# MATH 704: Methods of Applied Mathematics-2 | UW–Madison

[View on UW Courses](https://uwcourses.com/courses/MATH_704)

## Dataset

### revision

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### built at

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### term

1272

### departments

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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 704

### course uid

course\_a0150f21af89cd5e021aa199

### catalog version id

f0a2c8d450680cfa0c7d23f83581c71dbf61d3ab195fceb194a8501332aae2a3

### course number

704

### subjects

* MATH

### title

METHODS OF APPLIED MATHEMATICS-2

### description

Derivation, nature and solution of canonical partial differential equations of applied mathematics. Conservation laws, advection, diffusion. First order PDEs, characteristics, shocks. Traffic flow, eikonal and Hamilton-Jacobi equations. Higher order PDEs: classification, Fourier analysis, well-posedness. Series solutions and integral transforms. Green's functions and distributions. Similarity solutions. Asymptotics of Fourier integrals. Laplace's method, stationary phase. Ship waves. Perturbation methods. Knowledge of undergraduate linear algebra, analysis and complex analysis is strongly recommended.

### requirements text

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

### credit offering ids

None recorded.

### llm job id

enrich-f516c4d3e82cfe326b4f5f54

### 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

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### llm search status

valid

### llm summary

Methods of applied mathematics focusing on the derivation and solution of canonical partial differential equations.

### llm topics

* Conservation laws, advection, and diffusion
* Traffic flow, eikonal, and Hamilton-Jacobi equations
* Ship waves

### llm skills

* Derivation and solution of canonical PDEs
* Analysis of first-order PDEs, characteristics, and shocks
* Classification and Fourier analysis of higher-order PDEs
* Series solutions, integral transforms, and Green's functions
* Similarity solutions and asymptotic methods
* Perturbation methods

### llm assumed background

* Undergraduate linear algebra, analysis, and complex analysis

### llm search phrases

* partial differential equations
* applied mathematics methods
* characteristics shocks
* Green's functions
* asymptotic 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

MATH 704

#### current instructors

None recorded.

#### difficulty workload

Historical reviews of Jean Luc Thiffeault: The course is rated as moderately difficult with a difficulty score of 3.

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#### errors

None recorded.

#### historical context

Historical reviews for Jean Luc Thiffeault describe him as highly intelligent and passionate about mathematics. One reviewer rated his teaching quality highly, noting his enjoyment of the subject.

```json
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#### offered

false

#### profile hash

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#### quick take

Historical reviews describe Jean Luc Thiffeault as highly intelligent and passionate about mathematics, resulting in a positive student experience.

```json
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Recent recorded grades — Spring 2024: 4.00 GPA, 100.0% A/AB (n=18 letter grades); Spring 2025: 3.95 GPA, 96.4% A/AB (n=28 letter grades); Spring 2026: 3.95 GPA, 100.0% A/AB (n=11 letter grades).

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#### student experience

Historical reviews of Jean Luc Thiffeault: Students appreciate the instructor's evident enjoyment of math and life, contributing to a high quality rating.

```json
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#### task hash

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#### teaching history

JEAN-LUC THIFFEAULT is recorded teaching in Spring 2017, Spring 2019, Spring 2020, Spring 2023, Spring 2024, Spring 2025. 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

n0

#### status

parsed

### instructors

None recorded.

### offerings

None recorded.

### sections

None recorded.

### grade instructors

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  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 704",
    "course_uid": "course_a0150f21af89cd5e021aa199",
    "term_id": "1244",
    "term_name": "Spring 2024",
    "instructors": [
      "Jean-Luc Thiffeault"
    ],
    "a": 18,
    "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": 18,
    "source_aliases": [
      "MATH 704"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 704",
    "course_uid": "course_a0150f21af89cd5e021aa199",
    "term_id": "1254",
    "term_name": "Spring 2025",
    "instructors": [
      "Jean-Luc Thiffeault"
    ],
    "a": 26,
    "ab": 1,
    "b": 1,
    "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": 28,
    "source_aliases": [
      "MATH 704"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 704",
    "course_uid": "course_a0150f21af89cd5e021aa199",
    "term_id": "1264",
    "term_name": "Spring 2026",
    "instructors": [
      "SAMUEL STECHMANN"
    ],
    "a": 10,
    "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": 11,
    "source_aliases": [
      "MATH 704"
    ]
  }
]
```

### statistics

#### gpa

3.778

#### graded

356

#### counts

* 275
* 40
* 29
* 4
* 4
* 0
* 4

### grade conflicts

None recorded.

