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Week |
Subject |
Related Preparation |
1) |
Rings and ideals. Morphisms of rings. |
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2) |
Fields and vector spaces. |
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3) |
Examples of rings and fields. |
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4) |
Zero divisors. Principal Ideal Domains and Integral Domains. |
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5) |
Euclidean Domains. Unique Factorizations Domains. |
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6) |
Principal ideals, primary ideals, prime ideals and maximal ideals. |
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7) |
Radicals of ideals and rings. Nil radical and Jacobson radical. |
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8) |
Local and semi-local rings. |
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9) |
Basics of Lie algebras and Lie brackets. Structure constants. Jacobi identity. |
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10) |
Residue field and the cotangent space of a local ring. |
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11) |
The lattice of ideals of a ring, and operations in this lattice. |
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12) |
Alexandroff topology in a poset. Distributive lattices and Birhoff transform. |
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13) |
Selected topics from ring theory. |
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14) |
Selected topics from ring theory. |
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Program Outcomes |
Level of Contribution |
1) |
Ability to assimilate mathematic related concepts and associate these concepts with each other.
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2) |
Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
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3) |
Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. |
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4) |
Ability to make individual and team work on issues related to working and social life. |
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5) |
Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. |
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6) |
Ability to use mathematical knowledge in technology. |
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7) |
To apply mathematical principles to real world problems. |
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8) |
Ability to use the approaches and knowledge of other disciplines in Mathematics. |
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9) |
Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. |
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10) |
To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. |
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11) |
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. |
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12) |
To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, |
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