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Course Code: 
MATH 312
Semester: 
Spring
Course Type: 
Core
P: 
3
Lab: 
0
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
5
Course Language: 
English
Course Objectives: 
To provide information about the local and global structures of curves and surfaces in three dimensions.
Course Content: 

Curves in plane and 3-space, the local theory of curves, Serret-Frenet formulas. Closed curves, isoperimetric inequality and four-vertex theorem. Surfaces, first and second fundamental forms. Geometry of Gauss map. Structure equations. Theorema Egregium. Formulation with differential forms. Gauss-Bonnet theorem. Intrinsic and extrinsic geometry of surfaces.

Course Methodology: 
1: Lecture, 2: Problem Solving
Course Evaluation Methods: 
A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes

Teaching Methods

Assessment Methods

1) Learns the local behaviour of curves

1

A

2) Learns the local behaviour of surfaces

1

A

3) Learns how to distinguish local and global behaviours of curves

1

A

4) Learns how to distinguish local and global behaviours of surfaces

1

A

5) Learns how to obtain global information about curves

1

A

6) Learns how to obtain global information about surfaces

1

A

Course Flow

Week

Topics

Study Materials

1

Local Curve Theory in 2D

From textbook 2.1-2.3

2

Local Curve Theory in 3D

2.4-2.6

3

Global Theory of Plane Curves

3.1-3.3

4

Global Theory of Plane Curves

3.4-3.6

5

 MIDTERM and discussion of solutions

 

6

Local Surface Theory (First and Second Fundamental Forms)

4.1-4.3, 4.7

7

Local Surface Theory (Parallelism and Curvatures)

4.4-4.6, 4.8,

8

Local Surface Theory ( Fundamental Theorem of Surfaces)

4.10

9

Local Surface Theory ( Theorema Egregium)

4.9

10

MIDTERM and discussion of solutions

 

11

Global Theory of Space Curves

5.1-5.3

12

Global Theory of Surfaces (Curvature, Orientability)

6.1-6.3

13

Global Theory of Surfaces (Gauss-Bonnet Formula)

6.4-6.6

14

Global Theory of Surfaces (Index of a Vector Field)

6.7

Recommended Sources

Textbook

R.S. Millman, G.D. Parker, Elements of Differential Geometry, Pearson, 1977

Additional Resources

 

Material Sharing

Documents

 

Assignments

 

Exams

 

Assessment

IN-TERM STUDIES

NUMBER

PERCENTAGE

Mid-terms

2

100

Quizzes

-

-

Assignments

-

-

Total

 

100

CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE

 

40

CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE

 

60

Total

 

100

 

COURSE CATEGORY

Expertise/Field Courses

Course’s Contribution to Program

No

Program Learning Outcomes

Contribution

1

2

3

4

5

1

The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)

 

x

     

2

Acquiring fundamental knowledge on fundamental research fields in mathematics

       

x

3

Ability form and interpret the relations between research topics in mathematics

       

x

4

Ability to define, formulate and solve mathematical problems

       

x

5

Consciousness of professional ethics and responsibilty

   

x

   

6

Ability to communicate actively

   

x

   

7

Ability of self-development in fields of interest

     

x

 

8

Ability to learn, choose and use necessary information technologies

   

x

   

9

Lifelong education

   

x

   

ECTS

Activities

Quantity

Duration
(Hour)

Total
Workload
(Hour)

Course Duration (14x Total course hours)

14

3

42

Hours for off-the-classroom study (Pre-study, practice)

14

3

42

Mid-terms (Including self study)

2

12

24

Quizzes

-

-

-

Assignments

-

-

-

Final examination (Including self study)

1

24

24

Total Work Load

 

 

132

Total Work Load / 25 (h)

 

 

5.28

ECTS Credit of the Course

 

 

5