# MATH 751: Introductory Topology I | UW–Madison

[View on UW Courses](https://uwcourses.com/courses/MATH_751)

## Dataset

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### departments

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## course

### run id

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### semester

1272

### observed at

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### course number

751

### subjects

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### title

INTRODUCTORY TOPOLOGY I

### description

An introduction to algebraic and differential topology. Elements of homotopy theory, fundamental group, covering spaces. Differentiable manifolds, tangent vectors, regular values, transversality, examples of compact Lie groups. Homological algebra, chain complexes, cell complexes, singular and cellular homology, calculations for surfaces, spheres, projective spaces, etc. Familiarity with undergraduate algebra and topologyMATH 541or551) is strongly recommended.

### requirements text

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

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### llm summary

MATH 751 introduces algebraic and differential topology, covering homotopy, manifolds, and homology.

### llm topics

* Homotopy theory and fundamental group
* Differentiable manifolds and Lie groups
* Homological algebra and homology

### llm skills

* Introduction to algebraic and differential topology
* Homotopy theory and covering spaces
* Differentiable manifolds and transversality
* Homological algebra and homology calculations

### llm assumed background

* Undergraduate algebra and topology

### llm search phrases

* algebraic topology
* differential topology
* homotopy theory
* manifolds
* homology

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#### errors

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#### historical context

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#### quick take

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#### teaching history

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#### term name

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#### version

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#### notes

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#### root

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#### status

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### statistics

#### gpa

3.691

#### graded

398

#### counts

* 255
* 79
* 45
* 7
* 8
* 4
* 0

### grade conflicts

None recorded.

### evidence

#### history

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_f5b6bdfc443b676b16f5eb9d-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_f5b6bdfc443b676b16f5eb9d-0.json)

#### traces

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_f5b6bdfc443b676b16f5eb9d-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_f5b6bdfc443b676b16f5eb9d-0.json)

#### meetings

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/meetings/course\_f5b6bdfc443b676b16f5eb9d-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/meetings/course_f5b6bdfc443b676b16f5eb9d-0.json)

#### results

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_f5b6bdfc443b676b16f5eb9d-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_f5b6bdfc443b676b16f5eb9d-0.json)

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

## context

### all

#### term



#### gpa

3.690954773869347

#### count

398

#### university

##### size

4146

##### gpa Percentile

47

##### count Percentile

69

##### median Count

193

##### 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 | 10    | false   |
| 2.8–3.2 | 326   | false   |
| 3.2–3.6 | 1185  | false   |
| 3.6–4.0 | 2625  | true    |

#### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 97,
      "gpaPercentile": 53,
      "countPercentile": 59,
      "medianCount": 297,
      "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": 2,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 31,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 16,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 48,
          "current": true
        }
      ]
    }
  }
]
```

### terms

#### 1072

##### term

1072

##### gpa

3.8529411764705883

##### count

17

##### departments

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

#### 1082

##### term

1082

##### gpa

3.8214285714285716

##### count

14

##### departments

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

#### 1092

##### term

1092

##### gpa

3.5625

##### count

16

##### departments

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

#### 1102

##### term

1102

##### gpa

3.3076923076923075

##### count

13

##### departments

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

#### 1112

##### term

1112

##### gpa

3.269230769230769

##### count

13

##### departments

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

#### 1122

##### term

1122

##### gpa

3.923076923076923

##### count

13

##### departments

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

#### 1132

##### term

1132

##### gpa

3.473684210526316

##### count

19

##### departments

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

#### 1142

##### term

1142

##### gpa

3.888888888888889

##### count

18

##### departments

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

#### 1152

##### term

1152

##### gpa

3.5789473684210527

##### count

19

##### departments

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

#### 1162

##### term

1162

##### gpa

3.736842105263158

##### count

19

##### departments

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

#### 1172

##### term

1172

##### gpa

4

##### count

12

##### departments

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

#### 1182

##### term

1182

##### gpa

3.5357142857142856

##### count

14

##### departments

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

#### 1192

##### term

1192

##### gpa

3.8392857142857144

##### count

28

##### departments

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

#### 1202

##### term

1202

##### gpa

3.7083333333333335

##### count

24

##### departments

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

#### 1212

##### term

1212

##### gpa

3.6

##### count

20

##### departments

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

#### 1222

##### term

1222

##### gpa

3.1346153846153846

##### count

26

##### departments

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

#### 1232

##### term

1232

##### gpa

4

##### count

35

##### university

###### size

1216

###### gpa Percentile

95

###### count Percentile

12

###### median Count

66

###### 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 | 14    | false   |
| 2.8–3.2 | 174   | false   |
| 3.2–3.6 | 356   | false   |
| 3.6–4.0 | 670   | true    |

##### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 43,
      "gpaPercentile": 95,
      "countPercentile": 17,
      "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": 1,
          "current": false
        },
        {
          "range": "2.4–2.8",
          "count": 4,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 17,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 14,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 7,
          "current": true
        }
      ]
    }
  }
]
```

