# MATH 856: Topics in Differential Topology | UW–Madison

[View on UW Courses](https://uwcourses.com/courses/MATH_856)

## Dataset

### revision

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### repository

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### term

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### departments

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| PORTUG    | 33    |
| PSYCH     | 101   |
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| RADIOL    | 11    |
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| RELIGST   | 90    |
| RHABMED   | 9     |
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| URBRPL    | 60    |
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## course

### run id

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### semester

1272

### observed at

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### course number

856

### subjects

* MATH

### title

TOPICS IN DIFFERENTIAL TOPOLOGY

### description

The theory of differential manifolds such as differential forms and de Rham theorem, cobordism groups, Lie groups, homogeneous spaces, fiber bundles, characteristic classes.

### requirements text

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### llm search status

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### llm summary

MATH 856 covers topics in differential topology, including manifolds, forms, Lie groups, and fiber bundles.

### llm topics

* Differential manifolds and de Rham theorem
* Cobordism groups
* Lie groups, homogeneous spaces, and fiber bundles

### llm skills

* Understanding differential manifolds, forms, and theorems
* Analyzing advanced topological structures and groups

### llm assumed background

None recorded.

### llm search phrases

* differential manifolds theory
* de Rham theorem cobordism
* Lie groups fiber bundles
* characteristic classes topology

### llm requirements status

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#### errors

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#### offered

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#### quick take

Recent recorded grades — Fall 2015: 4.00 GPA, 100.0% A/AB (n=21 letter grades); Fall 2017: 4.00 GPA, 100.0% A/AB (n=6 letter grades); Fall 2021: 4.00 GPA, 100.0% A/AB (n=15 letter grades).

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    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 10,
    "source_aliases": [
      "MATH 856"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 856",
    "course_uid": "course_c1a73ebc105c65d7c9e8a04d",
    "term_id": "1082",
    "term_name": "Fall 2007",
    "instructors": [
      "YONG-GEUN OH"
    ],
    "a": 13,
    "ab": 0,
    "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": 14,
    "source_aliases": [
      "MATH 856"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 856",
    "course_uid": "course_c1a73ebc105c65d7c9e8a04d",
    "term_id": "1112",
    "term_name": "Fall 2010",
    "instructors": [
      "YONG-GEUN OH"
    ],
    "a": 7,
    "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": 7,
    "source_aliases": [
      "MATH 856"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 856",
    "course_uid": "course_c1a73ebc105c65d7c9e8a04d",
    "term_id": "1134",
    "term_name": "Spring 2013",
    "instructors": [
      "YONG-GEUN OH"
    ],
    "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 856"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 856",
    "course_uid": "course_c1a73ebc105c65d7c9e8a04d",
    "term_id": "1162",
    "term_name": "Fall 2015",
    "instructors": [
      "LU WANG"
    ],
    "a": 21,
    "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": 21,
    "source_aliases": [
      "MATH 856"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 856",
    "course_uid": "course_c1a73ebc105c65d7c9e8a04d",
    "term_id": "1182",
    "term_name": "Fall 2017",
    "instructors": [
      "AMIR ASSADI"
    ],
    "a": 6,
    "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": 6,
    "source_aliases": [
      "MATH 856"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 856",
    "course_uid": "course_c1a73ebc105c65d7c9e8a04d",
    "term_id": "1222",
    "term_name": "Fall 2021",
    "instructors": [
      "Chenxi Wu"
    ],
    "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 856"
    ]
  }
]
```

### statistics

#### gpa

3.989

#### graded

88

#### counts

* 87
* 0
* 1
* 0
* 0
* 0
* 0

### grade conflicts

None recorded.

### evidence

#### history

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_c1a73ebc105c65d7c9e8a04d-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_c1a73ebc105c65d7c9e8a04d-0.json)

#### traces

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_c1a73ebc105c65d7c9e8a04d-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_c1a73ebc105c65d7c9e8a04d-0.json)

#### results

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_c1a73ebc105c65d7c9e8a04d-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_c1a73ebc105c65d7c9e8a04d-0.json)

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

## context

### all

#### term



#### gpa

3.9886363636363638

#### count

88

#### university

##### size

3045

##### gpa Percentile

94

##### count Percentile

46

##### median Count

98

##### 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 | 424   | false   |
| 3.2–3.6 | 1012  | false   |
| 3.6–4.0 | 1582  | true    |

#### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 76,
      "gpaPercentile": 92,
      "countPercentile": 39,
      "medianCount": 117,
      "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": 4,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 29,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 13,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 29,
          "current": true
        }
      ]
    }
  }
]
```

### terms

#### 1074

##### term

1074

##### gpa

4

##### count

10

##### departments

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

#### 1082

##### term

1082

##### gpa

3.9285714285714284

##### count

14

##### departments

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

#### 1112

##### term

1112

##### gpa

4

##### count

7

##### departments

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

#### 1134

##### term

1134

##### gpa

4

##### count

15

##### departments

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

#### 1162

##### term

1162

##### gpa

4

##### count

21

##### departments

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

#### 1182

##### term

1182

##### gpa

4

##### count

6

##### departments

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

#### 1222

##### term

1222

##### gpa

4

##### count

15

##### departments

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

### benchmarks

#### all

##### school

###### size

3045

###### gpa

3.5753570024206764

###### top Share

76.66717122298573

###### count

98

##### MATH

###### size

76

###### gpa

3.396159998751156

###### top Share

66.69285547353557

###### count

117

#### 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

##### 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

##### 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

##### 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

##### 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

##### 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

##### 1222

###### school

###### size

1157

###### gpa

3.563052311875811

###### top Share

76.64869058732418

###### count

64

###### MATH

###### size

39

###### gpa

3.2083447119296955

###### top Share

56.75007696473496

###### count

63

## instructor Trends

```json
[
  {
    "uid": "instructor_cdee516dd316c178fc57fc60",
    "name": "YONG-GEUN OH",
    "count": 46,
    "terms": [
      {
        "term": "1074",
        "count": 10,
        "sections": 1,
        "gpa": 4
      },
      {
        "term": "1082",
        "count": 14,
        "sections": 1,
        "gpa": 3.9285714285714284
      },
      {
        "term": "1112",
        "count": 7,
        "sections": 1,
        "gpa": 4
      },
      {
        "term": "1134",
        "count": 15,
        "sections": 1,
        "gpa": 4
      }
    ]
  },
  {
    "uid": "instructor_c4bb9475d87ea8defd8f9a55",
    "name": "LU WANG",
    "count": 21,
    "terms": [
      {
        "term": "1162",
        "count": 21,
        "sections": 1,
        "gpa": 4
      }
    ]
  },
  {
    "uid": "instructor_09b1c1be00e1b7fd397c55cf",
    "name": "CHENXI WU",
    "count": 15,
    "terms": [
      {
        "term": "1222",
        "count": 15,
        "sections": 1,
        "gpa": 4
      }
    ]
  },
  {
    "uid": "instructor_e4128e249cb9e36c3c1d6985",
    "name": "AMIR ASSADI",
    "count": 6,
    "terms": [
      {
        "term": "1182",
        "count": 6,
        "sections": 1,
        "gpa": 4
      }
    ]
  }
]
```

## following

None recorded.
