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| Course Description |
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| Course Name |
: |
Advanced Calculus I |
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| Course Code |
: |
MT 241 |
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| Course Type |
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Compulsory |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
2 |
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| Course Semester |
: |
Fall (16 Weeks) |
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| ECTS |
: |
7 |
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| Name of Lecturer(s) |
: |
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| Learning Outcomes of the Course |
: |
Knows the concept of the Dedekind cut that forms the field of real numbers.
Knows the limit theorems in sequences.
Knows subsequences and the Bolzano-Weierstrass Theorem.
Knows the Cauchy convergence criterion and that it is equivalent to the completeness of real numbers.
Knows the convergence of infinite series, and conditional and absolute convergence tests.
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| Mode of Delivery |
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Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
The student who has learned the analytical techniques in general in the MT131 and MT 132 courses, will learn the structure of real numbers with all their proofs in this course. Thus, the student will be provided with the basic background of real-analytic concepts and will be able to comprehend the concepts of advanced analysis. |
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| Course Contents |
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Induction, Real Numbers, Sequences, Series. |
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| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Classrooms of Faculty of Science and Letters |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
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1 |
Induction and inequalities |
Required readings |
Lecture and discussion |
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2 |
Algebraic and order properties of real numbers |
Required readings |
Lecture and discussion |
|
3 |
Completeness property that forms the basis of real numbers |
Required readings |
Lecture and discussion |
|
4 |
Results of completeness properties |
Required readings |
Lecture and discussion |
|
5 |
Topology of real numbers |
Required readings |
Lecture and discussion |
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6 |
Convergence of sequences and sequences |
Required readings |
Lecture and discussion |
|
7 |
Limit theorems in sequences. |
Required readings |
Lecture and discussion |
|
8 |
Mid-term exam |
Review of topics discussed in the lecture notes and sources |
Written Exam |
|
9 |
Monotone sequences and properties. |
Required readings |
Lecture and discussion |
|
10 |
Subsquences and the Bolzano-Weierstrass Theorem |
Required readings |
Lecture and discussion |
|
11 |
Cauchy sequences and completeness in terms of Cauchy sequences of real numbers |
Required readings |
Lecture and discussion |
|
12 |
Divergent series and properties. |
Required readings |
Lecture and discussion |
|
13 |
Infinite series and convergence |
Required readings |
Lecture and discussion |
|
14 |
Convergence tests for series with positive terms |
Required readings |
Lecture and discussion |
|
15 |
Conditional convergence, absolute convergence and convergence tests |
Review of the relevant pages from sources |
Narration and discussion |
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16/17 |
Final exam |
Review of topics discussed in the lecture notes and sources |
Written Exam |
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Required Course Resources |
| Resource Type | Resource Name |
| Recommended Course Material(s) |
 Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert
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| |
| Required Course Material(s) |
Principles of Mathematical Analysis, Walter Rudin
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Assessment Methods and Assessment Criteria |
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Semester/Year Assessments |
Number |
Contribution Percentage |
|
Mid-term Exams (Written, Oral, etc.) |
1 |
80 |
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Homeworks/Projects/Others |
5 |
20 |
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Total |
100 |
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Rate of Semester/Year Assessments to Success |
40 |
| |
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Final Assessments
|
100 |
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Rate of Final Assessments to Success
|
60 |
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Total |
100 |
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| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
5 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
5 |
|
3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
2 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
1 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
1 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
3 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
5 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
4 |
|
9 |
Knows at least one computer programming language |
4 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
0 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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| Student Workload - ECTS |
| Works | Number | Time (Hour) | Total Workload (Hour) |
| Course Related Works |
|
Class Time (Exam weeks are excluded) |
14 |
4 |
56 |
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Out of Class Study (Preliminary Work, Practice) |
14 |
5 |
70 |
| Assesment Related Works |
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Homeworks, Projects, Others |
5 |
5 |
25 |
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Mid-term Exams (Written, Oral, etc.) |
1 |
15 |
15 |
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Final Exam |
1 |
20 |
20 |
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Total Workload: | 186 |
| Total Workload / 25 (h): | 7.44 |
| ECTS Credit: | 7 |
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