### evidence

#### history

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_a0150f21af89cd5e021aa199-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_a0150f21af89cd5e021aa199-0.json)

#### traces

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_a0150f21af89cd5e021aa199-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_a0150f21af89cd5e021aa199-0.json)

#### reviews

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course\_a0150f21af89cd5e021aa199-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course_a0150f21af89cd5e021aa199-0.json)

#### results

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_a0150f21af89cd5e021aa199-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_a0150f21af89cd5e021aa199-0.json)

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

## context

### all

#### term



#### gpa

3.7780898876404496

#### count

356

#### university

##### size

4298

##### gpa Percentile

58

##### count Percentile

69

##### 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": 65,
      "countPercentile": 64,
      "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

3.6666666666666665

##### count

12

##### departments

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

#### 1084

##### term

1084

##### gpa

3.857142857142857

##### count

14

##### departments

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

#### 1094

##### term

1094

##### gpa

3.5625

##### count

8

##### departments

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

#### 1104

##### term

1104

##### gpa

3.5833333333333335

##### count

12

##### departments

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

#### 1124

##### term

1124

##### gpa

4

##### count

17

##### departments

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

#### 1134

##### term

1134

##### gpa

3.6818181818181817

##### count

11

##### departments

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

#### 1144

##### term

1144

##### gpa

3.5

##### count

11

##### departments

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

#### 1154

##### term

1154

##### gpa

3.303030303030303

##### count

33

##### university

###### size

935

###### gpa Percentile

38

###### count Percentile

5

###### median Count

63

###### 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 | 38    | false   |
| 2.8–3.2 | 237   | false   |
| 3.2–3.6 | 326   | true    |
| 3.6–4.0 | 334   | false   |

##### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 33,
      "gpaPercentile": 88,
      "countPercentile": 6,
      "medianCount": 69,
      "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": 10,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 15,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 6,
          "current": true
        },
        {
          "range": "3.6–4.0",
          "count": 2,
          "current": false
        }
      ]
    }
  }
]
```

#### 1164

##### term

1164

##### gpa

3.175

##### count

20

##### departments

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

#### 1174

##### term

1174

##### gpa

3.8620689655172415

##### count

29

##### departments

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

#### 1184

##### term

1184

##### gpa

3.71875

##### count

16

##### departments

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

#### 1194

##### term

1194

##### gpa

3.9318181818181817

##### count

44

##### university

###### size

1040

###### gpa Percentile

89

###### count Percentile

26

###### median Count

67

###### 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 | 23    | false   |
| 2.8–3.2 | 220   | false   |
| 3.2–3.6 | 342   | false   |
| 3.6–4.0 | 454   | true    |

##### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 38,
      "gpaPercentile": 92,
      "countPercentile": 27,
      "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": 1,
          "current": false
        },
        {
          "range": "2.4–2.8",
          "count": 6,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 18,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 6,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 7,
          "current": true
        }
      ]
    }
  }
]
```

#### 1204

##### term

1204

##### gpa

4

##### count

25

##### departments

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

#### 1224

##### term

1224

##### gpa

3.9

##### count

15

##### departments

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

#### 1234

##### term

1234

##### gpa

3.96875

##### count

32

##### university

###### size

1188

###### gpa Percentile

92

###### count Percentile

5

###### 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 | 3     | false   |
| 2.4–2.8 | 17    | false   |
| 2.8–3.2 | 144   | false   |
| 3.2–3.6 | 374   | false   |
| 3.6–4.0 | 650   | true    |

##### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 41,
      "gpaPercentile": 98,
      "countPercentile": 3,
      "medianCount": 67,
      "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": 5,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 13,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 14,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 7,
          "current": true
        }
      ]
    }
  }
]
```

#### 1244

##### term

1244

##### gpa

4

##### count

18

##### departments

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

#### 1254

##### term

1254

##### gpa

3.9464285714285716

##### count

28

##### departments

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

#### 1264

##### term

1264

##### gpa

3.9545454545454546

##### count

11

##### 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_ba5b41fe7dad67a1d6af17a1",
    "name": "JEAN-LUC THIFFEAULT",
    "count": 176,
    "terms": [
      {
        "term": "1174",
        "count": 29,
        "sections": 1,
        "gpa": 3.8620689655172415
      },
      {
        "term": "1194",
        "count": 44,
        "sections": 1,
        "gpa": 3.9318181818181817
      },
      {
        "term": "1204",
        "count": 25,
        "sections": 1,
        "gpa": 4
      },
      {
        "term": "1234",
        "count": 32,
        "sections": 1,
        "gpa": 3.96875
      },
      {
        "term": "1244",
        "count": 18,
        "sections": 1,
        "gpa": 4
      },
      {
        "term": "1254",
        "count": 28,
        "sections": 1,
        "gpa": 3.9464285714285716
      }
    ]
  },
  {
    "uid": "instructor_e8033b131444ac21313c075f",
    "name": "SAMUEL STECHMANN",
    "count": 117,
    "terms": [
      {
        "term": "1134",
        "count": 11,
        "sections": 1,
        "gpa": 3.6818181818181817
      },
      {
        "term": "1144",
        "count": 11,
        "sections": 1,
        "gpa": 3.5
      },
      {
        "term": "1154",
        "count": 33,
        "sections": 1,
        "gpa": 3.303030303030303
      },
      {
        "term": "1164",
        "count": 20,
        "sections": 1,
        "gpa": 3.175
      },
      {
        "term": "1184",
        "count": 16,
        "sections": 1,
        "gpa": 3.71875
      },
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      }
    ]
  }
]
```

## following

None recorded.
