# MATH 761: Differentiable Manifolds | UW–Madison

[View on UW Courses](https://uwcourses.com/courses/MATH_761)

## Dataset

### revision

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### repository

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### built at

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### current instructors

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### term

1272

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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 761

### course uid

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### catalog version id

bda12a7e64aa76920c7f5efbafbdf157397d42dfdae6f131be9268217ac11b11

### course number

761

### subjects

* MATH

### title

DIFFERENTIABLE MANIFOLDS

### description

Differentiable manifolds, vector bundles, implicit function theorem, submersions and immersions, vector fields and flows, foliations and Frobenius theorem, differential forms and exterior calculus, integration and Stokes' theorem, De Rham theory, Riemannian metrics. Familiarity with basic undergraduate analysis coursesMATH 521and522orMATH 621) is strongly recommended.

### requirements text

Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

### credits min

3

### credits max

3

### credit offering ids

* 1272:600:011758

### llm job 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

MATH 761 covers differentiable manifolds, vector bundles, differential forms, and Riemannian metrics.

### llm topics

* Differentiable manifolds and vector bundles
* Vector fields, flows, and foliations
* Differential forms and De Rham theory
* Riemannian metrics

### llm skills

* Study of differentiable manifolds, vector bundles, and differential forms.

### llm assumed background

* Basic undergraduate analysis courses (MATH 521, MATH 522, or MATH 621) are strongly recommended.

### llm search phrases

* differentiable manifolds course
* MATH 761 differential geometry
* graduate manifolds analysis

### 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

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          {
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        "text": "Sean Paul receives polarized feedback regarding his teaching organization and lecture style. One reviewer found his lectures unorganized and lacking notes, while another found them exciting and helpful for concentration. Review 2 notes his homework is difficult, while Review 1 finds exams easy."
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#### difficulty workload

Homework assignments are difficult and require significant time to solve step-by-step.

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#### errors

None recorded.

#### historical context

Historical reviews for Alex Waldron describe difficult lectures and harsh grading that diagnose student problems. One reviewer found the professor difficult to get along with.

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    {
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#### offered

true

#### profile hash

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#### quick take

Sean Paul's teaching style elicits polarized reactions, with students describing his lectures as either unorganized and unhelpful or exciting and engaging.

```json
{
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```

Recent recorded grades — Spring 2024: 3.96 GPA, 100.0% A/AB (n=24 letter grades); Fall 2024: 3.71 GPA, 85.7% A/AB (n=14 letter grades); Fall 2025: 3.69 GPA, 79.3% A/AB (n=29 letter grades).

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```

#### student experience

Students may find the lack of lecture notes and disorganized structure frustrating, leading to a perception that they learn little from the instruction.

```json
{
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      "type": "review"
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```

#### task hash

74fb0997943e888960bbc9e47db8c4fd12e4292d55c20509d8d89db6a9910f68

#### teaching history

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

```json
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      "term_id": "1252",
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}
```

SEAN PAUL is recorded teaching in Fall 2013, Spring 2019, Spring 2022. Recorded history may be incomplete and does not establish a future schedule.

```json
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#### term id

1272

#### term name

2026 Fall

#### version

2

### requirements

#### nodes

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#### notes

None recorded.

#### root

n2

#### status

parsed

### instructors

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    "term_id": "1182",
    "term_name": "Fall 2017",
    "instructors": [
      "LU WANG"
    ],
    "a": 12,
    "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": 12,
    "source_aliases": [
      "MATH 761"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 761",
    "course_uid": "course_963da18c52ee0091bf4904b6",
    "term_id": "1194",
    "term_name": "Spring 2019",
    "instructors": [
      "Sean Paul"
    ],
    "a": 15,
    "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": 15,
    "source_aliases": [
      "MATH 761"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 761",
    "course_uid": "course_963da18c52ee0091bf4904b6",
    "term_id": "1204",
    "term_name": "Spring 2020",
    "instructors": [
      "GAO CHEN"
    ],
    "a": 12,
    "ab": 1,
    "b": 0,
    "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": 14,
    "source_aliases": [
      "MATH 761"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 761",
    "course_uid": "course_963da18c52ee0091bf4904b6",
    "term_id": "1224",
    "term_name": "Spring 2022",
    "instructors": [
      "Sean Paul"
    ],
    "a": 12,
    "ab": 0,
    "b": 0,
    "bc": 0,
    "c": 1,
    "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": 14,
    "source_aliases": [
      "MATH 761"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 761",
    "course_uid": "course_963da18c52ee0091bf4904b6",
    "term_id": "1234",
    "term_name": "Spring 2023",
    "instructors": [
      "Andrew Zimmer"
    ],
    "a": 7,
    "ab": 8,
    "b": 8,
    "bc": 0,
    "c": 3,
    "d": 0,
    "f": 0,
    "satisfactory": 0,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 1,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 27,
    "source_aliases": [
      "MATH 761"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 761",
    "course_uid": "course_963da18c52ee0091bf4904b6",
    "term_id": "1244",
    "term_name": "Spring 2024",
    "instructors": [
      "Chenxi Wu"
    ],
    "a": 22,
    "ab": 2,
    "b": 0,
    "bc": 0,
    "c": 0,
    "d": 0,
    "f": 0,
    "satisfactory": 0,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 2,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 26,
    "source_aliases": [
      "MATH 761"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 761",
    "course_uid": "course_963da18c52ee0091bf4904b6",
    "term_id": "1252",
    "term_name": "Fall 2024",
    "instructors": [
      "Alex Waldron"
    ],
    "a": 8,
    "ab": 4,
    "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": 14,
    "source_aliases": [
      "MATH 761"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 761",
    "course_uid": "course_963da18c52ee0091bf4904b6",
    "term_id": "1262",
    "term_name": "Fall 2025",
    "instructors": [
      "Tullia Dymarz"
    ],
    "a": 17,
    "ab": 6,
    "b": 6,
    "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": 29,
    "source_aliases": [
      "MATH 761"
    ]
  }
]
```

