| Course Type | Elective Course |
|---|
| Course Level | Doctorate Of Science |
|---|
| Year of Study | - |
|---|
| Semester | - |
|---|
| ECTS | 10 |
|---|
| Name of Lecturer(s) |
- |
| Learning Outcomes |
At the end of this course, the students;
- Know the main topics of the history and the philosophy of mathematics.
- Know why and how to use the history of mathematics in the teaching and learning of mathematics.
- Know the impact of the knowledge about the history and philosophy of mathematics to the teaching and learning of mathematics.
|
| Mode of Delivery | Face to face |
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| Prerequisites | No |
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| Recommended Optional Programme Components | None. |
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| Course Description | The mathematical landscape; Varieties of mathematical experience; Outer issues; Inner issues, Selected topics in mathematics; Teaching and learning; From certainty to fallibility. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
The Current State of Mathematics; What is Mathematics?; Where is Mathematics?; The Mathematics Community; Supporting Tools and Resources; How Much Mathematics is Known Today?; Ulam?s Dilemma; How Much Mathematics Could There Be? |
|
2nd Week |
The Diversity of Mathematical Experience; Individual and Collective Consciousness Today; The Ideal Mathematician; A Physicist?s Perspective on Mathematics. |
|
3rd Week |
I. R. Shafarevich and Neoplatonism; Anomalies; The Individual and Culture. |
|
4th Week |
External Issues; Why Does Mathematics Work: A Traditional Answer; Mathematical Models. |
|
5th Week |
Usefulness; Beneath the Fig Leaf; Abstraction and Scholastic Theology. |
|
6th Week |
Internal Issues; Symbols, Abstraction, Generalization, Formalization; Mathematical Objects and Structures: Existence, Proof, Infinity or The Magic Cube of Mathematics; The Taut Wire, Tyche's Coin, The Aesthetic Component, Pattern, Order, and Chaos. |
|
7th Week |
Algorithmic vs. Dialectical Mathematics; Achieving Abstraction and Generalization; The Chinese Remainder Theorem: A Case Study; Mathematics as an Enigma; Unity in Diversity. |
|
8th Week |
Midterm |
|
9th Week |
Selected Topics in Mathematics: Group Theory and the Classification of Simple Finite Groups, The Prime Number Theorem, Non-Euclidean Geometry. |
|
10th Week |
Non-Cantorian Set Theory, Non-Standard Analysis, Fourier Analysis. |
|
11th Week |
Teaching and Learning, Confessions of a High School Mathematics Teacher, The Crisis of Understanding and Pedagogy in Traditional Classrooms, Polya's Craft of Discovery. |
|
12th Week |
The Creation of New Mathematics: An Application of Lakatos' Discovery Strategy, Comparative Aesthetics, The Non-Analytic Aspects of Mathematics. |
|
13th Week |
From Certainty to Falsifiability, Platonism, Formalism, Constructivism; The Philosophical Position of the Working Mathematician; The Myth of Euclid. |
|
14th Week |
General Review |
|
15th Week |
Foundations Discovered and Lost; Formalist Philosophy of Mathematics; Lakatos and the Philosophy of Skepticism. |
|
| Recommended or Required Reading | Required Reading:
Philip J. Davis, Reuben Hersh, Elena Anne Marchisotto, The Mathematical Experience, Birkhauser, 1995
Optional Reading:
Adnan Baki, Matematik Tarihi ve Felsefesi, Pegem Akademi, 2014
Victor J. Katz, A History of Mathematics: An Introduction, 3rd Edition, Addison-Wesley (Pearson), 2009
Burton, The History of Mathematics: An Introduction, 6th Edition, McGraw-Hill, 2006
John Stillwell, Mathematics and Its History, 3rd Edition, Springer, 2010. |
|---|
| Planned Learning Activities and Teaching Methods |
- Discussion
- Questions/Answers
- Other
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
30 |
| Assignment |
3 |
30 |
| Total(%) |
|
60 |
| Contribution of In-term Studies to Overall Grade(%) |
|
60 |
| Contribution of Final Examination to Overall Grade(%) |
|
40 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
3 |
3 |
| Preparation for Quiz |
|
|
|
| Individual or group work |
13 |
10 |
130 |
| Preparation for Final exam |
1 |
40 |
40 |
| Course hours |
13 |
3 |
39 |
| Preparation for Midterm exam |
1 |
25 |
25 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
3 |
3 |
| Homework |
3 |
20 |
60 |
| Total Work Load | 300 |
| Total Work Load / 30 (h) | 10 |
| ECTS Credit of the Course | 10 |
|
| Language of Instruction | Turkish |
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| Work Placement(s) | No |
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