "subject": "STAT",
    "comparison": {
      "size": 25,
      "gpaPercentile": 96,
      "countPercentile": 4,
      "medianCount": 70,
      "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": 0,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 6,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 11,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 8,
          "current": true
        }
      ]
    }
  }
]
```

#### 1194

##### term

1194

##### gpa

3.8703703703703702

##### count

27

##### departments

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

#### 1204

##### term

1204

##### gpa

3.7

##### count

10

##### departments

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

#### 1224

##### term

1224

##### gpa

3.4722222222222223

##### count

18

##### departments

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

#### 1234

##### term

1234

##### gpa

3.566666666666667

##### count

15

##### departments

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

#### 1244

##### term

1244

##### gpa

3.6578947368421053

##### count

38

##### university

###### size

1241

###### gpa Percentile

51

###### count Percentile

17

###### 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": 86,
      "countPercentile": 14,
      "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
        }
      ]
    }
  },
  {
    "subject": "STAT",
    "comparison": {
      "size": 29,
      "gpaPercentile": 82,
      "countPercentile": 14,
      "medianCount": 62,
      "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": 0,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 8,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 13,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 8,
          "current": true
        }
      ]
    }
  }
]
```

#### 1254

##### term

1254

##### gpa

3.9642857142857144

##### count

28

##### departments

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

#### 1264

##### term

1264

##### gpa

3.4473684210526314

##### count

19

##### departments

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

### benchmarks

#### all

##### school

###### size

3857

###### gpa

3.6765573337568056

###### top Share

82.9558451655162

###### count

147

##### MATH

###### size

101

###### gpa

3.496341535514786

###### top Share

72.36232771746849

###### count

173

##### STAT

###### size

61

###### gpa

3.5806627676835294

###### top Share

77.80958779672933

###### count

253

#### terms

##### 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

###### STAT

###### size

14

###### gpa

3.0970281238579784

###### top Share

51.741770775379614

###### count

74.5

##### 1154

###### school

###### size

935

###### gpa

3.4282378385810093

###### top Share

67.66674668721691

###### count

63

###### MATH

###### size

33

###### gpa

2.9834698949629033

###### top Share

46.71989715257013

###### count

69

###### STAT

###### size

19

###### gpa

3.247335845906281

###### top Share

58.329434774225824

###### count

57

##### 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

###### STAT

###### size

21

###### gpa

3.317795716655057

###### top Share

62.84642273068802

###### count

69

##### 1174

###### school

###### size

955

###### gpa

3.4597947384071412

###### top Share

69.5290038366363

###### count

69

###### MATH

###### size

32

###### gpa

2.992971960864239

###### top Share

44.393513280464695

###### count

89

###### STAT

###### size

22

###### gpa

3.3391231320477925

###### top Share

62.80825113292103

###### count

71.5

##### 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

###### STAT

###### size

25

###### gpa

3.460210558661105

###### top Share

70.42953406269322

###### count

70

##### 1194

###### school

###### size

1040

###### gpa

3.4906527436719808

###### top Share

71.74728845515045

###### count

67

###### MATH

###### size

38

###### gpa

3.133406260873163

###### top Share

53.17595010634325

###### count

71.5

###### STAT

###### size

23

###### gpa

3.3818127863152334

###### top Share

66.9295898310719

###### count

79

##### 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

###### STAT

###### size

27

###### gpa

3.6537351147420534

###### top Share

80.87794592686507

###### count

56

##### 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

###### STAT

###### size

27

###### gpa

3.4650681869904103

###### top Share

69.88606041738046

###### count

74

##### 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

###### STAT

###### size

25

###### gpa

3.396227416481204

###### top Share

66.8429997070879

###### 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

###### STAT

###### size

29

###### gpa

3.390846810323202

###### top Share

64.2629736611174

###### count

62

##### 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

###### STAT

###### size

28

###### gpa

3.4752654121860003

###### top Share

68.35873780152826

###### count

70

##### 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

###### STAT

###### size

26

###### gpa

3.343399816676682

###### top Share

63.23102425546245

###### count

66

## instructor Trends

```json
[
  {
    "uid": "instructor_bec15c77aa953cbac45042f2",
    "name": "TIMO SEPPALAINEN",
    "count": 68,
    "terms": [
      {
        "term": "1154",
        "count": 13,
        "sections": 1,
        "gpa": 3.423076923076923
      },
      {
        "term": "1194",
        "count": 27,
        "sections": 1,
        "gpa": 3.8703703703703702
      },
      {
        "term": "1254",
        "count": 28,
        "sections": 1,
        "gpa": 3.9642857142857144
      }
    ]
  },
  {
    "uid": "instructor_11da40ed2a2bb6d06bf52104",
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]
```

## following

None recorded.