### statistics

#### gpa

3.805

#### graded

277

#### counts

* 220
* 25
* 24
* 1
* 6
* 0
* 1

### grade conflicts

None recorded.

### evidence

#### history

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_963da18c52ee0091bf4904b6-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_963da18c52ee0091bf4904b6-0.json)

#### traces

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_963da18c52ee0091bf4904b6-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_963da18c52ee0091bf4904b6-0.json)

#### reviews

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course\_963da18c52ee0091bf4904b6-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course_963da18c52ee0091bf4904b6-0.json)

#### meetings

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/meetings/course\_963da18c52ee0091bf4904b6-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/meetings/course_963da18c52ee0091bf4904b6-0.json)

#### results

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_963da18c52ee0091bf4904b6-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_963da18c52ee0091bf4904b6-0.json)

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

## context

### all

#### term



#### gpa

3.8050541516245486

#### count

277

#### university

##### size

4829

##### gpa Percentile

62

##### count Percentile

67

##### median Count

155

##### 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 | 358   | false   |
| 3.2–3.6 | 1347  | false   |
| 3.6–4.0 | 3110  | true    |

#### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 119,
      "gpaPercentile": 64,
      "countPercentile": 63,
      "medianCount": 165,
      "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": 31,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 25,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 60,
          "current": true
        }
      ]
    }
  }
]
```

### terms

#### 1072

##### term

1072

##### gpa

3.6923076923076925

##### count

13

##### departments

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

#### 1082

##### term

1082

##### gpa

4

##### count

12

##### departments

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

#### 1092

##### term

1092

##### gpa

3.8666666666666667

##### count

15

##### departments

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

#### 1102

##### term

1102

##### gpa

4

##### count

6

##### departments

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

#### 1112

##### term

1112

##### gpa

3.3125

##### count

8

##### departments

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

#### 1122

##### term

1122

##### gpa

3.7777777777777777

##### count

9

##### departments

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

#### 1132

##### term

1132

##### gpa

4

##### count

14

##### departments

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

#### 1142

##### term

1142

##### gpa

4

##### count

13

##### departments

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

#### 1152

##### term

1152

##### gpa

3.6666666666666665

##### count

12

##### departments

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

#### 1162

##### term

1162

##### gpa

3.857142857142857

##### count

14

##### departments

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

#### 1172

##### term

1172

##### gpa

4

##### count

15

##### departments

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

#### 1182

##### term

1182

##### gpa

4

##### count

12

##### departments

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

#### 1194

##### term

1194

##### gpa

4

##### count

15

##### departments

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

#### 1204

##### term

1204

##### gpa

3.9615384615384617

##### count

13

##### departments

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

#### 1224

##### term

1224

##### gpa

3.8461538461538463

##### count

13

##### departments

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

#### 1234

##### term

1234

##### gpa

3.3076923076923075

##### count

26

##### departments

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

#### 1244

##### term

1244

##### gpa

3.9583333333333335

##### count

24

##### departments

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

#### 1252

##### term

1252

##### gpa

3.7142857142857144

##### count

14

##### departments

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

#### 1262

##### term

1262

##### gpa

3.689655172413793

##### count

29

##### departments

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

### benchmarks

#### all

##### school

###### size

4829

###### gpa

3.6622001412009633

###### top Share

81.95612036710932

###### count

155

##### MATH

###### size

119

###### gpa

3.5337333306520042

###### top Share

74.15454404009111

###### count

165

#### terms

##### 1072

###### school

###### size

723

###### gpa

3.344595727439471

###### top Share

62.012941427864526

###### count

67

###### MATH

###### size

21

###### gpa

2.878188611674867

###### top Share

40.4748751710427

###### count

115

##### 1082

###### school

###### size

723

###### gpa

3.3583896732335172

