# MATH 722: Complex Analysis | UW–Madison

[View on UW Courses](https://uwcourses.com/courses/MATH_722)

## Dataset

### revision

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### repository

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### term

1272

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## course

### run id

20260907T155543-ce3781c4

### semester

1272

### observed at

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### record version id

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### course id

MATH 722

### course uid

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### catalog version id

6d00fe2fff346435f74e707699194cfa662c31744e44d827569118c316741441

### course number

722

### subjects

* MATH

### title

COMPLEX ANALYSIS

### description

The basic theory of functions of one complex variable including Cauchy formula, singularities and residues, meromorphic functions, conformal mappings, harmonic functions, approximation and the nonhomogeneous d-bar equation. Requires knowledge of undergraduate analysis (e.g. the sequenceMATH 521and522).

### requirements text

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

### credit offering ids

None recorded.

### llm job id

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### llm output id

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### llm model revision

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### llm task version

14

### llm search status

valid

### llm summary

Complex Analysis covers the theory of functions of one complex variable, including Cauchy formula, residues, conformal mappings, and the d-bar equation.

### llm topics

* Cauchy formula, singularities, residues, meromorphic functions, conformal mappings, harmonic functions, approximation, d-bar equation

### llm skills

* Theory of functions of one complex variable, Cauchy formula, singularities, residues, meromorphic functions, conformal mappings, harmonic functions, approximation, nonhomogeneous d-bar equation.

### llm assumed background

* Undergraduate analysis sequence covering real analysis, topology, and differential calculus in normed spaces.

### llm search phrases

* complex analysis graduate
* Cauchy formula residues
* conformal mappings harmonic functions
* MATH 722 prerequisites

### llm requirements status

needs\_review

### 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

A historical review assigned a difficulty rating of 1, suggesting the course was perceived as easy under that instructor.

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#### errors

None recorded.

#### historical context

No current instructor is listed for MATH 722. Historical reviews for Alexander Nagel describe him as one of the finest professors at the UW, noting that he made the material clear and interesting.

```json
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#### offered

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#### profile hash

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#### quick take

Historical reviews describe Alexander Nagel as one of the finest professors at UW, noting that he made the material clear and interesting.

```json
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Recent recorded grades — Spring 2024: 3.60 GPA, 76.0% A/AB (n=25 letter grades); Spring 2025: 3.53 GPA, 68.8% A/AB (n=16 letter grades); Spring 2026: 3.44 GPA, 59.3% A/AB (n=27 letter grades).

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#### student experience

Historical reviews of Alexander Nagel: Students found the instruction clear and the material interesting when taught by Alexander Nagel.

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#### task hash

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#### teaching history

ALEXANDER NAGEL is recorded teaching in Spring 2007, Spring 2009, Spring 2012. 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

* Requirements are based on standing or program membership, not specific course prerequisites. No linked courses are provided for MATH 722.

#### root

root

#### status

needs\_review

### instructors

None recorded.

### offerings

None recorded.

### sections

None recorded.