#### 1242

##### term

1242

##### gpa

3.8333333333333335

##### count

27

##### departments

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

#### 1252

##### term

1252

##### gpa

3.6363636363636362

##### count

22

##### departments

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

#### 1262

##### term

1262

##### gpa

3.810344827586207

##### count

29

##### departments

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

### benchmarks

#### all

##### school

###### size

4146

###### gpa

3.655576857310451

###### top Share

81.61127984016484

###### count

193

##### MATH

###### size

97

###### gpa

3.5110850672888794

###### top Share

72.940720357223

###### count

297

#### 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

##### 1192

###### school

###### size

1077

###### gpa

3.50327634323125

###### top Share

72.44641925727845

###### count

67

###### MATH

###### size

39

###### gpa

3.1003216533236415

###### top Share

50.01588968281552

###### count

99

##### 1202

###### school

###### size

1102

###### gpa

3.5102605987403313

###### top Share

72.78244569053733

###### count

68

###### MATH

###### size

40

###### gpa

3.1467748801316944

###### top Share

52.57847974231038

###### count

90.5

##### 1212

###### school

###### size

1111

###### gpa

3.5856416028074487

###### top Share

77.58926748660845

###### count

68

###### MATH

###### size

41

###### gpa

3.3211331103538813

###### top Share

59.85093623917685

###### count

87

##### 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

##### 1232

###### school

###### size

1216

###### gpa

3.575457431972425

###### top Share

77.33712216234007

###### count

66

###### MATH

###### size

43

###### gpa

3.2486774162409366

###### top Share

56.56203211471963

###### count

69

##### 1242

###### school

###### size

1295

###### gpa

3.595302892737449

###### top Share

78.36291889885307

###### count

67

###### MATH

###### size

43

###### gpa

3.2449031633350183

###### top Share

58.03783489438137

###### count

80

##### 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_49a66e28b37e5752a789849c",
    "name": "LAURENTIU MAXIM",
    "count": 93,
    "terms": [
      {
        "term": "1102",
        "count": 13,
        "sections": 1,
        "gpa": 3.3076923076923075
      },
      {
        "term": "1112",
        "count": 13,
        "sections": 1,
        "gpa": 3.269230769230769
      },
      {
        "term": "1152",
        "count": 19,
        "sections": 1,
        "gpa": 3.5789473684210527
      },
      {
        "term": "1222",
        "count": 26,
        "sections": 1,
        "gpa": 3.1346153846153846
      },
      {
        "term": "1252",
        "count": 22,
        "sections": 1,
        "gpa": 3.6363636363636362
      }
    ]
  },
  {
    "uid": "instructor_cfd7c53959806f45e66d2292",
    "name": "AUTUMN KENT",
    "count": 66,
    "terms": [
      {
        "term": "1132",
        "count": 19,
        "sections": 1,
        "gpa": 3.473684210526316
      },
      {
        "term": "1172",
        "count": 12,
        "sections": 1,
        "gpa": 4
      },
      {
        "term": "1232",
        "count": 35,
        "sections": 1,
        "gpa": 4
      }
    ]
  },
  {
    "uid": "instructor_bc7acc9f38e7d8108854c8c5",
    "name": "TULLIA DYMARZ",
    "count": 46,
    "terms": [
      {
        "term": "1142",
        "count": 18,
        "sections": 1,
        "gpa": 3.888888888888889
      },
      {
        "term": "1192",
        "count": 28,
        "sections": 1,
        "gpa": 3.8392857142857144
      }
    ]
  },
  {
    "uid": "instructor_78d8427e395048f488ebf606",
    "name": "HSIAN-HUA TSENG",
    "count": 30,
    "terms": [
      {
        "term": "1082",
        "count": 14,
        "sections": 1,
        "gpa": 3.8214285714285716
      },
      {
        "term": "1092",
        "count": 16,
        "sections": 1,
        "gpa": 3.5625
      }
    ]
  },
  {
    "uid": "instructor_0661a671fd34e712f2db8fc6",
    "name": "MARISSA LOVING",
    "count": 29,
    "terms": [
      {
        "term": "1262",
        "count": 29,
        "sections": 1,
        "gpa": 3.810344827586207
      }
    ]
  },
  {
    "uid": "instructor_18ef1d7d9b98466965984778",
    "name": "CAGLAR UYANIK",
    "count": 27,
    "terms": [
      {
        "term": "1242",
        "count": 27,
        "sections": 1,
        "gpa": 3.8333333333333335
      }
    ]
  },
  {
    "uid": "instructor_beaa2ba123a3ed1dfa42136b",
    "name": "SHAOSAI HUANG",
    "count": 24,
    "terms": [
      {
        "term": "1202",
        "count": 24,
        "sections": 1,
        "gpa": 3.7083333333333335
      }
    ]
  },
  {
    "uid": "instructor_bb4ab5ae7dbecb56c2cd59db",
    "name": "BOTONG WANG",
    "count": 20,
    "terms": [
      {
        "term": "1212",
        "count": 20,
        "sections": 1,
        "gpa": 3.6
      }
    ]
  },
  {
    "uid": "instructor_3753748fa7dd09581055ebda",
    "name": "MANUEL GONZALEZ VILLA",
    "count": 19,
    "terms": [
      {
        "term": "1162",
        "count": 19,
        "sections": 1,
        "gpa": 3.736842105263158
      }
    ]
  },
  {
    "uid": "instructor_48e572d2049f84b83f04af8a",
    "name": "KE ZHU",
    "count": 17,
    "terms": [
      {
        "term": "1072",
        "count": 17,
        "sections": 1,
        "gpa": 3.8529411764705883
      }
    ]
  },
  {
    "uid": "instructor_c63c73a7dbde3b5fdf6cfb42",
    "name": "ALEXANDRA KJUCHUKOVA",
    "count": 14,
    "terms": [
      {
        "term": "1182",
        "count": 14,
        "sections": 1,
        "gpa": 3.5357142857142856
      }
    ]
  },
  {
    "uid": "instructor_cdee516dd316c178fc57fc60",
    "name": "YONG-GEUN OH",
    "count": 13,
    "terms": [
      {
        "term": "1122",
        "count": 13,
        "sections": 1,
        "gpa": 3.923076923076923
      }
    ]
  }
]
```

## following

None recorded.