###### top Share

62.932746798940194

###### count

68

###### MATH

###### size

20

###### gpa

2.8603540012311925

###### top Share

39.28661748894661

###### count

122

##### 1092

###### school

###### size

732

###### gpa

3.374660709520374

###### top Share

63.690339324346596

###### count

70

###### MATH

###### size

22

###### gpa

2.8820162698417926

###### top Share

39.71597770466243

###### count

131

##### 1102

###### school

###### size

774

###### gpa

3.36712622366007

###### top Share

63.703228532165696

###### count

67

###### MATH

###### size

27

###### gpa

2.936619140855453

###### top Share

42.28372460948232

###### count

76

##### 1112

###### school

###### size

805

###### gpa

3.3737773184830386

###### top Share

63.91039244872789

###### count

66

###### MATH

###### size

26

###### gpa

2.9941347625171355

###### top Share

43.79682105650899

###### count

87

##### 1122

###### school

###### size

804

###### gpa

3.3737149752667013

###### top Share

63.65118790117902

###### count

70

###### MATH

###### size

27

###### gpa

2.898067749128924

###### top Share

42.09489165698714

###### count

103

##### 1132

###### school

###### size

851

###### gpa

3.391128778809763

###### top Share

64.69509437122704

###### count

66

###### MATH

###### size

25

###### gpa

2.9605395515107897

###### top Share

42.794601137643824

###### count

108

##### 1142

###### school

###### size

853

###### gpa

3.3941849959684913

###### top Share

65.28450334228523

###### count

67

###### MATH

###### size

31

###### gpa

3.009040780059457

###### top Share

45.87481076818359

###### count

77

##### 1152

###### school

###### size

918

###### gpa

3.408733538594633

###### top Share

66.06693005846735

###### count

65

###### MATH

###### size

34

###### gpa

3.0803080141506425

###### top Share

49.72677618758506

###### count

82

##### 1162

###### school

###### size

954

###### gpa

3.43726781345039

###### top Share

68.05645304987395

###### count

64.5

###### MATH

###### size

36

###### gpa

3.1059509777204544

###### top Share

50.071044743474

###### count

74.5

##### 1172

###### school

###### size

991

###### gpa

3.465129042641772

###### top Share

69.42600667567366

###### count

67

###### MATH

###### size

36

###### gpa

3.098601909983034

###### top Share

48.67573746500224

###### count

66

##### 1182

###### school

###### size

1025

###### gpa

3.474159360325319

###### top Share

70.34861441764347

###### count

69

###### MATH

###### size

36

###### gpa

3.0839531022443034

###### top Share

48.116975859522796

###### count

80

##### 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

##### 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

##### 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

##### 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

##### 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

##### 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_eb98a96c05ac474b321e9170",
    "name": "SEAN PAUL",
    "count": 41,
    "terms": [
      {
        "term": "1142",
        "count": 13,
        "sections": 1,
        "gpa": 4
      },
      {
        "term": "1194",
        "count": 15,
        "sections": 1,
        "gpa": 4
      },
      {
        "term": "1224",
        "count": 13,
        "sections": 1,
        "gpa": 3.8461538461538463
      }
    ]
  },
  {
    "uid": "instructor_b9a630b0e3b3db4a0fe1de98",
    "name": "GLORIA MARI-BEFFA",
    "count": 35,
    "terms": [
      {
        "term": "1102",
        "count": 6,
        "sections": 1,
        "gpa": 4
      },
      {
        "term": "1112",
        "count": 8,
        "sections": 1,
        "gpa": 3.3125
      },
      {
        "term": "1122",
        "count": 9,
        "sections": 1,
        "gpa": 3.7777777777777777
      },
      {
        "term": "1152",
        "count": 12,
        "sections": 1,
        "gpa": 3.6666666666666665
      }
    ]
  },
  {
    "uid": "instructor_bc7acc9f38e7d8108854c8c5",
    "name": "TULLIA DYMARZ",
    "count": 29,
    "terms": [
      {
        "term": "1262",
        "count": 29,
        "sections": 1,
        "gpa": 3.689655172413793
      }
    ]
  },
  {
    "uid": "instructor_180bf94a3d2f4343128d8704",
    "name": "JEFF VIACLOVSKY",
    "count": 28,
    "terms": [
      {
        "term": "1072",
        "count": 13,
        "sections": 1,
        "gpa": 3.6923076923076925
      },
      {
        "term": "1092",
        "count": 15,
        "sections": 1,
        "gpa": 3.8666666666666667
      }
    ]
  },
  {
    "uid": "instructor_c4bb9475d87ea8defd8f9a55",
    "name": "LU WANG",
    "count": 27,
    "terms": [
      {
        "term": "1172",
        "count": 15,
        "sections": 1,
        "gpa": 4
      },
      {
        "term": "1182",
        "count": 12,
        "sections": 1,
        "gpa": 4
      }
    ]
  },
  {
    "uid": "instructor_192e932c9d86d7d925e021f3",
    "name": "ANDREW ZIMMER",
    "count": 26,
    "terms": [
      {
        "term": "1234",
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    ]
  }
]
```

## following

None recorded.