### grade instructors

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    "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": 11,
    "source_aliases": [
      "MATH 722"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 722",
    "course_uid": "course_f14af393237e30c6a39c8fb8",
    "term_id": "1194",
    "term_name": "Spring 2019",
    "instructors": [
      "Xianghong Gong"
    ],
    "a": 7,
    "ab": 2,
    "b": 3,
    "bc": 1,
    "c": 1,
    "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 722"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 722",
    "course_uid": "course_f14af393237e30c6a39c8fb8",
    "term_id": "1204",
    "term_name": "Spring 2020",
    "instructors": [
      "Xianghong Gong"
    ],
    "a": 8,
    "ab": 0,
    "b": 2,
    "bc": 0,
    "c": 0,
    "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": 11,
    "source_aliases": [
      "MATH 722"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 722",
    "course_uid": "course_f14af393237e30c6a39c8fb8",
    "term_id": "1224",
    "term_name": "Spring 2022",
    "instructors": [
      "Alexei Poltoratski"
    ],
    "a": 19,
    "ab": 0,
    "b": 4,
    "bc": 0,
    "c": 0,
    "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": 24,
    "source_aliases": [
      "MATH 722"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 722",
    "course_uid": "course_f14af393237e30c6a39c8fb8",
    "term_id": "1234",
    "term_name": "Spring 2023",
    "instructors": [
      "Alexei Poltoratski"
    ],
    "a": 20,
    "ab": 0,
    "b": 6,
    "bc": 0,
    "c": 2,
    "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": 28,
    "source_aliases": [
      "MATH 722"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 722",
    "course_uid": "course_f14af393237e30c6a39c8fb8",
    "term_id": "1244",
    "term_name": "Spring 2024",
    "instructors": [
      "Alexei Poltoratski"
    ],
    "a": 19,
    "ab": 0,
    "b": 4,
    "bc": 0,
    "c": 1,
    "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": 25,
    "source_aliases": [
      "MATH 722"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 722",
    "course_uid": "course_f14af393237e30c6a39c8fb8",
    "term_id": "1254",
    "term_name": "Spring 2025",
    "instructors": [
      "Xianghong Gong"
    ],
    "a": 10,
    "ab": 1,
    "b": 3,
    "bc": 0,
    "c": 2,
    "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": 16,
    "source_aliases": [
      "MATH 722"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 722",
    "course_uid": "course_f14af393237e30c6a39c8fb8",
    "term_id": "1264",
    "term_name": "Spring 2026",
    "instructors": [
      "Alexei Poltoratski"
    ],
    "a": 16,
    "ab": 0,
    "b": 7,
    "bc": 0,
    "c": 4,
    "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": 28,
    "source_aliases": [
      "MATH 722"
    ]
  }
]
```

### statistics

#### gpa

3.657

#### graded

312

#### counts

* 200
* 41
* 57
* 1
* 12
* 0
* 1

### grade conflicts

None recorded.

### evidence

#### history

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_f14af393237e30c6a39c8fb8-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_f14af393237e30c6a39c8fb8-0.json)

#### traces

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_f14af393237e30c6a39c8fb8-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_f14af393237e30c6a39c8fb8-0.json)

#### reviews

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course\_f14af393237e30c6a39c8fb8-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course_f14af393237e30c6a39c8fb8-0.json)

#### results

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_f14af393237e30c6a39c8fb8-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_f14af393237e30c6a39c8fb8-0.json)

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

## context

### all

#### term



#### gpa

3.657051282051282

#### count

312

#### university

##### size

4298

##### gpa Percentile

43

##### count Percentile

66

##### median Count

170

##### 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 | 316   | false   |
| 3.2–3.6 | 1235  | false   |
| 3.6–4.0 | 2735  | true    |

#### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 104,
      "gpaPercentile": 55,
      "countPercentile": 59,
      "medianCount": 218.5,
      "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": 6,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 27,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 22,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 49,
          "current": true
        }
      ]
    }
  }
]
```

