Tensor product, Subspaces and factor spaces, Direct decompositions, Linear mappings, Tensor product of several vector spaces, Dual spaces, Finite dimensional vector spaces, Tensor product of vector spaces with additional structure, Tensor product of algebras,Tensor algebra, Tensors,Skew symmetric tensors,Skew symmetric mappings, Exterior algebra, mixed exterior algebra, The algebra ^(E,E*), Poincaré isomorphism, Homomorphisms, derivations and antiderivations, The operator i(a), Applications to linear transformations, Multilinear functions as tensors.
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| Week |
Subject |
Related Preparation |
| 1) |
Preliminaries |
|
| 2) |
Preliminaries |
|
| 3) |
Tensor product |
|
| 4) |
Examples of tensor product |
|
| 5) |
Subspaces and factor spaces, Direct decompositions,Linear mappings |
|
| 6) |
Tensor product of several vector spaces, Dual spaces, Finite dimensional vector spaces |
|
| 7) |
Examples |
|
| 8) |
Tensor product of vector spaces with additional structure,Tensor product of algebras |
|
| 9) |
Tensor algebra, Tensors |
|
| 10) |
Skew symmetric tensors, The factor algebra × E/N(E) |
|
| 11) |
Skew symmetric mappings, Exterior algebra |
|
| 12) |
Mixed exterior algebra, The algebra ^(E,E*), The Poincaré isomorphism |
|
| 13) |
Homomorphisms, derivations and antiderivations, The operator i(a) |
|
| 14) |
Applications to linear transformations, Multilinear functions as tensors |
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| |
Program Outcomes |
Level of Contribution |
| 1) |
To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics |
5 |
| 2) |
To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods, |
5 |
| 3) |
To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials, |
4 |
| 4) |
To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, |
4 |
| 5) |
To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way, |
3 |
| 6) |
To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,
|
4 |
| 7) |
To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement, |
1 |
| 8) |
To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, |
|
| 9) |
By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere, |
|
| 10) |
To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning, |
|
| 11) |
To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school, |
5 |
| 12) |
To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. |
2 |
BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