### terms

#### 1074

##### term

1074

##### gpa

3.92

##### count

25

##### departments

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

#### 1084

##### term

1084

##### gpa

4

##### count

7

##### departments

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

#### 1094

##### term

1094

##### gpa

3.4444444444444446

##### count

27

##### departments

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

#### 1104

##### term

1104

##### gpa

4

##### count

8

##### departments

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

#### 1124

##### term

1124

##### gpa

3.8461538461538463

##### count

13

##### departments

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

#### 1134

##### term

1134

##### gpa

4

##### count

11

##### departments

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

#### 1144

##### term

1144

##### gpa

3.5681818181818183

##### count

22

##### departments

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

#### 1154

##### term

1154

##### gpa

3.6

##### count

15

##### departments

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

#### 1164

##### term

1164

##### gpa

3.5714285714285716

##### count

14

##### departments

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

#### 1174

##### term

1174

##### gpa

3.65625

##### count

16

##### departments

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

#### 1184

##### term

1184

##### gpa

3.5454545454545454

##### count

11

##### departments

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

#### 1194

##### term

1194

##### gpa

3.4642857142857144

##### count

14

##### departments

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

#### 1204

##### term

1204

##### gpa

3.8

##### count

10

##### departments

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

#### 1224

##### term

1224

##### gpa

3.8260869565217392

##### count

23

##### departments

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

#### 1234

##### term

1234

##### gpa

3.642857142857143

##### count

28

##### departments

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

#### 1244

##### term

1244

##### gpa

3.6

##### count

25

##### departments

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

#### 1254

##### term

1254

##### gpa

3.53125

##### count

16

##### departments

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

#### 1264

##### term

1264

##### gpa

3.4444444444444446

##### count

27

##### departments

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

### benchmarks

#### all

##### school

###### size

4298

###### gpa

3.6599169512129595

###### top Share

81.92066096643725

###### count

170

##### MATH

###### size

104

###### gpa

3.489755928725373

###### top Share

72.34164691083211

###### count

218.5

#### 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

##### 1084

###### school

###### size

720

###### gpa

3.3670742938849725

###### top Share

63.42064564712246

###### count

70

###### MATH

###### size

22

###### gpa

2.977459424628873

###### top Share

44.52710820759676

###### count

88.5

##### 1094

###### school

###### size

758

###### gpa

3.3891454428111527

###### top Share

64.36369814389255

###### count

71

###### MATH

###### size

19

###### gpa

2.861322177541941

###### top Share

40.26350030907326

###### count

108

##### 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

##### 1114

###### school

###### size

804

###### gpa

3.3696004653806844

###### top Share

64.0389334741844

###### count

68

###### MATH

###### size

26

###### gpa

2.9090822348911582

###### top Share

41.14706210117883

###### count

83.5

##### 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

##### 1134

###### school

###### size

852

###### gpa

3.4138934207568203

###### top Share

66.35946578182744

###### count

66

###### MATH

###### size

26

###### gpa

2.938004331770204

###### top Share

42.318323348030226

###### count

83.5

##### 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

##### 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

##### 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

##### 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

##### 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

##### 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

##### 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

##### 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_7d24ffb9e92a280f073bd9d1",
    "name": "ALEXEI POLTORATSKI",
    "count": 103,
    "terms": [
      {
        "term": "1224",
        "count": 23,
        "sections": 1,
        "gpa": 3.8260869565217392
      },
      {
        "term": "1234",
        "count": 28,
        "sections": 1,
        "gpa": 3.642857142857143
      },
      {
        "term": "1244",
        "count": 25,
        "sections": 1,
        "gpa": 3.6
      },
      {
        "term": "1264",
        "count": 27,
        "sections": 1,
        "gpa": 3.4444444444444446
      }
    ]
  },
  {
    "uid": "instructor_12d87346f1e3d02a2dacf52c",
    "name": "XIANGHONG GONG",
    "count": 89,
    "terms": [
      {
        "term": "1084",
        "count": 7,
        "sections": 1,
        "gpa": 4
      },
      {
        "term": "1154",
        "count": 15,
        "sections": 1,
        "gpa": 3.6
      },
      {
        "term": "1174",
        "count": 16,
        "sections": 1,
        "gpa": 3.65625
      },
      {
        "term": "1184",
        "count": 11,
        "sections": 1,
        "gpa": 3.5454545454545454
      },
      {
        "term": "1194",
        "count": 14,
        "sections": 1,
        "gpa": 3.4642857142857144
      },
      {
        "term": "1204",
        "count": 10,
        "sections": 1,
        "gpa": 3.8
      },
      {
        "term": "1254",
        "count": 16,
        "sections": 1,
        "gpa": 3.53125
      }
    ]
  },
  {
    "uid": "instructor_f00d358fd7c1650bfb3e8b33",
    "name": "ALEXANDER NAGEL",
    "count": 65,
    "terms": [
      {
        "term": "1074",
        "count": 25,
        "sections": 1,
        "gpa": 3.92
      },
      {
        "term": "1094",
        "count": 27,
        "sections": 1,
        "gpa": 3.4444444444444446
      },
      {
        "term": "1124",
        "count": 13,
        "sections": 1,
        "gpa": 3.8461538461538463
      }
    ]
  },
  {
    "uid": "instructor_76f9c7d76a0cb5d9c1ddc816",
    "name": "BING WANG",
    "count": 22,
    "terms": [
      {
        "term": "1144",
        "count": 22,
        "sections": 1,
        "gpa": 3.5681818181818183
      }
    ]
  },
  {
    "uid": "instructor_e930b3f6ec9d1140d6f286c3",
    "name": "SERGUEI DENISSOV",
    "count": 14,
    "terms": [
      {
        "term": "1164",
        "count": 14,
        "sections": 1,
        "gpa": 3.5714285714285716
      }
    ]
  },
  {
    "uid": "instructor_c0289d403f78c76ec800e7ea",
    "name": "BRIAN STREET",
    "count": 11,
    "terms": [
      {
        "term": "1134",
        "count": 11,
        "sections": 1,
        "gpa": 4
      }
    ]
  },
  {
    "uid": "instructor_3584679bc66cd68602ec043d",
    "name": "JEAN-PIERRE ROSAY",
    "count": 8,
    "terms": [
      {
        "term": "1104",
        "count": 8,
        "sections": 1,
        "gpa": 4
      }
    ]
  }
]
```

## following

None recorded.
